literature review and current state of the art

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J Grad Med Educ
v.14(6); 2022 Dec

Understanding State-of-the-Art Literature Reviews

Erin s. barry.

Erin S. Barry, MS, is Assistant Professor, Department of Military & Emergency Medicine and Department of Anesthesiology, F. Edward Hébert School of Medicine, Uniformed Services University of the Health Sciences, and Doctoral Candidate, School of Health Professions Education, Maastricht University, Maastricht, the Netherlands

Jerusalem Merkebu

Jerusalem Merkebu, PhD, is Assistant Professor, Department of Medicine, F. Edward Hébert School of Medicine, Uniformed Services University of the Health Sciences

Lara Varpio

Lara Varpio, PhD, is Professor of Medicine, Department of Medicine, F. Edward Hébert School of Medicine, Uniformed Services University of the Health Sciences

Sometimes the literature review you need isn't one that answers a narrow question: for that we would use a systematic review to determine, for example, the best workplace-based assessment tool for a pediatric residency program. Sometimes educators are not interested in how individual theories addressing a phenomenon align and differ, an answer you would find via an integrative review. Instead, educators may need to know how the modern conceptualization of a specific phenomenon became the norm—including the history that informed current understanding, what that understanding is, and what might develop in the future. For example, to understand resident assessment, you might want to know its history, what the current orientation is, and what future expansions might occur. To answer such questions, educators and researchers turn to State-of-the-Art (SotA) literature reviews .

Foundations

What is a sota review.

SotA literature reviews provide a time-based overview of the current state of knowledge about a phenomenon and suggest directions for future research. 1 They are organized in relation to how the understanding of the phenomena has evolved over time. Structured around turning points in the history of knowledge development, SotA reviews articulate: This is where we are now. This is how we got here. This is where we should go next . By synthesizing how the main characteristics of a topic have changed over time to give rise to current understandings, SotA reviews offer a modern knowledge synthesis that “tend[s] to address more current matters in contrast to other combined retrospective and current [literature review] approaches.” 1 SotA reviews are used prolifically in many fields, such as biomedical science, medicine, and engineering, to provide information on the current understanding of a topic, the historical roots that shaped the understanding, and potential next directions for future research.

How Are SotA Literature Reviews Different From Other Knowledge Syntheses?

Given their time-based and turning point-based orientations, SotA reviews are inherently different from other types of knowledge synthesis. For example, systematic reviews focus on specific research questions that are narrow in scope; in contrast, SotA reviews present a broader historical overview of knowledge development. Scoping reviews focus on mapping the present state of knowledge about a phenomenon, including, for example, the data currently available, the nature of that data, and the gaps in knowledge. Conversely, SotA reviews offer interpretations of the historical progression of knowledge relating to a phenomenon, centered on significant shifts that occurred during that history. 2

When Might SotA Reviews Be Used in Graduate Medical Education?

SotA reviews are especially useful within graduate medical education due to their purpose: these knowledge syntheses focus on the turning points that ended older ways of thinking and gave rise to current insights, while also evaluating where the field should go next. Thus, by conducting this type of review, educators and researchers in graduate medical education will be positioned to understand and apply modern best practices and to influence future directions. The Box illustrates the Case of Dr. Smith, which continues throughout this Journal of Graduate Medical Education (JGME) special review series, considering the same question using different review methodologies.

Processes and Considerations

What are the orienting assumptions of sota reviews.

Although SotA reviews are frequently published in peer-reviewed journals, there are few descriptions of how to conduct these knowledge syntheses, their markers of methodical rigor, and their reporting standards. We set out to address this gap by: (1) analyzing all publicly available and indexed methods-related publications describing SotA reviews, and (2) studying all SotA reviews (n=398) published between 2016 and 2020 to identify the foundational principles and techniques underpinning them. 3 Through this work, we developed a 6-stage process for conducting SotA reviews, 3 which aligns with the existing brief descriptions. 1 , 2 , 4 - 7 These 6 stages are summarized in a short how-to guide accompanying this article. 8 Here, we explain the orienting premises that shape SotA reviews.

Foundations of SotA Reviews

SotA literature reviews are founded on the principle that there is no single objectively true or correct synthesis of a body of literature. Instead, SotA reviews rest on the premise that literature is open for interpretation and that the context in which the review is conducted will shape the synthesis developed. SotA literature reviews are steeped in a relativist ontology: the nature of reality is socially and experientially informed and constructed. Consequently, SotA reviews do not require the literature included in the review to use identical methodology to support meta-analyses to generate a right answer. That is, not all findings synthesized in the review need to be carried out in the same way to enable cross-study data amalgamations. Instead—because SotA reviews assume that multiple different understandings of a phenomenon are available—this synthesis does not exclude research using different methodologies.

In terms of epistemology (the origins, nature, and limits of knowledge about reality), SotA literature reviews embrace subjectivism , the premise that knowledge generated from the review is a construction, not an objective fact. The knowledge generated through the review is value-dependent; it grows out of the subjective interpretations of the researchers who performed the synthesis. SotA reviews generate an interpretation of the literature informed by the expertise, experiences, and social context of the review team. Furthermore, the knowledge developed through SotA reviews is informed by the point in time when the review was conducted. A SotA review from 2000 reflects the contemporary knowledge of the year 2000; a SotA review from 2022 would report different knowledge reflecting that year's perspectives.

Purpose of SotA Reviews

SotA literature reviews seek (1) to create a critical summary of contemporary thinking about a topic; (2) to describe historical progressions and patterns in the literature; (3) to discuss how such modern perspectives have evolved over time; and (4) to propose a direction the field could take moving forward. Further, the SotA review presents an argument for how the literature could be interpreted; it is not a definitive statement about how the literature should or must be understood. The purpose of the SotA review is to engage in this critical summary at a specific point in time; it highlights the pivot points shaping the historical development of a topic, the factors that informed those changes in understanding, and the ways of thinking about and studying the topic that could newly inform the generation of further insights. Ultimately, the purpose of SotA literature reviews is to create a 3-part argument: This is where we are now in our understanding of this topic. This is how we got here. This is where we could go next .

To illustrate, Schuwirth and van der Vleuten's article, “A History of Assessment in Medical Education,” 9 offers a temporally organized overview of the evolving thinking in medical education about learner assessment. The authors describe how learner assessment was originally perceived as a problem of measurement, where the goal was to differentiate competent learners from incompetent ones. Historically, assessment was concerned with tool validity and replicability; human judgement was largely ignored. Even when assessment moved to include workplace-based assessment methods, the field continued to foreground assessment as a measurement problem. When human judgment was considered, the field focused on training assessors to minimize bias. Modern perspectives conceive of assessment as a whole system. Today, assessment data are integrated together to meaningfully triangulate data into a fair and defensible whole. Human judgement is recognized, but not as a bias to be mitigated. Instead, learners and assessors work together “to create a meaningful holistic narrative rather than a set of individual measurements.” 9 The authors suggest that the future of learner assessment will continue to focus on determining if a learner possesses and can apply appropriate knowledge and skills; in addition, information technologies and the availability of big data will shape future assessment considerations. These technologies will also require a reexamination of the knowledge and skills that will be required of future clinicians. Schuwirth and van der Vleuten's article thus offers a SotA review by providing an interpretation of the past, present, and future of learner assessment. 9

Strengths and Weaknesses of SotA Reviews

A significant contribution of a SotA review is the historical overview of how thinking about a phenomenon has changed over time. Such descriptions are particularly valuable for those exploring a new phenomenon or field of inquiry, and for those seeking to identify contemporary best practices and conceptualizations. Further, a SotA review provides a comprehensive time-based overview of a body of knowledge. Educators and researchers have an opportunity not only to assess past, present, and future trends, but also to characterize the unique shifts and patterns occurring over a specific period of time. Finally, the scope of a SotA review can extend beyond peer-reviewed literature.

The purpose and foundations upon which SotA reviews are built constrains them from providing a direct answer to specific, narrow research questions. They do not offer definitive answers to readers; instead, they are subjective reviews offering one interpretation of how the literature could be interpreted. Alternative interpretations exist. Moreover, the moment in history when the review is conducted and the specific review team engaging in the synthesis will shape the SotA review. Thus, reflexivity considerations by the team should be provided so that readers fully understand how the research team reached their conclusions.

Markers of a SotA Review's Rigor

While many knowledge syntheses have reporting standards, no such guidance exists for SotA reviews. SotA reviews offer interpretations of a specific body of literature; therefore, appraising the quality of the literature and preserving objectivity of the analysis processes is not relevant. Instead, indicators of the quality of a review are connected to its transparency , including considerations such as: How was the collection of articles included in the synthesis created? What inclusion and exclusion criteria controlled the selection? What reflexivity considerations shaped the perspectives of the authors? What contextual factors contributed to shaping the analysis? The final search strategy must be included in the manuscript so that others can replicate the process. The purpose of a replication would not be to confirm the interpretations offered in the SotA review; instead, it would be for another team of researchers to offer their unique interpretations and insights. Another consideration is the breadth of literature included in the review. It is advisable to incorporate a wide range of papers (eg, commentaries, research articles, grey literature) since part of the purpose of a SotA review is to identify how and when a field of inquiry took on its current state. Such information is not necessarily found only in peer-reviewed journal articles.

A SotA review can be deemed a success if it offers a coherent description regarding the current state of knowledge of a phenomenon: This is where we are now in our current understanding of this topic. This is how we got here. This is where we could go next .

Conclusions

Until very recently, SotA reviews were highly used but underdescribed: no robust methodologies were offered, and no information existed about their epistemological and ontological backgrounds. We hope to redress this gap. It is important when reading older SotA reviews to look for the 6 stages presented in the accompanying short article 8 to help make meaning of the findings (additional resources are provided in the Table ). We recommend that the structure of future SotA reviews clearly articulate these 6 stages so that researchers can more easily assess the interpretations offered within.

Resources for Conducting a State-of-the-Art (SotA) Literature Review

Box The Case of Dr. Smith

Dr. Smith, a program director, has been tasked to develop an interprofessional education (IPE) experience for the residency. Dr. Smith decides that conducting a literature review would be a savvy way to examine the existing evidence and generate a publication useful to others. After running a quick Google search using the term “interprofessional education,” she finds more than 11 million hits, and a similar PubMed search generates 24 000+ matches—far too many to review. Dr. Smith begins to randomly sample articles and notes the huge diversity in how IPE is conceptualized and in the types of articles, from randomized trials to qualitative investigations to critical perspectives on issues of concern.

As Dr. Smith is interested in learning how IPE is currently conceptualized, how the field came to hold this conceptualization, and where the field should go next, she decides to complete a State-of-the-Art review. This will allow Dr. Smith to identify the seminal moments when thinking about how IPE has changed in graduate medical education, to understand today's conceptualization of IPE, how that conceptualization came to be, and to offer new ideas about where IPE should go next.

Disclaimer: The opinions and assertions contained herein are those of the authors and are not to be construed as reflecting the views of the Uniformed Services University of the Health Sciences or the US Department of Defense.

Which review is that? A guide to review types.

Which review is that?
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Critical Review
Integrative Review
Narrative Review

State of the Art Review

Narrative Summary
Systematic Review
Meta-analysis
Comparative Effectiveness Review
Diagnostic Systematic Review
Network Meta-analysis
Prognostic Review
Psychometric Review
Review of Economic Evaluations
Systematic Review of Epidemiology Studies
Living Systematic Reviews
Umbrella Review
Review of Reviews
Rapid Review
Rapid Evidence Assessment
Rapid Realist Review
Qualitative Evidence Synthesis
Qualitative Interpretive Meta-synthesis
Qualitative Meta-synthesis
Qualitative Research Synthesis
Framework Synthesis - Best-fit Framework Synthesis
Meta-aggregation
Meta-ethnography
Meta-interpretation
Meta-narrative Review
Meta-summary
Thematic Synthesis
Mixed Methods Synthesis
Narrative Synthesis
Bayesian Meta-analysis
EPPI-Centre Review
Critical Interpretive Synthesis
Realist Synthesis - Realist Review
Scoping Review
Mapping Review
Systematised Review
Concept Synthesis
Expert Opinion - Policy Review
Technology Assessment Review
Methodological Review
Systematic Search and Review

State of the art reviews "generally focus on recently published literature to assess current matters. A state-of-the-art review will often highlight new ideas or gaps in research with no official quality assessment". "

Example

Wang, L., Kolios, A., Liu, X., Venetsanos, D., & Rui, C. (2022). Reliability of offshore wind turbine support structures: A state-of-the-art review. Renewable and Sustainable Energy Reviews , 161 , 112250. Full Text

References Baguss, J. (2020). The Systematic Review Research Process: 8 Types of Systematic Reviews You Should Know. Evidence Partners. Link

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Foundations

Processes and considerations, strengths and weaknesses of sota reviews, conclusions, understanding state-of-the-art literature reviews.

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Erin S. Barry , Jerusalem Merkebu , Lara Varpio; Understanding State-of-the-Art Literature Reviews. J Grad Med Educ 1 December 2022; 14 (6): 659–662. doi: https://doi.org/10.4300/JGME-D-22-00705.1

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What Is a SotA Review?

How Are SotA Literature Reviews Different From Other Knowledge Syntheses?

When Might SotA Reviews Be Used in Graduate Medical Education?

What Are the Orienting Assumptions of SotA Reviews?

Foundations of SotA Reviews

Purpose of SotA Reviews

Markers of a SotA Review's Rigor

Resources for Conducting a State-of-the-Art (SotA) Literature Review

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State Of The Art Literature Reviews

Top Reasons they lead to Non-Conformances

Under the MEDDEV 2.7/1 rev 4 regulations that came into effect on May 26, 2021, literature reviews play an important role in several areas of the CER , including establishment of State of the Art (SOTA). Therefore, anyone involved in Clinical Evaluation Reports (CERs) for medical devices will find themselves undertaking many more literature reviews .

The state of the art “describes what is currently and generally considered standard of care, or best practice, for the medical condition or treatment for which the device is used.” This is central to the CER and its best practice to dedicate a section of the CER to establishing the SOTA. You can then reference as needed throughout.

A considerable amount of the data that supports the SOTA comes from reviewing published literature for relevant information. You must conduct the SOTA literature review systematically, using sound and objective methods, according to the guidance provided by the regulators.

However, there are many issues that can arise in the literature review process, which will also increase the risk of failing an audit.

A State of the Art (SOTA) literature review is a thorough investigation and analysis of the most up-to-date knowledge, advancements, and trends of medical devices. This type of review aims to provide a comprehensive understanding of the current landscape, including the latest technologies, regulatory changes, clinical studies, and emerging innovations related to medical devices. It serves as a valuable resource for researchers, manufacturers, and regulatory authorities to stay informed about the cutting-edge developments in the medical device industry.

Research methodology must be valid. It is advisable to use a framework such as PICO and set out each aspect of the search. It is important to formulate a research question.

We must show all potentially relevant articles in the results. If anything considered relevant is missing, it can raise the question of validity within the entire literature review.

Despite the availability of literature review software, spreadsheets remain a big part of the review process in many organisations. But, as handy as they are, spreadsheets can’t keep track of connections between data and source documents, timestamps, proof of participation, or provide version control. When the Notified Bodies ask, you’ll need to produce this type of data to verify that you conducted the literature review thoroughly and with full adherence to a prescribed process.

Ensure that there is search and appraisal evidence. The appraisal plan needs to be clear and applied consistently and all searches should be saved. Any excluded articles also need to be listed and reasons why they have been omitted given.

The Process

Manufacturers should define a literature search protocol that scopes out the plan, clarifies any problems, and conforms with existing guidelines before beginning the search. The guidance provided in MEDDEV 2.7/1 rev 4 calls for a systematic approach to literature reviews. Many reviews lack the thorough, documented process that the notified bodies are looking for. The data should be reported in a scientific manner, avoiding an bias.

When updating the CER, it is expected that the manufacturer will repeat literature searches to identify new data on the device under evaluation but also to verify that the device remains the state of the art, as discussed in section 3.1.1 above. This is also a requirement of the PMS plan per Annex III. Therefore, i t’s vital for manufacturers to build a solid literature search technique that we can readily repeat and validate throughout future CER revision. Ultimately, if you gave the process to someone who wasn’t involved in the literature search, would the same result occur?

Manufacturers must consult applicable standards and guidance documents in the corresponding medical device field to determine the current state of the art. Using information on the medical condition managed with the device, benchmark devices, and medical alternatives available to the target population would be beneficial.

You also need to ensure that you have adequate justification for the selection of databases used and their suitability. There are results filters that can provide SoTA filter justifications and give an overview of the initial generation of search syntax and justification of its suitability.

Scientific databases are required, and not ‘grey’ databases such as internet searches, non-published data, and citations. CER’s commonly use scientific databases such as Cochrane, EMBASE, Pubmed, CHINAHL, SCOPUS, Cochrane Library or PROQUEST databases for literature search.

The Efficiency

The use of automated software can undertake tasks such as data collation and report preparation. The higher the number of required literature reviews, the more important it is to manage the workload more efficiently. By automating repetitive takes, it can make the review process quicker and produce better quality data.

In the literature review, any mistake can be disastrous. Typos, inconsistencies in data entry, transcription errors, or undocumented manual decisions can all negatively affect your literature review. You should implement proper tools to negate these possibilities.

CLIN-r+ Recommendations

Medical device producers will face stricter regulations due to the introduction of EU MDR . The Clinical Evaluation workflow is the area where the standards have increased the most, placing the expectations high for medical writers. Getting experienced CER writers and consultants onboard early improves the likelihood of executing a SOTA and CER to ensure a successful NB audit.

Always remember that a SoTA is free clinical data. It is much more cost effective than planning or executing a Clinical Investigation, so focus on meeting all the SoTA requirements mentioned in the MDCG 2020-13 . This will ensure you define the performance and safety range for your device category and alternative therapies. Having this benchmark will ensure you clearly show you meet the GSPR and establish if you have adequate data. It also identifies if data is missing and what PMCF studies you need to undertake.

Partner early with Clinical Evaluation experts to save resources and time so you can focus on other areas. As the Clinical Evaluation is a key workflow that automatically audits your QMS system and highlights areas of concern, it’s the most efficient and cost-effective area to bring in experts. Experienced CER consultants will not only identify problems upstream, but also advise on solutions, best practices deployed by the medical device industry, and efficient workflows to overcome problems later on. Consultancies also come with resources such as systematic review software, access to literature databases, and industry expert reviewers, helping expand your companies’ capabilities cost-effectively.

Consider partnering with a consultancy for the maintenance of your CER. Just because certification is obtained it doesn’t mean the work is over. CLIN-r+ can update documents and create reports as new data arises—and periodically as required—so that you always comply. Investing in ongoing maintenance also helps streamline updates to risk management and SSCP s, and the creation of PSUR s. Interested? Get in touch!

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literature review and current state of the art

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Revised medical device and in vitro diagnostic guidelines have challenged manufacturers looking to achieve or maintain regulatory compliance for new and existing products sold in Europe. First introduced in 2017, the MDR defines this requirement as a systematic and planned process to continuously generate, collect, analyze and assess the clinical data pertaining to a device in order to verify the safety and performance, including clinical benefits, of the device when used as intended by the manufacturer. Among the more segments of MDR are the literature review and the clinical evaluation report (CER), which are known to cause anguish for manufacturers due to the complexity and thoroughness required by notified bodies.

Literature reviews play a critical role in supporting the CER, which consists largely of clinical data collected during investigations of the product and from studies of devices deemed to be substantially equivalent to the product(s) under review. For devices currently on the market, the CER also includes references to post-market clinical follow-up (PMCF) data. Requirements for the clinical evaluation report are found in Annex XIV, Part A of Regulation (EU) 2017/745.

As part of conducting a thorough literature review and clinical evaluation report for the MDR, it is important to establish a framework that accounts for the generally accepted current knowledge, or the state of the art (SOTA). References to state of the art are found throughout Regulation (EU) 2017/745 as well as in MEDDEV 2.7/1 revision 4 , an industry guidance document on best practices for MDR clinical evaluations.

Far from being a simple term that must be included or considered in literature reviews, the state-of-the-art framework plays an active role in the entire clinical evaluation process, impacting key MDR components such as risk management, demonstration of equivalence rationales, risk-benefit analysis, executive summaries, clinical investigations, literature reviews, post-market clinical follow-up, and post-market surveillance.

Defining State of the Art and Understanding Its Importance

There are nearly 40 mentions of SOTA in MEDDEV 2.7/1 revision 4 , which defines state of the art as “the currently and generally agreed upon standard of care, or best practices, of the medical condition or treatment for which the device is used.”

Section 8.2 of MEDDEV 2.7/1 revision 4 describes SOTA as including applicable standards and guidance documents, data related to benchmark devices, other devices, critical components and medical alternatives or to the specific medical conditions and patient populations intended to be managed with the device. The data are typically needed in order to:

Describe the clinical background and identify the current knowledge/state of the art in the corresponding medical field
Identify potential clinical hazards (including hazards due to substances and technologies, manufacturing procedures and impurity profiles)
Justify the validity of criteria used for the demonstration of equivalence (if equivalence is claimed)
Justify the validity of surrogate endpoints (if surrogate endpoints are used)

Illustration of the core role of state of the art

SOTA also includes domain knowledge such as changes to applicable standards and guidance documents, new information relating to the medical condition managed with the device and its natural course, and medical alternatives available to the target population.

Finally, it is important to note that SOTA, as it pertains to technology, does not necessarily refer to the latest, most cutting-edge tools that have been invented. Rather, the state of the art around a specific medical condition is often well-established technology that has already achieved CE mark status, having been thoroughly vetted in terms of clinical safety, performance, benefit, and risk. This stands in contrast to emerging technologies that may still be under investigation or review for CE mark approval, which, despite their relative technological advances, may still be unproven in clinical practice over time.

Having defined SOTA, it becomes clear how ubiquitous a comprehensive state-of-the-art framework should be throughout the various MDR clinical evaluation components previously mentioned. As Figure 1 indicates, a strongly defined set of currently accepted therapeutic and technological options, as well as an understanding of how these options affect the risk, benefit, safety, and performance of devices under review, can assist in providing thorough evidence of device equivalence to products already on the market. This background research justifies the results of the literature search, which require SOTA research studies, and the findings of the CER, which provides information on competitor products.

In short, SOTA serves as an underlying foundation supporting the safety, efficacy, and performance claims of the device under review. Literature reviews, meanwhile, serve as a critical data source to their timely management and submission.

Requirements and Challenges for SOTA

Despite the numerous references to state of the art in both the MDR and the MEDDEV documents, some challenges remain for manufacturers attempting to establish a SOTA framework for the product families included in their MDR submissions. Specifically, manufacturers must take deliberate efforts to avoid issues when determining which content to include in the CER to demonstrate state of the art, as well as when implementing best practices for performing a SOTA literature search to establish safety and performance and claims of device equivalence. Interpretation of what constitutes state of the art can vary within an organization.

Obtaining sufficient SOTA data via an equivalent device literature search can also pose problems, particularly for those performing literature reviews manually. Manual literature reviews are time-consuming and error-prone. They can negatively impact the clinical evaluation process by introducing potential bias, mistakes and bottlenecks that could lead to market launch delays and rejected submissions.

Here’s a step-by-step approach to establishing a SOTA framework:

Define SOTA for Each Product Family

Regardless of the product being submitted for MDR certification, a CER that accounts for the SOTA framework should include a number of key sections. Specifically, background information provides the clinical context of the product family under review. This section should include summaries of the intended patient population, clinical indications and contraindications of the device(s), intended users, and specific clinical use cases for the product(s).

Within the SOTA framework, it is also important to provide treatment alternatives to the proposed medical device, which would be available for each medical condition cited in the background segment. These alternatives should be well-established, gold-standard options rather than experimental or untested products. A thorough literature search with well defined search parameters will retrieve the necessary data which can be used to establish evidence of device equivalence.

The results will lend further weight to claims of product safety and performance, particularly if the product is deemed equivalent in biological, clinical, and technical characteristics. Finally, any current standards, applicable guidelines, and evidence of the functional status of the product relative to its clinical indication can further assist in ensuring CER compliance with SOTA requirements.

These definitions will vary from one product family to the next, and sometimes from one product to another. However, the approach to thoroughly defining an appropriate SOTA framework for each product should remain consistent across the manufacturer’s portfolio.

Perform a Literature Search and a SOTA Search

Once manufacturers define state of the art for each product family under review, the process for arriving at a compliant literature search that can support the CER requires the following steps:

Framing an appropriately focused literature search question
Performing the literature search using multiple databases
Posing a specific SOTA question
Conducting a SOTA search using multiple keywords and the patient, intervention, comparison, outcome (PICO) strategy
Preparing the report that summarizes the findings

The foundation of an effective literature search is an appropriately scoped research question that returns a comprehensive yet focused and relevant list of articles. Ultimately, procuring adequate references is merely a way to ensure that the review of published data on the product family, including the SOTA, is comprehensive and not superficial.

The literature search identifies clinical data outside of the manufacturer’s domain that is needed to provide a substantial clinical evaluation of the device, justifying its candidacy for regulatory approval or compliance.

When performing the literature search, it is important to consult adequate databases in order to ensure broad capture of relevant sources. Requirements for clinical data found in the literature search are laid out in Regulation (EU) 2017/745 Annex XIV, Part A , Sections 1-4.

In contrast to a literature search, the SOTA search has a slightly different endpoint than the clinical literature review. Whereas the literature review is meant to provide evidence that justifies the safety and performance of the product for any given medical indications, the SOTA review is focused on providing evidence that the existing well-established technologies or products on the market (or the current state of the art) can be effectively compared with the device under review.

Any product outside of the specific product family under compliance review should be considered in the SOTA search rather than the literature search.

Literature search terms verifying the safety and performance of a product compare product claims (made on the product label) against clinical data (both favorable and unfavorable) from multiple sources. SOTA terms should reflect current medical practices and treatments independent of the similarity of the product(s) under review.

Review and Extract Full-Text Articles to Ensure Data Quality

Once a parsed down list of relevant research abstracts has been agreed upon in the SOTA search, full-text articles must be extracted in order to fully characterize the clinical data within. This technical task can be quite burdensome for large SOTA searches, particularly when performed manually by medical writers. MDCG 2020-13, Section D indicates that full-text article extraction is a best practice to evaluate the biological, technical, and clinical characteristics of devices in use. Given the imperative nature of this task, finding practice efficiencies is thus paramount to performing a solid SOTA review.

SOTA search data quality should be assessed to ensure compliance with Annex 5, Section 3 of MEDDEV 2.7/1 revision 4 and with the requirements of proposed CER content listed in Appendix A9 of the same document.

Best Practices and Strategies For Compliant EU MDR Literature Reviews

Having complete understanding of best practices and strategies pertaining to state of the art in literature reviews is therefore imperative for MDR compliance. The purpose of literature reviews is to provide substantial evidence and clinical data to justify product claims of safety and performance compared to state-of-the-art medical treatment.

These claims can be made of new products that are being introduced into the market, enhancements or upgrades to an existing product already on the market, or competitor products deemed to be equivalent to the device under review.

Literature reviews are designed to support the CER, as outlined in Chapter VI ( Article 61 , Paragraph 12) of the MDR as well as in Annex II (Technical Documentation) and Annex XIV , Part A (Clinical Evaluation). CERs integrate a substantial amount of clinical data and non-clinical evidence from key findings of literature review and post-market surveillance efforts to support device safety and performance. The literature review lifecycle listed below is a consistent methodology to ensure completion of a thorough and compliant review.

Literature Review Strategies For Relevant SOTA Search

Despite the differences between the literature search and the SOTA search, there is substantial overlap between the two when it comes to the processes used to evaluate search results, research papers, references, and clinical data. The same databases, such as EMBASE and PubMed, should be used during search execution.

Adverse event databases such as the such as the Manufacturer and User Facility Device Experience (MAUDE) database (a non-EU source) should be consulted to include relevant post-market surveillance data and field performance in order to fully characterize the clinical performance of the device(s).

Initially, it will be easier to parse through research abstracts rather than full-text papers, given the volume of data that SOTA searches produce. MDCG 2020-13 , Section D indicates that abstracts are a good choice for first-pass reviews. Abstracts should be triaged to determine if they are clinically relevant to the product under review (i.e., similar medical indications or use cases) or potentially equivalent devices (via biological, clinical, and technical characteristics) and if the study meets quality standards (i.e., a well-designed, conducted, and reported cohort study).

Strong rationales should be provided for articles excluded from consideration in the SOTA review to assist with traceability and further justify the methods used to establish the state-of-the-art framework.

A literature review management platform, such as DistillerSR , can help reviewers screen references by title and abstract and select relevant data. From there, they can build their inclusion/exclusion criteria, which will provide a consistent and repeatable process for determining which references to keep for the data extraction stage of the review. DistillerSR manages all the literature review data in one central repository, eliminating the need to collate individual spreadsheets and inclusion/exclusion responses for data processing and analysis. It enables reviewers to detect and remove duplicate citations preventing skew and bias caused by studies included more than once.

Annex 5, Section 3 of MEDDEV 2.7/1 revision 4 lists recommendations and methods for literature review screening. These guidelines can be used to structure adequate state-of-the-art search protocols and procedures within a manufacturer’s roadmap.

State of the art literature reviews require transparent, repeatable, and auditable processes that enable manufacturers to create and implement a standard framework.

Automated software platforms, like DistillerSR, automate the management of literature collection, screening and assessment using AI and intelligent workflows.

State of the Art, a Continuous Methodology

The SOTA review methods should be listed in the literature review protocol, as outlined in MEDDEV 2.7/1 revision 4, Annex 5, Section 3 . Processes should be repeatable, in the case that new clinical data becomes available that may challenge prior claims of device equivalence, clinical safety, or performance. For example, while a product’s key claims or specifications may not change from one version to another, adverse events or substantial changes to the literature may alter the fundamental state-of-the-art framework, thus requiring a new SOTA review. The ability to archive numerous SOTA reviews is therefore an extremely useful feature of automated software programs.

When establishing a state-of-the-art framework to support a device’s clinical evaluation, the use of professional guidelines and guidance documents published by the MDCG, industry consultation groups, and the European Commission is critical.

Manufacturers seeking MDR compliance across a portfolio of products must also ensure the replicability of methods from one product family to another. The use of automated software designed to rapidly perform literature searches, SOTA reviews, inclusion/exclusion calculations, full-text extraction, protocol generation, and report creation can substantially improve regulatory effort efficiency, compliance rates, and cost effectiveness. These tools provide a systematic methodology that can be leveraged to ensure repeatable, consistent, and transparent processes related to the state-of-the-art framework used in the clinical evaluation of devices under MDR review.

State of the art literature reviews can be continuously maintained in the DistillerSR platform and periodically updated as new reference material becomes available.

Reviewers can automatically import newly published references, keeping literature reviews always up to date.

DistillerSR’s add-on module CuratorCR is a research knowledge center that centrally and dynamically manages an organization’s evidence-based research, allowing medical researchers to continuously collect, share, update, and reuse data across literature reviews and teams.

Ultimately, the strategies employed in establishing a state-of-the-art framework may vary from one manufacturer to the next and from one product family to another. Industry guidelines should be consulted and followed whenever possible, and the use of automated software tailored to performing SOTA literature reviews can greatly enhance the success of these complex regulatory efforts.

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1 Introduction

2 hydrogen versus natural gas fuels, 3 combustion emissions from hydrogen (no x ), 4 no x control technologies and techniques, 5 current status of hydrogen turbine emissions control, 6 conclusions, acknowledgment, data availability statement, nomenclature, a literature review of no x emissions in current and future state-of-the-art gas turbines.

Turbomachinery Technical Conference & Exposition, Hynes Convention Center, June 26–30, 2023. Turbo Expo 2023.

The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

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Dennis, R., Long, H. A., III, and Jesionowski, G. (January 29, 2024). "A Literature Review of NO x Emissions in Current and Future State-of-the-Art Gas Turbines." ASME. J. Eng. Gas Turbines Power . March 2024; 146(3): 030801. https://doi.org/10.1115/1.4063836

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Current U.S. government policy seeks to achieve a completely carbon-free economy by 2050, with a carbon-free electricity sector by 2035 (per executive orders #14008 and #14057). To address these goals, the U.S. Department of Energy is evaluating strategies and technologies that support the production, utilization, transport, and storage of hydrogen (via initiatives such as Department of Energy's (DOE) Energy Earthshot—Hydrogen and various DOE funding opportunity announcements). A carbon-free fuel such as hydrogen cannot be overvalued in a dynamic electric energy sector seeking to decarbonize. One of the most important technologies needed to achieve the goal of a carbon-free electricity sector is a 100% hydrogen-fueled gas turbine. Accommodating hydrogen-based fuels has been a key goal for various original engine manufacturers (OEMs) for many years, but much more research and development (R&D) is needed. The purpose of this paper is to highlight the current state-of-the- art of hydrogen turbine technology, especially regarding nitrogen oxide (NO X ) emissions compared to natural gas-fueled turbines. NO X is the primary criteria pollutant from thermally driven combustion turbines and should be controlled to levels that are equivalent to or below existing standards (as reported “existing standards” for hydrogen-fueled gas turbines may need to be rebaselined). This paper will provide an overview of hydrogen as a fuel and various NO X emissions control techniques that are relevant for hydrogen-based fuels. A conclusion from this overview is that, with some level of R&D, NO X emissions from hydrogen-fueled gas turbines can be controlled to levels similar to those produced by state-of-the-art (SOTA) natural gas-fueled combustion turbines while remaining competitive in terms of performance and efficiency.

In 2021, the President of the United States released Executive Order #14008 (Tackling the Climate Crisis at Home and Abroad) [ 1 ] with the goal of reaching a completely carbon-free economy by 2050. One of the milestones for this plan was to achieve a carbon-free electricity sector by 2035. The U.S. DOE approach to achieving this goal includes engaging in key R&D initiatives that enable hydrogen (H 2 ) to meet current and future energy needs of the United States. One of the most important technologies needed to achieve the goal of a hydrogen-based electricity sector is a 100% hydrogen-fueled gas turbine. Various OEMs have been developing hydrogen-based combustion technologies that can accommodate fuels of various blending levels of hydrogen over the past several years, but much more R&D is needed. The purpose of this paper is to highlight the current SOTA for hydrogen-based gas turbine technology, as well as to provide an overview of hydrogen as a fuel and various NO X control techniques that are relevant for hydrogen-based fuels. The most important parameters for future hydrogen turbines are long lifespan and comparable maintenance schedule compared to natural gas turbines, consistent and reliable operation, safety (in terms of explosion risk), high efficiency, and low emissions (especially nitrogen oxide [NO X ]).

Currently, natural gas is the standard primary fuel that is used in most gas turbines (GTs). As will be covered in later sections, forcing GTs to switch to 100% hydrogen requires that special considerations in the design of the GT combustor (emphasis on NO X emissions) be made. Hydrogen differs from natural gas in a few key aspects that are relevant to combustion in gas turbines, outlined as follows:

2.1 Low Mass and Energy Density.

Hydrogen has the lowest mass density of any substance in the universe, with an atomic weight of only 2.0. It is approximately eight times lighter than methane (CH 4 ) [ 2 ]. Because of this, there is a common misconception that hydrogen is a superior fuel to natural gas because of its larger heating value (141.86 MJ/kg for H 2 versus 55.53 MJ/kg for pure methane). However, this is due to hydrogen's low density , not because it contains a large amount of energy. On a molecular basis, more energy is contained within four C–H bonds compared to a single H–H bond. Also, gas turbine combustors are of fixed volume and designed to work at specific operating pressures with little room for deviation. Therefore, the amount of hydrogen that can be used in a particular gas turbine is limited by volume. Indeed, looking at the energy content on a per-unit-volume or mole basis reveals that natural gas has more than three times the energy density of hydrogen by volume (10,050 kJ/m 3 H 2 versus 32,560 kJ/m 3 CH 4 ) [ 2 ]. Thus, in order to accommodate hydrogen fuel, hydrogen GTs will either require larger combustors, incorporate higher max pressures to reduce gas volumes, or both in order to operate with the same energy input as natural gas turbines. Therefore, to achieve performance and emissions ratings similar to those of their natural gas counterparts, hydrogen turbines may be more costly to produce.

2.2 High Flame Temperature.

The adiabatic flame temperature of hydrogen in air is 2254 °C (4089 °F) under stoichiometric and standard conditions, whereas that of methane is only 1963 °C (3565 °F) under the same conditions. This results in three primary issues of concern: (1) increased metal temperatures, which will require localized cooling or some other technique to protect downstream turbine components from thermal stresses; (2) higher thermal NO X emissions; and (3) changes to thermal acoustics (higher temperatures cause changes in thermal loads, which cause pressure fluctuations in the combustor. This, in turn, leads to vibrations that could potentially damage various components). Figure 1 shows chemiluminescence images of natural gas flames both with and without hydrogen. Note the greater chemical activity in the plot on the right, which indicates higher heat generation. The majority of hydrogen flames have lower overall luminosity since most of the energy will be released as heat instead of light. Techniques to control the temperature of hydrogen to mitigate these effects are discussed in later sections.

Chemiluminescence images for natural gas (left) and hydrogen (right) fuels

2.3 High Flame Speed.

The last major issue of concern with hydrogen as a fuel is its high flame speed. This is perhaps the single most challenging issue to overcome for hydrogen. Compared to natural gas, hydrogen's flame speed is an order of magnitude faster (∼3 m/s for H 2 versus ∼0.3 m/s NG). The high flame speed can also increase local flame temperature (in addition to the high natural flame temperature), which exacerbates the issues discussed previously [ 3 ]. Nilsson et al. [ 4 ] examined the effects of hydrogen on flame speed for various premixed flames at various fuel–air equivalence ratios (actual fuel–air ratio divided by the stoichiometric fuel–air ratio) and found that a 70% hydrogen blend by volume effectively has a flame speed of triple that of a pure natural gas flame.

Conventional gas turbines make use of velocity-driven diffusion flames or lean-air premixed flames. This means that they are designed with a specific flame speed in mind. If the flame speed is significantly higher than the actual fluid velocity, the flame will propagate backward (“flashback”) into the fuel mixing zone, which causes explosions and/or damage to the injectors and other components through exposure to high local temperatures [ 3 – 5 ]. Conversely, a higher fluid velocity can push the reacting species out of the combustor or extinguish the flame completely (“blowout” or “blow-off”) [ 4 ]. For hydrogen, simply raising the injection velocity is not an option for existing machines because higher velocities will create higher pressure drops across the combustor, which impacts machine work output, efficiency, reliability, maintenance, and life expectancy. Due to the operational limits of gas turbines, newer machines are currently being developed to accommodate the higher fluid speeds while maintaining high combustion efficiency, keeping NO X production in check, and having 100% reliable and safe operation.

As a pure element, hydrogen contains no inherent pollutants. Thus, aside from pollutants resulting from the combustion of trace substances that may remain after the hydrogen production and purification processes, the only noteworthy pollutants that arise from hydrogen combustion are nitrogen oxides (NO X ).

The actual formation of NO X is not straightforward, and determining the amount of potential NO X production from any fuel combustion process requires an understanding of chemical kinetics. There are three generalized categories of NO X : fuel NO X , prompt NO X , and thermal NO X . Each category has its own independent formation mechanism(s), which are discussed in Secs. 3.1 – 3.3 .

3.1 Fuel NO X .

The most straightforward NO X formation mechanism proceeds when nitrogen bound to the fuel itself is oxidized directly. The resulting NO X is called “fuel NO X ” and is only prominent in fuels that have significant nitrogen content (greater than 0.3% N 2 ). The mechanism involves the production of nitrous intermediates, such as hydrogen cyanide (HCN) and ammonia (NH 3 ), due to thermal decomposition, which are then combusted into nitrogen dioxide (NO 2 ), carbon dioxide (CO 2 ), and water (H 2 O) [ 6 – 8 ]. One common misconception is that fuel and prompt NO X make up very little of the actual total NO X and that thermal NO X is the most abundant source of NO X due to high combustion temperatures. In reality, the balance depends on the nitrogen content of the fuel. For most fuels (solid fuels in particular), fuel NO X tends to be the most dominant form of NO X , and thermal NO X does not typically achieve a clear majority for average combustion temperatures below 1500 °C (2732 °F), as demonstrated in Fig. 2 . In the case of hydrogen and natural gas, which generally do not have fuel-bound nitrogen, the misconception turns out to be technically true.

NO X emissions by mechanism versus temperature (biomass combustion)—data from De-Nevers [ 6 ]

3.2 Prompt NO X .

Prompt NO X is usually the least significant type of NO X . For the mechanism, nitrogen in the air reacts directly with the fuel, which creates an intermediate, such as cyanide (HCN) for carbon-based fuels or NNH for hydrogen. Oxygen from the air that combusts the fuel will convert this intermediate into NO X . Prompt NO X is, therefore, related to, but is not the same as, fuel NO X . Oftentimes, the two are analyzed together via a single mechanism. In the case of carbon-based fuels such as natural gas, this is known as the Fenimore mechanism (shown in Fig. 3 ) [ 9 , 10 ].

Fennimore mechanism [ 9 ]

For the NNH mechanism, nitrogen bonds with hydrogen molecules, forming an NNH intermediate (2N 2 + H 2 ↔ 2NNH), which is later combusted to produce NO X [ 11 ]. The word “prompt” refers to the fact that this class of NO X tends to form during the early stages of combustion and is responsible for most of the NO X formed during these early stages, most prominently under low-temperature conditions in particularly fuel-rich flames [ 7 , 12 , 13 ]. Prompt NO X is mostly unaffected by parameters such as residence times [ 14 ] and temperature [ 13 ], but it can be mitigated through fuel-air premixing [ 13 , 14 ].

3.3 Thermal NO X .

For most high-temperature combustion applications, thermal NO X is the most prevalent class of NO X emissions (at temperatures higher than 1500 °C). Thermal NO X is created by direct oxidation of free nitrogen within the air (N 2 + O 2 → 2NO). Per its name, thermal NO X formation rates are a strong function of temperature in addition to residence time and oxygen content [ 7 , 11 , 12 ]. The overall process takes place via the Zeldovich mechanism, which is given by reactions R1– R7 [ 7 , 9 , 15 ]. In regions of the flame where there is a lack of oxygen, nitrous oxide (N 2 O) can also be formed from the under-oxidation of nitrogen, as shown by reaction R8. N 2 O can also be further oxidized into nitric oxide (NO) or nitrogen dioxide (NO 2 ), so N 2 O formation during combustion is generally very rare compared to other NO X compounds [ 16 ]. Thus, such intermediate mechanisms are beyond the scope of this paper.

The Zeldovich Mechanism

Here, reactions R3, R4, and R7 make up the core Zeldovich mechanism [ 9 , 12 ], while the remaining reactions are necessary to obtain the equilibrium concentrations of key intermediates and complete the mechanism [ 15 ].

The simplest method of mitigating thermal NO X is by reducing the maximum combustion temperature. Controlled mixing burners, for example, can be used to reduce turbulence in the combustion zone, which reduces the reaction rate. Premixed combustion allows heat energy to be more evenly distributed in the combustion chamber to keep the maximum temperature low. Flue gas recirculation (FGR) and/or nitrogen/water/steam dilution can be used to cool the flame directly. Finally, fuel-staged or oxygen-staged combustion can be used to control the fuel-air ratio and different parts of the combustion process, which effectively controls the temperature and limits the amount of NO X that can be formed when combined with premixed combustion, as shown in Fig. 4 (note that the data in the figure are for total NO X , not just thermal NO X ).

NO x emissions in premixed/diffusion flames [ 12 ]

From the figure, using a premixed flame with either a significant (>15–20% excess) amount of oxygen or a substoichiometric amount of oxygen limits thermal NO X production. For high excess air schemes, the lower amount of fuel means that less energy is released per unit mass, and the released heat will be absorbed by the surrounding gases. For substoichiometric combustion, lower reaction rates will result in a slower energy release, allowing more time for the heat to dissipate, lowering the mean temperature and the frequency of hot spots. Modern combustors will often use an early fuel-lean premixed flame and a much more fuel-rich flame downstream. Combining the two exhaust streams in a final “burnout zone” further downstream results in complete combustion with minimized NO X [ 12 ].

3.4 Effects of Hydrogen on NO X in Gas Turbines.

In summary, for gaseous fuels with low fuel-bound nitrogen, thermal NO X is the primary category of NO X created in gas turbines. In the case of hydrogen, this problem is exacerbated by higher flame speed, which is not only indicative of a higher reaction rate but it also induces combustion instabilities due to thermoacoustics [ 17 ]. As a result, for flames with uncontrolled NO X emissions, hydrogen is expected to produce more than eight times more NO X than natural gas under similar conditions [ 18 ]. However, for lean premixed flames, these emissions can be mitigated to the point that downstream NO X control technologies can reduce the total NO X emission to levels that are compliant with current U.S. Environmental Protection Agency regulations, if not comparable to those produced by ordinary natural gas turbines. It is thus predicted that hydrogen gas turbines of the future will be able to compete with current natural gas engines.

Several modern techniques for reducing NO X emissions are compatible with gas turbines. The three most prominent techniques include altering the design of the combustor fuel injection zone, various flame dilution strategies, and postcombustion selective catalytic or noncatalytic reduction (SCR or SNCR). One strategy that has seen great success with Rankine cycle plants (coal- and natural gas-fired) is oxy-fuel combustion, where air separation is used to create nearly 100% pure oxygen to perform the combustion, eliminating thermal NO X completely. This strategy, however, is much more complex and costly for gas turbines, and though there is a growing body of research on this technique, it is not currently actively practiced in industry [ 19 – 21 ].

4.1 Combustor Geometry and Fuel Injection Schemes.

The most widely implemented technology to control NO X involves designing the combustor in a way that encourages specific thermo-fluid behavior in order to limit NO X production. The cost of hydrogen fuels and the difficulty of developing these combustors are the primary reasons why pure hydrogen-fueled turbines have not fully entered mainstream use, as a single combustor design may not necessarily be able to handle hydrogen in the same way it can accommodate natural gas (for the reasons mentioned previously).

Figure 5 shows a simplified representation of a dry, low-NO X (DLN) combustion chamber. The primary injection region occurs on the sides of the chamber. In this region, approximately 83% of the fuel is combusted under oxygen-lean conditions. The remaining 17% of the fuel flows through the central tube under highly oxygen-rich conditions. As discussed earlier, both fuel–air ratios lead to reduced NO X formation compared to stoichiometric conditions. The two streams combine in the downstream dilution zone, where the remaining air from the central injector completes the overall combustion process [ 22 ].

Early low-NO X combustor design – from GE gas power [ 22 ]

To accommodate hydrogen in the fuels, the geometry of these combustors will need to be reworked to accommodate hydrogen's high flame speed and reactivity. In addition, injection nozzle diameters may need to be widened to allow more fuel into the chamber to ensure similar total fuel energy input rates. Overcoming these challenges remains an important point of research, and changes in the combustor geometry can affect performance and operation in other areas, such as the compressor and turbine sections.

4.2 Flame Dilution.

If a given combustor design is not able to meet local NO X emissions targets, one strategy to employ is injecting another fluid into the combustor to dilute the flame. This other fluid will usually be water/steam or nitrogen (CO 2 can also be used). In this case, the flame is directly quenched to provide a heat sink, which reduces the rate of thermal NO X formation. In addition, due to the extra mass present, the turbine section of the gas turbine will produce higher gross power at the same expansion ratio. However, the additional parasitic work required to compress the injected fluid(s) will offset this. Therefore, the effect on net power/efficiency varies case-by-case. For an integrated gasification combined cycle, an air separation unit will often be used to generate oxygen for the gasifier. In cases such as this, the extra parasitic loads for making use of leftover nitrogen for diluting the gas turbine combustor flame are minimal compared to the increased turbine power, usually improving the efficiency.

Water/steam can be injected as either a gas or as atomized water droplets. Water injection has the greatest NO X reduction potential due to lower liquid temperatures and latent heat. However, it is important to remember that this technique, as well as the previously mentioned staged combustion technique, only affects thermal NO X formation, and, in particular, water or steam injection may actually increase the rate of fuel NO X formation, depending on the fuel [ 23 ]. As always, careful experimentation/testing to optimize the performance and emissions of select engines or cycles is required. Alternatively, FGR can be used to reduce the combustor peak temperature. Through FGR, approximately 30–50% of the flue gas is fed back into the gas turbine compressor intake, which not only dilutes the flame but also has the added benefit of raising the CO 2 concentration in the exhaust (for carbon-based fuels). This raises the capture efficiency of any downstream CO 2 capture units needed to achieve a target CO 2 emission level [ 24 , 25 ].

4.3 Selective Catalytic and Noncatalytic Reduction.

If no combination of the previously mentioned techniques can achieve the required NO X emission targets, a potential remedy is the use of SCR or SNCR technology. Both techniques involve the injection of a reagent, usually ammonia or urea, into the flue gas. The only difference between the techniques is that, per their names, SCR uses a catalyst to increase the reaction rate and lower the NO X concentration equilibrium point. and SNCR does not. However, each method has different temperature requirements and follows a different injection scheme to maximize effectiveness, with SNCR generally requiring higher temperatures due to the absence of a catalyst [ 26 – 29 ]. The general chemical reaction scheme governing these processes is given by reactions R8–R10.

Selective Reduction

Typical catalysts used for SCR include titanium dioxide (TiO 2 ) and vanadium-5 oxide (V 2 O 5 ); however, other catalysts such as other base metal oxides, precious metal oxides, or activated carbon have been used [ 30 ]. A general simplified diagram of both technologies in coal boiler systems is shown in Fig. 6 for comparison. In the figure, note the honeycomb catalyst grid put in place for the SCR scheme that is not present for the SNCR scheme. A rough summary of the performance and costs of both technologies can be reviewed in Table 1 . In general, SNCR is much cheaper to implement than SCR due to the lack of catalyst, but it requires higher temperatures to be effective. Additionally, SNCR is less effective in flue gas with low base NO X concentrations, and it has more variability in how much NO X can be eliminated (and even then, it cannot reach the reduction levels possible with SCR) [ 26 , 28 , 29 ]. Typical SNCR reduction of NO X is 40–60% on average, but removal rates as low as 25% or as high as 85% have been reported, depending on application and reagent choice.

SNCR (left) versus SCR (right) as used in Rankine cycle boilers

SCR versus SNCR (capital costs in 2003 USD, operating costs in 1999 USD) [ 26 , 28 , 29 ]

Note that SNCR is generally not suitable for gas turbines for the previously mentioned reasons but is included here for completeness. Gas turbines, through various NO X reduction techniques, have low NO X concentrations in the flue gas and low flue gas temperatures (900–1200 °F, depending on frame type). SNCR is well suited for systems with temperatures in the range of 1600–1900 °F, NO X concentrations of more than 200 parts per million (ppm), and high particulate matter concentrations [ 29 , 30 ].

One last point of consideration for SCR/SNCR is ammonia slip, where unreacted ammonia will find its way into the flue gas. Ammonia is itself an unregulated pollutant and typical ammonia slip levels will be of the order of 2–10 ppm, which is not high enough to affect plume formation or act as a human health hazard [ 31 ]. The primary issues with ammonia slip are the formation of ammonia salts, which can deposit on and corrode downstream components and ductwork, and the deposition of ammonia onto ash particles (solid fuels only), which can affect ash disposal and reuse. Two primary salts that can form from ammonia slip are ammonium sulfate [(NH 4 ) 2 SO 4 ] and ammonium nitrate (NH 4 NO 3 ). The former is only a primary concern for fuels with high sulfur content, but the latter will readily form when excess ammonia reacts with NO X . Both salts form more readily when high amounts of sulfur oxides (SO X ) and water are present in the flue gas, which deactivate catalyst reaction sites [ 31 ]. In addition, both salts are contributors to secondary particulate matter (PM) emissions, particularly those less than 2.5 microns in size (PM2.5) [ 32 , 33 ]. One competing technology, called the SCONO X ™ process, removes both carbon monoxide (CO) and NO X from flue gas via a platinum catalyst and potassium carbonate adsorbent, with no ammonia required. However, SCONO X requires dilute H 2 and CO 2 gas to remove the captured NO X from the adsorbent to regenerate it. In addition, several practical issues with SCONO X have limited its market penetration, including a high exhaust gas pressure drop, safety and reliability issues, and costs [ 33 ].

Most major turbine manufacturers have made progress in both the design of low-NO X combustors and the implementation of hydrogen into their turbine fuel profiles. A significant amount of research into hydrogen combustion in turbines, boilers, and other engines/reactors has been performed for many decades. The following sections will focus on General Electric (GE), Siemens, and Mitsubishi heavy industries, which are the three largest turbine manufacturers in the world in terms of market share as of 2022. Other manufacturers' research progress and state-of-the-art turbines will be collectively discussed later. Table 2 offers a brief summary of several commercial technologies produced by these three original OEMs that enable gas turbines to achieve some level of commercially viable hydrogen combustion [ 34 ].

Hydrogen combustion technologies from the three largest OEMs as of 2019 [ 34 ]

5.1 General Electric.

GE Gas Power (henceforth called “GE”) is the largest manufacturer of gas turbines in the world by market share as of 2022 and has been a leading pioneer in hydrogen turbine R&D for more than 30 years, having more than 75 current turbine models able to run on hydrogen-based fuels. GE's most recent commercial combustor design—the DLN 2.6e—uses an advanced premixer technology developed in part through DOE's High Hydrogen Turbine Program [ 35 ]. This combustor uses miniature tubes to increase the speed at which premixing occurs. This allows high-reactivity fuels, such as hydrogen, to be premixed safely and reduces the risk of premature combustion. The current hydrogen capabilities of GE's turbines are summarized in Fig. 7 .

Hydrogen capabilities of GE gas turbines [ 36 ]

For NO X emissions reduction, GE has also led several development efforts for both traditional methods of reduction and DLN combustors. GE-developed DLN combustion systems have been used in more than 200 different engines, including retrofits of older machines [ 22 ]. GE engines with DLN technology were some of the first machines to achieve single-digit ppm NO X emissions in the early 1990s. A comparison of the NO X and CO emissions of some of these engines is shown in Table 3 . As seen in the table, some engines can reach NO X concentrations as low as 9 ppm (newer engines can reach as low as 5 ppm [ 37 ]). As of 2019, GE's DLN 2.6e has operated for more than 70 × 10 −6 hours and has successfully been implemented in both F- and H-class turbines [ 38 ].

NO X and CO emissions from GE gas turbines (with natural gas fuel) [ 22 ]

5.2 Siemens.

Siemens Energy (“Siemens”) has also made progress in incorporating hydrogen fuels into their turbines. On average, Siemens engines can handle approximately 30–60% hydrogen in the gas turbine fuel. Siemens offers a control and hardware upgrade package called “H2DeCarb” to enable E- and F-class turbines to combust larger quantities of hydrogen (typically 50–60%), and Siemens aeroderivative engines have been able to combust 100% hydrogen safely for many years using wet, low-emissions combustors that utilize water injection [ 35 ]. A chart of the hydrogen capabilities of select Siemens turbines is shown in Fig. 8 . As of 2019, Siemens also achieved a research breakthrough (still proprietary) that allows hydrogen-tolerant turbine parts to be integrated into existing structures with no welds, significantly reducing construction times [ 39 ].

Hydrogen capabilities of Siemens gas turbines [ 40 ]

Siemens has been researching and expanding the use of hydrogen in its gas turbines since the 1960s [ 41 ], and with the rest of the European Association of Gas and Steam Turbine Manufacturers (EUTurbines), is progressing research with the goal of developing a full fleet of 100% hydrogen industrial gas turbines by 2030 [ 42 ], the first of which is scheduled for completion by 2023 [ 41 ]. Also, as with GE, some aeroderivative turbines are already capable of 100% hydrogen. However, to keep NO X emissions low (less than 25 ppm), which will be a key factor in the environmental success of hydrogen combustion turbines, the wet, low-emissions combustors require approximately 20 metric tons, or 20,000 liters, of water every hour. This is also compounded by the fact that the water needs to be demineralized, which further increases operating costs [ 41 ].

Siemens' biggest contribution to a global zero-emissions electricity economy thus far is the construction of a zero-emissions test facility/demonstration plant in Finspång, Sweden, which was developed in collaboration with the Zero-emissions hydrogen turbine center. The project will demonstrate zero-carbon electricity generated by green hydrogen. The hydrogen will be created via electrolysis powered by excess electricity from nearby prototype turbine testing and solar electrolysis [ 41 , 42 ]. The plant first began operation in June of 2021 [ 42 ]. Project partners include the Chalmers University of Technology, the University of Bologna, and Linde [ 41 ].

5.3 Mitsubishi Heavy Industries.

Finally, Mitsubishi heavy industries, specifically its subsidiary, Mitsubishi Power (“Mitsubishi”), has also been making progress on developing hydrogen turbines and supporting infrastructure. In late October 2020, then-Japanese Prime Minister Yoshihide Suga declared that Japan would become a decarbonized nation by 2050, echoing previously announced plans from the European Union and the United States. Up to this point, Mitsubishi had already successfully developed a turbine engine that could reliably utilize 30% hydrogen in the fuel. Mitsubishi anticipates the release of a 100% hydrogen engine by 2025 [ 43 , 44 ]. In addition, they have achieved numerous advances in gas turbine technology in the past, including the development of the world's first (and, as of this writing, the only) J-Class gas turbines (the M501J and M701J-series) boasting turbine inlet temperatures of 1600 °C (2912 °F), more than 100 °C higher than equivalent engines at the time [ 45 ]. For hydrogen deployment, Mitsubishi is developing a green hydrogen energy solutions package called Hydaptive TM , which acts as a power balancing resource that allows gas turbine power cycles to ramp up and down more rapidly through the integration of hydrogen and natural gas plants. Hydaptive also includes a storage paradigm called “Hystore” [ 43 , 46 ], which provides for hydrogen production off-site and storage options to ensure a steady hydrogen supply during peak operating times. Hydaptive and Hystore are being used in multiple projects throughout the United States (mostly in Appalachia) and Europe, including the Advanced Clean Energy Systems Project, which is codeveloped by Magnum Deployment and uses wind and solar power to produce green hydrogen stored in an underground salt dome [ 43 ]. This makes Hydaptive and Hystore the world's first commercially available hydrogen infrastructure and supply packages. Figures 9 and 10 show schematics of an integrated thermal cycle using the Hydaptive system and the Hydaptive storage package, respectively.

Mitsubishi's hydaptive system [ 43 ]

Mitsubishi's hystore system [ 43 ]

With unmitigated NO X , many pure diffusion turbine combustors from Mitsubishi are compatible with 100% hydrogen. To meet current NO X emission standards, innovative NO X control technologies must be developed. In this regard, the majority of Mitsubishi's current fleet of turbines can operate using up to 30% hydrogen in the fuel, as shown in Fig. 11 . To achieve 100% hydrogen capability, Mitsubishi has been developing a unique “multicluster” turbine combustor, which is slated to be deployed in 2024 [ 47 ]. The combustor makes use of multiple small air and fuel nozzles arranged coaxially, which create a fuel-lean mixture much faster than in conventional combustors. In addition, the combustor design allows for “flame lifting,” using directional adjustment of the air jets to force the flame to initialize an appreciable distance away from the actual burner, reducing flashback risks. The technology has been in development since 2008, has achieved success at lab-scale, and has successfully been tested in an H-class machine [ 48 ].

Mitsubishi's current hydrogen turbine capabilities [ 47 ]

5.4 Others.

Many smaller gas turbine OEMs have also made contributions to hydrogen and NO X reduction research and have also worked to increase the tolerable levels of acceptable hydrogen fuel in their machines. After the three OEMs discussed previously, the largest manufacturer by market share as of 2022 is Solar Turbines (“Solar”) [ 49 ]. Over the past decade, Solar's Titan and Taurus engines have been operating on coke oven gas (COG) created as a by-product during steel production (alongside petcoke). COG will typically contain between 55 and 60% hydrogen by volume. Most of Solar's COG turbines are used in China, where they have operated for more than 1.4 million cumulative hours. Solar's SoLoNOx™ brand of DLN combustors is able to operate with up to 20% hydrogen in the fuel without significant modification [ 35 ] and can achieve NO X emissions of 25 ppm (42 ppm on smaller machines) [ 50 ] or lower. Solar also participated in a DOE-funded project in collaboration with Precision Combustion Inc., which aimed to develop a full-scale rich catalytic hydrogen (RCH1) injector. The results confirmed that the technology was able to achieve low single-digit NO X emissions with a mixture of 42% hydrogen (remainder being nitrogen diluent) [ 51 ]. Finally, Solar was selected for a research grant under the DOE's Funding Opportunity Announcement (FOA) 2400 [ 52 ] to develop a DLN gas turbine combustor designed for 100% hydrogen (and blends of natural gas).

Rolls-Royce Power Systems has also begun decarbonizing its products and operations, including gas turbines. In 2015, Rolls-Royce launched its Green and High-Tech Program to create and test new mobile engines on 100% hydrogen fuel. The aim of the program is to reduce pollutant emissions and materials consumption in the stationary turbine and marine energy industries [ 53 ]. While specific data on Rolls-Royce hydrogen turbines could not be found in the literature, the company spent $2.1 × 10 −9 USD in R&D (with international support) for the advancement of hydrogen technologies with the goal of completely decarbonizing all products and business operations by 2050 [ 54 ].

Ansaldo Energia is a smaller manufacturer that offers hydrogen turbines capable of burning fuels with 25–50% hydrogen content by volume. Internal testing confirmed that Ansaldo's engines could generally handle 30% hydrogen content without modification, with one engine having demonstrated the ability to combust fuels containing up to 70% hydrogen by volume. Ansaldo has since developed a retrofitted “flamesheet combustor” as a commercial solution for E- and F-class turbines, boosting the hydrogen limit to 40% by volume. Several GE engines have also made use of this technology, and a simple retrofit is all that is needed to apply it to other commercial engines [ 35 ].

Baker Hughes is another smaller manufacturer that experienced significant growth in 2019 after it was spun off from GE. Baker Hughes generally specializes in smaller turbines (40 megawatts [MW] or less) but has developed several light industrial-scale turbines in the 100-MW range. From the technology rights inherited from GE, as well as through continued R&D, Baker Hughes turbines can currently handle approximately 30–60% hydrogen, with most high-hydrogen-capable turbines being aeroderivatives such as the LM 2500 and LM 5000™ series [ 55 ]. Their newest line of turbines, the NovaLT™ series, is currently under R&D to increase the fuel flexibility, allowing up to 100% hydrogen. Finally, Baker Hughes is currently collaborating with Enel Labs to create novel burner technologies to increase the reliability of lean, premixed combustion of high-hydrogen fuels [ 35 ].

MAN Energy Solutions has a portfolio consisting mostly of microturbines (6–12 MW). These turbines typically use standard diffusion flame combustors, which can reliably handle fuels with up to 60% hydrogen by volume but require postcombustion NO X treatment in order to reach emissions targets. Several turbines are equipped with DLE technology, which can achieve very low NO X without flame dilution. However, the allowable hydrogen percentage drops to 20% under such conditions. In collaboration with the German Aerospace Center (Deutsches Zentrum für Luft und Raumfahrt [DLR]) at Stuttgart, MAN continues to conduct theoretical and experimental studies with the goal of achieving 100% hydrogen capability with low NO X emissions [ 35 ].

Finally, Kawasaki Heavy Industries is working on implementing new combustion technologies and techniques to improve the reliability of hydrogen combustion in its turbines. To this end, current R&D efforts are focusing on a new “Micro-Mix” combustor to reduce the effects of instabilities created by hydrogen combustion, helping to reduce NO X . This technology is being developed in collaboration with Aachen University in Germany [ 56 , 57 ]. The technology was successfully demonstrated in 2020, making Kawasaki the first turbine manufacturer to successfully verify a 100% hydrogen-fueled turbine with DLN combustion technology. The demonstration project was carried out in partnership with Japan's New Energy and Industrial Technology Development Organization (NEDO) and Obayashi Corporation [ 58 ]. Using 100% hydrogen, the test system was able to provide 2800 kilowatts (kW) of heating steam and hot water and 1100 kW of electricity to various neighboring facilities while using water injection to achieve NO X emissions of approximately 50 ppm. While this may seem high, it is important to remember that this is well below the 70-ppm threshold set by Japan's Air Pollution Control Act [ 59 ].

Hydrogen combustion research is ongoing, and while achieving 100% clean hydrogen combustion in gas turbines remains challenging, many endeavors have come to fruition. Aeroderivative engines appear to have made the most progress, with many models supposedly already able to utilize 100% hydrogen fuel with low NO X emissions. As mentioned previously, companies such as GE and Siemens claim that several of their turbines are already capable of 100% hydrogen with diffusion combustors. However, such turbines are not feasible because their unmitigated NO X emissions are too high.

The major challenge with designing a 100% hydrogen combustion turbine is balancing the increased hydrogen usage limits against keeping NO X emissions in check without sacrificing turbine efficiency. In addition, there is a corrosion issue downstream in the turbine due to the high temperature/pressure steam generated by hydrogen combustion. Such challenges have been the subject of extensive R&D over the past several decades, and they continue to this day. Without proper NO X abatement techniques (SCR, SNCR, SoLoNOx, etc.) and combustor development, experts predict that the use of hydrogen will increase NO X emissions. However, with modern cocombustion and postcombustion abatement techniques, the studies and research efforts presented in this paper demonstrate that a fully commercialized, low-NO X , high-hydrogen turbine can be developed within the next 20 years with enough R&D.

Both public and private research initiatives are currently underway with the goal of achieving a fully commercialized hydrogen gas turbine power plant, as most operational issues associated with hydrogen fuels have been resolved. Most OEMs continue to make progress advancing the technology toward full compatibility with 100% hydrogen fuels. It is likely that most of the industry will be capable of producing commercial-grade, 100% hydrogen engines by 2030 based on current research progress and publicly announced forecasts.

The authors would like to thank the OEM representatives who provided the specification data cited in the review study behind this paper, especially representatives from GE, Siemens, and Mitsubishi for providing and granting permission to use several of the figures shown in this paper. Finally, the authors would like to thank the Department of Energy personnel that provided advance review comments and granted approval for the publication of this paper so it can be shared with industry, research personnel, and the general public.

This project was funded by the United States Department of Energy, National Energy Technology Laboratory, in part, through a site support contract. Neither the United States Government nor any agency thereof, nor any of their employees, nor the support contractor, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

The authors attest that all data for this study are included in the paper.

air separation unit

carbon capture and sequestration/storage

coke oven gas

dry, low-emissions

dry, low-NO X

flue gas recirculation

gas turbine

integrated gasification combined cycle

natural gas

natural gas combined cycle

nitrogen oxides

original equipment/engine manufacturer

research and development

rich catalytic hydrogen (injector)

selective catalytic reduction

selective noncatalytic reduction

state-of-the-art

wet, low-NO X

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A systematic literature review of the current discussion on mathematical modelling competencies: state-of-the-art developments in conceptualizing, measuring, and fostering

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Published: 15 October 2021
Volume 109 , pages 205–236, ( 2022 )

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Mustafa Cevikbas 1 ,
Gabriele Kaiser ORCID: orcid.org/0000-0002-6239-0169 1 , 2 &
Stanislaw Schukajlow 3

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Mathematical modelling competencies have become a prominent construct in research on the teaching and learning of mathematical modelling and its applications in recent decades; however, current research is diverse, proposing different theoretical frameworks and a variety of research designs for the measurement and fostering of modelling competencies. The study described in this paper was a systematic literature review of the literature on modelling competencies published over the past two decades. Based on a full-text analysis of 75 peer-reviewed studies indexed in renowned databases and published in English, the study revealed the dominance of an analytical, bottom-up approach for conceptualizing modelling competencies and distinguishing a variety of sub-competencies. Furthermore, the analysis showed the great richness of methods for measuring modelling competencies, although a focus on (non-standardized) tests prevailed. Concerning design and offering for fostering modelling competencies, the majority of the papers reported training strategies for modelling courses. Overall, the current literature review pointed out the necessity for further theoretical work on conceptualizing mathematical modelling competencies while highlighting the richness of developed empirical approaches and their implementation at various educational levels.

Modelling Competencies: Past Development and Further Perspectives

Fostering Mathematical Modelling Competencies: A Systematic Literature Review

Empirical research on teaching and learning of mathematical modelling: a survey on the current state-of-the-art

S. Schukajlow, G. Kaiser & G. Stillman

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Modelling and applications are essential components of mathematics, and applying mathematical knowledge in the real world is a core competence of mathematical literacy; thus, fostering students’ competence in solving real-world problems is a widely accepted goal of mathematics education, and mathematical modelling is included in many curricula across the world. Despite this consensus on the relevance of mathematical modelling competencies, various influential approaches exist that define modelling competencies differently. In psychological discourse, competencies are mainly defined as cognitive abilities for solving specific problems, complemented by affective components, such as the volitional and social readiness to use the problem solutions (Weinert, 2001 ). In the mathematics educational discourse, Niss and Højgaard ( 2011 , 2019 ) emphasized cognitive abilities as the core of mathematical competencies within their extensive framework, an updated version of which has recently been published; therefore, the question of how to conceptualize competence as an overall construct, with competency and competencies as associated derivations, remains open.

The discussion on the teaching and learning of mathematical modelling, which began in the 1980s, has emphasized the practical application of mathematical modelling skills; for example, the prologue of the proceedings of the first conference on the teaching and learning of mathematical modelling and applications (hereafter ICTMA) stated: “To become proficient in modelling, you must fully experience it – it is no good just watching somebody else do it, or repeat what somebody else has done – you must experience it yourself” (Burghes, 1984 , p. xiii). This strong connection to proficiency may be one reason for the early development of the discourse on modelling competencies compared to other domains, such as teacher education.

Despite this broad consensus on the importance of modelling competencies and the relevance of the modelling cycle in specifying the expected modelling steps and phases, no worldwide accepted research evidence exists on the effects of short- and long-term mathematical modelling examples and courses in school and higher education on the development of modelling competencies. One reason for this research gap may be the diversity of instruments for measuring modelling competencies and the lack of agreed-upon standards for investigating the effects of fostering mathematical modelling competencies at various educational levels, which depends on reliable and valid measurement instruments. Finally, only a few approaches have addressed or further developed the construct of mathematical modelling competencies and/or its descriptions and components. Precise conceptualizations of mathematical modelling competence as a construct are needed to underpin reliable and valid measurement instruments and implementation studies to foster mathematical modelling competencies effectively.

With this systematic literature review, the results of which are presented in this paper, we aimed to analyze current state-of-the-art research regarding the development of modelling competencies and their conceptualization, measurement, and fostering. This analysis hopefully will contribute to a better understanding of the previously mentioned research gaps and may encourage further research.

1 Theoretical frameworks as the basis for the research questions and analysis

To date, only one comprehensive literature review on modelling competencies—a classical literature search on modelling competencies by Kaiser and Brand ( 2015 )—has been conducted, constituting an important starting point for the current discourse on mathematical modelling. Contrasting with the present systematic literature review using reputable databases, this classical literature review was based on the proceedings of the biennial ICTMA series. A study by the International Commission on Mathematics Instruction (ICMI) on modelling and applications (the 14th ICMI Study), conducted at the International Congress of Mathematical Education’s (ICME’s) international quadrennial congresses, reviewed related books published by special groups, together with special issues of mathematics educational journals and other journal papers. Based on this literature survey, the development of the discourse on modelling competencies since the start of the international conference series in 1983 was reconstructed by Kaiser and Brand ( 2015 ).

The review indicated that the early discourse addressed the constructs of modelling skills or modelling abilities, including metacognitive skills. The first widespread use of the modelling competence construct emerged with the 14th ICMI Study on Applications and Modelling, a separate part of which was devoted to modelling competencies (Blum et al., 2007 ). More or less simultaneously, the discussion on modelling competence, and its conceptualization and measurement, started at ICTMA12 (Haines et al., 2007 ) and continued at ICTMA14 (Kaiser et al., 2011 ), with both proceedings containing sections on modelling competencies.

In their literature review, Kaiser and Brand ( 2015 ) distinguished four central perspectives on mathematical modelling competencies with different emphases and foci. These four perspectives were characterized as follows:

Introduction of modelling competencies and an overall comprehensive concept of competencies by the Danish KOM project (Niss & Højgaard, 2011 , 2019 )

Measurement of modelling skills and the development of measurement instruments by a British-Australian group (Haines et al., 1993 ; Houston & Neill, 2003 )

Development of a comprehensive concept of modelling competencies based on sub-competencies and their evaluation by a German modelling group (Kaiser, 2007 ; Maaß, 2006 )

Integration of metacognition into modelling competencies by an Australian modelling group (Galbraith et al., 2007 ; Stillman, 2011 ; Stillman et al., 2010 ).

These perspectives shaping the discourse on modelling competencies followed two distinct approaches to understanding and defining mathematical modelling competence: a holistic understanding and an analytic description of modelling competencies, referred to as top-down and bottom-up approaches by Niss and Blum ( 2020 ).

In the following, we describe these two diametrically opposite approaches and identify intermediate approaches.

1.1 A holistic approach to mathematical modelling competence—the top-down approach

The Danish KOM project first clarified the concept of modelling competence, which was embedded by Niss and Højgaard ( 2011 ) into an overall concept of mathematical competence consisting of eight mathematical competencies. The modelling competency was defined as one of the eight competencies, which were seen as aspects of a holistic description of mathematical competency, in the sense of Shavelson ( 2010 ). The modelling competency was defined by Niss and Højgaard ( 2011 ) as follows:

This competency involves, on the one hand, being able to analyze the foundations and properties of existing models and being able to assess their range and validity. Belonging to this is the ability to ‘de-mathematise’ (traits of) existing mathematical models; i.e. being able to decode and interpret model elements and results in terms of the real area or situation which they are supposed to model. On the other hand, competency involves being able to perform active modelling in given contexts; i.e. mathematising and applying it to situations beyond mathematics itself. (p. 58)

In their revised version of the definition of mathematical competence, Niss and Højgaard ( 2019 ) explicitly excluded affective aspects such as volition and focused on cognitive components. Referring to the mastery of the modelling competency, Blomhøj and Højgaard Jensen ( 2007 ) developed three dimensions for evaluation:

Degree of coverage, referring to the part of the modelling process the students work with and the level of their reflection

Technical level, describing the kind of mathematics students use

Radius of action, denoting the domain of situations in which students perform modeling activities.

Niss and Blum’s ( 2020 ) description of these approaches called this definition the “top-down” definition, referring explicitly to the expression “modelling competency” as singular, denoting a “distinct, recognizable and more or less well-defined entity” (p. 80).

Concerning the fostering of modelling competencies, Blomhøj and Jensen ( 2003 ) distinguished holistic and atomistic approaches. The holistic approach depends on a full-scale modelling process, with the students working through all phases of the modelling process. In the atomistic approach, students concentrate on selected phases of the modelling process, especially the processes of mathematizing and analyzing models mathematically, because these phases are seen as especially demanding. However, the authors issued a strong plea for a balance between these two approaches, since neither of them alone was seen as adequate.

1.2 An analytic approach to modelling competencies and sub-competencies—the bottom-up approach

The analytic definition of competence refers to the seminal work of Weinert ( 2001 ), which described it as “the cognitive abilities and skills available to individuals or learnable through them to solve specific problems, as well as the associated motivational, volitional and social readiness and abilities to use problem solutions successfully and responsibly in variable situations” (Weinert, 2001 , p. 27f). Based on this definition, modelling competencies were distinguished from modelling abilities: “Modelling competencies include, in contrast to modelling abilities, not only the ability but also the willingness to work out problems, with mathematical aspects taken from reality, through mathematical modelling” (Kaiser, 2007 , p. 110). Similarly, Maaß ( 2006 ) described modelling competencies as the ability and willingness to work out problems with mathematical means, including knowledge as the inevitable basis for competencies. The emphasis on knowledge as part of competence is in line with the discussion on competencies in the professional development of teachers; the most recent approach within this discussion on competence as a continuum aims to connect dispositions, including knowledge and beliefs, with situation-specific skills and classroom performance (Blömeke et al., 2015 ). Due to the fact that no standard methods exist for mathematical modelling as a means to find solutions to real-world problems, many cognitive and affective barriers must be overcome. This situation makes metacognitive skills and knowledge needed to monitor modelling activities highly relevant to the development of non-standard approaches. The construct of metacognition has been introduced into the broad discussion about the teaching and learning of mathematical modelling and plays an increasing role within the current modelling discourse, which was called for by Stillman and Galbraith in 1998 and further developed by, among others, Stillman ( 2011 ) and Vorhölter ( 2018 ).

Departing from the developments described above, a distinction has been developed between global modelling competencies and the sub-competencies of mathematical modelling within the mathematical modelling discourse (Kaiser, 2007 ; Maaß, 2006 ). Global modelling competencies are defined as the abilities necessary to perform and reflect on the whole modelling process, to at least partially solve a real-world problem through a model developed by oneself, to reflect on the modelling process using meta-knowledge, and to develop insight into the connections between mathematics and reality and into the subjectivity of mathematical modelling. Furthermore, social competencies, such as the ability to work in groups and communicate about and via mathematics, are part of global competencies.

The sub-competencies of mathematical modelling relate to the modelling cycle, of which different descriptions exist, including the different competencies essential for performing individual steps of the modelling cycle. Based on early work by Blum and Kaiser ( 1997 ) and subsequent extensive empirical studies, the following sub-competencies of modelling competence were distinguished by Kaiser ( 2007 , p. 111) and similarly by Maaß ( 2006 ):

Competencies to understand real-world problems and to develop a real-world model

Competencies to create a mathematical model out of a real-world model

Competencies to solve mathematical problems within a mathematical model

Competencies to interpret the mathematical results in a real-world model or a real-world situation

Competencies to challenge the developed solution and carry out the modelling process again, if necessary

Due to the strong reference to sub-competencies as part of the construct competence, this approach is called the analytic approach or, according to Niss and Blum ( 2020 ), the “bottom-up approach” (p. 80). Stillman et al. ( 2015 ) noted in their summarized description of this perspective the comprehensive character of this approach, referring to the early development of assessment instruments with multiple-choice items mapped to indicators of each sub-competence (e.g., Haines et al., 1993 ), which was adopted by further studies. Additionally, different levels of modelling competence were distinguished based, for example, on various test instruments (Maaß, 2006 ; Kaiser, 2007 ) and metacognitive frameworks (Stillman, 2011 ).

1.3 Further approaches to mathematical modelling competence

Further approaches concerning the construct of mathematical modelling competence can be distinguished, which this section briefly summarizes.

In their survey paper for the ICMI study on mathematical modelling and applications, Niss et al. ( 2007 ) proposed an enrichment of the top-down method, which integrated the main characteristics of the top-down approach with elements of the bottom-up approach. Referring to the holistic approach to competency, they defined mathematical modelling competency as follows:

[The] ability to identify relevant questions, variables, relations or assumptions in a given real world situation, to translate these into mathematics and to interpret and validate the solution of the resulting mathematical problem in relation to the given situation, as well as the ability to analyze or compare given models by investigating the assumptions being made, checking properties and scope of a given model etc. in short: modelling competency in our sense denotes the ability to perform the processes that are involved in the construction and investigation of mathematical models. (p. 12–13)

Furthermore, social competencies and mathematical competencies were included in this approach, which had (at least initially) some similarities to the bottom-up approach; however, with the inclusion of a critical analysis of modelling activities, this approach can be seen as resembling the top-down approach. In our systematic literature review, we call this approach a top-down enriched approach.

Other approaches have also been developed in the past, and hierarchical level-oriented approaches in particular have received some attention; for example, Henning and Keune ( 2007 ) focused on the cognitive demands of modelling competencies and distinguished them as follows: level one recognition and understanding of modelling, level two independent modelling, and level three meta-reflection on modelling. Furthermore, design-based model-eliciting activity principles, which had been developed as assessment tools for modelling competencies, were proposed as competence framework (Lesh et al., 2000 ). Another framework taken up within the discourse was the framework for the successful implementation of mathematical modelling (Stillman et al., 2007 ).

Summarizing the description of the theoretical approaches to mathematical modelling competencies, we can state that only a few established theoretical frameworks currently exist, which are difficult to discriminate between, as they refer to each other and the ongoing discourse. Overall, although modelling competencies are clearly conceptualized, as evidenced by the inclusion of current approaches in the ongoing discussion, we could not identify a rich variety of conceptualizations on which to build our literature review.

1.4 Research questions

Building upon the above-mentioned theoretical frameworks for conceptualizing modelling competencies and ways to measure and foster them, our study systematically reviewed the existing literature in the field of modelling competencies. In order to reveal how cumulative progress has been made in research over the past few decades, we endeavored to answer the following research questions and analyze them over time (i.e., the last three decades):

1.4.1 Study characteristics and research methodologies

How are the studies on modelling competencies distributed, and how can they be characterized by the country of origin of the authors, appearance over time, type of paper (theoretical or empirical; conference proceedings papers or journal papers), use of research methods, educational level involved, previous modelling experience before implementing the study, and type of modelling task used?

1.4.2 Characteristics of the studies concerning the conceptualization, measurement, and fostering of modelling competencies

How have researchers conceptualized modelling competencies? Are the theoretical perspectives identified and described in the theoretical frameworks also reflected in the various empirical studies? Are modelling competencies conceptualized as a holistic construct, or are they further differentiated as analytic constructs using various sub-competencies?

Which instruments for measuring modelling competencies have researchers used to study (preservice) teachers’ or school students’ modelling competencies? Specifically, what types of instruments and data collection methods were used, which groups were targeted, and what were the sample sizes?

Which interventions for fostering and measuring modelling competencies have researchers used to support (preservice) teachers’ or school students’ modelling competencies?

In the following section, we describe the methods used for this literature review before we present the results. The paper closes with an outlook on further perspectives on the work based on this systematic literature review and on the contributions of the papers in this special issue of Educational Studies in Mathematics on modelling competencies.

2 Methodology of the systematic literature review

2.1 search strategies and manuscript selection procedure.

To uncover the current state of the research conceptualizing mathematical modelling competencies and their measurement and fostering, we conducted a systematic literature review. This approach involves “a review of a clearly formulated question that uses systematic and explicit methods to identify, select, and critically appraise relevant research, and to collect and analyze data from the studies that are included in the review” (Moher et al., 2009 , p. 1).

The current review followed the most recent Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines (Page et al., 2021 ). The final literature search was carried out on March 17, 2021 in the following databases: (1) Web of Science (WoS) Core Collection, (2) Scopus, (3) PsycINFO, (4) ERIC, (5) Teacher Reference Center, (6) IEEEXplore Digital Library, (7) SpringerLink, (8) Taylor & Francis Online Journals, (9) zbMATH Open, (10) JSTOR, (11) MathSciNet, and (12) Education Source. These databases have high-quality indexing standards and a high international reputation. Furthermore, they contain many studies in the field of educational sciences, particularly in mathematics education research. In order to capture the relevant studies in the field of mathematics education research, search strings with Boolean operators and asterisks were used in the systematic review, as shown in Table 1 .

The current survey focused on studies conducted in the field of mathematics education, published in English, which closely related to the conceptualization, measurement, or fostering of mathematical modelling competencies. Our search embraced studies conducted at all levels of mathematics education and did not restrict the publication year of the studies. Overall, to specify eligible manuscripts for the review, we used five inclusion and five exclusion criteria as presented in Table 2 ; since not all exclusion criteria were exact opposites of the inclusion criteria, we separated exclusion and inclusion criteria. All the authors of this study were responsible for determining the eligibility of the papers for inclusion.

In addition to the electronic database search, on the basis of the first four criteria (IC1-IC4 and EC1-EC4), we conducted a hand-search for key conference proceedings that are important for mathematical modelling research, although they were not indexed in the electronic databases (amongst others as they were not registered by their publishers). We therefore screened the ICTMA proceedings from 1984 to 2009 and the recently published ICTMA19 proceedings. There was no need to manually screen the remaining ICTMA proceedings since they were already indexed in databases covered by IC5. Hand-searching is an accepted way of identifying the most recent studies that have not yet been included in or indexed by academic databases (Hopewell et al., 2007 ).The manuscript selection process was conducted in three main stages: (1) identification, (2) screening, and (3) inclusion (Page et al., 2021 ). In the identification stage, search strings from Table 1 were used, and a literature search of the 12 listed databases yielded 6,146 records. Endnote served as bibliographic software for managing references and removing duplicate records. After discarding 670 duplicate records, we moved to the initial screening of 5,476 records. Additionally, we found 411 potentially eligible records through hand-searching and screened all 5,887 reports based on their titles, abstracts, and keywords. First, we used the “refine” or “limit to” features of the electronic databases to exclude 3,276 papers by selecting the document type as journal article, book chapter, or conference proceedings; the language as English (all databases); and subject areas as education/educational research and educational scientific disciplines (WoS), education (Taylor & Francis Online Journals, SpringerLink, and JSTOR), social sciences (Scopus), and mathematics (WoS and Scopus). We then manually screened the remaining 2,611 reports’ titles, abstracts, and keywords on the basis of our ICs and ECs and found 204 potentially relevant studies through independent examination by the authors. At the end of the screening stage, we examined the full-text versions of these 204 studies based on our eligibility criteria, as mentioned in Table 2 . Ultimately, we included 75 studies in the systematic review with the full agreement of all the authors. Figure 1 illustrates the flow chart for the entire manuscript selection process.

Flow diagram of the manuscript selection process

2.2 Data analysis

Our analysis included 75 papers, which are described in Tables 9 , 10 , 11 , and 12 in the Appendix and displayed in the electronic supplementary material. The analysis of the current review mainly consisted of a screening and a coding procedure. First, the eligible studies were screened three times by the authors and examined in-depth. A coding scheme was then developed, and the codes were structured around our research questions according to four overarching categories:

Study characteristics and research methodologies (research question 1)

Theoretical frameworks for modelling competencies (research question 2)

Measuring mathematical modelling competencies (research question 3)

Fostering mathematical modelling competencies (research question 4)

Table 3 exemplifies our coding concerning the theoretical conceptualization of the reviewed papers.

The analysis was carried out according to the qualitative content analysis method (Miles & Huberman, 1994 ), focusing on the topics the reviewed studies addressed. We analyzed the studies that concerned our research interests, systematized according to the four main categories. First, concerning research question 1, we categorized the general characteristics of the reviewed studies and the research methodologies they had used based on ten sub-categories (e.g., publication year, document type, geographic distribution, research methods, sample/participants, participants’ level of education, sample size, participants’ previous experience in modelling, task types and modelling activities, and data collection methods). Second, with a special focus on research question 2, we analyzed the theoretical frameworks for modelling competencies that motivated the studies. Regarding research questions 3 and 4, we identified the measurement and fostering strategies developed, used, or suggested in the reviewed studies.

The main parts of the coding manual can be found in the Appendix, displayed in the electronic supplementary material (Tables 9 , 10 , 11 , and 12 ) with a sample coding in Table 12 . Our initial coding was conducted by the first author, and multiple strategies were then used to check the coding reliability using Miles and Huberman’s ( 1994 , p.64) formula: “reliability = number of agreements / (total number of agreements + disagreements).” First, we applied a code-recode strategy, which involved recoding all the studies after an interval of four weeks, and the consistency rate between the two distinct coding sessions was computed as 0.97. Second, to test coding reliability, 20% of the reviewed papers were randomly selected and cross-checked for coherence by a coder other than the authors, who had previous experience in mathematical modelling research area and qualitative data analysis. The intercoder reliability was found to be 0.93. Third, the first two authors separately coded the theoretical frameworks of all the included studies because these frameworks for modelling competencies were more complex to code than the other categories due to more interpretative elements. After double coding all the data concerning the theoretical frameworks underpinning the studies, the intercoder reliability rate was 0.91. After applying these strategies, all coders discussed the coding schedule, with a particular focus on the discrepancies between different codes, to achieve full consensus. All the computed reliability rates illustrated that the coding system was sufficiently reliable (Creswell, 2013 ).

3 Results of the systematic literature review on mathematical modelling competencies

3.1 study characteristics and research methodologies of the papers (research question 1), 3.1.1 types of documents and publication years.

The 75 papers included in our study consisted of 67 empirical studies, 4 theoretical studies, 3 survey or overview studies, and 1 document analysis study with the following distribution of papers: 31 journal articles, 42 conference proceedings, and 2 book chapters. Eligible papers were published in 21 different scientific journals, including 10 mathematics education journals, 5 educational journals, and 4 interdisciplinary scientific journals focusing on science, technology, engineering, and mathematics (STEM) education. The reviewed articles published in mathematics education journals constituted only 7% of all the reviewed studies. Concerning conference proceedings, the majority of the eligible papers came from ICTMA proceedings ( n = 31), with only a few studies from other mathematics education conferences (mainly ICME, Psychology in Mathematics Education [PME], and Congress of the European Society for Research in Mathematics Education [CERME]). Concerning publication years, the reviewed studies appeared between 2003 and 2021, and an increase was observed in studies on modelling competencies in 2020 (see Fig. 2 ). The visualization in Fig. 2 does not show steady progress over time, especially regarding the impact of the biennial ICTMA conferences and their subsequently published proceedings. We called papers stemming from the books from the ICTMA conference series as conference proceedings, although the books have not been named like that in the past decade due to their selectivity and rigorous peer-review process carried out.

Numbers of annual studies on mathematical modelling competencies

3.1.2 Geographic distribution

The results concerning geographic distribution revealed the contributions of researchers from different countries to research on mathematical modelling competencies. An analysis conducted separately based on all authors’ affiliations and first authors’ affiliations found few important differences; thus, only the results based on all authors’ country affiliations are tabulated. When reviewing the studies, geographical origins were critical, as the classification criteria reflected the research culture of the countries to a certain extent; for example, the competence construct is especially prominent in Europe, whereas in other parts of the world, other constructs, such as proficiency, are more common. We therefore found as expected that most authors came from Europe, followed by Asia, Africa, and America, and only one came from Australia. In particular, the authors came from 18 different countries, with Germany being the most prominent. Table 4 indicates the distribution of the authors by country and continent.

3.1.3 Research designs and data collection methods

The analysis revealed that roughly one-third of the reviewed studies (32%, n = 24) used quantitative research methods (e.g., experimental, quasi-experimental, comparative, correlational research, survey, and relational survey models), followed by qualitative research methods (e.g., case study and grounded theory; 27%, n = 20) and design-based research methods (5%, n = 4). Only one study used both qualitative and quantitative research methods, and another study relied on document analysis. A few theoretical studies (5%, n = 4) and overview/survey studies (4%, n = 3) were counted among the remainder. For 18 eligible studies (24%), it was not possible to identify the research method used.

Various data collection methods were used in the reviewed studies, with (non-standardized) test instruments being the most frequently used method (see Fig. 3 ). The majority of the studies (44 of 75 studies, 59%) used more than one data collection method, whereas 23 studies (31%) used only one method. Seven papers reporting theoretical and overview/survey studies were not applicable to this category. We took into account that data collection might not be restricted to the evaluation of modelling competencies, but could include in addition other constructs, such as beliefs or attitudes.

Data collection methods used in the reviewed studies

3.1.4 Focus samples, sample sizes, and study participants’ levels of education

In this review study, we analyzed the sample characteristics of the reviewed studies. When we categorized the participants of the studies, we took into consideration the authors’ reports concerning the educational level of the participants. There is no clear international distinction between elementary and lower secondary education with elementary education covering year 1 to 4 or 1 to 6, which has to be taken into account.

The analysis showed that the majority of the reviewed studies (45%, n = 34) recruited secondary school students (grades 6–12), and 20% ( n = 15) used samples of preservice (mathematics) teachers. Moreover, 12 studies (16%) focused on university students, including engineering students ( n = 8), mathematics and natural science students ( n = 1), and students from an interdisciplinary program ( n = 1), an introductory and interdisciplinary study program in science ( n = 1), and STEM education ( n = 1). Additionally, three studies (4%) used mixed samples of students, preservice teachers, and experienced teachers as their participants. Only two studies (3%) dealt with elementary school students (one group focusing on first graders and the other on fifth graders). One study did not mention the sample. The remaining eight studies (11%) were not applicable to this category, as they did not report on an empirical study or were of a theoretical nature. Figure 4 illustrates the distribution of the reviewed studies’ participants.

Participants in the reviewed studies

Table 5 shows the analysis of the sample sizes of the studies. The majority of the studies (32%, n = 24) recruited 0-50 participants, and overall, 51% ( n = 38) had less than 200 participants. Additionally, 14 studies (19%) conducted research with 201-500 participants, and 3 large-scale studies (4%) had more than 1,000 participants. We also analyzed the sample sizes of the studies based on the participants’ levels of education, and we used two categories (school/university students and preservice teachers). The results for these two categories did not differ substantially from each other; the most striking difference seemed to be in the range of 201-500 participants who were school students. The table illustrates the difficulties in higher education in collecting data from larger samples.

3.1.5 Participants’ previous modelling experience and modelling task types

Since participants’ previous modelling experience was mentioned as an important factor for success by several studies, we analyzed this information given in the papers. Our results showed that in 25% ( n = 19) of the studies, participants had very limited or no experience in modelling (i.e., they had participated in only one or two modelling activities by the time of the study). Furthermore, two studies reported that their participants had previous modelling experience (e.g., experience gained by attending modelling courses and seminars) before the research interventions. One study mentioned that the participants were heterogeneous in terms of their experience in modelling. Besides these results, we found that the majority of the reviewed studies (65%, n = 45) did not provide any information regarding participants’ previous experience in modelling.

In our review, we also evaluated how modelling activities were carried out during the research interventions and which types of tasks were used by the studies. The results revealed that modelling activities were predominantly performed in group work (37%, n = 28), 5 studies (7%) reported that they guided participants in individual/independent modelling activities, and the other 6 studies (8%) stated that they used both individual and group work. However, numerous reviewed studies (39%, n = 29) did not state how they performed modelling activities.

The types of modelling tasks used in the studies were not clearly described in the majority of the reviewed studies (59%, n = 44). We did not use a predefined classification, but used the classification given by the authors as in many papers no detailed information about the task was provided. This did not allow to use a predefined classification scheme, although we admit the advantages of predefined classifications. In this sense, we found that 11 studies (15%) applied more than 1 task type in the research; however, 18 reviewed studies (24%) employed a single type of modelling task. The results on type of tasks used by the reviewed studies are displayed in Table 6 .

Connected to the low information to the task type is the missing information about the context of the modelling examples (e.g., closeness to students’ world, workplace, citizenship, etc.) in many papers, which did not allow us to analyze this important category.

3.2 Results concerning the theoretical frameworks for modelling competencies (research question 2)

In our review, we classified the theoretical frameworks of the studies for mathematical modelling competencies into six categories. The main approaches used were as described in the theoretical part of this paper, and the results are displayed in Fig. 5 . The most prevalent theoretical framework was the bottom-up approach; other different theoretical frameworks comprised model-eliciting activities and principles as assessment tools for modelling competencies (Lesh et al., 2000 ), level-oriented descriptions of modelling competencies (Henning & Keune, 2007 ), or the framework for success in modelling (Stillman et al., 2007 ). Overall, the results indicated a scarcity of theoretical frameworks underpinning studies that investigated modelling competencies.

Theoretical frameworks of the studies on modelling competencies

3.3 Results concerning the measurement of modelling competencies (research question 3)

Our results revealed that a number of methods were used to measure modelling competencies. The most prevalent approaches used (mainly non-standardized) test instruments (55%, n = 41), written reports, and audio/video and screen recordings (24%, n = 18). The least-used methods were multidimensional item response theory (IRT) approaches ( n = 1) and field notes ( n = 1). Table 7 illustrates the methods described by the researchers for measuring modelling competencies.

The reviewed studies applied 16 different approaches to measure mathematical modelling competencies: 33% ( n = 25) of the studies used one method, 27% ( n = 20) applied two methods, 17% ( n = 13) used three methods, 7% ( n = 5) followed four methods, 4% ( n = 3) applied 5 methods, and 1 study used 6 different measurement methods for modelling competencies. For one of the reviewed studies, the modelling competency measurement method was not specified.

3.4 Results concerning the fostering of modelling competencies (research question 4)

The analysis revealed that the majority of the reviewed studies (79%, n = 59) contributed to the discourse on fostering modelling competencies by designing, developing, testing, or discussing various activities, including recommendations for the improvement of these activities. The remaining 16 studies (21%) did not mention results about fostering modelling competencies. The activities suggested in the reviewed studies for fostering modelling competencies could be divided into eight groups (see Table 8 ).

In detail, about half of the studies (48%, n = 36) designed and/or used training strategies (e.g., modelling courses/seminars, teaching units, professional development programs, and modelling projects) to foster students’ modelling competencies. Most researchers conducted studies as part of ongoing teaching activities (in schools or universities) or modelling-oriented projects, or they designed specific teaching units aimed at fostering students’ modelling competencies. Concerning modelling tasks, roughly one-third of the studies (31%, n = 23) found that the development of modelling tasks supported students’ modelling competencies. About 9% ( n = 7) of the reviewed studies reported that psychological factors (e.g., motivation, self-efficacy, attitudes, and beliefs) can affect students’ modelling competencies. The analysis revealed that studies found positive correlations between students’ modelling competencies and their levels of self-efficacy and motivation as well as their attitudes and beliefs towards modelling. Moreover, 6 eligible studies (8%) reported that metacognitive factors influenced the modelling competencies of the study participants. A few studies (5%, n = 4) focused on the effects of digital technologies/tools on modelling competencies. The results indicated that using digital devices, such as programmable calculators, special mathematical software (e.g., MATLAB), and dynamic geometry software (e.g., GeoGebra), fostered students’ modelling competencies. Three other eligible studies (4%) discussed the efficiency of the holistic and atomistic approaches to supporting modelling competencies, which we report in detail due to their relevance to the theoretical discourse: The empirical results of these studies illustrated that both approaches foster students’ modelling competencies, although both approaches have weaknesses and strengths. Kaiser and Brand ( 2015 ) found in their comparison of both approaches that the holistic approach had larger effects in interpreting and validating, the atomistic approach had larger effects on working mathematically, and there were mixed results on mathematizing and simplifying. Furthermore, the holistic approach seemed to be more effective than the atomistic approach for students who have relatively weak performance in mathematics (Brand, 2014 ). To summarize, from a developmental perspective, Blomhøj and Jensen ( 2003 ) highlighted the importance of a balance between holistic and atomistic approach to foster students’ modelling competencies.

Seven eligible studies (9%) provided other fostering strategies to develop students’ modelling competencies, as reported in Table 7 .

Overall, the results of the literature review confirmed the richness of the implementation strategies for modelling competencies and emphasized the focus of the current discourse on implementing (or at least suggesting) teaching strategies.

4 Discussion and limitations of the study and further prospects

This review study systematically investigated the current state of research on mathematical modelling competencies through analyzing 75 included papers. Our major focus concerned basic study characteristics, the conceptualization of modelling competencies, and theoretical frameworks and strategies for measuring and fostering modelling competencies.

4.1 Discussion of the results and limitations of the study

Concerning our first research question, our results indicated that the number of reported studies on modelling competencies relatively reached a satisfactory level, with a substantial increase in 2020, but there is still a need for further studies on this topic. Moreover, the vast majority of the reviewed studies were empirical studies, with only a few theoretical or survey studies, and Kaiser and Brand’s ( 2015 ) literature review on modelling competencies, which differed in nature from this one, remains the only other one to date. Conference proceedings, especially ICTMA proceedings, constituted an important proportion of the reviewed studies, followed by journal articles. Notably, the articles published in mathematics education journals accounted for only 7% of the reviewed papers. These results indicate that specialized international mathematics education conferences have a major impact on modelling competence research. Moreover, many articles in high-ranking journals have been written by psychologists rather than mathematics educators, confirming the well-known impression of the low visibility of research on mathematical modelling competencies in mathematics education.

Most authors from reviewed studies came from Europe, particularly Germany; several authors stemmed from Africa and Asia; a very limited number of authors came from North and South America; and only one from Australia. On the one hand, we need to consider the cultural contexts of studies that investigate modelling competencies, and from this point of view, there are plenty of opportunities for future intercultural research on modelling competencies. On the other hand, these results might be influenced by the fact that the competence discussion has been strongly guided by European, especially German, scholars, and that in other discourses, other terminology (e.g., performance, proficiency, skill, and ability) may be used. Further studies should focus on how modelling competencies are conceptualized and identified and consider the terms used for modelling competencies, thus enabling studies to identify the differences or similarities between different approaches to modelling competencies across different countries or cultures. Our review study illustrates that the ICTMA conferences have an influence on the distribution of the papers in terms of country affiliations of the authors. For example, ICTMA18 conducted in Cape Town (South Africa) had a great influence on the number of reviewed papers from South Africa; however, there is no similar effect for South American papers following the ICTMA16 conference held in Blumenau (Brazil), probably reflecting other theoretical perspectives such as socio-cultural approaches, in which modelling competencies play a less pronounced role (Kaiser & Sriraman, 2006 ). Furthermore, institutional restrictions may play an important role concerning the differences in country distribution of these studies.

Our results revealed that approximately one-third of the reviewed studies relied on quantitative research methods, followed by qualitative and design-based research methods. No researcher had named their study approach as mixed-methods research, but only one author reported that both quantitative and qualitative research methods were used. Overall, it is promising that the reviewed studies used a wide variety of data collection methods and more than half of them applied more than one data collection approach, which supports the development of a reliable database (Cevikbas & Kaiser, 2021 ). Moreover, a significant number of the studies focused on secondary school students as participants, followed by preservice teachers and university students from engineering, STEM, and interdisciplinary study programs. However, only two studies recruited elementary school students as participants. In line with these results, the majority of the studies were conducted in secondary education, followed by higher education, but no studies investigated early childhood education or adult education. These results showed that research is needed on modelling competencies in these areas (i.e., early childhood education, elementary education, and adult education).

Notably, interpreting study results regarding students’ modelling competencies crucially depends on knowing the participants’ previous modelling experience, but the majority of the studies provided no information about their participants’ experience in modelling. Additionally, a quarter of the studies reported that their participants had either extremely limited or no experience in modelling, and only two studies stated that their participants had substantial previous experience in mathematical modelling. These results imply that teachers and teacher educators should put great effort into developing students’ modelling experience during their school and university education. Overall, it seems advisable to share information concerning the study participants’ previous experience in modelling to enable readers to make accurate inferences from the study results and compare the results of different studies.

Furthermore, our results indicated that many reviewed studies did not mention which type of task they had used. The analysis of the remaining studies showed that various types of modelling tasks had been implemented. As the core of modelling activities are the modelling tasks or problems, it is crucial to know for the modelling discourse, which modelling tasks are used in studies and what their characteristics are. Using diverse types of modelling tasks can allow researchers to investigate the strengths and weaknesses of these tasks for teaching and learning mathematical modelling and for the promotion of students’ modelling competencies. Using different types of tasks can provide rich opportunities in the learning and teaching of modelling. Further studies should investigate which types of tasks are most effective for developing students’ modelling competencies and should make recommendations for teachers or teacher educators.

Concerning the theoretical frameworks, the results indicated that the predominant framework used by the studies was the bottom-up approach and only a few studies adopted top-down or top-down enriched approaches or other frameworks. Therefore, there is a great need to investigate modelling competencies using a variety of theoretical frameworks and to extend existing frameworks by using innovative approaches. The lack of diversity within the frameworks used directly relates to the conceptualization of modelling competencies; therefore, more theoretical research focusing on the conceptualization of modelling competencies is needed.

The strategies of the reviewed studies for measuring modelling competencies were aligned with their research methods; hence, the results showed that modelling competencies tended to be measured using (mainly non-standardized) test instruments and questionnaires. It is promising that the reviewed studies used various approaches to measure modelling competencies; however, we could not identify any study investigating which method or strategy was most effective for measuring the modelling competencies of students (e.g., focusing on the strengths and weaknesses of different measurement approaches and comparing the capabilities of these approaches to measure students’ modelling competencies). Future studies should focus on producing new tools or strategies to extend existing approaches to measuring students’ modelling competencies by, for example, using digital technologies to measure students’ modelling competencies according to these technologies’ pedagogical potential.

Although the studies reported that students’ or preservice teachers’ mathematical modelling competencies were still far from reaching an expert level, their modelling competencies could be fostered by the various strategies mentioned above (see Results 3.4). In this vein, the reviewed studies contributed to the discourse on fostering modelling competencies by designing, developing, testing, or recommending specific modelling activities. To foster students’ modelling competencies, most of the reviewed studies used instructional strategies that focused on practice in modelling and gaining experience through modelling tasks.

Moreover, several studies found that motivation, self-efficacy, beliefs, and attitudes regarding modelling, and metacognitive competencies, could affect students’ modelling competencies. A few of the studies recommended maintaining a balance between holistic and analytic approaches in the teaching and learning of modelling. Furthermore, few studies have analyzed the use of digital technologies/tools to promote students’ modelling competencies. Accordingly, using mathematical software (e.g., MATLAB and GeoGebra) for modelling has been identified as an effective strategy for fostering modelling competencies, but only a limited number of studies have focused on how and what types of technologies could be used to improve students’ modelling competencies.

In summary, we emphasize that the main foci of this systematic review (i.e., the conceptualization of modelling competencies and the related theoretical frameworks for measuring and fostering modelling competencies) are closely interrelated. Fostering and measuring strategies for modelling competency depend on its conceptualization. To this end, theoretical and empirical studies could contribute strongly to both the epistemology of modelling and its application and are greatly needed.

The results of our systematic literature review are limited by several restrictions. The first significant limitation relates to the restrictions of the databases: The exclusion of papers published in books and journals not included in WoS, Scopus, and the other high-ranking databases led to the exclusion of local/national journals that may have had the potential to provide interesting research studies. Furthermore, the exclusion of papers not written in English excluded many potentially interesting papers, especially those from the Spanish/Portuguese-speaking countries. Further research should try to overcome this limitation by including native speakers from this language area.

Other restrictions related to the automated selection process (i.e., the so-called jingle-jangle fallacy; Gonzalez et al., 2021 ). In our systematic literature review, we used the terms modelling and competence; however, we identified studies that used modelling competence differently, particularly regarding the use of modelling competencies in psychometric or educational modelling (large-scale studies) or in economics or engineering. Manual screening could help overcome this problem; however, we could not prevent the omission of papers that examined modelling competencies but used different terms, such as modelling performance or modelling proficiency. We therefore might have missed an important number of studies that employed other terminology. This is a systemic problem of our approach. Further studies should use a broader theoretical framework to identify and examine these other types of studies.

4.2 Contributions of this special issue to the discourse on modelling competencies

With this present special issue, which the current systematic literature review introduces, we aim to present advances in the research on mathematical modelling competencies. A broad body of past research has investigated modelling processes and students’ barriers to solving modelling problems. Descriptive analyses of students’ solution processes have identified the importance of specific sub-processes and related sub-competencies, such as comprehension, structuring, simplifying, mathematizing, interpretation of mathematical results, and validation of mathematical results and mathematical models for mathematical modelling. However, only a limited amount of research has investigated the effects of short- and long-term interventions on the implementation of mathematical modelling in schools and higher education institutes using rigorous methodological standards. These observations are consistent with the systematic review presented in the previous section, which identified only a limited number of studies contributing to these research aims. In line with these considerations, we argue that much more research effort should be devoted to evaluating measurement instruments and approaches to fostering mathematical modelling in schools and universities (Schukajlow et al., 2018 ). The papers in this special issue contribute to closing these significant gaps by addressing (1) the measurement and (2) the fostering of modelling competencies as well as (3) comparing groups of participants with different expertise or participants from different cultures.

The first group of papers presented assessment instruments for measuring modelling competencies. Based on their conceptualization of modelling competencies, Brady and Jung developed an assessment instrument for analyzing classroom modelling cultures. Their quantitative analysis of the modelling activities of secondary school students demonstrated differences between classroom cultures and revealed shifts in cultures within a classroom, and their qualitative analysis of students’ discourse during presentations of their solutions in classrooms offered an explanation for the phenomenon identified by the quantitative analysis. Brady and Jung interpreted these results as indicative of the validity of the measurement instrument. The new contribution of this study laid in pointing out the importance of using this new assessment instrument to analyze classroom modelling cultures in future studies.

Noticing competencies during mathematical modelling is considered important for research on modelling and on teachers’ situation-specific competencies. Alwast and Vorhölter answered the call to be more specific in the assessment of teachers’ competencies and focused on situation-specific modelling competencies in their study. Alwast and Vorhölter developed staged videos and used these videos as prompts for the assessment of preservice teachers’ noticing competencies in mathematical modelling. They performed a series of studies that aimed to collect evidence of the validity of the new instrument. This instrument could be used in the future to analyze the development of preservice teachers’ noticing skills and to examine the relationship between teachers’ noticing and their decisions and interventions in classrooms.

Students’ creativity, as a research field with a long tradition, has rarely been analyzed in relation to mathematical modelling competencies in the past. Lu and Kaiser identified the importance of creativity for the assessment of modelling competencies and evaluated students’ creative solutions to modelling problems by analyzing three central dimensions of mathematical creativity: usefulness, fluency, and originality. Their analysis of upper secondary school students’ responses indicated a close association between fluency and originality, which has important theoretical implications for the assessment of modelling competencies and the relationship between factors that contribute to mathematical creativity.

The second group of papers examined various approaches to fostering modelling sub-competencies. Geiger, Galbraith, and Niss developed a task design and implementation framework for mathematical modelling tasks aimed at supporting the instructional modelling competence of in-service teachers. The core of this approach was researcher-teacher collaboration over a long period. The results of this study have theoretical implications for implementation research by connecting the task design and task implementation streams of research in a joint model. Furthermore, this research extended the concept of pedagogical competence from numeracy to mathematical modelling competence.

Reading comprehension is an essential part of modelling processes, and improving reading comprehension can help to foster modelling competencies. Krawitz, Chang, Yang, and Schukajlow analyzed the effects of reading comprehension prompts on competence to construct a real-world model of the situation and interest of secondary school students in Germany and Taiwan. Reading comprehension prompts did not affect modelling, but they did affect interest. In-depth analysis of students’ responses indicated a positive relationship between reading comprehension and modelling. Krawitz et al. suggested that the high-quality responses to reading prompts are essential for modelling and should be given more attention in research and practice.

Teaching methods and their impact on the modelling competencies and attitudes of engineering students were the focus of the contribution by Durandt, Blum, and Lindl. The researchers analyzed the effects of independence-oriented and teacher-guided teaching styles in South Africa. The group of students taught according to the independence-oriented teaching style had the strongest competency growth and reported more positive attitudes after the treatment. Students’ independent work supported by adaptive teacher interventions and by a metacognitive scaffold, which encourage individual solutions, is a promising approach that should be analyzed in future studies and evaluated in teaching practice for mathematical modelling competencies.

Greefrath, Siller, Klock, and Wess investigated the effects of two teaching interventions on preservice secondary teachers’ pedagogical content knowledge for teaching mathematical modelling. Preservice teachers in one group designed modelling tasks for use with students, and those in another group were trained to support mathematical modelling processes. Both groups improved some facets of pedagogical content knowledge compared to a third group that received no modelling intervention. As one practical implication of the study, Greefrath et al. underlined the importance of practical sessions for improving preservice teachers’ pedagogical content knowledge of modelling.

The third group of papers included two contributions to comparative studies and a commentary. Preservice teachers’ professional modelling competencies are essential for the teaching of modelling. Yang, Schwarz, and Leung compared this construct in Germany, Mainland China, and Hong Kong. The results indicated that preservice teachers in Germany had higher levels of mathematical content knowledge and mathematical pedagogical knowledge of modelling. Yang et al. suggested that possible reasons for these results might lie in the history of mathematical modelling in mathematics curricula, teacher education, and the teaching cultures in these three regions. Future research should pay more attention to international comparative studies regarding modelling competencies.

Cai, LaRochelle, Hwang, and Kaiser compared expert and novice (preservice) secondary teachers’ competencies in noticing students’ thinking about modelling. The expert teachers noticed the students’ needed to make assumptions to complete the task more often than the novice teachers did. The researchers identified many important characteristics of the differences between experts and novices. Future research should analyze the development of preservice teachers’ and experts teachers’ competencies for noticing students’ thinking about modelling and identify what components of noticing affect the teaching of mathematical modelling competencies.

Finally, Frejd and Vos analyzed the contributions of the papers in this special issue and reflected on further developments in a commentary paper.

Summarizing the contributions of the systematic literature survey and the papers in this special issue, we recognize––despite certain limitations––many insights offered by the special issue that can enhance the current discourse on mathematical modelling competencies. The papers point to a great need for further theoretical work on the conceptualization of modelling competencies, although most papers have adopted a clear theoretical framework in their study. The low number of theoretical papers in this area strongly confirms the need for approaches that have the potential to further develop the current theoretical frameworks, especially taking socio-cultural and socio-critical aspects into account (Maass et al., 2019 ). Furthermore, the development of more standardized test instruments should be encouraged, and an exchange of these instruments within the modelling community (similar to the tests developed by Haines et al., 1993 ) is desirable. In addition, the inclusion of qualitatively oriented, in-depth studies within quantitative studies, leading to mixed-methods designs, seems to be highly desirable. Concerning teachers’ professional competencies, it seems essential to use more recent approaches to competence development, such as developing situation-specific noticing skills of preservice teachers, which should be included in further studies. Scaling-up of established learning environments within implementations under controlled conditions (e.g., by laboratory studies) seems to be highly necessary in order to strengthen the link to psychological research in this area. Despite the high methodological standards in the studies examined in the systematic literature survey and in this special issue, more studies with rigorous methodological standards that rely on the theory of modelling competencies seem to be necessary. One theoretical prediction is that knowledge about modelling and the modelling cycle is a prerequisite for developing modelling competencies. In earlier research, students’ knowledge (e.g., their procedural and conceptual knowledge of modelling as addressed by Achmetli et al., 2019 ) was analyzed as a decisive factor. Future research should assess the various facets of teachers’ modelling competence in relation to its overall construct and students’ modelling competence to contribute to the validation of theories of modelling competencies.

Change history

25 february 2022.

The original version of this paper was updated to add the missing compact agreement Open Access funding note.

Asterisk denotes inclusion in the database.

Achmetli, K., Schukajlow, S., & Rakoczy, K. (2019). Multiple solutions to solve real-world problems and students’ procedural and conceptual knowledge. International Journal of Science and Mathematics Education, 17 , 1605–1625.

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Cevikbas, M., Kaiser, G. & Schukajlow, S. A systematic literature review of the current discussion on mathematical modelling competencies: state-of-the-art developments in conceptualizing, measuring, and fostering. Educ Stud Math 109 , 205–236 (2022). https://doi.org/10.1007/s10649-021-10104-6

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Foundations of SotA Reviews

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Best Practices and Strategies For Compliant EU MDR Literature Reviews

Literature Review Strategies For Relevant SOTA Search

State of the Art, a Continuous Methodology

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1 Introduction

2.1 Low Mass and Energy Density.

2.2 High Flame Temperature.

2.3 High Flame Speed.

3.1 Fuel NO X .

3.2 Prompt NO X .

3.3 Thermal NO X .

The Zeldovich Mechanism

3.4 Effects of Hydrogen on NO X in Gas Turbines.

4.1 Combustor Geometry and Fuel Injection Schemes.

4.2 Flame Dilution.

4.3 Selective Catalytic and Noncatalytic Reduction.

Selective Reduction

5.1 General Electric.

5.2 Siemens.

5.3 Mitsubishi Heavy Industries.

5.4 Others.

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A systematic literature review of the current discussion on mathematical modelling competencies: state-of-the-art developments in conceptualizing, measuring, and fostering

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Modelling Competencies: Past Development and Further Perspectives

Fostering Mathematical Modelling Competencies: A Systematic Literature Review

Empirical research on teaching and learning of mathematical modelling: a survey on the current state-of-the-art

1 Theoretical frameworks as the basis for the research questions and analysis

1.1 A holistic approach to mathematical modelling competence—the top-down approach

1.2 An analytic approach to modelling competencies and sub-competencies—the bottom-up approach

1.3 Further approaches to mathematical modelling competence

1.4 Research questions

1.4.1 Study characteristics and research methodologies