experimental research topics in mathematics

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Mathematics Theses, Projects, and Dissertations

Theses/projects/dissertations from 2024 2024.

On Cheeger Constants of Knots , Robert Lattimer

Information Based Approach for Detecting Change Points in Inverse Gaussian Model with Applications , Alexis Anne Wallace

Theses/Projects/Dissertations from 2023 2023

DNA SELF-ASSEMBLY OF TRAPEZOHEDRAL GRAPHS , Hytham Abdelkarim

An Exposition of the Curvature of Warped Product Manifolds , Angelina Bisson

Jackknife Empirical Likelihood Tests for Equality of Generalized Lorenz Curves , Anton Butenko

MATHEMATICS BEHIND MACHINE LEARNING , Rim Hammoud

Statistical Analysis of Health Habits for Incoming College Students , Wendy Isamara Lizarraga Noriega

Reverse Mathematics of Ramsey's Theorem , Nikolay Maslov

Distance Correlation Based Feature Selection in Random Forest , Jose Munoz-Lopez

Constructing Hyperbolic Polygons in the Poincaré Disk , Akram Zakaria Samweil

KNOT EQUIVALENCE , Jacob Trubey

Theses/Projects/Dissertations from 2022 2022

SYMMETRIC GENERATIONS AND AN ALGORITHM TO PROVE RELATIONS , Diddier Andrade

The Examination of the Arithmetic Surface (3, 5) Over Q , Rachel J. Arguelles

Error Terms for the Trapezoid, Midpoint, and Simpson's Rules , Jessica E. Coen

de Rham Cohomology, Homotopy Invariance and the Mayer-Vietoris Sequence , Stacey Elizabeth Cox

Symmetric Generation , Ana Gonzalez

SYMMETRIC PRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Samar Mikhail Kasouha

Simple Groups and Related Topics , Simrandeep Kaur

Homomorphic Images and Related Topics , Alejandro Martinez

LATTICE REDUCTION ALGORITHMS , Juan Ortega

THE DECOMPOSITION OF THE SPACE OF ALGEBRAIC CURVATURE TENSORS , Katelyn Sage Risinger

Verifying Sudoku Puzzles , Chelsea Schweer

AN EXPOSITION OF ELLIPTIC CURVE CRYPTOGRAPHY , Travis Severns

Theses/Projects/Dissertations from 2021 2021

Non-Abelian Finite Simple Groups as Homomorphic Images , Sandra Bahena

Matroids Determinable by Two Partial Representations , Aurora Calderon Dojaquez

SYMMETRIC REPRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Connie Corona

Symmetric Presentation of Finite Groups, and Related Topics , Marina Michelle Duchesne

MEASURE AND INTEGRATION , JeongHwan Lee

A Study in Applications of Continued Fractions , Karen Lynn Parrish

Partial Representations for Ternary Matroids , Ebony Perez

Theses/Projects/Dissertations from 2020 2020

Sum of Cubes of the First n Integers , Obiamaka L. Agu

Permutation and Monomial Progenitors , Crystal Diaz

Tile Based Self-Assembly of the Rook's Graph , Ernesto Gonzalez

Research In Short Term Actuarial Modeling , Elijah Howells

Hyperbolic Triangle Groups , Sergey Katykhin

Exploring Matroid Minors , Jonathan Lara Tejeda

DNA COMPLEXES OF ONE BOND-EDGE TYPE , Andrew Tyler Lavengood-Ryan

Modeling the Spread of Measles , Alexandria Le Beau

Symmetric Presentations and Related Topics , Mayra McGrath

Minimal Surfaces and The Weierstrass-Enneper Representation , Evan Snyder

ASSESSING STUDENT UNDERSTANDING WHILE SOLVING LINEAR EQUATIONS USING FLOWCHARTS AND ALGEBRAIC METHODS , Edima Umanah

Excluded minors for nearly-paving matroids , Vanessa Natalie Vega

Theses/Projects/Dissertations from 2019 2019

Fuchsian Groups , Bob Anaya

Tribonacci Convolution Triangle , Rosa Davila

VANISHING LOCAL SCALAR INVARIANTS ON GENERALIZED PLANE WAVE MANIFOLDS , Brian Matthew Friday

Analogues Between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle , Lacey Taylor James

Geodesics on Generalized Plane Wave Manifolds , Moises Pena

Algebraic Methods for Proving Geometric Theorems , Lynn Redman

Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle , Antonio Saucedo Jr.

THE EFFECTIVENESS OF DYNAMIC MATHEMATICAL SOFTWARE IN THE INSTRUCTION OF THE UNIT CIRCLE , Edward Simons

CALCULUS REMEDIATION AS AN INDICATOR FOR SUCCESS ON THE CALCULUS AP EXAM , Ty Stockham

Theses/Projects/Dissertations from 2018 2018

PROGENITORS, SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS , Diana Aguirre

Monomial Progenitors and Related Topics , Madai Obaid Alnominy

Progenitors Involving Simple Groups , Nicholas R. Andujo

Simple Groups, Progenitors, and Related Topics , Angelica Baccari

Exploring Flag Matroids and Duality , Zachary Garcia

Images of Permutation and Monomial Progenitors , Shirley Marina Juan

MODERN CRYPTOGRAPHY , Samuel Lopez

Progenitors, Symmetric Presentations, and Related Topics , Joana Viridiana Luna

Symmetric Presentations, Representations, and Related Topics , Adam Manriquez

Toroidal Embeddings and Desingularization , LEON NGUYEN

THE STRUGGLE WITH INVERSE FUNCTIONS DOING AND UNDOING PROCESS , Jesus Nolasco

Tutte-Equivalent Matroids , Maria Margarita Rocha

Symmetric Presentations and Double Coset Enumeration , Charles Seager

MANUAL SYMMETRIC GENERATION , Joel Webster

Theses/Projects/Dissertations from 2017 2017

Investigation of Finite Groups Through Progenitors , Charles Baccari

CONSTRUCTION OF HOMOMORPHIC IMAGES , Erica Fernandez

Making Models with Bayes , Pilar Olid

An Introduction to Lie Algebra , Amanda Renee Talley

SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS , Ulyses Velasco

CONSTRUCTION OF FINITE GROUP , Michelle SoYeong Yeo

Theses/Projects/Dissertations from 2016 2016

Upset Paths and 2-Majority Tournaments , Rana Ali Alshaikh

Regular Round Matroids , Svetlana Borissova

GEODESICS IN LORENTZIAN MANIFOLDS , Amir A. Botros

REALIZING TOURNAMENTS AS MODELS FOR K-MAJORITY VOTING , Gina Marie Cheney

Solving Absolute Value Equations and Inequalities on a Number Line , Melinda A. Curtis

BIO-MATHEMATICS: INTRODUCTION TO THE MATHEMATICAL MODEL OF THE HEPATITIS C VIRUS , Lucille J. Durfee

ANALYSIS AND SYNTHESIS OF THE LITERATURE REGARDING ACTIVE AND DIRECT INSTRUCTION AND THEIR PROMOTION OF FLEXIBLE THINKING IN MATHEMATICS , Genelle Elizabeth Gonzalez

LIFE EXPECTANCY , Ali R. Hassanzadah

PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS , Sean M. Hearon

A Dual Fano, and Dual Non-Fano Matroidal Network , Stephen Lee Johnson

Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity , Nitish Mittal

The Kauffman Bracket and Genus of Alternating Links , Bryan M. Nguyen

Probabilistic Methods In Information Theory , Erik W. Pachas

THINKING POKER THROUGH GAME THEORY , Damian Palafox

Indicators of Future Mathematics Proficiency: Literature Review & Synthesis , Claudia Preciado

Ádám's Conjecture and Arc Reversal Problems , Claudio D. Salas

AN INTRODUCTION TO BOOLEAN ALGEBRAS , Amy Schardijn

The Evolution of Cryptology , Gwendolyn Rae Souza

Theses/Projects/Dissertations from 2015 2015

SYMMETRIC PRESENTATIONS AND RELATED TOPICS , Mashael U. Alharbi

Homomorphic Images And Related Topics , Kevin J. Baccari

Geometric Constructions from an Algebraic Perspective , Betzabe Bojorquez

Discovering and Applying Geometric Transformations: Transformations to Show Congruence and Similarity , Tamara V. Bonn

Symmetric Presentations and Generation , Dustin J. Grindstaff

HILBERT SPACES AND FOURIER SERIES , Terri Joan Harris Mrs.

SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS , Leonard B. Lamp

Simple Groups and Related Topics , Manal Abdulkarim Marouf Ms.

Elliptic Curves , Trinity Mecklenburg

A Fundamental Unit of O_K , Susana L. Munoz

CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES , Jessica Luna Ramirez

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• 14 May 2024

Why mathematics is set to be revolutionized by AI

• Thomas Fink 0

Thomas Fink is the director of the London Institute for Mathematical Sciences, UK.

You can also search for this author in PubMed   Google Scholar

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Giving birth to a conjecture — a proposition that is suspected to be true, but needs definitive proof — can feel to a mathematician like a moment of divine inspiration. Mathematical conjectures are not merely educated guesses. Formulating them requires a combination of genius, intuition and experience. Even a mathematician can struggle to explain their own discovery process. Yet, counter-intuitively, I think that this is the realm in which machine intelligence will initially be most transformative.

In 2017, researchers at the London Institute for Mathematical Sciences, of which I am director, began applying machine learning to mathematical data as a hobby. During the COVID-19 pandemic, they discovered that simple artificial intelligence (AI) classifiers can predict an elliptic curve’s rank 1 — a measure of its complexity. Elliptic curves are fundamental to number theory, and understanding their underlying statistics is a crucial step towards solving one of the seven Millennium Problems, which are selected by the Clay Mathematics Institute in Providence, Rhode Island, and carry a prize of US$1 million each. Few expected AI to make a dent in this high-stakes arena.

AI now beats humans at basic tasks — new benchmarks are needed, says major report

AI has made inroads in other areas, too. A few years ago, a computer program called the Ramanujan Machine produced new formulae for fundamental constants 2 , such as π and e . It did so by exhaustively searching through families of continued fractions — a fraction whose denominator is a number plus a fraction whose denominator is also a number plus a fraction and so on. Some of these conjectures have since been proved, whereas others remain open problems.

Another example pertains to knot theory, a branch of topology in which a hypothetical piece of string is tangled up before the ends are glued together. Researchers at Google DeepMind, based in London, trained a neural network on data for many different knots and discovered an unexpected relationship between their algebraic and geometric structures 3 .

How has AI made a difference in areas of mathematics in which human creativity was thought to be essential?

First, there are no coincidences in maths. In real-world experiments, false negatives and false positives abound. But in maths, a single counterexample leaves a conjecture dead in the water. For example, the Pólya conjecture states that most integers below any given integer have an odd number of prime factors. But in 1960, it was found that the conjecture does not hold for the number 906,180,359. In one fell swoop, the conjecture was falsified.

Second, mathematical data — on which AI can be trained — are cheap. Primes, knots and many other types of mathematical object are abundant. The On-Line Encyclopedia of Integer Sequences (OEIS) contains almost 375,000 sequences — from the familiar Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, ...) to the formidable Busy Beaver sequence (0, 1, 4, 6, 13, …), which grows faster than any computable function. Scientists are already using machine-learning tools to search the OEIS database to find unanticipated relationships.

DeepMind AI outdoes human mathematicians on unsolved problem

AI can help us to spot patterns and form conjectures. But not all conjectures are created equal. They also need to advance our understanding of mathematics. In his 1940 essay A Mathematician’s Apology , G. H. Hardy explains that a good theorem “should be one which is a constituent in many mathematical constructs, which is used in the proof of theorems of many different kinds”. In other words, the best theorems increase the likelihood of discovering new theorems. Conjectures that help us to reach new mathematical frontiers are better than those that yield fewer insights. But distinguishing between them requires an intuition for how the field itself will evolve. This grasp of the broader context will remain out of AI’s reach for a long time — so the technology will struggle to spot important conjectures.

But despite the caveats, there are many upsides to wider adoption of AI tools in the maths community. AI can provide a decisive edge and open up new avenues for research.

Mainstream mathematics journals should also publish more conjectures. Some of the most significant problems in maths — such as Fermat’s Last Theorem, the Riemann hypothesis, Hilbert’s 23 problems and Ramanujan’s many identities — and countless less-famous conjectures have shaped the course of the field. Conjectures speed up research by pointing us in the right direction. Journal articles about conjectures, backed up by data or heuristic arguments, will accelerate discovery.

Last year, researchers at Google DeepMind predicted 2.2 million new crystal structures 4 . But it remains to be seen how many of these potential new materials are stable, can be synthesized and have practical applications. For now, this is largely a task for human researchers, who have a grasp of the broad context of materials science.

Similarly, the imagination and intuition of mathematicians will be required to make sense of the output of AI tools. Thus, AI will act only as a catalyst of human ingenuity, rather than a substitute for it.

Nature 629 , 505 (2024)

doi: https://doi.org/10.1038/d41586-024-01413-w

He, Y.-H., Lee, K.-H., Oliver, T. & Pozdnyakov, A. Preprint at arXiv https://doi.org/10.48550/arXiv.2204.10140 (2024).

Raayoni, G. et al. Nature 590 , 67–73 (2021).

Article   PubMed   Google Scholar  

Davies, A. et al. Nature 600 , 70–74 (2021).

Merchant, A. et al. Nature 624 , 80–85 (2023).

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200+ Experimental Quantitative Research Topics For STEM Students In 2023

STEM means Science, Technology, Engineering, and Math, which is not the only stuff we learn in school. It is like a treasure chest of skills that help students become great problem solvers, ready to tackle the real world’s challenges.

In this blog, we are here to explore the world of Research Topics for STEM Students. We will break down what STEM really means and why it is so important for students. In addition, we will give you the lowdown on how to pick a fascinating research topic. We will explain a list of 200+ Experimental Quantitative Research Topics For STEM Students.

And when it comes to writing a research title, we will guide you step by step. So, stay with us as we unlock the exciting world of STEM research – it is not just about grades; it is about growing smarter, more confident, and happier along the way.

What Is STEM?

Table of Contents

STEM is Science, Technology, Engineering, and Mathematics. It is a way of talking about things like learning, jobs, and activities related to these four important subjects. Science is about understanding the world around us, technology is about using tools and machines to solve problems, engineering is about designing and building things, and mathematics is about numbers and solving problems with them. STEM helps us explore, discover, and create cool stuff that makes our world better and more exciting.

Why STEM Research Is Important?

STEM research is important because it helps us learn new things about the world and solve problems. When scientists, engineers, and mathematicians study these subjects, they can discover cures for diseases, create new technology that makes life easier, and build things that help us live better. It is like a big puzzle where we put together pieces of knowledge to make our world safer, healthier, and more fun.

• STEM research leads to new discoveries and solutions.
• It helps find cures for diseases.
• STEM technology makes life easier.
• Engineers build things that improve our lives.
• Mathematics helps us understand and solve complex problems.

How to Choose a Topic for STEM Research Paper

Here are some steps to choose a topic for STEM Research Paper:

Step 1: Identify Your Interests

Think about what you like and what excites you in science, technology, engineering, or math. It could be something you learned in school, saw in the news, or experienced in your daily life. Choosing a topic you’re passionate about makes the research process more enjoyable.

Step 2: Research Existing Topics

Look up different STEM research areas online, in books, or at your library. See what scientists and experts are studying. This can give you ideas and help you understand what’s already known in your chosen field.

Step 3: Consider Real-World Problems

Think about the problems you see around you. Are there issues in your community or the world that STEM can help solve? Choosing a topic that addresses a real-world problem can make your research impactful.

Step 4: Talk to Teachers and Mentors

Discuss your interests with your teachers, professors, or mentors. They can offer guidance and suggest topics that align with your skills and goals. They may also provide resources and support for your research.

Step 5: Narrow Down Your Topic

Once you have some ideas, narrow them down to a specific research question or project. Make sure it’s not too broad or too narrow. You want a topic that you can explore in depth within the scope of your research paper.

Here we will discuss 200+ Experimental Quantitative Research Topics For STEM Students: 

Qualitative Research Topics for STEM Students:

Qualitative research focuses on exploring and understanding phenomena through non-numerical data and subjective experiences. Here are 10 qualitative research topics for STEM students:

• Exploring the experiences of female STEM students in overcoming gender bias in academia.
• Understanding the perceptions of teachers regarding the integration of technology in STEM education.
• Investigating the motivations and challenges of STEM educators in underprivileged schools.
• Exploring the attitudes and beliefs of parents towards STEM education for their children.
• Analyzing the impact of collaborative learning on student engagement in STEM subjects.
• Investigating the experiences of STEM professionals in bridging the gap between academia and industry.
• Understanding the cultural factors influencing STEM career choices among minority students.
• Exploring the role of mentorship in the career development of STEM graduates.
• Analyzing the perceptions of students towards the ethics of emerging STEM technologies like AI and CRISPR.
• Investigating the emotional well-being and stress levels of STEM students during their academic journey.

Easy Experimental Research Topics for STEM Students:

These experimental research topics are relatively straightforward and suitable for STEM students who are new to research:

•  Measuring the effect of different light wavelengths on plant growth.
•  Investigating the relationship between exercise and heart rate in various age groups.
•  Testing the effectiveness of different insulating materials in conserving heat.
•  Examining the impact of pH levels on the rate of chemical reactions.
•  Studying the behavior of magnets in different temperature conditions.
•  Investigating the effect of different concentrations of a substance on bacterial growth.
•  Testing the efficiency of various sunscreen brands in blocking UV radiation.
•  Measuring the impact of music genres on concentration and productivity.
•  Examining the correlation between the angle of a ramp and the speed of a rolling object.
•  Investigating the relationship between the number of blades on a wind turbine and energy output.

Research Topics for STEM Students in the Philippines:

These research topics are tailored for STEM students in the Philippines:

•  Assessing the impact of climate change on the biodiversity of coral reefs in the Philippines.
•  Studying the potential of indigenous plants in the Philippines for medicinal purposes.
•  Investigating the feasibility of harnessing renewable energy sources like solar and wind in rural Filipino communities.
•  Analyzing the water quality and pollution levels in major rivers and lakes in the Philippines.
•  Exploring sustainable agricultural practices for small-scale farmers in the Philippines.
•  Assessing the prevalence and impact of dengue fever outbreaks in urban areas of the Philippines.
•  Investigating the challenges and opportunities of STEM education in remote Filipino islands.
•  Studying the impact of typhoons and natural disasters on infrastructure resilience in the Philippines.
•  Analyzing the genetic diversity of endemic species in the Philippine rainforests.
•  Assessing the effectiveness of disaster preparedness programs in Philippine communities.

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Good Research Topics for STEM Students:

These research topics are considered good because they offer interesting avenues for investigation and learning:

•  Developing a low-cost and efficient water purification system for rural communities.
•  Investigating the potential use of CRISPR-Cas9 for gene therapy in genetic disorders.
•  Studying the applications of blockchain technology in securing medical records.
•  Analyzing the impact of 3D printing on customized prosthetics for amputees.
•  Exploring the use of artificial intelligence in predicting and preventing forest fires.
•  Investigating the effects of microplastic pollution on aquatic ecosystems.
•  Analyzing the use of drones in monitoring and managing agricultural crops.
•  Studying the potential of quantum computing in solving complex optimization problems.
•  Investigating the development of biodegradable materials for sustainable packaging.
•  Exploring the ethical implications of gene editing in humans.

Unique Research Topics for STEM Students:

Unique research topics can provide STEM students with the opportunity to explore unconventional and innovative ideas. Here are 10 unique research topics for STEM students:

•  Investigating the use of bioluminescent organisms for sustainable lighting solutions.
•  Studying the potential of using spider silk proteins for advanced materials in engineering.
•  Exploring the application of quantum entanglement for secure communication in the field of cryptography.
•  Analyzing the feasibility of harnessing geothermal energy from underwater volcanoes.
•  Investigating the use of CRISPR-Cas12 for rapid and cost-effective disease diagnostics.
•  Studying the interaction between artificial intelligence and human creativity in art and music generation.
•  Exploring the development of edible packaging materials to reduce plastic waste.
•  Investigating the impact of microgravity on cellular behavior and tissue regeneration in space.
•  Analyzing the potential of using sound waves to detect and combat invasive species in aquatic ecosystems.
•  Studying the use of biotechnology in reviving extinct species, such as the woolly mammoth.

Experimental Research Topics for STEM Students in the Philippines

Research topics for STEM students in the Philippines can address specific regional challenges and opportunities. Here are 10 experimental research topics for STEM students in the Philippines:

•  Assessing the effectiveness of locally sourced materials for disaster-resilient housing construction in typhoon-prone areas.
•  Investigating the utilization of indigenous plants for natural remedies in Filipino traditional medicine.
•  Studying the impact of volcanic soil on crop growth and agriculture in volcanic regions of the Philippines.
•  Analyzing the water quality and purification methods in remote island communities.
•  Exploring the feasibility of using bamboo as a sustainable construction material in the Philippines.
•  Investigating the potential of using solar stills for freshwater production in water-scarce regions.
•  Studying the effects of climate change on the migration patterns of bird species in the Philippines.
•  Analyzing the growth and sustainability of coral reefs in marine protected areas.
•  Investigating the utilization of coconut waste for biofuel production.
•  Studying the biodiversity and conservation efforts in the Tubbataha Reefs Natural Park.

Capstone Research Topics for STEM Students in the Philippines:

Capstone research projects are often more comprehensive and can address real-world issues. Here are 10 capstone research topics for STEM students in the Philippines:

•  Designing a low-cost and sustainable sanitation system for informal settlements in urban Manila.
•  Developing a mobile app for monitoring and reporting natural disasters in the Philippines.
•  Assessing the impact of climate change on the availability and quality of drinking water in Philippine cities.
•  Designing an efficient traffic management system to address congestion in major Filipino cities.
•  Analyzing the health implications of air pollution in densely populated urban areas of the Philippines.
•  Developing a renewable energy microgrid for off-grid communities in the archipelago.
•  Assessing the feasibility of using unmanned aerial vehicles (drones) for agricultural monitoring in rural Philippines.
•  Designing a low-cost and sustainable aquaponics system for urban agriculture.
•  Investigating the potential of vertical farming to address food security in densely populated urban areas.
•  Developing a disaster-resilient housing prototype suitable for typhoon-prone regions.

Experimental Quantitative Research Topics for STEM Students:

Experimental quantitative research involves the collection and analysis of numerical data to conclude. Here are 10 Experimental Quantitative Research Topics For STEM Students interested in experimental quantitative research:

•  Examining the impact of different fertilizers on crop yield in agriculture.
•  Investigating the relationship between exercise and heart rate among different age groups.
•  Analyzing the effect of varying light intensities on photosynthesis in plants.
•  Studying the efficiency of various insulation materials in reducing building heat loss.
•  Investigating the relationship between pH levels and the rate of corrosion in metals.
•  Analyzing the impact of different concentrations of pollutants on aquatic ecosystems.
•  Examining the effectiveness of different antibiotics on bacterial growth.
•  Trying to figure out how temperature affects how thick liquids are.
•  Finding out if there is a link between the amount of pollution in the air and lung illnesses in cities.
•  Analyzing the efficiency of solar panels in converting sunlight into electricity under varying conditions.

Descriptive Research Topics for STEM Students

Descriptive research aims to provide a detailed account or description of a phenomenon. Here are 10 topics for STEM students interested in descriptive research:

•  Describing the physical characteristics and behavior of a newly discovered species of marine life.
•  Documenting the geological features and formations of a particular region.
•  Creating a detailed inventory of plant species in a specific ecosystem.
•  Describing the properties and behavior of a new synthetic polymer.
•  Documenting the daily weather patterns and climate trends in a particular area.
•  Providing a comprehensive analysis of the energy consumption patterns in a city.
•  Describing the structural components and functions of a newly developed medical device.
•  Documenting the characteristics and usage of traditional construction materials in a region.
•  Providing a detailed account of the microbiome in a specific environmental niche.
•  Describing the life cycle and behavior of a rare insect species.

Research Topics for STEM Students in the Pandemic:

The COVID-19 pandemic has raised many research opportunities for STEM students. Here are 10 research topics related to pandemics:

•  Analyzing the effectiveness of various personal protective equipment (PPE) in preventing the spread of respiratory viruses.
•  Studying the impact of lockdown measures on air quality and pollution levels in urban areas.
•  Investigating the psychological effects of quarantine and social isolation on mental health.
•  Analyzing the genomic variation of the SARS-CoV-2 virus and its implications for vaccine development.
•  Studying the efficacy of different disinfection methods on various surfaces.
•  Investigating the role of contact tracing apps in tracking & controlling the spread of infectious diseases.
•  Analyzing the economic impact of the pandemic on different industries and sectors.
•  Studying the effectiveness of remote learning in STEM education during lockdowns.
•  Investigating the social disparities in healthcare access during a pandemic.
• Analyzing the ethical considerations surrounding vaccine distribution and prioritization.

Research Topics for STEM Students Middle School

Research topics for middle school STEM students should be engaging and suitable for their age group. Here are 10 research topics:

• Investigating the growth patterns of different types of mold on various food items.
• Studying the negative effects of music on plant growth and development.
• Analyzing the relationship between the shape of a paper airplane and its flight distance.
• Investigating the properties of different materials in making effective insulators for hot and cold beverages.
• Studying the effect of salt on the buoyancy of different objects in water.
• Analyzing the behavior of magnets when exposed to different temperatures.
• Investigating the factors that affect the rate of ice melting in different environments.
• Studying the impact of color on the absorption of heat by various surfaces.
• Analyzing the growth of crystals in different types of solutions.
• Investigating the effectiveness of different natural repellents against common pests like mosquitoes.

Technology Research Topics for STEM Students

Technology is at the forefront of STEM fields. Here are 10 research topics for STEM students interested in technology:

• Developing and optimizing algorithms for autonomous drone navigation in complex environments.
• Exploring the use of blockchain technology for enhancing the security and transparency of supply chains.
• Investigating the applications of virtual reality (VR) and augmented reality (AR) in medical training and surgery simulations.
• Studying the potential of 3D printing for creating personalized prosthetics and orthopedic implants.
• Analyzing the ethical and privacy implications of facial recognition technology in public spaces.
• Investigating the development of quantum computing algorithms for solving complex optimization problems.
• Explaining the use of machine learning and AI in predicting and mitigating the impact of natural disasters.
• Studying the advancement of brain-computer interfaces for assisting individuals with
• disabilities.
• Analyzing the role of wearable technology in monitoring and improving personal health and wellness.
• Investigating the use of robotics in disaster response and search and rescue operations.

Scientific Research Topics for STEM Students

Scientific research encompasses a wide range of topics. Here are 10 research topics for STEM students focusing on scientific exploration:

• Investigating the behavior of subatomic particles in high-energy particle accelerators.
• Studying the ecological impact of invasive species on native ecosystems.
• Analyzing the genetics of antibiotic resistance in bacteria and its implications for healthcare.
• Exploring the physics of gravitational waves and their detection through advanced interferometry.
• Investigating the neurobiology of memory formation and retention in the human brain.
• Studying the biodiversity and adaptation of extremophiles in harsh environments.
• Analyzing the chemistry of deep-sea hydrothermal vents and their potential for life beyond Earth.
• Exploring the properties of superconductors and their applications in technology.
• Investigating the mechanisms of stem cell differentiation for regenerative medicine.
• Studying the dynamics of climate change and its impact on global ecosystems.

Interesting Research Topics for STEM Students:

Engaging and intriguing research topics can foster a passion for STEM. Here are 10 interesting research topics for STEM students:

• Exploring the science behind the formation of auroras and their cultural significance.
• Investigating the mysteries of dark matter and dark energy in the universe.
• Studying the psychology of decision-making in high-pressure situations, such as sports or
• emergencies.
• Analyzing the impact of social media on interpersonal relationships and mental health.
• Exploring the potential for using genetic modification to create disease-resistant crops.
• Investigating the cognitive processes involved in solving complex puzzles and riddles.
• Studying the history and evolution of cryptography and encryption methods.
• Analyzing the physics of time travel and its theoretical possibilities.
• Exploring the role of Artificial Intelligence  in creating art and music.
• Investigating the science of happiness and well-being, including factors contributing to life satisfaction.

Practical Research Topics for STEM Students

Practical research often leads to real-world solutions. Here are 10 practical research topics for STEM students:

• Developing an affordable and sustainable water purification system for rural communities.
• Designing a low-cost, energy-efficient home heating and cooling system.
• Investigating strategies for reducing food waste in the supply chain and households.
• Studying the effectiveness of eco-friendly pest control methods in agriculture.
• Analyzing the impact of renewable energy integration on the stability of power grids.
• Developing a smartphone app for early detection of common medical conditions.
• Investigating the feasibility of vertical farming for urban food production.
• Designing a system for recycling and upcycling electronic waste.
• Studying the environmental benefits of green roofs and their potential for urban heat island mitigation.
• Analyzing the efficiency of alternative transportation methods in reducing carbon emissions.

Experimental Research Topics for STEM Students About Plants

Plants offer a rich field for experimental research. Here are 10 experimental research topics about plants for STEM students:

• Investigating the effect of different light wavelengths on plant growth and photosynthesis.
• Studying the impact of various fertilizers and nutrient solutions on crop yield.
• Analyzing the response of plants to different types and concentrations of plant hormones.
• Investigating the role of mycorrhizal in enhancing nutrient uptake in plants.
• Studying the effects of drought stress and water scarcity on plant physiology and adaptation mechanisms.
• Analyzing the influence of soil pH on plant nutrient availability and growth.
• Investigating the chemical signaling and defense mechanisms of plants against herbivores.
• Studying the impact of environmental pollutants on plant health and genetic diversity.
• Analyzing the role of plant secondary metabolites in pharmaceutical and agricultural applications.
• Investigating the interactions between plants and beneficial microorganisms in the rhizosphere.

Qualitative Research Topics for STEM Students in the Philippines

Qualitative research in the Philippines can address local issues and cultural contexts. Here are 10 qualitative research topics for STEM students in the Philippines:

• Exploring indigenous knowledge and practices in sustainable agriculture in Filipino communities.
• Studying the perceptions and experiences of Filipino fishermen in coping with climate change impacts.
• Analyzing the cultural significance and traditional uses of medicinal plants in indigenous Filipino communities.
• Investigating the barriers and facilitators of STEM education access in remote Philippine islands.
• Exploring the role of traditional Filipino architecture in natural disaster resilience.
• Studying the impact of indigenous farming methods on soil conservation and fertility.
• Analyzing the cultural and environmental significance of mangroves in coastal Filipino regions.
• Investigating the knowledge and practices of Filipino healers in treating common ailments.
• Exploring the cultural heritage and conservation efforts of the Ifugao rice terraces.
• Studying the perceptions and practices of Filipino communities in preserving marine biodiversity.

Science Research Topics for STEM Students

Science offers a diverse range of research avenues. Here are 10 science research topics for STEM students:

• Investigating the potential of gene editing techniques like CRISPR-Cas9 in curing genetic diseases.
• Studying the ecological impacts of species reintroduction programs on local ecosystems.
• Analyzing the effects of microplastic pollution on aquatic food webs and ecosystems.
• Investigating the link between air pollution and respiratory health in urban populations.
• Studying the role of epigenetics in the inheritance of acquired traits in organisms.
• Analyzing the physiology and adaptations of extremophiles in extreme environments on Earth.
• Investigating the genetics of longevity and factors influencing human lifespan.
• Studying the behavioral ecology and communication strategies of social insects.
• Analyzing the effects of deforestation on global climate patterns and biodiversity loss.
• Investigating the potential of synthetic biology in creating bioengineered organisms for beneficial applications.

Correlational Research Topics for STEM Students

Correlational research focuses on relationships between variables. Here are 10 correlational research topics for STEM students:

• Analyzing the correlation between dietary habits and the incidence of chronic diseases.
• Studying the relationship between exercise frequency and mental health outcomes.
• Investigating the correlation between socioeconomic status and access to quality healthcare.
• Analyzing the link between social media usage and self-esteem in adolescents.
• Studying the correlation between academic performance and sleep duration among students.
• Investigating the relationship between environmental factors and the prevalence of allergies.
• Analyzing the correlation between technology use and attention span in children.
• Studying how environmental factors are related to the frequency of allergies.
• Investigating the link between parental involvement in education and student achievement.
• Analyzing the correlation between temperature fluctuations and wildlife migration patterns.

Quantitative Research Topics for STEM Students in the Philippines

Quantitative research in the Philippines can address specific regional issues. Here are 10 quantitative research topics for STEM students in the Philippines

• Analyzing the impact of typhoons on coastal erosion rates in the Philippines.
• Studying the quantitative effects of land use change on watershed hydrology in Filipino regions.
• Investigating the quantitative relationship between deforestation and habitat loss for endangered species.
• Analyzing the quantitative patterns of marine biodiversity in Philippine coral reef ecosystems.
• Studying the quantitative assessment of water quality in major Philippine rivers and lakes.
• Investigating the quantitative analysis of renewable energy potential in specific Philippine provinces.
• Analyzing the quantitative impacts of agricultural practices on soil health and fertility.
• Studying the quantitative effectiveness of mangrove restoration in coastal protection in the Philippines.
• Investigating the quantitative evaluation of indigenous agricultural practices for sustainability.
• Analyzing the quantitative patterns of air pollution and its health impacts in urban Filipino areas.

Things That Must Keep In Mind While Writing Quantitative Research Title 

Here are few things that must be keep in mind while writing quantitative research tile:

1. Be Clear and Precise

Make sure your research title is clear and says exactly what your study is about. People should easily understand the topic and goals of your research by reading the title.

2. Use Important Words

Include words that are crucial to your research, like the main subjects, who you’re studying, and how you’re doing your research. This helps others find your work and understand what it’s about.

3. Avoid Confusing Words

Stay away from words that might confuse people. Your title should be easy to grasp, even if someone isn’t an expert in your field.

4. Show Your Research Approach

Tell readers what kind of research you did, like experiments or surveys. This gives them a hint about how you conducted your study.

5. Match Your Title with Your Research Questions

Make sure your title matches the questions you’re trying to answer in your research. It should give a sneak peek into what your study is all about and keep you on the right track as you work on it.

STEM students, addressing what STEM is and why research matters in this field. It offered an extensive list of research topics , including experimental, qualitative, and regional options, catering to various academic levels and interests. Whether you’re a middle school student or pursuing advanced studies, these topics offer a wealth of ideas. The key takeaway is to choose a topic that resonates with your passion and aligns with your goals, ensuring a successful journey in STEM research. Choose the best Experimental Quantitative Research Topics For Stem Students today!

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Experimental Research about Effect of Mathematics Anxiety, Working Memory Capacity on Students' Mathematical Performance With Three Different Types of …

2011, ARPN Journal of Science and Technology (ISSN: 2225-7217)

The paper has shown the relationship between mathematics anxiety, mathematics performance and academic hardiness in high school students in term of students learning method (Cooperative learning vs. traditional learning). For students who are working in small math cooperative groups, researchers have found that they can develop problem solving. The main aim of this study is to show that how much learning method could be helpful for learner with high math anxiety. The sample comprised 263 (134 males and 129 females) college students were tested on Mathematics Anxiety Rating Scale, Academic Hardiness Scale and Mathematics examination. Results obtained indicated that students work together with low or high mathematics anxiety had better performance in mathematics score. Also, results have revealed that mathematics anxiety has significant negative correlation with mathematics performance and academic hardiness. It is also found that the gender differences in mathematics anxiety are significant, whereas no significant differences are detected between boys and girls in mathematics performance and academic hardiness. In addition, the result of the study showed that students who work together with low or high mathematics anxiety had better performance in mathematics score.

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saeed daneshamooz

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Psychology and Education , Andrea Leigh G. Angeles , Celine Jhoy P. Sanone , Mizalette Glenn E. Bambo

This study aimed to determine the correlational analysis or whether math anxiety and mathematical performance of Grade 10 students in Morong National High School have a significant relationship with each other. It also focused on determining the level of math anxiety of Grade 10 students, describing their mathematical performance, and identifying the factors influencing their math anxiety. This study used a mixed method to answer the research questions as part of the descriptive, correlational design using a survey to determine the relationship between the two variables. The study was conducted in Morong National High School with 253 respondents out of 829 10th Grade students. The probability sampling was employed through simple random sampling on 10th Grade students regardless of their age, gender, section, or academic achievement in Mathematics. According to the statistical analysis of the results, the Pearson coefficient value suggests a weak negative correlation between math anxiety and mathematical performance, however, the magnitude of the correlation is quite small, indicating that there is only minimal relationship between the two variables. The result was produced from a Pearson coefficient of-0.058 and a p-value of 0.349 which exceeds a 0.05 level of significance, from a total of 253 respondents indicates that the observed correlation coefficient is not statistically significant at the chosen significant level of 0.05 (α=0.05).There is a weak negative correlation between math anxiety and mathematical performance of Grade 10 students in Morong National High School. Furthermore, the results of the scaling of math anxiety level resulted in quite a bit of anxiety with an overall weighted mean of 3.45 and an average of 83.66 on the respondent's mathematical performance. Many factors are also identified that influence the students' math anxiety: the level of difficulty of math lessons, level of difficulty of math problems, oral recitation, low self-esteem, lack of knowledge in math, and surprise quizzes.

Procedia - Social and Behavioral Sciences

Norazah Nordin

Science Park Research Organization & Counselling

Present project assess the effectiveness of cooperative learning over the mathematic anxiety and review the behavior of help seeking in first grade high school girl students. The experimental research procedure was in the form of pre-post tests after a period of 8 sessions of teaching. To measure the variables, the questionnaire of mathematic anxiety (Shokrani, 2002) and the questionnaire of help seeking technique (Ghadampour, 1998) were practiced (accepting or avoiding help seeking).To perform the assignment, 40 girl students from two schools were selected randomly and based on the highest mark of mathematic anxiety in pretest level and also after completing the two questionnaires; centered on matching process; they were placed in two groups of control and experimental. Teaching methodology of mathematic courses was offered in traditional method in control group but in experimental group, teaching methodology was cooperative learning method. After concluding the teaching sessions, once more, two questionnaires of mathematic anxiety and help seeking behavior were accomplished for the students. To analyze the data, the statistics method of analysis of covariance (ANCOVA) was implemented. The accomplished results indicated that cooperative learning method, in comparison with traditional technique, significantly decreases mathematic anxiety in students and increases help seeking behavior and decline the avoidance factors (p<0.05). These changes are, therefore, marked and meaningful in control group. Consequently, it is determined that the cooperative learning method can decrease the mathematic anxiety and increase help seeking behavior in students.

Akinremi Tunde

This study examined the Effect and Relationship of Mathematics Anxiety in Senior Secondary School Student Achievement in Mathematics. The students in Senior Secondary School I (SSS I) and Senior Secondary School II (SSS II) in Government College School Surulere (GCSS), Lagos State, were used for the study. Two hundred and seven (207) students were sampled. Mathematics Anxiety Questionnaire (MAQ) and Mathematics Achievement Test (MAT) were designed and the validity of the instruments was assessed by experts. The hypotheses was analyzed using t-test and Pearson Product Moment Correlation (PPMC) and the research question was analyzed with mean and standard deviation. The findings of the study showed that if teachers have bad behavior and did not use appropriate strategy for teaching of mathematics can make students not to like mathematics, also the bad mathematical orientation the students acquired from senior ones that mathematics is unfriendly reduce their love for mathematics and make it difficult for them to study and understand the subject. All the causes of mathematics anxiety mostly affect the High anxious student at times some moderate anxious student. But for the low and most moderate mathematics anxious student the bad orientation they heard from their senior ones does not make them to dislike mathematics and they do not see mathematics as a boring subject rather interesting subject. Then, the hypothesis result show that there is significant influence of gender on students’ achievement in mathematics, there is significant influence of gender in students’ anxiety in mathematics and that there is significant relationship between mathematics anxiety and students’ achievement in mathematics. It was recommended that teacher should inculcate good behavior in teaching of mathematics, appropriate strategy should be used in teaching of mathematics and that student too should be positive in their attitudes toward mathematics lesson.

CERN European Organization for Nuclear Research - Zenodo

Mubasshira Ansari

International Journal of Science and Research (IJSR)

Mohammad Anouti

This research study aims at examining the relationship between math anxiety and students' performance, through their overall grade averages in mathematics, in the intermediate and secondary classes excluding grade twelve. For this research study, the researchers were not interested in determining the cause and effect between students' math anxiety, the independent variable, and their performance, the dependent variable, so they have remained observers during the process. The sample of the study has consisted of 124 participants out of 1620 students, 84 in classes of the intermediate level and 40 in the first and second year secondary, from two different private schools. First, the researchers have determined students' overall mathematical grade averages based on grade cards delivered by the administrations of both private schools at the end of the academic year. After that, the researchers have employed a standardized five point likert scale survey questionnaire for math anxiety self-test as the research instrument. Through the quantitative approach, the researchers have adopted the correlation design to explore the possible relationship between students' math anxiety and their performance, through their overall mathematical grade averages. For statistics, the researchers have used the bar diagram and the scatter plot to represent the data collected, the correlation coefficient and the one way ANOVA test for analysis. Results of the study have revealed that anxiety has a strong negative correlation and a significant effect on the overall mathematical grade averages of the sample of students in the intermediate and secondary levels excluding grade twelve. The researchers recommend teachers to detect if math anxiety is negatively affecting students' performance and adopt the students-centered approach to support the learning and performance of the highly anxious students. In addition, future researches should be dedicated to examining the impact of math exams anxiety in grade 12 and primary classes, and determining math chapters that trigger students' math anxiety the most.

Dr. Kamruzzaman Mollah

The present study described the causes of Mathematics anxiety, its' impacts on students and way of mitigation from Mathematics anxiety. Mathematics anxiety can be manifested as psychological, physical as well as behavioral expression. It has negative impact on performance, achievement and social development of the students. There are so many different reasons to create Mathematics anxiety such as teacher's negative attitude, un-psychological teaching methods, negative classroom experience of students, parents' unrealistic expectation and high stake test pressure. If the issue of Mathematics anxiety is not dealt with sincerely, it could have grim effect in many areas of our whole education system. In this issue teacher should most responsible and they should follow the teaching learning procedure 'concrete to abstract' and easy mathematical problem to harder. To mitigate the Mathematics anxiety the external support system is not only teachers' activities but also includes parents' attitude and peer groups.

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• Published: 23 June 2015

Experimental study of learning support through examples in mathematical problem posing

• Kazuaki Kojima 1 ,
• Kazuhisa Miwa 2 &
• Tatsunori Matsui 3  

Research and Practice in Technology Enhanced Learning volume  10 , Article number:  1 ( 2015 ) Cite this article

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When using mathematics to solve problems in everyday life, problem solvers must recognize and formulate problems by themselves because structured problems are not provided. Therefore, in general education, fostering learner problem posing is an important task. Because novice learners have difficulty in composing mathematical structures ( solutions ) in problem posing, learning support to improve the composition of solutions is required. Although learning by solving examples is adopted in general education, it may not be sufficiently effective in fostering learner problem posing because cognitive skills differ between problem solving and problem posing. This study discusses and experimentally investigates the effects of learning from examples on composing solutions when problem posing. We studied three learning activities: learning by solving an example, learning by reproducing an example, and learning by evaluating an example. In our experiment, undergraduates were asked to pose their own new, unique problems from a base problem initially presented after the students learned an example by solving, reproducing, or evaluating it. The example allowed the undergraduates to gain ideas for composing a novel solution. The results indicated that learning by reproducing the example was the most effective in fostering the composition of solutions.

In addition to solving problems provided by a teacher or textbook, problem posing, by which learners create problems, has also been identified as an important activity in mathematics education. In fact, some mathematicians and mathematics educators have pointed out that problem posing lies at the heart of mathematical activity (English 1997 ; Polya 1945 ; Silver 1994 ). Problem posing is a necessary skill for problem solving in everyday life. Because structured problems are not provided when using mathematics in everyday life, problem solvers must recognize and formulate problems by themselves (Ishida and Inoue 1983 ; Singer and Voica 2013 ). Therefore, it is an important task in general education to foster learner problem posing. Several studies have addressed this issue in terms of a learning activity to improve problem solving, despite insufficiently addressing the skill of learner problem posing itself.

The problem-posing research has empirically confirmed that novice learners succeeded in posing new problems based on mathematical structures provided in formulae or equations, whereas they had difficulty in composing novel mathematical structures on their own (Christou et al. 2005 ; Kojima et al. 2010 ). Because problem posing in everyday life is performed under various constraints with different materials, fostering the skill to pose diverse problems appropriately is highly desirable. In human problem solving, two attributes of problems are recognized as crucial: one is surface features such as contextual settings in problem texts (e.g., purchase of goods or transfer by vehicles) and the other is structural features such as mathematical structures (Gentner 1983 ; Forbus et al. 1995 ; Holyoak and Thagard 1996 ). We refer to these two attributes as situations and solutions . Studies in cognitive science have demonstrated that novice learners are strongly influenced by situations in problem solving and often fail in understanding solutions and adapting them to problem solving (e.g., Novick 1988 ; Reed et al. 1985 ; Ross 1987 ). Similarly in problem posing, composing novel solutions is more difficult than generating new situations. Therefore, learning support is required to improve the composition of solutions by novice learners. Here, composition of solutions is a process in which a problem poser generates mathematical relationships and then forms equations and stories in texts along with the relationships. Problem posing in everyday life must require composition of solutions from information given to or generated by the poser. Our study addressed improvement of solution composition as prerequisite for fostering problem-posing skill.

To support novice learners, using examples is efficient and effective. Examples are indispensable for learning in any domain, including mathematics. In general mathematics education, procedures for solving problems are initially taught using examples. Cognitive science studies have also argued how to foster transfer of a solution learned in an example to problem solving (e.g., Gick and Holyoak 1983 ; Novick and Holyoak 1991 ). However, the general method of learning from examples in problem solving may not be sufficiently effective in problem posing because cognitive skills in problem solving and problem posing are different. We refer to the former task as a comprehension task and the latter as a production task. In fact, some researchers report that learning tasks such as comprehension and production have no mutual influence (Singley and Anderson 1989 ). Accordingly, to improve composition of solutions in problem posing, learning examples using production tasks may be more effective than those using comprehension tasks.

To provide a basis for computational support that uses examples in problem posing, this study discussed and experimentally investigated the effects of activities for learning from an example on composing solutions in problem posing. In our experiment, undergraduates were asked to pose their own new, unique problems from a base problem initially presented after they had learned an example. We compared three activities for learning from an example adopted in general mathematical education or computational support systems for problem posing. In the next session, we discussed problem posing and the activities of learning from problem-posing examples.

Theoretical background

Relationships and differences between problem solving and problem posing.

Although problem solving and problem posing differ, they are not entirely different cognitive activities but are closely related. Several researchers have experimentally confirmed that problem-solving ability and problem-posing performance are correlated and that problem posing positively influences problem solving (Bernardo 2001 ; Ellerton 1986 ; Nikata and Shimada 2005 ; Silver and Cai 1996 ). Problem posing offers many benefits: For example, it enhances problem-solving ability and the grasp of mathematical concepts, generates diverse and flexible thinking, alerts both teachers and learners to misunderstandings, and improves learners’ attitudes and confidence in mathematics (English 1998 ; Silver 1994 ). Although problem posing is rarely adopted in general education owing to certain constraints in practical classrooms, it is as critical a skill as problem solving.

Problem solving and problem posing differ, of course, in the features and formats of their tasks. Problem solving is a comprehension task, by which a learner extracts a mathematical structure from given information and reaches a correct answer. In contrast, problem posing is a production task that requires generation of information and its synthesis. Learners show difficulty in problem posing even if they can easily solve the problems. Akay and Boz ( 2009 ) asked prospective science teachers to respond to questionnaires about problem posing after participation in a course oriented to mathematical problem posing. The prospective teachers responded that problem posing was difficult because of its nature (e.g., not knowing the steps of problem posing), their abilities (not being creative), or lack of mathematical knowledge (having difficulties understanding abstractions) although they were not novices but had been trained as teachers.

Base (A 1 ): I bought some 60-yen oranges and 120-yen apples for 1020 yen. The total number of oranges and apples was 12. How many oranges and apples did I buy?

Let x denote the number of oranges and y denote the number of apples.

x  +  y = 12

60 x  + 120 y = 1020

According to the equations above, x  = 7 and y  = 5.

We investigated problems posed by novices to understand the difficulties they encounter in problem posing (Kojima et al. 2010 ). Undergraduates were asked to generate new problems from problems initially presented as bases. The bases were simple word problems easily solved by equations. The undergraduates were then encouraged to generate problems as varied and unique as possible. The variety of problems they posed was evaluated according to the four categories shown in Fig.  1 , indicating similarities in the situations and solutions between each of their problems and the bases. Category I/I indicates problems that are almost the same as the bases, D/I indicates problems generated by altering the situations of the bases, I/D indicates problems generated by altering the solutions, and D/D indicates problems generated by combining alterations in both situations and solutions. Figure  2 presents examples of problems posed in each category that were solved by simultaneous equations. The results confirmed that the undergraduates posed many problems in categories I/I and D/I and few problems in I/D. They also revealed that D/I problems with situations different from the bases were appropriately composed. On the other hand, problems in I/D and D/D, where solutions differed from the bases, were relatively simple and inappropriate. Although the bases were elementary problems, many of the posed problems were simpler than the bases. These results indicate that the novices could generate novel situations, but failed to create new solutions in problem posing; thus, even if they can easily solve problems, undergraduates have difficulty in posing new problems. Therefore, because problem posing is more difficult than problem solving, it requires additional support.

Categories for evaluating posed problems

Examples of posed problems in each category

Computational support of learning by problem posing has already been developed in various domains (Barak and Rafaeli 2004 ; Hirashima et al. 2007 ; Hirashima et al. 2010 ; Hirai et al. 2009 ; Takagi and Teshigawara 2006 ; Yu et al. 2005 ). However, such computational support focuses mainly on improving performance of comprehension tasks through problem posing, such as understanding domain knowledge or procedures in problem solving. Some studies empirically analyzed problems posed by learners (e.g., Cankoy 2014 ; English 1998 ; Leung 1997 ; Yu and Wu 2013 ); however, these studies have not addressed learning from examples in problem posing.

The effects of examples in problem posing

The research field of Intelligent Tutoring Systems/Artificial Intelligence in Education has long addressed learning from examples. Interactive scaffolding that enhances learning from examples has been implemented, and its effects have been discussed (e.g., Conati and VanLehn 2000 ; Koedinger and Aleven 2007 ; Schwonke et al. 2009 ; McLaren and Isotani 2011 ). However, the central issue in such research is basically limited to problem solving and does not include problem posing.

Even so, some studies have addressed learning from examples in problem posing. Hsiao et al. ( 2013 ) experimentally confirmed the effect of seeing worked examples on problems posed by undergraduates in the business mathematics domain. The undergraduates posed problems with a web-based learning management system in three homework exercises after lecture classes. In each exercise, half of the students were provided two problems as examples solved through concepts or formulae learned in the lecture classes. The results demonstrated the effects of the examples: undergraduates who provided examples posed fewer problems not oriented to what they had learned in the lecture classes than those who provided no examples. Hsiao et al. also examined problems posed by undergraduates in terms of complexities. However, the examples’ effects on the problems’ complexities were limited—the examples did not expand the average complexity of each posed problem. Because Hsiao et al. provided each as a worked example, the undergraduates must have read only its solution, indicating that they learned the example through comprehension tasks.

We implemented a support system to facilitate learners’ posing of diverse problems by using examples (Kojima and Miwa 2008 ). In the system, learners engage in the same task as the one described above (Kojima et al. 2010 ). They pose new problems and input the texts and equations of their solutions into the system. The system automatically understands the situations and solutions in the problems and evaluates their variety. It can also present learners with problems as examples to provide hints for idea generation. The variety of learners’ problems is evaluated, and the presentation of examples is controlled on the four-category basis shown in Fig.  1 . Experimental evaluations of the system confirmed that to some extent, it could facilitate learners’ posing of diverse problems. The number of problems posed in the I/I category decreased and those in D/I and D/D increased after the learners had posed problems with the system, and the system showed them various examples belonging to D/I and I/D. However, the presentation of examples did not increase the number of problems in I/D. The lack of problem posing in I/D was consistent with the results obtained by Kojima et al. ( 2010 ).

Although the system presents examples to learners and prompts them to compare the base with their posed problems, it does not give any instructions on how to learn from the examples. The examples are merely shown to the learners. We have not examined how the learners actually learned from the presented examples: the learners may have simply read the presented examples. In other words, the learners may have understood the examples through performing a comprehension task. The comprehension of examples may have helped in generating various situations; however, it may not have necessarily facilitated understanding of the solution structures. For learners to adequately study the solutions from examples and transfer that knowledge to their problem posing, further support must be introduced. Because problem posing is a production task, it effectively allows a learner to examine each example through a productive activity.

Learning activities of examples in problem posing

Learning by solving examples.

Solving examples and understanding the solution is of course one of the most popular activities in mathematical learning. As mentioned above, however, learning by solving may not be effective in improving the composition of solutions in learner problem posing because problem solving differs from problem posing.

Learning by reproducing examples

We designed a method of learning from examples through imitation, a learning activity adopted in productive task domains (Kojima et al. 2013 ). Imitation—the method by which learners reproduce existing example works—has long been adopted as a major learning activity in the domains of creative generation, such as art and music. The relationship between imitation and creation has been consistently noted in such domains and the effects of imitation have been documented. For example, Ishibashi and Okada ( 2006 ) argue that imitating examples can prompt imitators’ understanding of examples and their conceptual background; imitation facilitates a creative performance by imitators. In their experiment, subjects were engaged in an artistic drawing task before and after they created copies of a presented example. Results showed that the subjects deeply understood the example through its imitation, and understanding the example then elicited understanding of the subjects’ own expressions.

Based on this insight, we implemented a system for learning by reproducing examples in problem posing (Kojima et al. 2013 ) as an enhancement of the system previously described (Kojima and Miwa 2008 ). Learning by reproduction of an example allows learners to understand the ideas used in formulating the example from the viewpoint of the poser.

Figure  3 indicates the basic framework for learning by reproducing examples. In learning with the system, a learner is required to pose new problems from an initially given base. The learner is also presented with problems as examples, each generated by altering the base. When a learner studies an example generated from the base, the system hides the example itself and shows its generation process information to indicate how it was generated (bold black arrows in Fig.  3 ). Generation process information also includes sufficient information to reproduce the example. The learner generates a problem identical to the example by reproducing alteration of the base as indicated in generation process information (Fig.  3(a )). This prevents the learner from merely duplicating the characters and symbols that compose the text and solution of the example. From a poser’s viewpoint, this learning activity can facilitate understanding of the essential ideas used to generate the example, particularly those for composing a solution. The learner then transfers what is learned through reproduction into the posing of new problems (Fig.  3(b )).

Basic framework of learning by reproducing examples

We experimentally verified that learning by reproducing an example facilitated problem posing through directly adopting ideas used in the example’s generation (Kojima et al. 2013 ). However, we have not yet confirmed whether such learning can foster composition of solutions in the learner’s own problem posing.

Learning by evaluating examples

Some computational systems for supporting learning by problem posing (e.g., Barak and Rafaeli 2004 ; Hirai et al. 2009 ; Takagi and Teshigawara, 2006 ; Yu et al. 2005 ) adopt problem evaluation among learners as an activity in addition to problem posing. Experiments have shown that learning through such activities improves learning performance as well as the quality of learner problems. These studies basically designed the systems from the viewpoint of collaborative learning and focused on improving understanding of domain knowledge through problem posing. Although it is empirically confirmed that evaluations of problems posed by learners had predictive effects on the problems’ qualities (Yu and Wu 2013 ), these studies have not immediately produced evidence about the cognitive impacts of a learner evaluating activity on problem posing by the learners themselves.

Evaluation is a process involved in the creative generation of ideas or products. The importance of evaluative skills in creativity has been documented (Runco and Chand 1994 ). Furthermore, the effects of evaluating examples on the evaluator’s idea generation have been empirically demonstrated. Lonergan et al. ( 2004 ) experimentally observed that evaluation of examples according to certain standards improved the originality and feasibility of ideas generated by the evaluators, depending on the qualities of the examples and standards. Therefore, evaluation of existing ideas or products can be regarded as a production task because evaluation is a cognitive activity that can contribute to creative generation.

According to the above-mentioned studies, we experimentally investigated the effects of learning from an example on solution composition for problem posing. In the investigation, we studied the learning activities of reproducing and evaluating an example. To examine differences between comprehension and production tasks, we also studied the effects of learning by solving the same example. Because novice learners pose few such problems as examples, the investigation used an I/D problem as an example of a problem having a solution more complex than the base. As mentioned above, it is important to foster posing such problems because composing novel solutions is necessary but difficult, whereas generation of new situations is easy.

Procedures and materials

Undergraduates participated in the experimental investigation conducted in three classes of a cognitive science lecture from 2010 to 2012. The undergraduates were first given a learning task in the domain of word problems solved with simultaneous equations. They were told that the learning task’s purpose was to instruct them how to pose a novel problem from a base. The base in the learning task was the problem A 1 (see Fig.  2 ). The undergraduates learned the following problem, A 2 , as an example of output in the domain of A 1 .

A 2 : Last year, I bought some 40-yen pencils and 110-yen pens. The total number was 13. This year, I bought 2 times as many pencils as last year, as many pens as last year, and a 300-yen pen case for 1430 yen. How many pencils and pens did I buy last year?

Let x denote the number of pencils and y denote the number of pens.

x  +  y  = 13

40 × 2 x  + 110 y  = 1430–300

According to the equations above, x = 10 and y = 3.

The solution of A 2 was composed by an alteration that added two parameters and operations to A 1 . Thus, this process can hint at composing complex solutions in problem posing by the undergraduates. A 2 is an I/D problem more complex than the base and difficult to pose for novice learners. The undergraduates had to learn the example in 15 min.

The learning task was followed by a problem-posing task, in which the undergraduates were asked to pose their own problems in the domain of word problems solved with unitary equations. The base in the problem-posing task was the following problem B.

B: I want to buy some boxes of cookies. If I buy 110-yen boxes of cookies, then I have 50 yen left. If I buy 120-yen boxes of chocolate cookies, then I need 20 yen more. How many boxes do I want?

Let x denote the number of boxes.

110 x  + 50 = 120 x  − 20

According to the above equation, x  = 7.

Prior to the problem-posing task, the undergraduates were instructed to pose as many diverse and unique problems as possible in 20 min.

Condition groups

Undergraduates in the same school of the same university participated as one of the three condition groups each year. Because it is an interdisciplinary school, the background of the undergraduates varied but no one majored in mathematics. All of the undergraduates had trained to solve problems in the domain of word problems solved with linear equations in middle and high school education.

In the 2010 class, undergraduates were provided sheets of paper on which the text and solution of A 1 and the text of A 2 were printed. They were asked to solve A 2 and write the answer on the sheet. The undergraduates were hence referred to as the solving group.

In 2011, undergraduates were first presented A 1 and A 2 on a screen. After A 2 had been removed from the screen, they were provided printed sheets with A 1 and generation process information indicating how to compose A 2 from A 1 . The generation process information had been created by the system mentioned above (Kojima et al. 2013 ). The undergraduates were asked to reproduce, according to the information, the same problem as A 2 . They were also told that their problems’ texts did not need to be identical with the example as long as the problems could be solved by a solution identical to the example. We refer to the undergraduates as the reproduction group. Appendix 1 shows the information presented to this group.

In 2012, undergraduates were provided sheets on which A 1 and A 2 were printed. They were asked to evaluate A 2 with a view toward originality and feasibility as a mathematical problem by using a 5-point scale and to describe the reasons for the evaluations. These viewpoints are generally used in researching creative thinking (e.g., Finke et al. 1996 ). We refer to these undergraduates as the evaluation group.

In fact, transfer of the example enabled posing I/D problems whose solutions were more complex than the base by altering the solution of the base. To verify the effect, we examined the following research questions:

RQ1: Do the undergraduates pose I/D problems after learning the example?

RQ2: Do the undergraduates learn how to compose solutions by altering the example and transferring it to their problem posing?

RQ3: After they learn the example, are the undergraduates fostered to compose solutions more complex than the base?

Problems posed by the undergraduates were analyzed in terms of variety, strategies to alter solutions, and complexities of solutions. To examine RQ1, the variety of each problem was evaluated on the basis of the four categories shown in Fig.  1 . The example A 2 is a problem in category I/D.

To examine RQ2, strategies to alter solutions of problems posed by the undergraduates were evaluated by comparing each problem’s solution structure with that of the base. The undergraduates’ problems were classified into not altered , partially altered (adding/removing operations to/from the solution of the base), or overall altered (composing a solution entirely different from the base). A 2 was posed with partially altered.

To examine RQ3, the complexities of the undergraduates’ problems were estimated by comparing the numbers of operations required to reach the answers with the number required for the base. The number of operations in the base is three. Only the complexities of I/D and D/D problems were analyzed because the structure of solutions in I/I and D/I problems are always equal to the base.

In the study previously described (Kojima et al. 2010 ), we acquired problems posed by undergraduates in the same task without any learning through example in another class of the cognitive science lecture in 2009. The effects of learning with the example were verified through a comparison of the solving, reproduction, or evaluation groups in this investigation as experimental groups with those of the previous study as a control group . The procedures and material of the problem-posing task in the control group were the same as those described in the “ Procedures and materials ” section. For the comparison, this study used the same problem-posing task.

In the reproduction group, some undergraduates did not reproduce A 2 and instead posed problems that were slightly different from A 2 (e.g., changing parameters or operations in A 2 ); some others did not complete reproduction in the learning task. Such undergraduates were excluded from the analysis. Some others in the reproduction group failed to reproduce A 2 . Although they wrote the same solution as A 2 , their problem texts were contradictory to the solution. Therefore, the data of those who failed in the learning task ( reproduction-f group ) were separately described from those who succeeded ( reproduction-s group ). Appendix 2 shows an example of a contradictory problem posed by the reproduction-f group.

In the solving group, 62 undergraduates participated; in the reproduction group, 132; and in the evaluation group, 25. In the reproduction group, 44 did not reproduce A 2 , and 8 did not complete reproduction. In the others, 52 were in the reproduction-s group, and 28 were in the reproduction-f group. Undergraduates in the solving, reproduction-s, reproduction-f, and evaluation groups posed 372 problems in the problem-posing task, 68 of which were excluded because they were in domains other than the base (e.g., solved with inequalities) or unsolvable due to insufficient or contradictory constraints. Because the undergraduates were instructed to pose problems in the domain of the base, posing any problems in other domains was a violation of the instruction. In case of unsolvable problems, solutions described by undergraduates were inconsistent with problem text that they described. Thus, problems that the undergraduates tried to pose were unclear. Appendix 3 shows some examples of problems posed in the experimental groups. In the control group, 76 undergraduates participated. They posed 146 problems and 29 were excluded in the same manner.

Figure  4 indicates the proportions of posed problems in each category, and Table  1 indicates differences in the numbers between the control and each of the experimental groups. As mentioned above, the control group posed few I/D problems. The experimental groups posed more I/D problems than the control group. We compared the control group with the solving group using the chi-square test; the result indicated a significant difference between the solving and control groups ( χ 2 (3) = 11.51, p  < .01). Furthermore, the results of residual analysis indicated that the number of D/I problems was significantly high in the control group but significantly low in the solving group. The number of I/D problems was significantly high in the solving group but significantly low in the control group. Similarly, a significant difference existed between the reproduction-s and control groups ( χ 2 (3) = 15.26, p  < .01). The number of I/I problems was significantly high in the control group but significantly low in the reproduction-s group. The number of I/D problems was significantly high in the reproduction-s group but significantly low in the control group. There was also a significant difference between the evaluation and control groups ( χ 2 (3) = 14.48, p  < .01). The number of D/I problems was significantly high in the control group but significantly low in the evaluation group, whereas the number of I/D problems was significantly high in the evaluation group but significantly low in the control group. There was no difference between the reproduction-f and control groups ( χ 2 (3) = 4.64, n.s.).

Proportions of posed problems in each category

Solution-altering strategies

Figure  5 indicates the proportions of posed problems composed with each solution-altering strategy in each group, and Table  2 indicates differences in the numbers between the control and each of the experimental groups. The chi-square test indicated a significant difference between the solving and control groups ( χ 2 (2) = 7.98, p  < .05). Furthermore, the results of residual analysis indicated that the number of not altered problems was significantly high in the control group but significantly low in the solving group, whereas the number of fully altered problems was significantly high in the solving group but significantly low in the control group. Similarly, there was a significant difference between the reproduction-s and control groups ( χ 2 (2) = 13.20, p  < .01). The results of residual analysis indicated that the number of not altered problems was significantly high in the control group but significantly low in the reproduction-s group. The number of partially altered problems was significantly high in the reproduction-s group but significantly low in the control group. There was also a significant difference between the evaluation and control groups ( χ 2 (2) = 8.20, p  < .05). The results of residual analysis indicated that the number of not altered problems was significantly high in the control group but significantly low in the evaluation group, whereas the number of partially altered problems was significantly high in the evaluation group but significantly low in the control group. There was a moderate but significant difference between the reproduction-f and control groups ( χ 2 (2) = 5.61, p  < .10). The results of residual analysis indicated that the number of partially altered problems was significantly high in the reproduction-f group but significantly low in the control group.

Proportions of posed problems with each solution-altering strategy

Complexities

Figure  6 indicates the proportions of I/D and D/D problems whose number of operations increased or decreased from the base, and Table  3 indicates differences in the numbers between the control and each of the experimental groups. In half of the I/D and D/D problems posed by the control group, the number of operations decreased from the base, implying that half of the I/D and D/D problems were simpler than the base. The number of such simple problems was smaller only in the reproduction-s group. We compared the control group with the solving, reproduction-s, reproduction-f, and evaluation groups using the chi-square test, with the results indicating a significant difference between the reproduction-s and control groups ( χ 2 (2) = 11.36, p  < .01). Furthermore, the results of residual analysis indicated that the number of decrease was significantly high in the control group but significantly low in the reproduction-s group. The number of increase was significantly high in the reproduction-s group but significantly low in the control group. There was no difference between the solving and control groups ( χ 2 (2) = 2.58, n.s.), the reproduction-f and control groups ( χ 2 (2) = 1.06, n.s.), or the evaluation and control groups ( χ 2 (2) = 0.06, n.s.).

Proportions of altered problems whose operations increased or decreased

Discussion and conclusion

The results presented above indicate that the experimental groups posed more I/D problems than the control group, indicating that the example facilitated posing I/D problems regardless of the learning activities. Thus, RQ1 was verified in all of the experimental groups.

On the other hand, there was a difference among the experimental groups in the solution-altering strategies. Overall altered problems posed increased in the solving group, whereas partially altered problems posed increased in the production-s, production-f, and evaluation groups. The latter three groups adapted ideas used in the example because it was composed by altering the base (partially altered). The solving group learned the example through a comprehension task, whereas the reproduction-s, reproduction-f, and evaluation groups did so through a production task. Therefore, RQ2 was verified in the reproduction-s, reproduction-f, and evaluation groups, demonstrating that learning the example through a production task facilitated its transfer to the undergraduates’ problem posing.

The results shown in Figs.  4 and 5 confirm that learning the example increased production of problems whose solutions differed from the base. As pointed out in the introduction, novices find it difficult to compose novel solutions when problem posing. The experimental groups posed problems with novel solutions in some senses, even though only the reproduction-s group posed many problems more complex than the base. The undergraduates could learn how to formulate more complex solutions by adding operations. However, such problem posing was performed only by those who had succeeded in reproducing the example. According to this, RQ3 was verified only in the reproduction-s group. Therefore, the answers to the research questions were as follows:

RQ1: Do the undergraduates pose I/D problems after learning the example? Yes, the example increased I/D problems.

RQ2: Do the undergraduates learn how to compose solutions by altering the example and transferring it to their problem posing? Partially, yes. Those who had learned the example through a production task transferred it.

RQ3: After they learn the example, are the undergraduates fostered to compose solutions more complex than the base? Partially, yes. Only those who succeeded in reproducing the example produced solutions more complex than the base.

The results indicate that learning by solving an example can increase I/D problems. In the previous study (Kojima and Miwa 2008 ), learners just viewed the examples. Therefore, involving learners with an example is effective to some extent in problem posing. On the other hand, such involvement is not sufficiently effective in fostering the composition of solutions.

The results also prove that in problem posing, learning an example through a production task is effective. The results also confirm that learning by reproducing an example is more effective in terms of a learning activity in a production task. However, this activity also involves difficulty. Although no one in the solving group failed in the learning task, the reproduction-f group did fail. Obviously, the example must be quite easy for undergraduates to solve. Although learning by reproduction is effective, it significantly challenges learners. Therefore, further supportive intervention must be introduced in learning from an example through a production task.

The reproduction-s and the evaluation groups both adapted the example to the problem-posing task. The evaluation group posed many I/D problems, as well as partially altered problems. However, like the control group, the evaluation group posed many I/D and D/D problems that were simpler than the base. Although this group evaluated the example as to its originality and feasibility, alternative viewpoints might be needed to improve an example’s effects. Furthermore, to enhance the effects of evaluation, presenting a nasty problem as an example is one alternative. A learner may devise a good idea through evaluating such an example and find how to improve the example. Further study is needed to thoroughly examine this point.

The results of the solving and reproduction-s groups were consistent with the report by Singley and Anderson ( 1989 ). They experimentally confirmed that there was little transfer from training of evaluating LISP code to generating LISP code and vice versa. In the same way, this study confirmed that solving the given example did not effectively transfer to posing new problems. On the other hand, reproducing the example fostered problem posing while transferring ideas used in the example. It indicates that experience to follow processes of generating the example was required for learning in problem posing. Therefore, the effects of learning the example were insufficient in the evaluation group because of the absence of such experience to follow generation processes.

This study has limitation in terms of influence of individual aspects of the undergraduates on problem posing. Mathematical abilities such as reasoning skills (Ellerton 1986 ) and some other variables such as self-efficacy in mathematics and attitudes toward mathematics (Akay and Boz 2010 ) can positively influence on behaviors and products in problem posing. This study has not addressed these aspects. We have to further study the influence of these aspects on the effects of learning examples in problem posing.

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Acknowledgements

This study was partially supported by the Grant-in-Aid for Young Scientists (B) 23700990 and 25870820 of the Ministry of Education, Culture, Sports, Science and Technology, Japan.

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Kazuaki Kojima

Graduate School of Information Science, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8601, Japan

Kazuhisa Miwa

Faculty of Human Sciences, Waseda University, 2-579-15 Mikajima, Tokorozawa, 359-1164, Japan

Tatsunori Matsui

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The authors declare that they have no competing interests.

Authors' contribution

KK conceived of the study, designed and conducted the experiment, performed the statistical analysis and drafted the manuscript. KM and TM contributed to conception of the study and interpretation of data, and was involved in drafting and critically revising the manuscript. All authors read and approved the final manuscript.

The example was composed by altering the base in the ways described below. According to these, make a problem identical to the example. It is unnecessary to exactly reproduce the text of the example as long as your problem is solved with the same solution.

Objects are altered to “pencils” and “pens”

x : pencils

Answers: x  = 10, y  = 3 (how many)

Numeric parameters in the text

Two parameters are added

Parameters: (total) 13, pen 110 yen, pencil 40 yen, pencil 2 times, (total) 1430 yen, pen case 300 yen

Third object (pen case and 300 yen) is added

Altered from the base

[ x pencils] + [ y pens] = [total 13]

[*1] × [ x pencils] + [110 yen pen] × [ y pens] = [*2]

*1 Operation [40 yen pencil] × [2 times pencils] is added

*2 Operation [total 1430 yen] − [pen case 300 yen] is added

Problem text

Keywords: last year, pencils, pens, total, buy, this year, the number, pen case

An example posed by the reproduction-f group in the learning task

Last year, I bought 40-yen pencils and 110-yen pens and a 300-yen pencil box for 1430 yen a . The total number of pencils and pens was 13. This year, I bought 2 times as many pencils as last year and as many pens as last year. The total number this year was also 13 b . Their sum was the same as last year, excluding the pencil box c . How many pencils and pens did I buy this year?

x  +  y  = 12

60 x  + 120 y  = 1020

According to the equations above, x  = 7 and y = 5.

a Not last year, but this year

b Not 13 this year

c The sums this year differed from last year

Examples of problems posed in the problem-posing task

D/i problem posed in the solving group.

A teacher planned to divide students into groups of equal numbers of students. If 5 students were assigned to each group, then 2 students were left. If 6 students were assigned to each group, then 4 additional students were needed. How many groups did the teacher want to make?

Let x denote the number of groups.

5 x  + 2 = 6 x  − 4

I/D problems posed in the production-s group

To buy 8 loaves of breads, I need 100 yen more. If 30 % is discounted from the price of a loaf, 284 yen is left after buying 8 loaves. Find the price of a loaf.

8 x  − 100 = 8 x  × (10–3)/10 + 284

(posed with partially altered)

A store sells a “tasty cookie”. A customer can buy a single cookie and a bag containing some cookies. A family of 3 persons bought 6 bags and each person ate the same number of cookies. Another family of 6 persons bought 10 bags and 10 single cookies and each person ate the same number of cookies. The numbers of cookies for one person were the same in both families. How many cookies does the bag contain?

Let x denote the number of cookies in a bag.

6 x /3 = (10 x  + 10)/6

(posed with overall altered)

D/D problems posed in the evaluation group

I drove from Tokyo to Nagoya. My car was driven at the speed of 100 km per hour on a highway and the journey took 4 h. Find the distance I drove.

Let x denote the distance I drove.

100 × 4 =  x

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Kojima, K., Miwa, K. & Matsui, T. Experimental study of learning support through examples in mathematical problem posing. RPTEL 10 , 1 (2015). https://doi.org/10.1007/s41039-015-0001-5

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Over the past couple of decades, teacher effectiveness has become a major focus to improve students’ mathematics learning. Teacher professional development (PD), in particular, has been at the center of efforts aimed at improving teaching practice and the mathematics learning of students. However, empirical evidence for the effectiveness of PD for improving student achievement is mixed and there is limited research-based knowledge about the features of effective PD not only in mathematics but also in other subject areas. In this quasi-experimental study, I examined the effect of a Math and Science Partnership (MSP) PD on student achievement trajectories. Results of hierarchical growth models for this study revealed that content-focused (Algebra1 and Geometry), ongoing PD was effective for improving student achievement (relative to a matched comparison group) in Algebra1 (both for high and low performing students) and in Geometry (for low performing students only). There was no effect of PD on students’ achievement in Algebra2, which was not the focus of the MSP-PD. By demonstrating an effect of PD on student achievement, this study contributes to our growing knowledge base about features of PD programs that appear to contribute to their effectiveness. Moreover, it provides a case study showing how the research design might contribute in important ways to the ability to detect an effect of PD -if one exists- on student achievement. For example, given the data I had from the district, I was able to examine student growth within all Algebra 1, Geometry and Algebra 2 courses, while matching classrooms on aggregate student characteristics and school contexts. This allowed me to eliminate the potential confound of curriculum and to utilize longitudinal models to examine PD effects on students’ growth (relative to a comparison sample) for matched classrooms. Findings of this study have implications for educational practitioners and policymakers in their efforts to design and support effective PD programs in mathematics, and these features likely transfer to the design of PD in all subject areas. Moreover, for educational researchers this study suggests potential strategies for demonstrating robust research-based evidence for the effectiveness of PD on student learning.

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Design Research in Mathematics Education

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Design-based research is a formative approach to research, in which a product or process (or “tool”) is envisaged, designed, developed, and refined through cycles of enactment, observation, analysis, and redesign, with systematic feedback from end users. In education, such tools might, for example, include innovative teaching methods, materials, professional development programs, and/or assessment tasks. Educational theory is used to inform the design and refinement of the tools and is itself refined during the research process. Its goals are to create innovative tools for others to use, describe and explain how these tools function, account for the range of implementations that occur, and develop principles and theories that may guide future designs. Ultimately, the goal is transformative ; we seek to create new teaching and learning possibilities and study their impact on teachers, children, and other end users.

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Centre for Research in Mathematics Education, Jubilee Campus, School of Education, University of Nottingham, Wollaton Road, Nottingham, NG8 1BB, UK

Malcolm Swan

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Correspondence to Malcolm Swan .

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Department of Education, Centre for Mathematics Education, London South Bank University, London, UK

Stephen Lerman

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Swan, M. (2014). Design Research in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_180

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DOI : https://doi.org/10.1007/978-94-007-4978-8_180

Published : 31 July 2014

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