solving problem of educational context

Why Every Educator Needs to Teach Problem-Solving Skills

Strong problem-solving skills will help students be more resilient and will increase their academic and career success .

Want to learn more about how to measure and teach students’ higher-order skills, including problem solving, critical thinking, and written communication?

Problem-solving skills are essential in school, careers, and life.

Problem-solving skills are important for every student to master. They help individuals navigate everyday life and find solutions to complex issues and challenges. These skills are especially valuable in the workplace, where employees are often required to solve problems and make decisions quickly and effectively.

Problem-solving skills are also needed for students’ personal growth and development because they help individuals overcome obstacles and achieve their goals. By developing strong problem-solving skills, students can improve their overall quality of life and become more successful in their personal and professional endeavors.

Problem-Solving Skills Help Students…

   develop resilience.

Problem-solving skills are an integral part of resilience and the ability to persevere through challenges and adversity. To effectively work through and solve a problem, students must be able to think critically and creatively. Critical and creative thinking help students approach a problem objectively, analyze its components, and determine different ways to go about finding a solution.  

This process in turn helps students build self-efficacy . When students are able to analyze and solve a problem, this increases their confidence, and they begin to realize the power they have to advocate for themselves and make meaningful change.

When students gain confidence in their ability to work through problems and attain their goals, they also begin to build a growth mindset . According to leading resilience researcher, Carol Dweck, “in a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment.”

    Set and Achieve Goals

Students who possess strong problem-solving skills are better equipped to set and achieve their goals. By learning how to identify problems, think critically, and develop solutions, students can become more self-sufficient and confident in their ability to achieve their goals. Additionally, problem-solving skills are used in virtually all fields, disciplines, and career paths, which makes them important for everyone. Building strong problem-solving skills will help students enhance their academic and career performance and become more competitive as they begin to seek full-time employment after graduation or pursue additional education and training.

  Resolve Conflicts

In addition to increased social and emotional skills like self-efficacy and goal-setting, problem-solving skills teach students how to cooperate with others and work through disagreements and conflicts. Problem-solving promotes “thinking outside the box” and approaching a conflict by searching for different solutions. This is a very different (and more effective!) method than a more stagnant approach that focuses on placing blame or getting stuck on elements of a situation that can’t be changed.

While it’s natural to get frustrated or feel stuck when working through a conflict, students with strong problem-solving skills will be able to work through these obstacles, think more rationally, and address the situation with a more solution-oriented approach. These skills will be valuable for students in school, their careers, and throughout their lives.

    Achieve Success

We are all faced with problems every day. Problems arise in our personal lives, in school and in our jobs, and in our interactions with others. Employers especially are looking for candidates with strong problem-solving skills. In today’s job market, most jobs require the ability to analyze and effectively resolve complex issues. Students with strong problem-solving skills will stand out from other applicants and will have a more desirable skill set.

In a recent opinion piece published by The Hechinger Report , Virgel Hammonds, Chief Learning Officer at KnowledgeWorks, stated “Our world presents increasingly complex challenges. Education must adapt so that it nurtures problem solvers and critical thinkers.” Yet, the “traditional K–12 education system leaves little room for students to engage in real-world problem-solving scenarios.” This is the reason that a growing number of K–12 school districts and higher education institutions are transforming their instructional approach to personalized and competency-based learning, which encourage students to make decisions, problem solve and think critically as they take ownership of and direct their educational journey.

Problem-Solving Skills Can Be Measured and Taught

Research shows that problem-solving skills can be measured and taught. One effective method is through performance-based assessments which require students to demonstrate or apply their knowledge and higher-order skills to create a response or product or do a task.

What Are Performance-Based Assessments?

With the No Child Left Behind Act (2002), the use of standardized testing became the primary way to measure student learning in the U.S. The legislative requirements of this act shifted the emphasis to standardized testing, and this led to a  decline in nontraditional testing methods .

But   many educators, policy makers, and parents have concerns with standardized tests. Some of the top issues include that they don’t provide feedback on how students can perform better, they don’t value creativity, they are not representative of diverse populations, and they can be disadvantageous to lower-income students.

While standardized tests are still the norm, U.S. Secretary of Education Miguel Cardona is encouraging states and districts to move away from traditional multiple choice and short response tests and instead use performance-based assessment, competency-based assessments, and other more authentic methods of measuring students abilities and skills rather than rote learning. 

Performance-based assessments  measure whether students can apply the skills and knowledge learned from a unit of study. Typically, a performance task challenges students to use their higher-order skills to complete a project or process. Tasks can range from an essay to a complex proposal or design.

Preview a Performance-Based Assessment

Want a closer look at how performance-based assessments work?  Preview CAE’s K–12 and Higher Education assessments and see how CAE’s tools help students develop critical thinking, problem-solving, and written communication skills.

Performance-Based Assessments Help Students Build and Practice Problem-Solving Skills

In addition to effectively measuring students’ higher-order skills, including their problem-solving skills, performance-based assessments can help students practice and build these skills. Through the assessment process, students are given opportunities to practically apply their knowledge in real-world situations. By demonstrating their understanding of a topic, students are required to put what they’ve learned into practice through activities such as presentations, experiments, and simulations. 

This type of problem-solving assessment tool requires students to analyze information and choose how to approach the presented problems. This process enhances their critical thinking skills and creativity, as well as their problem-solving skills. Unlike traditional assessments based on memorization or reciting facts, performance-based assessments focus on the students’ decisions and solutions, and through these tasks students learn to bridge the gap between theory and practice.

Performance-based assessments like CAE’s College and Career Readiness Assessment (CRA+) and Collegiate Learning Assessment (CLA+) provide students with in-depth reports that show them which higher-order skills they are strongest in and which they should continue to develop. This feedback helps students and their teachers plan instruction and supports to deepen their learning and improve their mastery of critical skills.

Explore CAE’s Problem-Solving Assessments

CAE offers performance-based assessments that measure student proficiency in higher-order skills including problem solving, critical thinking, and written communication.

• College and Career Readiness Assessment (CCRA+) for secondary education and
• Collegiate Learning Assessment (CLA+) for higher education.

Our solution also includes instructional materials, practice models, and professional development.

We can help you create a program to build students’ problem-solving skills that includes:

• Measuring students’ problem-solving skills through a performance-based assessment    
• Using the problem-solving assessment data to inform instruction and tailor interventions
• Teaching students problem-solving skills and providing practice opportunities in real-life scenarios
• Supporting educators with quality professional development

Get started with our problem-solving assessment tools to measure and build students’ problem-solving skills today! These skills will be invaluable to students now and in the future.

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Learn more about cae’s suite of products and let’s get started measuring and teaching students important higher-order skills like problem solving..

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• Published: 11 January 2023

The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature

• Enwei Xu   ORCID: orcid.org/0000-0001-6424-8169 1 ,
• Wei Wang 1 &
• Qingxia Wang 1  

Humanities and Social Sciences Communications volume  10 , Article number:  16 ( 2023 ) Cite this article

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Collaborative problem-solving has been widely embraced in the classroom instruction of critical thinking, which is regarded as the core of curriculum reform based on key competencies in the field of education as well as a key competence for learners in the 21st century. However, the effectiveness of collaborative problem-solving in promoting students’ critical thinking remains uncertain. This current research presents the major findings of a meta-analysis of 36 pieces of the literature revealed in worldwide educational periodicals during the 21st century to identify the effectiveness of collaborative problem-solving in promoting students’ critical thinking and to determine, based on evidence, whether and to what extent collaborative problem solving can result in a rise or decrease in critical thinking. The findings show that (1) collaborative problem solving is an effective teaching approach to foster students’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]); (2) in respect to the dimensions of critical thinking, collaborative problem solving can significantly and successfully enhance students’ attitudinal tendencies (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI[0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI[0.58, 0.82]); and (3) the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have an impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. On the basis of these results, recommendations are made for further study and instruction to better support students’ critical thinking in the context of collaborative problem-solving.

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Introduction.

Although critical thinking has a long history in research, the concept of critical thinking, which is regarded as an essential competence for learners in the 21st century, has recently attracted more attention from researchers and teaching practitioners (National Research Council, 2012 ). Critical thinking should be the core of curriculum reform based on key competencies in the field of education (Peng and Deng, 2017 ) because students with critical thinking can not only understand the meaning of knowledge but also effectively solve practical problems in real life even after knowledge is forgotten (Kek and Huijser, 2011 ). The definition of critical thinking is not universal (Ennis, 1989 ; Castle, 2009 ; Niu et al., 2013 ). In general, the definition of critical thinking is a self-aware and self-regulated thought process (Facione, 1990 ; Niu et al., 2013 ). It refers to the cognitive skills needed to interpret, analyze, synthesize, reason, and evaluate information as well as the attitudinal tendency to apply these abilities (Halpern, 2001 ). The view that critical thinking can be taught and learned through curriculum teaching has been widely supported by many researchers (e.g., Kuncel, 2011 ; Leng and Lu, 2020 ), leading to educators’ efforts to foster it among students. In the field of teaching practice, there are three types of courses for teaching critical thinking (Ennis, 1989 ). The first is an independent curriculum in which critical thinking is taught and cultivated without involving the knowledge of specific disciplines; the second is an integrated curriculum in which critical thinking is integrated into the teaching of other disciplines as a clear teaching goal; and the third is a mixed curriculum in which critical thinking is taught in parallel to the teaching of other disciplines for mixed teaching training. Furthermore, numerous measuring tools have been developed by researchers and educators to measure critical thinking in the context of teaching practice. These include standardized measurement tools, such as WGCTA, CCTST, CCTT, and CCTDI, which have been verified by repeated experiments and are considered effective and reliable by international scholars (Facione and Facione, 1992 ). In short, descriptions of critical thinking, including its two dimensions of attitudinal tendency and cognitive skills, different types of teaching courses, and standardized measurement tools provide a complex normative framework for understanding, teaching, and evaluating critical thinking.

Cultivating critical thinking in curriculum teaching can start with a problem, and one of the most popular critical thinking instructional approaches is problem-based learning (Liu et al., 2020 ). Duch et al. ( 2001 ) noted that problem-based learning in group collaboration is progressive active learning, which can improve students’ critical thinking and problem-solving skills. Collaborative problem-solving is the organic integration of collaborative learning and problem-based learning, which takes learners as the center of the learning process and uses problems with poor structure in real-world situations as the starting point for the learning process (Liang et al., 2017 ). Students learn the knowledge needed to solve problems in a collaborative group, reach a consensus on problems in the field, and form solutions through social cooperation methods, such as dialogue, interpretation, questioning, debate, negotiation, and reflection, thus promoting the development of learners’ domain knowledge and critical thinking (Cindy, 2004 ; Liang et al., 2017 ).

Collaborative problem-solving has been widely used in the teaching practice of critical thinking, and several studies have attempted to conduct a systematic review and meta-analysis of the empirical literature on critical thinking from various perspectives. However, little attention has been paid to the impact of collaborative problem-solving on critical thinking. Therefore, the best approach for developing and enhancing critical thinking throughout collaborative problem-solving is to examine how to implement critical thinking instruction; however, this issue is still unexplored, which means that many teachers are incapable of better instructing critical thinking (Leng and Lu, 2020 ; Niu et al., 2013 ). For example, Huber ( 2016 ) provided the meta-analysis findings of 71 publications on gaining critical thinking over various time frames in college with the aim of determining whether critical thinking was truly teachable. These authors found that learners significantly improve their critical thinking while in college and that critical thinking differs with factors such as teaching strategies, intervention duration, subject area, and teaching type. The usefulness of collaborative problem-solving in fostering students’ critical thinking, however, was not determined by this study, nor did it reveal whether there existed significant variations among the different elements. A meta-analysis of 31 pieces of educational literature was conducted by Liu et al. ( 2020 ) to assess the impact of problem-solving on college students’ critical thinking. These authors found that problem-solving could promote the development of critical thinking among college students and proposed establishing a reasonable group structure for problem-solving in a follow-up study to improve students’ critical thinking. Additionally, previous empirical studies have reached inconclusive and even contradictory conclusions about whether and to what extent collaborative problem-solving increases or decreases critical thinking levels. As an illustration, Yang et al. ( 2008 ) carried out an experiment on the integrated curriculum teaching of college students based on a web bulletin board with the goal of fostering participants’ critical thinking in the context of collaborative problem-solving. These authors’ research revealed that through sharing, debating, examining, and reflecting on various experiences and ideas, collaborative problem-solving can considerably enhance students’ critical thinking in real-life problem situations. In contrast, collaborative problem-solving had a positive impact on learners’ interaction and could improve learning interest and motivation but could not significantly improve students’ critical thinking when compared to traditional classroom teaching, according to research by Naber and Wyatt ( 2014 ) and Sendag and Odabasi ( 2009 ) on undergraduate and high school students, respectively.

The above studies show that there is inconsistency regarding the effectiveness of collaborative problem-solving in promoting students’ critical thinking. Therefore, it is essential to conduct a thorough and trustworthy review to detect and decide whether and to what degree collaborative problem-solving can result in a rise or decrease in critical thinking. Meta-analysis is a quantitative analysis approach that is utilized to examine quantitative data from various separate studies that are all focused on the same research topic. This approach characterizes the effectiveness of its impact by averaging the effect sizes of numerous qualitative studies in an effort to reduce the uncertainty brought on by independent research and produce more conclusive findings (Lipsey and Wilson, 2001 ).

This paper used a meta-analytic approach and carried out a meta-analysis to examine the effectiveness of collaborative problem-solving in promoting students’ critical thinking in order to make a contribution to both research and practice. The following research questions were addressed by this meta-analysis:

What is the overall effect size of collaborative problem-solving in promoting students’ critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills)?

How are the disparities between the study conclusions impacted by various moderating variables if the impacts of various experimental designs in the included studies are heterogeneous?

This research followed the strict procedures (e.g., database searching, identification, screening, eligibility, merging, duplicate removal, and analysis of included studies) of Cooper’s ( 2010 ) proposed meta-analysis approach for examining quantitative data from various separate studies that are all focused on the same research topic. The relevant empirical research that appeared in worldwide educational periodicals within the 21st century was subjected to this meta-analysis using Rev-Man 5.4. The consistency of the data extracted separately by two researchers was tested using Cohen’s kappa coefficient, and a publication bias test and a heterogeneity test were run on the sample data to ascertain the quality of this meta-analysis.

Data sources and search strategies

There were three stages to the data collection process for this meta-analysis, as shown in Fig. 1 , which shows the number of articles included and eliminated during the selection process based on the statement and study eligibility criteria.

This flowchart shows the number of records identified, included and excluded in the article.

First, the databases used to systematically search for relevant articles were the journal papers of the Web of Science Core Collection and the Chinese Core source journal, as well as the Chinese Social Science Citation Index (CSSCI) source journal papers included in CNKI. These databases were selected because they are credible platforms that are sources of scholarly and peer-reviewed information with advanced search tools and contain literature relevant to the subject of our topic from reliable researchers and experts. The search string with the Boolean operator used in the Web of Science was “TS = (((“critical thinking” or “ct” and “pretest” or “posttest”) or (“critical thinking” or “ct” and “control group” or “quasi experiment” or “experiment”)) and (“collaboration” or “collaborative learning” or “CSCL”) and (“problem solving” or “problem-based learning” or “PBL”))”. The research area was “Education Educational Research”, and the search period was “January 1, 2000, to December 30, 2021”. A total of 412 papers were obtained. The search string with the Boolean operator used in the CNKI was “SU = (‘critical thinking’*‘collaboration’ + ‘critical thinking’*‘collaborative learning’ + ‘critical thinking’*‘CSCL’ + ‘critical thinking’*‘problem solving’ + ‘critical thinking’*‘problem-based learning’ + ‘critical thinking’*‘PBL’ + ‘critical thinking’*‘problem oriented’) AND FT = (‘experiment’ + ‘quasi experiment’ + ‘pretest’ + ‘posttest’ + ‘empirical study’)” (translated into Chinese when searching). A total of 56 studies were found throughout the search period of “January 2000 to December 2021”. From the databases, all duplicates and retractions were eliminated before exporting the references into Endnote, a program for managing bibliographic references. In all, 466 studies were found.

Second, the studies that matched the inclusion and exclusion criteria for the meta-analysis were chosen by two researchers after they had reviewed the abstracts and titles of the gathered articles, yielding a total of 126 studies.

Third, two researchers thoroughly reviewed each included article’s whole text in accordance with the inclusion and exclusion criteria. Meanwhile, a snowball search was performed using the references and citations of the included articles to ensure complete coverage of the articles. Ultimately, 36 articles were kept.

Two researchers worked together to carry out this entire process, and a consensus rate of almost 94.7% was reached after discussion and negotiation to clarify any emerging differences.

Eligibility criteria

Since not all the retrieved studies matched the criteria for this meta-analysis, eligibility criteria for both inclusion and exclusion were developed as follows:

The publication language of the included studies was limited to English and Chinese, and the full text could be obtained. Articles that did not meet the publication language and articles not published between 2000 and 2021 were excluded.

The research design of the included studies must be empirical and quantitative studies that can assess the effect of collaborative problem-solving on the development of critical thinking. Articles that could not identify the causal mechanisms by which collaborative problem-solving affects critical thinking, such as review articles and theoretical articles, were excluded.

The research method of the included studies must feature a randomized control experiment or a quasi-experiment, or a natural experiment, which have a higher degree of internal validity with strong experimental designs and can all plausibly provide evidence that critical thinking and collaborative problem-solving are causally related. Articles with non-experimental research methods, such as purely correlational or observational studies, were excluded.

The participants of the included studies were only students in school, including K-12 students and college students. Articles in which the participants were non-school students, such as social workers or adult learners, were excluded.

The research results of the included studies must mention definite signs that may be utilized to gauge critical thinking’s impact (e.g., sample size, mean value, or standard deviation). Articles that lacked specific measurement indicators for critical thinking and could not calculate the effect size were excluded.

Data coding design

In order to perform a meta-analysis, it is necessary to collect the most important information from the articles, codify that information’s properties, and convert descriptive data into quantitative data. Therefore, this study designed a data coding template (see Table 1 ). Ultimately, 16 coding fields were retained.

The designed data-coding template consisted of three pieces of information. Basic information about the papers was included in the descriptive information: the publishing year, author, serial number, and title of the paper.

The variable information for the experimental design had three variables: the independent variable (instruction method), the dependent variable (critical thinking), and the moderating variable (learning stage, teaching type, intervention duration, learning scaffold, group size, measuring tool, and subject area). Depending on the topic of this study, the intervention strategy, as the independent variable, was coded into collaborative and non-collaborative problem-solving. The dependent variable, critical thinking, was coded as a cognitive skill and an attitudinal tendency. And seven moderating variables were created by grouping and combining the experimental design variables discovered within the 36 studies (see Table 1 ), where learning stages were encoded as higher education, high school, middle school, and primary school or lower; teaching types were encoded as mixed courses, integrated courses, and independent courses; intervention durations were encoded as 0–1 weeks, 1–4 weeks, 4–12 weeks, and more than 12 weeks; group sizes were encoded as 2–3 persons, 4–6 persons, 7–10 persons, and more than 10 persons; learning scaffolds were encoded as teacher-supported learning scaffold, technique-supported learning scaffold, and resource-supported learning scaffold; measuring tools were encoded as standardized measurement tools (e.g., WGCTA, CCTT, CCTST, and CCTDI) and self-adapting measurement tools (e.g., modified or made by researchers); and subject areas were encoded according to the specific subjects used in the 36 included studies.

The data information contained three metrics for measuring critical thinking: sample size, average value, and standard deviation. It is vital to remember that studies with various experimental designs frequently adopt various formulas to determine the effect size. And this paper used Morris’ proposed standardized mean difference (SMD) calculation formula ( 2008 , p. 369; see Supplementary Table S3 ).

Procedure for extracting and coding data

According to the data coding template (see Table 1 ), the 36 papers’ information was retrieved by two researchers, who then entered them into Excel (see Supplementary Table S1 ). The results of each study were extracted separately in the data extraction procedure if an article contained numerous studies on critical thinking, or if a study assessed different critical thinking dimensions. For instance, Tiwari et al. ( 2010 ) used four time points, which were viewed as numerous different studies, to examine the outcomes of critical thinking, and Chen ( 2013 ) included the two outcome variables of attitudinal tendency and cognitive skills, which were regarded as two studies. After discussion and negotiation during data extraction, the two researchers’ consistency test coefficients were roughly 93.27%. Supplementary Table S2 details the key characteristics of the 36 included articles with 79 effect quantities, including descriptive information (e.g., the publishing year, author, serial number, and title of the paper), variable information (e.g., independent variables, dependent variables, and moderating variables), and data information (e.g., mean values, standard deviations, and sample size). Following that, testing for publication bias and heterogeneity was done on the sample data using the Rev-Man 5.4 software, and then the test results were used to conduct a meta-analysis.

Publication bias test

When the sample of studies included in a meta-analysis does not accurately reflect the general status of research on the relevant subject, publication bias is said to be exhibited in this research. The reliability and accuracy of the meta-analysis may be impacted by publication bias. Due to this, the meta-analysis needs to check the sample data for publication bias (Stewart et al., 2006 ). A popular method to check for publication bias is the funnel plot; and it is unlikely that there will be publishing bias when the data are equally dispersed on either side of the average effect size and targeted within the higher region. The data are equally dispersed within the higher portion of the efficient zone, consistent with the funnel plot connected with this analysis (see Fig. 2 ), indicating that publication bias is unlikely in this situation.

This funnel plot shows the result of publication bias of 79 effect quantities across 36 studies.

Heterogeneity test

To select the appropriate effect models for the meta-analysis, one might use the results of a heterogeneity test on the data effect sizes. In a meta-analysis, it is common practice to gauge the degree of data heterogeneity using the I 2 value, and I 2  ≥ 50% is typically understood to denote medium-high heterogeneity, which calls for the adoption of a random effect model; if not, a fixed effect model ought to be applied (Lipsey and Wilson, 2001 ). The findings of the heterogeneity test in this paper (see Table 2 ) revealed that I 2 was 86% and displayed significant heterogeneity ( P  < 0.01). To ensure accuracy and reliability, the overall effect size ought to be calculated utilizing the random effect model.

The analysis of the overall effect size

This meta-analysis utilized a random effect model to examine 79 effect quantities from 36 studies after eliminating heterogeneity. In accordance with Cohen’s criterion (Cohen, 1992 ), it is abundantly clear from the analysis results, which are shown in the forest plot of the overall effect (see Fig. 3 ), that the cumulative impact size of cooperative problem-solving is 0.82, which is statistically significant ( z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]), and can encourage learners to practice critical thinking.

This forest plot shows the analysis result of the overall effect size across 36 studies.

In addition, this study examined two distinct dimensions of critical thinking to better understand the precise contributions that collaborative problem-solving makes to the growth of critical thinking. The findings (see Table 3 ) indicate that collaborative problem-solving improves cognitive skills (ES = 0.70) and attitudinal tendency (ES = 1.17), with significant intergroup differences (chi 2  = 7.95, P  < 0.01). Although collaborative problem-solving improves both dimensions of critical thinking, it is essential to point out that the improvements in students’ attitudinal tendency are much more pronounced and have a significant comprehensive effect (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]), whereas gains in learners’ cognitive skill are slightly improved and are just above average. (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

The analysis of moderator effect size

The whole forest plot’s 79 effect quantities underwent a two-tailed test, which revealed significant heterogeneity ( I 2  = 86%, z  = 12.78, P  < 0.01), indicating differences between various effect sizes that may have been influenced by moderating factors other than sampling error. Therefore, exploring possible moderating factors that might produce considerable heterogeneity was done using subgroup analysis, such as the learning stage, learning scaffold, teaching type, group size, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, in order to further explore the key factors that influence critical thinking. The findings (see Table 4 ) indicate that various moderating factors have advantageous effects on critical thinking. In this situation, the subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), learning scaffold (chi 2  = 9.03, P  < 0.01), and teaching type (chi 2  = 7.20, P  < 0.05) are all significant moderators that can be applied to support the cultivation of critical thinking. However, since the learning stage and the measuring tools did not significantly differ among intergroup (chi 2  = 3.15, P  = 0.21 > 0.05, and chi 2  = 0.08, P  = 0.78 > 0.05), we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving. These are the precise outcomes, as follows:

Various learning stages influenced critical thinking positively, without significant intergroup differences (chi 2  = 3.15, P  = 0.21 > 0.05). High school was first on the list of effect sizes (ES = 1.36, P  < 0.01), then higher education (ES = 0.78, P  < 0.01), and middle school (ES = 0.73, P  < 0.01). These results show that, despite the learning stage’s beneficial influence on cultivating learners’ critical thinking, we are unable to explain why it is essential for cultivating critical thinking in the context of collaborative problem-solving.

Different teaching types had varying degrees of positive impact on critical thinking, with significant intergroup differences (chi 2  = 7.20, P  < 0.05). The effect size was ranked as follows: mixed courses (ES = 1.34, P  < 0.01), integrated courses (ES = 0.81, P  < 0.01), and independent courses (ES = 0.27, P  < 0.01). These results indicate that the most effective approach to cultivate critical thinking utilizing collaborative problem solving is through the teaching type of mixed courses.

Various intervention durations significantly improved critical thinking, and there were significant intergroup differences (chi 2  = 12.18, P  < 0.01). The effect sizes related to this variable showed a tendency to increase with longer intervention durations. The improvement in critical thinking reached a significant level (ES = 0.85, P  < 0.01) after more than 12 weeks of training. These findings indicate that the intervention duration and critical thinking’s impact are positively correlated, with a longer intervention duration having a greater effect.

Different learning scaffolds influenced critical thinking positively, with significant intergroup differences (chi 2  = 9.03, P  < 0.01). The resource-supported learning scaffold (ES = 0.69, P  < 0.01) acquired a medium-to-higher level of impact, the technique-supported learning scaffold (ES = 0.63, P  < 0.01) also attained a medium-to-higher level of impact, and the teacher-supported learning scaffold (ES = 0.92, P  < 0.01) displayed a high level of significant impact. These results show that the learning scaffold with teacher support has the greatest impact on cultivating critical thinking.

Various group sizes influenced critical thinking positively, and the intergroup differences were statistically significant (chi 2  = 8.77, P  < 0.05). Critical thinking showed a general declining trend with increasing group size. The overall effect size of 2–3 people in this situation was the biggest (ES = 0.99, P  < 0.01), and when the group size was greater than 7 people, the improvement in critical thinking was at the lower-middle level (ES < 0.5, P  < 0.01). These results show that the impact on critical thinking is positively connected with group size, and as group size grows, so does the overall impact.

Various measuring tools influenced critical thinking positively, with significant intergroup differences (chi 2  = 0.08, P  = 0.78 > 0.05). In this situation, the self-adapting measurement tools obtained an upper-medium level of effect (ES = 0.78), whereas the complete effect size of the standardized measurement tools was the largest, achieving a significant level of effect (ES = 0.84, P  < 0.01). These results show that, despite the beneficial influence of the measuring tool on cultivating critical thinking, we are unable to explain why it is crucial in fostering the growth of critical thinking by utilizing the approach of collaborative problem-solving.

Different subject areas had a greater impact on critical thinking, and the intergroup differences were statistically significant (chi 2  = 13.36, P  < 0.05). Mathematics had the greatest overall impact, achieving a significant level of effect (ES = 1.68, P  < 0.01), followed by science (ES = 1.25, P  < 0.01) and medical science (ES = 0.87, P  < 0.01), both of which also achieved a significant level of effect. Programming technology was the least effective (ES = 0.39, P  < 0.01), only having a medium-low degree of effect compared to education (ES = 0.72, P  < 0.01) and other fields (such as language, art, and social sciences) (ES = 0.58, P  < 0.01). These results suggest that scientific fields (e.g., mathematics, science) may be the most effective subject areas for cultivating critical thinking utilizing the approach of collaborative problem-solving.

The effectiveness of collaborative problem solving with regard to teaching critical thinking

According to this meta-analysis, using collaborative problem-solving as an intervention strategy in critical thinking teaching has a considerable amount of impact on cultivating learners’ critical thinking as a whole and has a favorable promotional effect on the two dimensions of critical thinking. According to certain studies, collaborative problem solving, the most frequently used critical thinking teaching strategy in curriculum instruction can considerably enhance students’ critical thinking (e.g., Liang et al., 2017 ; Liu et al., 2020 ; Cindy, 2004 ). This meta-analysis provides convergent data support for the above research views. Thus, the findings of this meta-analysis not only effectively address the first research query regarding the overall effect of cultivating critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills) utilizing the approach of collaborative problem-solving, but also enhance our confidence in cultivating critical thinking by using collaborative problem-solving intervention approach in the context of classroom teaching.

Furthermore, the associated improvements in attitudinal tendency are much stronger, but the corresponding improvements in cognitive skill are only marginally better. According to certain studies, cognitive skill differs from the attitudinal tendency in classroom instruction; the cultivation and development of the former as a key ability is a process of gradual accumulation, while the latter as an attitude is affected by the context of the teaching situation (e.g., a novel and exciting teaching approach, challenging and rewarding tasks) (Halpern, 2001 ; Wei and Hong, 2022 ). Collaborative problem-solving as a teaching approach is exciting and interesting, as well as rewarding and challenging; because it takes the learners as the focus and examines problems with poor structure in real situations, and it can inspire students to fully realize their potential for problem-solving, which will significantly improve their attitudinal tendency toward solving problems (Liu et al., 2020 ). Similar to how collaborative problem-solving influences attitudinal tendency, attitudinal tendency impacts cognitive skill when attempting to solve a problem (Liu et al., 2020 ; Zhang et al., 2022 ), and stronger attitudinal tendencies are associated with improved learning achievement and cognitive ability in students (Sison, 2008 ; Zhang et al., 2022 ). It can be seen that the two specific dimensions of critical thinking as well as critical thinking as a whole are affected by collaborative problem-solving, and this study illuminates the nuanced links between cognitive skills and attitudinal tendencies with regard to these two dimensions of critical thinking. To fully develop students’ capacity for critical thinking, future empirical research should pay closer attention to cognitive skills.

The moderating effects of collaborative problem solving with regard to teaching critical thinking

In order to further explore the key factors that influence critical thinking, exploring possible moderating effects that might produce considerable heterogeneity was done using subgroup analysis. The findings show that the moderating factors, such as the teaching type, learning stage, group size, learning scaffold, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, could all support the cultivation of collaborative problem-solving in critical thinking. Among them, the effect size differences between the learning stage and measuring tool are not significant, which does not explain why these two factors are crucial in supporting the cultivation of critical thinking utilizing the approach of collaborative problem-solving.

In terms of the learning stage, various learning stages influenced critical thinking positively without significant intergroup differences, indicating that we are unable to explain why it is crucial in fostering the growth of critical thinking.

Although high education accounts for 70.89% of all empirical studies performed by researchers, high school may be the appropriate learning stage to foster students’ critical thinking by utilizing the approach of collaborative problem-solving since it has the largest overall effect size. This phenomenon may be related to student’s cognitive development, which needs to be further studied in follow-up research.

With regard to teaching type, mixed course teaching may be the best teaching method to cultivate students’ critical thinking. Relevant studies have shown that in the actual teaching process if students are trained in thinking methods alone, the methods they learn are isolated and divorced from subject knowledge, which is not conducive to their transfer of thinking methods; therefore, if students’ thinking is trained only in subject teaching without systematic method training, it is challenging to apply to real-world circumstances (Ruggiero, 2012 ; Hu and Liu, 2015 ). Teaching critical thinking as mixed course teaching in parallel to other subject teachings can achieve the best effect on learners’ critical thinking, and explicit critical thinking instruction is more effective than less explicit critical thinking instruction (Bensley and Spero, 2014 ).

In terms of the intervention duration, with longer intervention times, the overall effect size shows an upward tendency. Thus, the intervention duration and critical thinking’s impact are positively correlated. Critical thinking, as a key competency for students in the 21st century, is difficult to get a meaningful improvement in a brief intervention duration. Instead, it could be developed over a lengthy period of time through consistent teaching and the progressive accumulation of knowledge (Halpern, 2001 ; Hu and Liu, 2015 ). Therefore, future empirical studies ought to take these restrictions into account throughout a longer period of critical thinking instruction.

With regard to group size, a group size of 2–3 persons has the highest effect size, and the comprehensive effect size decreases with increasing group size in general. This outcome is in line with some research findings; as an example, a group composed of two to four members is most appropriate for collaborative learning (Schellens and Valcke, 2006 ). However, the meta-analysis results also indicate that once the group size exceeds 7 people, small groups cannot produce better interaction and performance than large groups. This may be because the learning scaffolds of technique support, resource support, and teacher support improve the frequency and effectiveness of interaction among group members, and a collaborative group with more members may increase the diversity of views, which is helpful to cultivate critical thinking utilizing the approach of collaborative problem-solving.

With regard to the learning scaffold, the three different kinds of learning scaffolds can all enhance critical thinking. Among them, the teacher-supported learning scaffold has the largest overall effect size, demonstrating the interdependence of effective learning scaffolds and collaborative problem-solving. This outcome is in line with some research findings; as an example, a successful strategy is to encourage learners to collaborate, come up with solutions, and develop critical thinking skills by using learning scaffolds (Reiser, 2004 ; Xu et al., 2022 ); learning scaffolds can lower task complexity and unpleasant feelings while also enticing students to engage in learning activities (Wood et al., 2006 ); learning scaffolds are designed to assist students in using learning approaches more successfully to adapt the collaborative problem-solving process, and the teacher-supported learning scaffolds have the greatest influence on critical thinking in this process because they are more targeted, informative, and timely (Xu et al., 2022 ).

With respect to the measuring tool, despite the fact that standardized measurement tools (such as the WGCTA, CCTT, and CCTST) have been acknowledged as trustworthy and effective by worldwide experts, only 54.43% of the research included in this meta-analysis adopted them for assessment, and the results indicated no intergroup differences. These results suggest that not all teaching circumstances are appropriate for measuring critical thinking using standardized measurement tools. “The measuring tools for measuring thinking ability have limits in assessing learners in educational situations and should be adapted appropriately to accurately assess the changes in learners’ critical thinking.”, according to Simpson and Courtney ( 2002 , p. 91). As a result, in order to more fully and precisely gauge how learners’ critical thinking has evolved, we must properly modify standardized measuring tools based on collaborative problem-solving learning contexts.

With regard to the subject area, the comprehensive effect size of science departments (e.g., mathematics, science, medical science) is larger than that of language arts and social sciences. Some recent international education reforms have noted that critical thinking is a basic part of scientific literacy. Students with scientific literacy can prove the rationality of their judgment according to accurate evidence and reasonable standards when they face challenges or poorly structured problems (Kyndt et al., 2013 ), which makes critical thinking crucial for developing scientific understanding and applying this understanding to practical problem solving for problems related to science, technology, and society (Yore et al., 2007 ).

Suggestions for critical thinking teaching

Other than those stated in the discussion above, the following suggestions are offered for critical thinking instruction utilizing the approach of collaborative problem-solving.

First, teachers should put a special emphasis on the two core elements, which are collaboration and problem-solving, to design real problems based on collaborative situations. This meta-analysis provides evidence to support the view that collaborative problem-solving has a strong synergistic effect on promoting students’ critical thinking. Asking questions about real situations and allowing learners to take part in critical discussions on real problems during class instruction are key ways to teach critical thinking rather than simply reading speculative articles without practice (Mulnix, 2012 ). Furthermore, the improvement of students’ critical thinking is realized through cognitive conflict with other learners in the problem situation (Yang et al., 2008 ). Consequently, it is essential for teachers to put a special emphasis on the two core elements, which are collaboration and problem-solving, and design real problems and encourage students to discuss, negotiate, and argue based on collaborative problem-solving situations.

Second, teachers should design and implement mixed courses to cultivate learners’ critical thinking, utilizing the approach of collaborative problem-solving. Critical thinking can be taught through curriculum instruction (Kuncel, 2011 ; Leng and Lu, 2020 ), with the goal of cultivating learners’ critical thinking for flexible transfer and application in real problem-solving situations. This meta-analysis shows that mixed course teaching has a highly substantial impact on the cultivation and promotion of learners’ critical thinking. Therefore, teachers should design and implement mixed course teaching with real collaborative problem-solving situations in combination with the knowledge content of specific disciplines in conventional teaching, teach methods and strategies of critical thinking based on poorly structured problems to help students master critical thinking, and provide practical activities in which students can interact with each other to develop knowledge construction and critical thinking utilizing the approach of collaborative problem-solving.

Third, teachers should be more trained in critical thinking, particularly preservice teachers, and they also should be conscious of the ways in which teachers’ support for learning scaffolds can promote critical thinking. The learning scaffold supported by teachers had the greatest impact on learners’ critical thinking, in addition to being more directive, targeted, and timely (Wood et al., 2006 ). Critical thinking can only be effectively taught when teachers recognize the significance of critical thinking for students’ growth and use the proper approaches while designing instructional activities (Forawi, 2016 ). Therefore, with the intention of enabling teachers to create learning scaffolds to cultivate learners’ critical thinking utilizing the approach of collaborative problem solving, it is essential to concentrate on the teacher-supported learning scaffolds and enhance the instruction for teaching critical thinking to teachers, especially preservice teachers.

Implications and limitations

There are certain limitations in this meta-analysis, but future research can correct them. First, the search languages were restricted to English and Chinese, so it is possible that pertinent studies that were written in other languages were overlooked, resulting in an inadequate number of articles for review. Second, these data provided by the included studies are partially missing, such as whether teachers were trained in the theory and practice of critical thinking, the average age and gender of learners, and the differences in critical thinking among learners of various ages and genders. Third, as is typical for review articles, more studies were released while this meta-analysis was being done; therefore, it had a time limit. With the development of relevant research, future studies focusing on these issues are highly relevant and needed.

Conclusions

The subject of the magnitude of collaborative problem-solving’s impact on fostering students’ critical thinking, which received scant attention from other studies, was successfully addressed by this study. The question of the effectiveness of collaborative problem-solving in promoting students’ critical thinking was addressed in this study, which addressed a topic that had gotten little attention in earlier research. The following conclusions can be made:

Regarding the results obtained, collaborative problem solving is an effective teaching approach to foster learners’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]). With respect to the dimensions of critical thinking, collaborative problem-solving can significantly and effectively improve students’ attitudinal tendency, and the comprehensive effect is significant (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

As demonstrated by both the results and the discussion, there are varying degrees of beneficial effects on students’ critical thinking from all seven moderating factors, which were found across 36 studies. In this context, the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have a positive impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. Since the learning stage (chi 2  = 3.15, P  = 0.21 > 0.05) and measuring tools (chi 2  = 0.08, P  = 0.78 > 0.05) did not demonstrate any significant intergroup differences, we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving.

Data availability

All data generated or analyzed during this study are included within the article and its supplementary information files, and the supplementary information files are available in the Dataverse repository: https://doi.org/10.7910/DVN/IPFJO6 .

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Acknowledgements

This research was supported by the graduate scientific research and innovation project of Xinjiang Uygur Autonomous Region named “Research on in-depth learning of high school information technology courses for the cultivation of computing thinking” (No. XJ2022G190) and the independent innovation fund project for doctoral students of the College of Educational Science of Xinjiang Normal University named “Research on project-based teaching of high school information technology courses from the perspective of discipline core literacy” (No. XJNUJKYA2003).

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Xu, E., Wang, W. & Wang, Q. The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature. Humanit Soc Sci Commun 10 , 16 (2023). https://doi.org/10.1057/s41599-023-01508-1

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Complex problem solving is an effective means to engage students in disciplinary content while also furnishing critical non-cognitive and life skills. Despite increased adoption of complex problem-solving methods in K-12 classrooms today (e.g., case-, project-, or problem-based learning), we know little about how to make these approaches accessible to linguistically and culturally diverse (LCD) students. In this paper, we promote a conceptual framework, based on an ethos of intentionality , that supports culturally responsive teaching (CRT). We provide specific questions to guide teachers’ implementation of an ethos of intentionality, through critical reflection and meaningful action, and discuss a framework for culturally relevant practice that operationalizes key central tenets (e.g., high expectations, cultural competence, and critical consciousness). Finally, we include strategies that can help teachers and designers translate the principles of the CRT framework into action with a specific focus on complex problem solving in classrooms.

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Chapter 9: Facilitating Complex Thinking

Problem-solving.

Somewhat less open-ended than creative thinking is problem solving , the analysis and solution of tasks or situations that are complex or ambiguous and that pose difficulties or obstacles of some kind (Mayer & Wittrock, 2006). Problem solving is needed, for example, when a physician analyzes a chest X-ray: a photograph of the chest is far from clear and requires skill, experience, and resourcefulness to decide which foggy-looking blobs to ignore, and which to interpret as real physical structures (and therefore real medical concerns). Problem solving is also needed when a grocery store manager has to decide how to improve the sales of a product: should she put it on sale at a lower price, or increase publicity for it, or both? Will these actions actually increase sales enough to pay for their costs?

Example 1: Problem Solving in the Classroom

Problem solving happens in classrooms when teachers present tasks or challenges that are deliberately complex and for which finding a solution is not straightforward or obvious. The responses of students to such problems, as well as the strategies for assisting them, show the key features of problem solving. Consider this example, and students’ responses to it. We have numbered and named the paragraphs to make it easier to comment about them individually:

Scene #1: A problem to be solved

A teacher gave these instructions: “Can you connect all of the dots below using only four straight lines?” She drew the following display on the chalkboard:

The problem itself and the procedure for solving it seemed very clear: simply experiment with different arrangements of four lines. But two volunteers tried doing it at the board, but were unsuccessful. Several others worked at it at their seats, but also without success.

Scene #2: Coaxing students to re-frame the problem

When no one seemed to be getting it, the teacher asked, “Think about how you’ve set up the problem in your mind—about what you believe the problem is about. For instance, have you made any assumptions about how long the lines ought to be? Don’t stay stuck on one approach if it’s not working!”

Scene #3: Alicia abandons a fixed response

After the teacher said this, Alicia indeed continued to think about how she saw the problem. “The lines need to be no longer than the distance across the square,” she said to herself. So she tried several more solutions, but none of them worked either.

The teacher walked by Alicia’s desk and saw what Alicia was doing. She repeated her earlier comment: “Have you assumed anything about how long the lines ought to be?”

Alicia stared at the teacher blankly, but then smiled and said, “Hmm! You didn’t actually say that the lines could be no longer than the matrix! Why not make them longer?” So she experimented again using oversized lines and soon discovered a solution:

Scene #4: Willem’s and Rachel’s alternative strategies

Meanwhile, Willem worked on the problem. As it happened, Willem loved puzzles of all kinds, and had ample experience with them. He had not, however, seen this particular problem. “It must be a trick,” he said to himself, because he knew from experience that problems posed in this way often were not what they first appeared to be. He mused to himself: “Think outside the box, they always tell you. . .” And that was just the hint he needed: he drew lines outside the box by making them longer than the matrix and soon came up with this solution:

When Rachel went to work, she took one look at the problem and knew the answer immediately: she had seen this problem before, though she could not remember where. She had also seen other drawing-related puzzles, and knew that their solution always depended on making the lines longer, shorter, or differently angled than first expected. After staring at the dots briefly, she drew a solution faster than Alicia or even Willem. Her solution looked exactly like Willem’s.

This story illustrates two common features of problem solving: the effect of degree of structure or constraint on problem solving, and the effect of mental obstacles to solving problems. The next sections discuss each of these features, and then looks at common techniques for solving problems.

The effect of constraints: well-structured versus ill-structured problems

Problems vary in how much information they provide for solving a problem, as well as in how many rules or procedures are needed for a solution. A well-structured problem provides much of the information needed and can in principle be solved using relatively few clearly understood rules. Classic examples are the word problems often taught in math lessons or classes: everything you need to know is contained within the stated problem and the solution procedures are relatively clear and precise. An ill-structured problem has the converse qualities: the information is not necessarily within the problem, solution procedures are potentially quite numerous, and a multiple solutions are likely (Voss, 2006). Extreme examples are problems like “How can the world achieve lasting peace?” or “How can teachers insure that students learn?”

By these definitions, the nine-dot problem is relatively well-structured—though not completely. Most of the information needed for a solution is provided in Scene #1: there are nine dots shown and instructions given to draw four lines. But not all necessary information was given: students needed to consider lines that were longer than implied in the original statement of the problem. Students had to “think outside the box,” as Willem said—in this case, literally.

When a problem is well-structured, so are its solution procedures likely to be as well. A well-defined procedure for solving a particular kind of problem is often called an algorithm ; examples are the procedures for multiplying or dividing two numbers or the instructions for using a computer (Leiserson, et al., 2001). Algorithms are only effective when a problem is very well-structured and there is no question about whether the algorithm is an appropriate choice for the problem. In that situation it pretty much guarantees a correct solution. They do not work well, however, with ill-structured problems, where they are ambiguities and questions about how to proceed or even about precisely what the problem is about. In those cases it is more effective to use heuristics , which are general strategies—“rules of thumb,” so to speak—that do not always work, but often do, or that provide at least partial solutions. When beginning research for a term paper, for example, a useful heuristic is to scan the library catalogue for titles that look relevant. There is no guarantee that this strategy will yield the books most needed for the paper, but the strategy works enough of the time to make it worth trying.

In the nine-dot problem, most students began in Scene #1 with a simple algorithm that can be stated like this: “Draw one line, then draw another, and another, and another.” Unfortunately this simple procedure did not produce a solution, so they had to find other strategies for a solution. Three alternatives are described in Scenes #3 (for Alicia) and 4 (for Willem and Rachel). Of these, Willem’s response resembled a heuristic the most: he knew from experience that a good general strategy that often worked for such problems was to suspect a deception or trick in how the problem was originally stated. So he set out to question what the teacher had meant by the word line , and came up with an acceptable solution as a result.

Common obstacles to solving problems

The example also illustrates two common problems that sometimes happen during problem solving. One of these is functional fixedness : a tendency to regard the functions of objects and ideas as fixed (German & Barrett, 2005). Over time, we get so used to one particular purpose for an object that we overlook other uses. We may think of a dictionary, for example, as necessarily something to verify spellings and definitions, but it also can function as a gift, a doorstop, or a footstool. For students working on the nine-dot matrix described in the last section, the notion of “drawing” a line was also initially fixed; they assumed it to be connecting dots but not extending lines beyond the dots. Functional fixedness sometimes is also called response set , the tendency for a person to frame or think about each problem in a series in the same way as the previous problem, even when doing so is not appropriate to later problems. In the example of the nine-dot matrix described above, students often tried one solution after another, but each solution was constrained by a set response not to extend any line beyond the matrix.

Functional fixedness and the response set are obstacles in problem representation , the way that a person understands and organizes information provided in a problem. If information is misunderstood or used inappropriately, then mistakes are likely—if indeed the problem can be solved at all. With the nine-dot matrix problem, for example, construing the instruction to draw four lines as meaning “draw four lines entirely within the matrix” means that the problem simply could not be solved. For another, consider this problem: “The number of water lilies on a lake doubles each day. Each water lily covers exactly one square foot. If it takes 100 days for the lilies to cover the lake exactly, how many days does it take for the lilies to cover exactly half of the lake?” If you think that the size of the lilies affects the solution to this problem, you have not represented the problem correctly. Information about lily size is not relevant to the solution, and only serves to distract from the truly crucial information, the fact that the lilies double their coverage each day. (The answer, incidentally, is that the lake is half covered in 99 days; can you think why?)

Strategies to assist problem solving

Just as there are cognitive obstacles to problem solving, there are also general strategies that help the process be successful, regardless of the specific content of a problem (Thagard, 2005). One helpful strategy is problem analysis —identifying the parts of the problem and working on each part separately. Analysis is especially useful when a problem is ill-structured. Consider this problem, for example: “Devise a plan to improve bicycle transportation in the city.” Solving this problem is easier if you identify its parts or component subproblems, such as (1) installing bicycle lanes on busy streets, (2) educating cyclists and motorists to ride safely, (3) fixing potholes on streets used by cyclists, and (4) revising traffic laws that interfere with cycling. Each separate subproblem is more manageable than the original, general problem. The solution of each subproblem contributes the solution of the whole, though of course is not equivalent to a whole solution.

Another helpful strategy is working backward from a final solution to the originally stated problem. This approach is especially helpful when a problem is well-structured but also has elements that are distracting or misleading when approached in a forward, normal direction. The water lily problem described above is a good example: starting with the day when all the lake is covered (Day 100), ask what day would it therefore be half covered (by the terms of the problem, it would have to be the day before, or Day 99). Working backward in this case encourages reframing the extra information in the problem (i. e. the size of each water lily) as merely distracting, not as crucial to a solution.

A third helpful strategy is analogical thinking —using knowledge or experiences with similar features or structures to help solve the problem at hand (Bassok, 2003). In devising a plan to improve bicycling in the city, for example, an analogy of cars with bicycles is helpful in thinking of solutions: improving conditions for both vehicles requires many of the same measures (improving the roadways, educating drivers). Even solving simpler, more basic problems is helped by considering analogies. A first grade student can partially decode unfamiliar printed words by analogy to words he or she has learned already. If the child cannot yet read the word screen , for example, he can note that part of this word looks similar to words he may already know, such as seen or green , and from this observation derive a clue about how to read the word screen . Teachers can assist this process, as you might expect, by suggesting reasonable, helpful analogies for students to consider.

Bassok, J. (2003). Analogical transfer in problem solving. In Davidson, J. & Sternberg, R. (Eds.). The psychology of problem solving. New York: Cambridge University Press.

German, T. & Barrett, H. (2005). Functional fixedness in a technologically sparse culture. Psychological Science, 16 (1), 1–5.

Leiserson, C., Rivest, R., Cormen, T., & Stein, C. (2001). Introduction to algorithms. Cambridge, MA: MIT Press.

Luchins, A. & Luchins, E. (1994). The water-jar experiment and Einstellung effects. Gestalt Theory: An International Interdisciplinary Journal, 16 (2), 101–121.

Mayer, R. & Wittrock, M. (2006). Problem-solving transfer. In D. Berliner & R. Calfee (Eds.), Handbook of Educational Psychology, pp. 47–62. Mahwah, NJ: Erlbaum.

Thagard, R. (2005). Mind: Introduction to Cognitive Science, 2nd edition. Cambridge, MA: MIT Press.

Voss, J. (2006). Toulmin’s model and the solving of ill-structured problems. Argumentation, 19 (3), 321–329.

• Educational Psychology. Authored by : Kelvin Seifert and Rosemary Sutton. Located at : https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=153 . License : CC BY: Attribution

• Author Rights
• Diversity, Equity & Inclusion

• JOLE 2023 Special Issue
• Editorial Staff
• 20th Anniversary Issue
• The Development of Problem-Solving Skills for Aspiring Educational Leaders

Jeremy D. Visone 10.12806/V17/I4/R3

Introduction

Solving problems is a quintessential aspect of the role of an educational leader. In particular, building leaders, such as principals, assistant principals, and deans of students, are frequently beset by situations that are complex, unique, and open-ended. There are often many possible pathways to resolve the situations, and an astute educational leader needs to consider many factors and constituencies before determining a plan of action. The realm of problem solving might include student misconduct, personnel matters, parental complaints, school culture, instructional leadership, as well as many other aspects of educational administration. Much consideration has been given to the development of problem-solving skills for educational leaders. This study was designed to answer the following research question: “How do aspiring educational leaders’ problem solving skills, as well as perceptions of their problem-solving skills, develop during a year-long graduate course sequence focused on school-level leadership that includes the presentation of real-world scenarios?” This mixed-methods study extends research about the development of problem-solving skills conducted with acting administrators (Leithwood & Steinbach, 1992, 1995).

The Nature of Problems

Before examining how educational leaders can process and solve problems effectively, it is worth considering the nature of problems. Allison (1996) posited simply that problems are situations that require thought and/or actions. Further, there are different types of problems presented to educational leaders. First, there are  well-structured problems , which can be defined as those with clear goals and relatively prescribed resolution pathways, including an easy way of determining whether goals were met (Allison, 1996).

Conversely,  ill-structured problems  are those with more open-ended profiles, whereby the goals, resolution pathways, or evidence of success are not necessarily clear. These types of problems could also be considered  unstructured  (Leithwood & Steinbach, 1995) or  open-design  (Allison, 1996). Many of the problems presented to educational leaders are unstructured problems. For example, a principal must decide how to discipline children who misbehave, taking into consideration their disciplinary history, rules and protocols of the school, and other contextual factors; determine how best to raise student achievement (Duke, 2014); and resolve personnel disputes among staff members. None of these problems point to singular solutions that can be identified as “right” or “wrong.” Surely there are responses that are less desirable than others (i.e. suspension or recommendation for expulsion for minor infractions), but, with justification and context, many possible solutions exist.

Problem-Solving Perspectives and Models

Various authors have shared perspectives about effective problem solving. Marzano, Waters, and McNulty (2005) outlined the “21 Responsibilities of the School Leader.” These responsibilities are highly correlated with student achievement based upon the authors’ meta- analysis of 69 studies about leadership’s effect on student achievement. The most highly correlated of the responsibilities was  situational awareness , which refers to understanding the school deeply enough to anticipate what might go wrong from day-to-day, navigate the individuals and groups within the school, and recognize issues that might surface at a later time (Marzano et al., 2005). Though the authors discuss the utility of situational awareness for long- term, large-scale decision making, in order for an educational leader to effectively solve the daily problems that come her way, she must again have a sense of situational awareness, lest she make seemingly smaller-scale decisions that will lead to large-scale problems later.

Other authors have focused on problems that can be considered more aligned with the daily work of educational leaders. Considering the problem-type classification dichotomies of Allison (1996) and Leithwood and Steinbach (1995), problems that educational leaders face on a daily basis can be identified as either well-structured or unstructured. Various authors have developed problem-solving models focused on unstructured problems (Bolman & Deal, 2008; Leithwood & Steinbach, 1995; Simon, 1993), and these models will be explored next.

Simon (1993) outlined three phases of the decision-making process. The first is to find problems that need attention. Though many problems of educational leaders are presented directly to them via, for example, an adult referring a child for discipline, a parent registering a complaint about a staff member, or a staff member describing a grievance with a colleague, there is a corollary skill of identifying what problems—of the many that come across one’s desk— require immediate attention, or ultimately, any attention, at all. Second, Simon identified “designing possible courses of action” (p. 395). Finally, educational leaders must evaluate the quality of their decisions. From this point of having selected a viable and positively evaluated potential solution pathway, implementation takes place.

Bolman and Deal (2008) outlined a model of reframing problems using four different frames, through which problems of practice can be viewed. These frames provide leaders with a more complete set of perspectives than they would likely utilize on their own. The  structural frame  represents the procedural and systems-oriented aspects of an organization. Within this frame, a leader might ask whether there is a supervisory relationship involved in a problem, if a protocol exists to solve such a problem, or what efficiencies or logical processes can help steer a leader toward a resolution that meets organizational goals. The  human resource frame  refers to the needs of individuals within the organization. A leader might try to solve a problem of practice with the needs of constituents in mind, considering the development of employees and the balance between their satisfaction and intellectual stimulation and the organization’s needs. The  political frame  includes the often competing interests among individuals and groups within the organization, whereby alliances and negotiations are needed to navigate the potential minefield of many groups’ overlapping aims. From the political frame, a leader could consider what the interpersonal costs will be for the leader and organization among different constituent groups, based upon which alternatives are selected. Last, the  symbolic frame  includes elements of meaning within an organization, such as traditions, unspoken rules, and myths. A leader may need to consider this frame when proposing a solution that might interfere with a long-standing organizational tradition.

Bolman and Deal (2008) identified the political and symbolic frames as weaknesses in most leaders’ consideration of problems of practice, and the weakness in recognizing political aspects of decision making for educational leaders was corroborated by Johnson and Kruse (2009). An implication for leadership preparation is to instruct students in the considerations of these frames and promote their utility when examining problems.

Authors have noted that experts use different processes than novice problem solvers (Simon, 1993; VanLehn, 1991). An application of this would be Simon’s (1993) assertion that experts can rely on their extensive experience to remember solutions to many problems, without having to rely on an extensive analytical process. Further, they may not even consider a “problem” identified by a novice a problem, at all. With respect to educational leaders, Leithwood and Steinbach (1992, 1995) outlined a set of competencies possessed by expert principals, when compared to their typical counterparts. Expert principals were better at identifying the nature of problems; possessing a sense of priority, difficulty, how to proceed, and connectedness to prior situations; setting meaningful goals for problem solving, such as seeking goals that are student-centered and knowledge-focused; using guiding principles and long-term purposes when determining the best courses of action; seeing fewer obstacles and constraints when presented with problems; outlining detailed plans for action that include gathering extensive information to inform decisions along the plan’s pathway; and responding with confidence and calm to problem solving. Next, I will examine how problem-solving skills are developed.

Preparation for Educational Leadership Problem Solving

How can the preparation of leaders move candidates toward the competencies of expert principals? After all, leading a school has been shown to be a remarkably complex enterprise (Hallinger & McCary, 1990; Leithwood & Steinbach, 1992), especially if the school is one where student achievement is below expectations (Duke, 2014), and the framing of problems by educational leaders has been espoused as a critically important enterprise (Bolman & Deal, 2008; Dimmock, 1996; Johnson & Kruse, 2009; Leithwood & Steinbach, 1992, 1995; Myran & Sutherland, 2016). In other disciplines, such as business management, simulations and case studies are used to foster problem-solving skills for aspiring leaders (Rochford & Borchert, 2011; Salas, Wildman, & Piccolo, 2009), and attention to problem-solving skills has been identified as an essential curricular component in the training of journalism and mass communication students (Bronstein & Fitzpatrick, 2015). Could such real-world problem solving methodologies be effective in the preparation of educational leaders? In a seminal study about problem solving for educational leaders, Leithwood and Steinbach (1992, 1995) sought to determine if effective problem-solving expertise could be explicitly taught, and, if so, could teaching problem- processing expertise be helpful in moving novices toward expert competence? Over the course of four months and four separate learning sessions, participants in the control group were explicitly taught subskills within six problem-solving components: interpretation of the problem for priority, perceived difficulty, data needed for further action, and anecdotes of prior experience that can inform action; goals for solving the problem; large-scale principles that guide decision making; barriers or obstacles that need to be overcome; possible courses of action; and the confidence of the leader to solve the problem. The authors asserted that providing conditions to participants that included models of effective problem-solving, feedback, increasingly complex problem-solving demands, frequent opportunities for practice, group problem-solving, individual reflection, authentic problems, and help to stimulate metacognition and reflection would result in educational leaders improving their problem-solving skills.

The authors used two experts’ ratings of participants’ problem-solving for both process (their methods of attacking the problem) and product (their solutions) using a 0-3 scale in a pretest-posttest design. They found significant increases in some problem-solving skills (problem interpretation, goal setting, and identification of barriers or obstacles that need to be overcome) after explicit instruction (Leithwood & Steinbach, 1992, 1995). They recommended conducting more research on the preparation of educational leaders, with particular respect to approaches that would improve the aspiring leaders’ problem-solving skills.

Solving problems for practicing principals could be described as constructivist, since most principals do solve problems within a social context of other stakeholders, such as teachers, parents, and students (Leithwood & Steinbach, 1992). Thus, some authors have examined providing opportunities for novice or aspiring leaders to construct meaning from novel scenarios using the benefits of, for example, others’ point of view, expert modeling, simulations, and prior knowledge (Duke, 2014; Leithwood & Steinbach, 1992, 1995; Myran & Sutherland, 2016; Shapira-Lishchinsky, 2015). Such collaborative inquiry has been effective for teachers, as well (DeLuca, Bolden, & Chan, 2017). Such learning can be considered consistent with the ideas of other social constructivist theorists (Berger & Luckmann, 1966; Vygotsky, 1978) as well, since individuals are working together to construct meaning, and they are pushing into areas of uncertainty and lack of expertise.

Shapira-Lishchinsky (2015) added some intriguing findings and recommendations to those of Leithwood and Steinbach (1992, 1995). In this study, 50 teachers with various leadership roles in their schools were presented regularly with ethical dilemmas during their coursework. Participants either interacted with the dilemmas as members of a role play or by observing those chosen. When the role play was completed, the entire group debriefed and discussed the ethical dilemmas and role-playing participants’ treatment of the issues. This method was shown, through qualitative analysis of participants’ discussions during the simulations, to produce rich dialogue and allow for a safe and controlled treatment of difficult issues. As such, the use of simulations was presented as a viable means through which to prepare aspiring educational leaders. Further, the author suggested the use of further studies with simulation-based learning that seek to gain information about aspiring leaders’ self-efficacy and psychological empowerment. A notable example of project-based scenarios in a virtual collaboration environment to prepare educational leaders is the work of Howard, McClannon, and Wallace (2014). Shapira-Lishchinsky (2015) also recommended similar research in other developed countries to observe the utility of the approaches of simulation and social constructivism to examine them for a wider and diverse aspiring administrator candidate pool.

Further, in an extensive review of prior research studies on the subject, Hallinger and Bridges (2017) noted that Problem-Based Learning (PBL), though applied successfully in other professions and written about extensively (Hallinger & Bridges, 1993, 2017; Stentoft, 2017), was relatively unheralded in the preparation of educational leaders. According to the authors, characteristics of PBL included problems replacing theory as the organization of course content, student-led group work, creation of simulated products by students, increased student ownership over learning, and feedback along the way from professors. Their review noted that PBL had positive aspects for participants, such as increased motivation, real-world connections, and positive pressure that resulted from working with a team. However, participants also expressed concerns about time constraints, lack of structure, and interpersonal dynamics within their teams. There were positive effects found on aspiring leaders’ problem-solving skill development with PBL (Copland, 2000; Hallinger & Bridges, 2017). Though PBL is much more prescribed than the scenarios strategy described in the Methods section below, the applicability of real-world problems to the preparation of educational leaders is summarized well by Copland (2000):

[I]nstructional practices that activate prior knowledge and situate learning in contexts similar to those encountered in practice are associated with the development of students’ ability to understand and frame problems. Moreover, the incorporation of debriefing techniques that encourage students’ elaboration of knowledge and reflection on learning appear to help students solidify a way of thinking about problems. (p. 604)

This study involved a one-group pretest-posttest design. No control group was assigned, as the pedagogical strategy in question—the use of real-world scenarios to build problem-solving skill for aspiring educational leaders—is integral to the school’s curriculum that prepares leaders, and, therefore, it is unethical to deny to student participants (Gay & Airasian, 2003). Thus, all participants were provided instruction with the use of real-world scenarios.

Participants.  Graduate students at a regional, comprehensive public university in the Northeast obtaining a 6 th -year degree (equivalent to a second master’s degree) in educational leadership and preparing for certification as educational administrators served as participants. Specifically, students in three sections of the same full-year, two-course sequence, entitled “School Leadership I and II” were invited to participate. This particular course was selected from the degree course sequence, as it deals most directly with the problem-solving nature and daily work of school administrators. Some key outcomes of the course include students using data to drive school improvement action plans, communicating effectively with a variety of stakeholders, creating a safe and caring school climate, creating and maintaining a strategic and viable school budget, articulating all the steps in a hiring process for teachers and administrators, and leading with cultural proficiency.

The three sections were taught by two different professors. The professors used real- world scenarios in at least half of their class meetings throughout the year, or in approximately 15 classes throughout the year. During these classes, students were presented with realistic situations that have occurred, or could occur, in actual public schools. Students worked with their classmates to determine potential solutions to the problems and then discussed their responses as a whole class under the direction of their professor, a master practitioner. Both professors were active school administrators, with more than 25 years combined educational leadership experience in public schools. It should be noted that the scenario presentation and discussions took place during the class sessions, only. These were not presented for homework or in online forums.

Of the 44 students in these three sections, 37 volunteered to participate at some point in the data collection sequence, but not all students in the pretest session attended the posttest session months later and vice versa. As a result, only 20 students’ data were used for the matched pairs analysis. All 37 participants were certified professional educators in public schools in Connecticut. The participants’ professional roles varied and included classroom teachers, instructional coaches, related service personnel, unified arts teachers, as well as other non- administrative educational roles. Characteristics of participants in the overall and matched pairs groups can be found in Table 1.

Table 1 Participant Characteristics

Procedure.  Participants’ data were compared between a fall of 2016 baseline data collection period and a spring of 2017 posttest data collection period. During the fall data collection period, participants were randomly assigned one of two versions of a Google Forms survey. After items about participant characteristics, the survey consisted of 11 items designed to elicit quantitative and qualitative data about participants’ perceptions of their problem-solving abilities, as well as their ability to address real-world problems faced by educational leaders. The participants were asked to rate their perception of their situational awareness, flexibility, and problem solving ability on a 10-point (1-10) Likert scale, following operational definitions of the terms (Marzano, Waters, & McNulty, 2005; Winter, 1982). They were asked, for each construct, to write open-ended responses to justify their numerical rating. They were then asked to write what they perceived they still needed to improve their problem-solving skills. The final four items included two real-world, unstructured, problem-based scenarios for which participants were asked to create plans of action. They were also asked to rate their problem-solving confidence with respect to their proposed action plans for each scenario on a 4-point (0-3) Likert scale.

During the spring data collection period, participants accessed the opposite version of the Google Forms survey from the one they completed in the fall. All items were identical on the two survey versions, except the scenarios, which were different on each survey version. The use of two versions was to ensure that any differences in perceived or actual difficulty among the four scenarios provided would not alter results based upon the timing of participant access (Leithwood & Steinbach, 1995). In order to link participants’ fall and spring data in a confidential manner, participants created a unique, six-digit alphanumeric code.

A focus group interview followed each spring data collection session. The interviews were recorded to allow for accurate transcription. The list of standard interview questions can be found in Table 2. This interview protocol was designed to elicit qualitative data with respect to aspiring educational leaders’ perceptions about their developing problem-solving abilities.

Table 2 Focus Group Interview Questions ___________________________________________________________________________________________

Please describe the development of your problem-solving skills as an aspiring educational leader over the course of this school year. In what ways have you improved your skills? Be as specific as you can.

What has been helpful to you (i.e. coursework, readings, experiences, etc.) in this development of your problem-solving skills? Why?

What do you believe you still need for the development in your problem-solving skills as an aspiring educational leader?

Discuss your perception of your ability to problem solve as an aspiring educational leader. How has this changed from the beginning of this school year? Why?

Please add anything else you perceive is relevant to this conversation about the development of your problem-solving skills as an aspiring educational leader.

___________________________________________________________________________________________

Data Analysis.

Quantitative data .  Data were obtained from participants’ responses to Likert-scale items relating to their confidence levels with respect to aspects of problem solving, as well as from the rating of participants’ responses to the given scenarios  against a rubric. The educational leadership problem-solving rubric chosen (Leithwood & Steinbach, 1995) was used with permission, and it reflects the authors’ work with explicitly teaching practicing educational leaders components of problem solving. The adapted rubric can be found in Figure 1. Through the use of this rubric, each individual response by a participant to a presented scenario was assigned a score from 0-15. It should be noted that affect data (representing the final 3 possible points on the 18-point rubric) were obtained via participants’ self-reporting their confidence with respect to their proposed plans of action. To align with the rubric, participants self-assessed their confidence through this item with a 0-3 scale.

0 = No Use of the Subskill 1 = There is Some Indication of Use of the Subskill 2 = The Subskill is Present to Some Degree 3 = The Subskill is Present to a Marked Degree; This is a Fine Example of this Subskill

Figure 1.  Problem-solving model for unstructured problems. Adapted from “Expert Problem Solving: Evidence from School and District Leaders,” by K. Leithwood and R. Steinbach, pp. 284-285. Copyright 1995 by the State University of New York Press.

I compared Likert-scale items and rubric scores via descriptive statistics and rubric scores also via a paired sample  t -test and Cohen’s  d , all using the software program IBM SPSS. I did not compare the Likert-scale items about situational awareness, flexibility, and problem solving ability with  t -tests or Cohen’s  d , since these items did not represent a validated instrument. They were only single items based upon participants’ ratings compared to literature-based definitions. However, the value of the comparison of means from fall to spring was triangulated with qualitative results to provide meaning. For example, to say that participants’ self-assessment ratings for perceived problem-solving abilities increased, I examined both the mean difference for items from fall to spring and what participants shared throughout the qualitative survey items and focus group interviews.

Prior to scoring participants’ responses to the scenarios using the rubric, and in an effort to maximize the content validity of the rubric scores, I calibrated my use of the rubric with two experts from the field. Two celebrated principals, representing more than 45 combined years of experience in school-level administration, collaboratively and comparatively scored participant responses. Prior to scoring, the team worked collaboratively to construct appropriate and comprehensive exemplar responses to the four problem-solving scenarios. Then the team blindly scored fall pretest scenario responses using the Leithwood and Steinbach (1995) rubric, and upon comparing scores, the interrater reliability correlation coefficient was .941, indicating a high degree of agreement throughout the team.

Qualitative data.  These data were obtained from open-ended items on the survey, including participants’ responses to the given scenarios, as well as the focus group interview transcripts. I analyzed qualitative data consistent with the grounded theory principles of Strauss and Corbin (1998) and the constant comparative methods of Glaser (1965), including a period of open coding of results, leading to axial coding to determine the codes’ dimensions and relationships between categories and their subcategories, and selective coding to arrive at themes. Throughout the entire data analysis process, I repeatedly returned to raw data to determine the applicability of emergent codes to previously analyzed data. Some categorical codes based upon the review of literature were included in the initial coding process. These codes were derived from the existing theoretical problem-solving models of Bolman and Deal (2008) and Leithwood and Steinbach (1995). These codes included  modeling ,  relationships , and  best for kids . Open codes that emerged from the participants’ responses included  experience ,  personality traits ,  current job/role , and  team . Axial coding revealed, for example, that current jobs or roles cited, intuitively, provided both sufficient building-wide perspective and situational memory (i.e. for special education teachers and school counselors) and insufficient experiences (i.e. for classroom teachers) to solve the given problems with confidence. From such understandings of the codes, categories, and their dimensions, themes were developed.

Quantitative Results.   First, participants’ overall, aggregate responses (not matched pairs) were compared from the fall to spring, descriptively. These findings are outlined in Table  3. As is seen in the table, each item saw a modest increase over the course of the year. Participant perceptions of their problem-solving abilities across the three constructs presented (situational awareness, flexibility, and problem solving) did increase over the course of the year, as did the average group score for the problem-solving scenarios. However, due to participant differences in the two data collection periods, these aggregate averages do not represent a matched-pair dataset.

Table 3 Fall to Spring Comparison of Likert-Scale and Rubric-Scored Items

a  These problem-solving dimensions from literature were rated by participants on a scale from 1- 10. b  Participants received a rubric score for each scenario between 0-18. Participants’ two scenario scores for each data collection period (fall, spring) were averaged to arrive at the scores represented here.

In order to determine the statistical significance of the increase in participants’ problem- solving rubric scores, a paired-samples  t -test was applied to the fall ( M  = 9.15;  SD  = 2.1) and spring ( M  = 9.25;  SD  = 2.3) averages. Recall that 20 participants had valid surveys for both the fall and spring. The  t -test ( t  = -.153;  df  = 19;  p  = .880) revealed no statistically significant change from fall to spring, despite the minor increase (0.10). I applied Cohen’s  d  to calculate the effect size. The small sample size ( n  = 20) for the paired-sample  t -test may have contributed to the lack of statistical significance. However, standard deviations were also relatively small, so the question of effect size was of particular importance. Cohen’s  d  was 0.05, which is also very small, indicating that little change—really no improvement, from a statistical standpoint—in participants’ ability to create viable action plans to solve real-world problems occurred throughout the year. However, the participants’ perceptions of their problem-solving abilities did increase, as evidenced by the increases in the paired-samples perception means shown in Table 3, though these data were only examined descriptively (from a quantitative perspective) due to the fact that these questions were individual items that are not part of a validated instrument.

Qualitative Results.   Participant responses to open-ended items on the questionnaire, responses to the scenarios, and oral responses to focus group interview questions served as sources of qualitative data. Since the responses to the scenarios were focused on participant competence with problem solving, as measured by the aforementioned rubric (Leithwood &  Steinbach, 1995), these data were examined separately from data collected from the other two sources.

Responses to scenarios.  As noted, participants’ rubric ratings for the scenarios did not display a statistically significant increase from fall to spring. As such, this outline will not focus upon changes in responses from fall to spring. Rather, I examined the responses, overall, through the lens of the Leithwood and Steinbach (1995) problem-solving framework indicators against which they were rated. Participants typically had outlined reasonable, appropriate, and logical solution processes. For example, in a potential bullying case scenario, two different participants offered, “I would speak to the other [students] individually if they have said or done anything mean to other student [ sic ] and be clear that it is not tolerable and will result in major consequences” and “I would initiate an investigation into the situation beginning with [an] interview with the four girls.” These responses reflect actions that the consulted experts anticipated from participants and deemed as logical and needed interventions. However, these two participants omitted other needed steps, such as addressing the bullied student’s mental health needs, based upon her mother’s report of suicidal ideations. Accordingly, participants earned points for reasonable and logical responses very consistently, yet, few full-credit responses were observed.

Problem interpretation scores were much more varied. For this indicator, some participants were able to identify many, if not all, the major issues in the scenarios that needed attention. For example, for a scenario where two teachers were not interacting professionally toward each other, many participants correctly identified that this particular scenario could include elements of sexual harassment, professionalism, teaching competence, and personality conflict. However, many other participants missed at least two of these key elements of the problem, leaving their solution processes incomplete. The categories of (a) goals and (b) principles and values also displayed a similarly wide distribution of response ratings.

One category, constraints, presented consistent difficulty for the participants. Ratings were routinely 0 and 1. Participants could not consistently report what barriers or obstacles would need addressing prior to success with their proposed solutions. To be clear, it was not a matter of participants listing invalid or unrealistic barriers or obstacles; rather, the participants were typically omitting constraints altogether from their responses. For example, for a scenario involving staff members arriving late and unprepared to data team meetings, many participants did not identify that a school culture of not valuing data-driven decision making or lack of norms for data team work could be constraints that the principal could likely face prior to reaching a successful resolution.

Responses to open-ended items.  When asked for rationale regarding their ratings for situational awareness, flexibility, and problem solving, participants provided open-ended responses. These responses revealed patterns worth considering, and, again, this discussion will consider, in aggregate, responses made in both the pre- and post- data collection periods, again due to the similarities in responses between the two data collection periods. The most frequently observed code (112 incidences) was  experience . Closely related were the codes  current job/role  (50 incidences). Together, these codes typically represented a theme that participants were linking their confidence with respect to problem solving with their exposure (or lack thereof) in their professional work. For example, a participant reported, “As a school counselor, I have a lot of contact with many stakeholders in the school -admin [ sic ], parents, teachers, staff, etc. I feel that I have a pretty good handle on the systemic issues.” This example is one of many where individuals working in counseling, instructional coaching, special education, and other support roles expressed their advanced levels of perspective based upon their regular contact with many stakeholders, including administrators. Thus, they felt they had more prior knowledge and situational memory about problems in their schools.

However, this category of codes also included those, mostly classroom or unified arts teachers, who expressed that their relative lack of experiences outside their own classrooms limited their perspective for larger-scale problem solving. One teacher succinctly summarized this sentiment, “I have limited experience in being part of situations outside of my classroom.” Another focused on the general problem solving skill in her classroom not necessarily translating to confidence with problem solving at the school level: “I feel that I have a high situational awareness as a teacher in the classroom, but as I move through these leadership programs I find that I struggle to take the perspective of a leader.” These experiences were presented in opposition to their book learning or university training. There were a number of instances (65 combined) of references to the value of readings, class discussions, group work, scenarios presented, research, and coursework in the spring survey. When asked what the participants need more, again, experience was referenced often. One participant summarized this concept, “I think that I, personally, need more experience in the day-to-day . . . setting.” Another specifically separated experiences from scenario work, “[T]here is [ sic ] some things you can not [ sic ] learn from merely discussing a ‘what if” scenario. A seasoned administrator learns problem solving skills on the job.”

Another frequently cited code was  personality traits  (63 incidences), which involved participants linking elements of their own personalities to their perceived abilities to process problems, almost exclusively from an assets perspective. Examples of traits identified by participants as potentially helpful in problem solving included: open-mindedness, affinity for working with others, not being judgmental, approachability, listening skills, and flexibility. One teacher exemplified this general approach by indicating, “I feel that I am a good listener in regards to inviting opinions. I enjoy learning through cooperation and am always willing to adapt my teaching to fit needs of the learners.” However, rare statements of personality traits interfering with problem solving included, “I find it hard to trust others [ sic ] abilities” and “my personal thoughts and biases.”

Another important category of the participant responses involved connections with others. First, there were many references to  relationships  (27 incidences), mostly from the perspective that building positive relationships leads to greater problem-solving ability, as the aspiring leader knows stakeholders better and can rely on them due to the history of positive interactions. One participant framed this idea from a deficit perspective, “Not knowing all the outlying relationships among staff members makes situational awareness difficult.” Another identified that established positive relationships are already helpful to an aspiring leader, “I have strong rapport with fellow staff members and administrators in my building.” In a related way, many instances of the code  team  were identified (29). These references overwhelmingly identified that solving problems within a team context is helpful. One participant stated, “I often team with people to discuss possible solutions,” while another elaborated,

I recognize that sometimes problems may arise for which I am not the most qualified or may not have the best answer. I realize that I may need to rely on others or seek out help/opinions to ensure that I make the appropriate decision.

Overall, participants recognized that problem-solving for leaders does not typically occur in a vacuum.

Responses to focus group interview questions.  As with the open-ended responses, patterns were evident in the interview responses, and many of these findings were supportive of the aforementioned themes. First, participants frequently referenced the power of group work to help build their understanding about problems and possible solutions. One participant stated, “hearing other people talk and realizing other concerns that you may not have thought of . . . even as a teacher sometimes, you look at it this way, and someone else says to see it this way.” Another added, “seeing it from a variety of persons [ sic ] point of views. How one person was looking at it, and how another person was looking at it was really helpful.” Also, the participants noted the quality of the discussion was a direct result of “professors who have had real-life experience” as practicing educational leaders, so they could add more realistic feedback and insight to the discussions.

Perhaps most notable in the participant responses during the focus groups was the emphasis on the value of real-world scenarios for the students. These were referenced, without prompting, in all three focus groups by many participants. Answers to the question about what has been most helpful in the development of their problem-solving skills included, “I think the real-world application we are doing,” “I think being presented with all the scenarios,” and “[the professor] brought a lot of real situations.”

With respect to what participants believed they still needed to become better and more confident problem solvers, two patterns emerged. First, students recognized that they have much more to learn, especially with respect to policy and law. It is noteworthy that, with few exceptions, these students had not taken the policy or law courses in the program, and they had not yet completed their administrative internships. Some students actually reported rating themselves as less capable problem solvers in the spring because they now understood more clearly what they lacked in knowledge. One student exemplified this sentiment, “I might have graded myself higher in the fall than I did now . . . [I now can] self identify areas I could improve in that I was not as aware of.” Less confidence in the spring was a minority opinion, however. In a more typical response, another participant stated, “I feel much more prepared for that than I did at the beginning of the year.”

Overall, the most frequently discussed future need identified was experience, either through the administrative internship or work as a formal school administrator. Several students summarized this idea, “That real-world experience to have to deal with it without being able to talk to 8 other people before having to deal with it . . . until you are the person . . . you don’t know” and “They tell you all they want. You don’t know it until you are in it.” Overall, most participants perceived themselves to have grown as problem solvers, but they overwhelmingly recognized that they needed more learning and experience to become confident and effective problem solvers.

This study continues a research pathway about the development of problem-solving skills for administrators by focusing on their preparation. The participants did not see a significant increase in their problem-solving skills over the year-long course in educational leadership.

Whereas, this finding is not consistent with the findings of others who focused on the development of problem-solving skills for school leaders (Leithwood & Steinbach, 1995; Shapira-Lishchinsky, 2015), nor is it consistent with PBL research about the benefits of that approach for aspiring educational leaders (Copland, 2000; Hallinger & Bridges, 2017), it is important to note that the participants in this study were at a different point in their careers. First, they were aspirants, as opposed to practicing leaders. Also, the studied intervention (scenarios) was not the same or nearly as comprehensive as the prescriptive PBL approach. Further, unlike the participants in either the practicing leader or PBL studies, because these individuals had not yet had their internship experiences, they had no practical work as educational leaders. This theme of lacking practical experience was observed in both open-ended responses and focus group interviews, with participants pointing to their upcoming internship experiences, or even their eventual work as administrators, as a key missing piece of their preparation.

Despite the participants’ lack of real gains across the year of preparation in their problem- solving scores, the participants did, generally, report an increase in their confidence in problem solving, which they attributed to a number of factors. The first was the theme of real-world context. This finding was consistent with others who have advocated for teaching problem solving through real-world scenarios (Duke, 2014; Leithwood & Steinbach, 1992, 1995; Myran & Sutherland, 2016; Shapira-Lishchinsky, 2015). This study further adds to this conversation, not only a corroboration of the importance of this method (at least in aspiring leaders’ minds), but also that participants specifically recognized their professors’ experiences as school administrators as important for providing examples, context, and credibility to the work in the classroom.

In addition to the scenario approach, the participants also recognized the importance of learning from one another. In addition to the experiences of their practitioner-professors, many participants espoused the value of hearing the diverse perspectives of other students. The use of peer discussion was also an element of instruction in the referenced studies (Leithwood & Steinbach, 1995; Shapira-Lishchinsky, 2015), corroborating the power of aspiring leaders learning from one another and supporting existing literature about the social nature of problem solving (Berger & Luckmann, 1966; Leithwood & Steinbach, 1992; Vygotsky, 1978).

Finally, the ultimate theme identified through this study is the need for real-world experience in the field as an administrator or intern. It is simply not enough to learn about problem solving or learn the background knowledge needed to solve problems, even when the problems presented are real-world in nature. Scenarios are not enough for aspiring leaders to perceive their problem-solving abilities to be adequate or for their actual problem-solving abilities to improve. They need to be, as some of the participants reasoned, in positions of actual responsibility, where the weight of their decisions will have tangible impacts on stakeholders, including students.

The study of participants’ responses to the scenarios connected to the Four Frames model of Bolman and Deal (2008). The element for which participants received the consistently highest scores was identifying solution processes. This area might most logically be connected to the structural and human resource frames, as solutions typically involve working to meet individuals’ needs, as is necessary in the human resource frame, and attending to protocols and procedures, which is the essence of the structural frame. As identified above, the political and symbolic frames have been cited by the authors as the most underdeveloped by educational leaders, and this assertion is corroborated by the finding in this study that participants struggled the most with identifying constraints, which can sometimes arise from an understanding of the competing personal interests in an organization (political frame) and the underlying meaning behind aspects of an organization (symbolic frame), such as unspoken rules and traditions. The lack of success identifying constraints is also consistent with participants’ statements that they needed actual experiences in leadership roles, during which they would likely encounter, firsthand, the types of constraints they were unable to articulate for the given scenarios. Simply, they had not yet “lived” these types of obstacles.

The study includes several notable limitations. First, the study’s size is limited, particularly with only 20 participants’ data available for the matched pairs analysis. Further, this study was conducted at one university, within one particular certification program, and over three sections of one course, which represented about one-half of the time students spend in the program. It is likely that more gains in problem-solving ability and confidence would have been observed if this study was continued through the internship year. Also, the study did not include a control group. The lack of an experimental design limits the power of conclusions about causality. However, this limitation is mitigated by two factors. First, the results did not indicate a statistically significant improvement, so there is not a need to attribute a gain score to a particular variable (i.e. use of scenarios), anyway, and, second, the qualitative results did reveal the perceived value for participants in the use of scenarios, without any prompting of the researcher. Finally, the participant pool was not particularly diverse, though this fact is not particularly unusual for the selected university, in general, representing a contemporary challenge the university’s state is facing to educate its increasingly diverse student population, with a teaching and administrative workforce that is predominantly White.

The findings in this study invite further research. In addressing some of the limitations identified here, expanding this study to include aspiring administrators across other institutions representing different areas of the United States and other developed countries, would provide a more generalizable set of results. Further, studying the development of problem-solving skills during the administrative internship experience would also add to the work outlined here by considering the practical experience of participants.

In short, this study illustrates for those who prepare educational leaders the value of using scenarios in increasing aspiring leaders’ confidence and knowledge. However, intuitively, scenarios alone are not enough to engender significant change in their actual problem-solving abilities. Whereas, real-world context is important to the development of aspiring educational leaders’ problem-solving skills, the best context is likely to be the real work of administration.

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Author Biography

Dr. Jeremy Visone is an Assistant Professor of Educational Leadership, Policy, & Instructional Technology. Until 2016, he worked as an administrator at both the elementary and secondary levels, most recently at Anna Reynolds Elementary School, a National Blue Ribbon School in 2016. Dr. Visone can be reached at  [email protected] .

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Why Teach with Context-Rich Problems?

Context-rich problems offer students opportunities to develop problem-solving skills they can apply in the real world. By engaging in this type of problem solving, students develop expert-like thinking in the discipline.

Educational benefits of context-rich problems

Context-rich problems have the following benefits for students (Heller & Hollabaugh, 1992) :

• Encourages students to use expert problem solving strategies
• Integrate the context in which the discipline lies relative to their own experience
• Increase the level of sophistication of the way students think about their world
• Provide practice in applying the fundamental concepts of the discipline
• Help students progress towards expert-like thinking

Grounded in learning theory

Cognitive apprenticeship research Context-rich problems follow a cognitive apprenticeship approach ( Brown, Collins, & Duguid, 1989 ). Historically, apprenticeship has been a successful teaching tool in learning a trade and cognitive apprenticeship transfers this model into the classroom. With this approach students watch the instructor go through the problem solving process, next begin to work through the problem solving process with help from the instructor and other students and finally are able to complete the process on their own. One of the central tenants of apprenticeship is that learning occurs in realistic situations, such as those provided by context-rich problems. Expert-novice problem solving research Research on learning shows that there is a qualitative difference between novices and experts in their approach to problem solving ( Chi, Feltovich, & Glaser, 1981 ). For example, novices tend to search through formulas they know to find one that includes the variables given in the problem, whereas an expert will first figure out what information is needed, then decide how to obtain that information. ( Bransford, Brown, & Cocking 1999 ) suggest that instructors should be intentional in helping students develop expert-like thinking. Incorporating context-rich problems into a class helps students learn when and where to use particular strategies as they solve these problems. In this way, students will develop the expert skill of recognizing core concepts independent of the varied contexts in which they are presented.

Additional evidence for the effectiveness of context-rich problems

The following selected references can provide a more in-depth analysis of the effectiveness of context-rich problems. More references are available on the reference page .

• Bangs, J. (2007). Teaching perfect and imperfect competition with context-rich problems . Social Science Research Network . This paper describes the experience of using context-rich problems in a principles of microeconomics course.
• Heller, P., Keith, R. & Anderson, S. (1992). Teaching problem solving through cooperative grouping. Part 1: Group versus individual problem solving . American Journal of Physics, 60 (7), 627-636. This paper describes using cooperative group learning in a physics course. The learning focused on problem solving abilities with the use of context-rich problems.
• Simkins, S. P. & Maier, M. (2008). Learning from physics education research: Lessons for economics education . Social Science Research Network . This paper highlights four specific examples of successful pedagogical innovations drawn from physics education - context-rich problems, concept tests, just-in-time teaching, and interactive lecture demonstrations - and illustrate how these practices can be adapted for economic education.

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Principals and Problem-Solving

• Posted November 13, 2014
• By Bari Walsh

If you’re a school principal, how does context matter when you’re facing a difficult problem? Where do you find your source of support, and do the people you turn to actually help you to reach effective solutions? Ebony Bridwell-Mitchell explores these questions in a paper published in Organization Science with co-author Theresa Lant, finding that the type of people principals surround themselves with, and to whom they turn for counsel, has a lot to do with how they think about their role and their challenges in the first place. This “cognitive context,” she found, helps determine their social context and is predictive of how they’ll go about solving problems or advancing their agenda.

Bridwell-Mitchell studies educational leadership, management, and organizations, often exploring the tension between structure and agency — “how we make choices within constraints,” as she describes it. “A lot of education policy is focused on what we can do to get people to make better choices — how we can spur them to be more gritty, or how we can incentivize them. But all the choices people make — even if they’re properly incentivized, even if they’re extra gritty — are constrained in some way by context. It turns out that when you look at differences across individuals, what best explains the variation is context. People in one context tend to think and do things a certain way, and very differently than people in another context.”

How Context Matters

In the recent paper, she set out to explore just how context matters when school principals are faced with decisions. She wanted to understand not only how principals’ social networks mattered, but also how cognitive context mattered — how they thought about or framed their problems.

She investigated two different ways in which principals might frame a pressing problem: as political, having to do with influence or power, or as strategic, having to do with performance and resources. She wanted to see whether that framing had an effect on the kinds of people they chose to go to for help.

She found that when people frame their problems politically, they are more likely to turn to advisors they think are trustworthy and have influence. But when they frame problems as being strategic, they are more likely to turn to people they think are accessible and have resources.

The Takeaway

What does all this mean in terms of helping principals solve problems? “If people have persistent patterns in how they see problems, then they have a tendency to choose certain kinds of people, irrespective of whether that’s what the problem actually is or those are the people they actually need,” says Bridwell-Mitchell. “You can imagine that people might be thinking about the problem in the wrong way and choosing the wrong people and not ending up with the solutions they need.”

“It really gives us an incentive to invest in what people often call shared decision making or shared leadership,” she continues. “What this is saying is, you need people to help you think carefully about these problems, so you can make sure you’re conceptualizing them in ways that will get you to the right people for help.”

Bridwell-Mitchell is doing a follow-up study to assess which cognitive contexts and social contexts may be more effective at solving which types of problems. She’s asking groups of principals to work through the issues involved in two randomly assigned scenarios, one about bullying and one about increasing achievement in middle-performing students, and then to come up with a solution. A set of experts — other principals and field experts — will assess and rate the solutions. The goal is to shed light on which factors were more helpful in arriving at effective solutions — cognitive framing, social context, or a combination of the two.

The bottom line is that context matters — perhaps more than any other factor — in effective leadership, says Bridwell-Mitchell. “If we’re not thinking about how much context matters, and how to change context, we’re losing most of the leverage that we have to actually get people to behave differently.”

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