sample research topics in mathematics education

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Mathematics Education Theses and Dissertations

Theses/dissertations from 2024 2024.

New Mathematics Teachers' Goals, Orientations, and Resources that Influence Implementation of Principles Learned in Brigham Young University's Teacher Preparation Program , Caroline S. Gneiting

Theses/Dissertations from 2023 2023

Impact of Applying Visual Design Principles to Boardwork in a Mathematics Classroom , Jennifer Rose Canizales

Practicing Mathematics Teachers' Perspectives of Public Records in Their Classrooms , Sini Nicole White Graff

Parents' Perceptions of the Importance of Teaching Mathematics: A Q-Study , Ashlynn M. Holley

Engagement in Secondary Mathematics Group Work: A Student Perspective , Rachel H. Jorgenson

Theses/Dissertations from 2022 2022

Understanding College Students' Use of Written Feedback in Mathematics , Erin Loraine Carroll

Identity Work to Teach Mathematics for Social Justice , Navy B. Dixon

Developing a Quantitative Understanding of U-Substitution in First-Semester Calculus , Leilani Camille Heaton Fonbuena

The Perception of At-Risk Students on Caring Student-Teacher Relationships and Its Impact on Their Productive Disposition , Brittany Hopper

Variational and Covariational Reasoning of Students with Disabilities , Lauren Rigby

Structural Reasoning with Rational Expressions , Dana Steinhorst

Student-Created Learning Objects for Mathematics Renewable Assignments: The Potential Value They Bring to the Broader Community , Webster Wong

Theses/Dissertations from 2021 2021

Emotional Geographies of Beginning and Veteran Reformed Teachers in Mentor/Mentee Relationships , Emily Joan Adams

You Do Math Like a Girl: How Women Reason Mathematically Outside of Formal and School Mathematics Contexts , Katelyn C. Pyfer

Developing the Definite Integral and Accumulation Function Through Adding Up Pieces: A Hypothetical Learning Trajectory , Brinley Nichole Stevens

Theses/Dissertations from 2020 2020

Mathematical Identities of Students with Mathematics Learning Dis/abilities , Emma Lynn Holdaway

Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures , Porter Peterson Nielsen

Student Use of Mathematical Content Knowledge During Proof Production , Chelsey Lynn Van de Merwe

Theses/Dissertations from 2019 2019

Making Sense of the Equal Sign in Middle School Mathematics , Chelsea Lynn Dickson

Developing Understanding of the Chain Rule, Implicit Differentiation, and Related Rates: Towards a Hypothetical Learning Trajectory Rooted in Nested Multivariation , Haley Paige Jeppson

Secondary Preservice Mathematics Teachers' Curricular Reasoning , Kimber Anne Mathis

“Don’t Say Gay. We Say Dumb or Stupid”: Queering ProspectiveMathematics Teachers’ Discussions , Amy Saunders Ross

Aspects of Engaging Problem Contexts From Students' Perspectives , Tamara Kay Stark

Theses/Dissertations from 2018 2018

Addressing Pre-Service Teachers' Misconceptions About Confidence Intervals , Kiya Lynn Eliason

How Teacher Questions Affect the Development of a Potential Hybrid Space in a Classroom with Latina/o Students , Casandra Helen Job

Teacher Graphing Practices for Linear Functions in a Covariation-Based College Algebra Classroom , Konda Jo Luckau

Principles of Productivity Revealed from Secondary Mathematics Teachers' Discussions Around the Productiveness of Teacher Moves in Response to Teachable Moments , Kylie Victoria Palsky

Theses/Dissertations from 2017 2017

Curriculum Decisions and Reasoning of Middle School Teachers , Anand Mikel Bernard

Teacher Response to Instances of Student Thinking During Whole Class Discussion , Rachel Marie Bernard

Kyozaikenkyu: An In-Depth Look into Japanese Educators' Daily Planning Practices , Matthew David Melville

Analysis of Differential Equations Applications from the Coordination Class Perspective , Omar Antonio Naranjo Mayorga

Theses/Dissertations from 2016 2016

The Principles of Effective Teaching Student Teachershave the Opportunity to Learn in an AlternativeStudent Teaching Structure , Danielle Rose Divis

Insight into Student Conceptions of Proof , Steven Daniel Lauzon

Theses/Dissertations from 2015 2015

Teacher Participation and Motivation inProfessional Development , Krystal A. Hill

Student Evaluation of Mathematical Explanations in anInquiry-Based Mathematics Classroom , Ashley Burgess Hulet

English Learners' Participation in Mathematical Discourse , Lindsay Marie Merrill

Mathematical Interactions between Teachers and Students in the Finnish Mathematics Classroom , Paula Jeffery Prestwich

Parents and the Common Core State Standards for Mathematics , Rebecca Anne Roberts

Examining the Effects of College Algebra on Students' Mathematical Dispositions , Kevin Lee Watson

Problems Faced by Reform Oriented Novice Mathematics Teachers Utilizing a Traditional Curriculum , Tyler Joseph Winiecke

Academic and Peer Status in the Mathematical Life Stories of Students , Carol Ann Wise

Theses/Dissertations from 2014 2014

The Effect of Students' Mathematical Beliefs on Knowledge Transfer , Kristen Adams

Language Use in Mathematics Textbooks Written in English and Spanish , Kailie Ann Bertoch

Teachers' Curricular Reasoning and MKT in the Context of Algebra and Statistics , Kolby J. Gadd

Mathematical Telling in the Context of Teacher Interventions with Collaborative Groups , Brandon Kyle Singleton

An Investigation of How Preservice Teachers Design Mathematical Tasks , Elizabeth Karen Zwahlen

Theses/Dissertations from 2013 2013

Student Understanding of Limit and Continuity at a Point: A Look into Four Potentially Problematic Conceptions , Miriam Lynne Amatangelo

Exploring the Mathematical Knowledge for Teaching of Japanese Teachers , Ratu Jared R. T. Bukarau

Comparing Two Different Student Teaching Structures by Analyzing Conversations Between Student Teachers and Their Cooperating Teachers , Niccole Suzette Franc

Professional Development as a Community of Practice and Its Associated Influence on the Induction of a Beginning Mathematics Teacher , Savannah O. Steele

Types of Questions that Comprise a Teacher's Questioning Discourse in a Conceptually-Oriented Classroom , Keilani Stolk

Theses/Dissertations from 2012 2012

Student Teachers' Interactive Decisions with Respect to Student Mathematics Thinking , Jonathan J. Call

Manipulatives and the Growth of Mathematical Understanding , Stacie Joyce Gibbons

Learning Within a Computer-Assisted Instructional Environment: Effects on Multiplication Math Fact Mastery and Self-Efficacy in Elementary-Age Students , Loraine Jones Hanson

Mathematics Teacher Time Allocation , Ashley Martin Jones

Theses/Dissertations from 2011 2011

How Student Positioning Can Lead to Failure in Inquiry-based Classrooms , Kelly Beatrice Campbell

Teachers' Decisions to Use Student Input During Class Discussion , Heather Taylor Toponce

A Conceptual Framework for Student Understanding of Logarithms , Heather Rebecca Ambler Williams

Theses/Dissertations from 2010 2010

Growth in Students' Conceptions of Mathematical Induction , John David Gruver

Contextualized Motivation Theory (CMT): Intellectual Passion, Mathematical Need, Social Responsibility, and Personal Agency in Learning Mathematics , Janelle Marie Hart

Thinking on the Brink: Facilitating Student Teachers' Learning Through In-the-Moment Interjections , Travis L. Lemon

Understanding Teachers' Change Towards a Reform-Oriented Mathematics Classroom , Linnae Denise Williams

Theses/Dissertations from 2009 2009

A Comparison of Mathematical Discourse in Online and Face-to-Face Environments , Shawn D. Broderick

The Influence of Risk Taking on Student Creation of Mathematical Meaning: Contextual Risk Theory , Erin Nicole Houghtaling

Uncovering Transformative Experiences: A Case Study of the Transformations Made by one Teacher in a Mathematics Professional Development Program , Rachelle Myler Orsak

Theses/Dissertations from 2008 2008

Student Teacher Knowledge and Its Impact on Task Design , Tenille Cannon

How Eighth-Grade Students Estimate with Fractions , Audrey Linford Hanks

Similar but Different: The Complexities of Students' Mathematical Identities , Diane Skillicorn Hill

Choose Your Words: Refining What Counts as Mathematical Discourse in Students' Negotiation of Meaning for Rate of Change of Volume , Christine Johnson

Mathematics Student Teaching in Japan: A Multi-Case Study , Allison Turley Shwalb

Theses/Dissertations from 2007 2007

Applying Toulmin's Argumentation Framework to Explanations in a Reform Oriented Mathematics Class , Jennifer Alder Brinkerhoff

What Are Some of the Common Traits in the Thought Processes of Undergraduate Students Capable of Creating Proof? , Karen Malina Duff

Probing for Reasons: Presentations, Questions, Phases , Kellyn Nicole Farlow

One Problem, Two Contexts , Danielle L. Gigger

The Main Challenges that a Teacher-in-Transition Faces When Teaching a High School Geometry Class , Greg Brough Henry

Discovering the Derivative Can Be "Invigorating:" Mark's Journey to Understanding Instantaneous Velocity , Charity Ann Gardner Hyer

Theses/Dissertations from 2006 2006

How a Master Teacher Uses Questioning Within a Mathematical Discourse Community , Omel Angel Contreras

Determining High School Geometry Students' Geometric Understanding Using van Hiele Levels: Is There a Difference Between Standards-based Curriculum Students and NonStandards-based Curriculum Students? , Rebekah Loraine Genz

The Nature and Frequency of Mathematical Discussion During Lesson Study That Implemented the CMI Framework , Andrew Ray Glaze

Second Graders' Solution Strategies and Understanding of a Combination Problem , Tiffany Marie Hessing

What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses? , Matthew M. Webb

Theses/Dissertations from 2005 2005

Fraction Multiplication and Division Image Change in Pre-Service Elementary Teachers , Jennifer J. Cluff

An Examination of the Role of Writing in Mathematics Instruction , Amy Jeppsen

Theses/Dissertations from 2004 2004

Reasoning About Motion: A Case Study , Tiffini Lynn Glaze

Theses/Dissertations from 2003 2003

An Analysis of the Influence of Lesson Study on Preservice Secondary Mathematics Teachers' View of Self-As Mathematics Expert , Julie Stafford

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251+ Math Research Topics [2024 Updated]

Mathematics, often dubbed as the language of the universe, holds immense significance in shaping our understanding of the world around us. It’s not just about crunching numbers or solving equations; it’s about unraveling mysteries, making predictions, and creating innovative solutions to complex problems. In this blog, we embark on a journey into the realm of math research topics, exploring various branches of mathematics and their real-world applications.

How Do You Write A Math Research Topic?

Writing a math research topic involves several steps to ensure clarity, relevance, and feasibility. Here’s a guide to help you craft a compelling math research topic:

• Identify Your Interests: Start by exploring areas of mathematics that interest you. Whether it’s pure mathematics, applied mathematics, or interdisciplinary topics, choose a field that aligns with your passion and expertise.
• Narrow Down Your Focus: Mathematics is a broad field, so it’s essential to narrow down your focus to a specific area or problem. Consider the scope of your research and choose a topic that is manageable within your resources and time frame.
• Review Existing Literature: Conduct a thorough literature review to understand the current state of research in your chosen area. Identify gaps, controversies, or unanswered questions that could form the basis of your research topic.
• Formulate a Research Question: Based on your exploration and literature review, formulate a clear and concise research question. Your research question should be specific, measurable, achievable, relevant, and time-bound (SMART).
• Consider Feasibility: Assess the feasibility of your research topic in terms of available resources, data availability, and research methodologies. Ensure that your topic is realistic and achievable within the constraints of your project.
• Consult with Experts: Seek feedback from mentors, advisors, or experts in the field to validate your research topic and refine your ideas. Their insights can help you identify potential challenges and opportunities for improvement.
• Refine and Iterate: Refine your research topic based on feedback and further reflection. Iterate on your ideas to ensure clarity, coherence, and relevance to the broader context of mathematics research.
• Craft a Title: Once you have finalized your research topic, craft a compelling title that succinctly summarizes the essence of your research. Your title should be descriptive, engaging, and reflective of the key themes of your study.
• Write a Research Proposal: Develop a comprehensive research proposal outlining the background, objectives, methodology, and expected outcomes of your research. Your research proposal should provide a clear roadmap for your study and justify the significance of your research topic.

By following these steps, you can effectively write a math research topic that is well-defined, relevant, and poised to make a meaningful contribution to the field of mathematics.

251+ Math Research Topics: Beginners To Advanced

• Prime Number Distribution in Arithmetic Progressions
• Diophantine Equations and their Solutions
• Applications of Modular Arithmetic in Cryptography
• The Riemann Hypothesis and its Implications
• Graph Theory: Exploring Connectivity and Coloring Problems
• Knot Theory: Unraveling the Mathematics of Knots and Links
• Fractal Geometry: Understanding Self-Similarity and Dimensionality
• Differential Equations: Modeling Physical Phenomena and Dynamical Systems
• Chaos Theory: Investigating Deterministic Chaos and Strange Attractors
• Combinatorial Optimization: Algorithms for Solving Optimization Problems
• Computational Complexity: Analyzing the Complexity of Algorithms
• Game Theory: Mathematical Models of Strategic Interactions
• Number Theory: Exploring Properties of Integers and Primes
• Algebraic Topology: Studying Topological Invariants and Homotopy Theory
• Analytic Number Theory: Investigating Properties of Prime Numbers
• Algebraic Geometry: Geometry Arising from Algebraic Equations
• Galois Theory: Understanding Field Extensions and Solvability of Equations
• Representation Theory: Studying Symmetry in Linear Spaces
• Harmonic Analysis: Analyzing Functions on Groups and Manifolds
• Mathematical Logic: Foundations of Mathematics and Formal Systems
• Set Theory: Exploring Infinite Sets and Cardinal Numbers
• Real Analysis: Rigorous Study of Real Numbers and Functions
• Complex Analysis: Analytic Functions and Complex Integration
• Measure Theory: Foundations of Lebesgue Integration and Probability
• Topological Groups: Investigating Topological Structures on Groups
• Lie Groups and Lie Algebras: Geometry of Continuous Symmetry
• Differential Geometry: Curvature and Topology of Smooth Manifolds
• Algebraic Combinatorics: Enumerative and Algebraic Aspects of Combinatorics
• Ramsey Theory: Investigating Structure in Large Discrete Structures
• Analytic Geometry: Studying Geometry Using Analytic Methods
• Hyperbolic Geometry: Non-Euclidean Geometry of Curved Spaces
• Nonlinear Dynamics: Chaos, Bifurcations, and Strange Attractors
• Homological Algebra: Studying Homology and Cohomology of Algebraic Structures
• Topological Vector Spaces: Vector Spaces with Topological Structure
• Representation Theory of Finite Groups: Decomposition of Group Representations
• Category Theory: Abstract Structures and Universal Properties
• Operator Theory: Spectral Theory and Functional Analysis of Operators
• Algebraic Number Theory: Study of Algebraic Structures in Number Fields
• Cryptanalysis: Breaking Cryptographic Systems Using Mathematical Methods
• Discrete Mathematics: Combinatorics, Graph Theory, and Number Theory
• Mathematical Biology: Modeling Biological Systems Using Mathematical Tools
• Population Dynamics: Mathematical Models of Population Growth and Interaction
• Epidemiology: Mathematical Modeling of Disease Spread and Control
• Mathematical Ecology: Dynamics of Ecological Systems and Food Webs
• Evolutionary Game Theory: Evolutionary Dynamics and Strategic Behavior
• Mathematical Neuroscience: Modeling Brain Dynamics and Neural Networks
• Mathematical Physics: Mathematical Models in Physical Sciences
• Quantum Mechanics: Foundations and Applications of Quantum Theory
• Statistical Mechanics: Statistical Methods in Physics and Thermodynamics
• Fluid Dynamics: Modeling Flow of Fluids Using Partial Differential Equations
• Mathematical Finance: Stochastic Models in Finance and Risk Management
• Option Pricing Models: Black-Scholes Model and Beyond
• Portfolio Optimization: Maximizing Returns and Minimizing Risk
• Stochastic Calculus: Calculus of Stochastic Processes and Itô Calculus
• Financial Time Series Analysis: Modeling and Forecasting Financial Data
• Operations Research: Optimization of Decision-Making Processes
• Linear Programming: Optimization Problems with Linear Constraints
• Integer Programming: Optimization Problems with Integer Solutions
• Network Flow Optimization: Modeling and Solving Flow Network Problems
• Combinatorial Game Theory: Analysis of Games with Perfect Information
• Algorithmic Game Theory: Computational Aspects of Game-Theoretic Problems
• Fair Division: Methods for Fairly Allocating Resources Among Parties
• Auction Theory: Modeling Auction Mechanisms and Bidding Strategies
• Voting Theory: Mathematical Models of Voting Systems and Social Choice
• Social Network Analysis: Mathematical Analysis of Social Networks
• Algorithm Analysis: Complexity Analysis of Algorithms and Data Structures
• Machine Learning: Statistical Learning Algorithms and Data Mining
• Deep Learning: Neural Network Models with Multiple Layers
• Reinforcement Learning: Learning by Interaction and Feedback
• Natural Language Processing: Statistical and Computational Analysis of Language
• Computer Vision: Mathematical Models for Image Analysis and Recognition
• Computational Geometry: Algorithms for Geometric Problems
• Symbolic Computation: Manipulation of Mathematical Expressions
• Numerical Analysis: Algorithms for Solving Numerical Problems
• Finite Element Method: Numerical Solution of Partial Differential Equations
• Monte Carlo Methods: Statistical Simulation Techniques
• High-Performance Computing: Parallel and Distributed Computing Techniques
• Quantum Computing: Quantum Algorithms and Quantum Information Theory
• Quantum Information Theory: Study of Quantum Communication and Computation
• Quantum Error Correction: Methods for Protecting Quantum Information from Errors
• Topological Quantum Computing: Using Topological Properties for Quantum Computation
• Quantum Algorithms: Efficient Algorithms for Quantum Computers
• Quantum Cryptography: Secure Communication Using Quantum Key Distribution
• Topological Data Analysis: Analyzing Shape and Structure of Data Sets
• Persistent Homology: Topological Invariants for Data Analysis
• Mapper Algorithm: Method for Visualization and Analysis of High-Dimensional Data
• Algebraic Statistics: Statistical Methods Based on Algebraic Geometry
• Tropical Geometry: Geometric Methods for Studying Polynomial Equations
• Model Theory: Study of Mathematical Structures and Their Interpretations
• Descriptive Set Theory: Study of Borel and Analytic Sets
• Ergodic Theory: Study of Measure-Preserving Transformations
• Combinatorial Number Theory: Intersection of Combinatorics and Number Theory
• Additive Combinatorics: Study of Additive Properties of Sets
• Arithmetic Geometry: Interplay Between Number Theory and Algebraic Geometry
• Proof Theory: Study of Formal Proofs and Logical Inference
• Reverse Mathematics: Study of Logical Strength of Mathematical Theorems
• Nonstandard Analysis: Alternative Approach to Analysis Using Infinitesimals
• Computable Analysis: Study of Computable Functions and Real Numbers
• Graph Theory: Study of Graphs and Networks
• Random Graphs: Probabilistic Models of Graphs and Connectivity
• Spectral Graph Theory: Analysis of Graphs Using Eigenvalues and Eigenvectors
• Algebraic Graph Theory: Study of Algebraic Structures in Graphs
• Metric Geometry: Study of Geometric Structures Using Metrics
• Geometric Measure Theory: Study of Measures on Geometric Spaces
• Discrete Differential Geometry: Study of Differential Geometry on Discrete Spaces
• Algebraic Coding Theory: Study of Error-Correcting Codes
• Information Theory: Study of Information and Communication
• Coding Theory: Study of Error-Correcting Codes
• Cryptography: Study of Secure Communication and Encryption
• Finite Fields: Study of Fields with Finite Number of Elements
• Elliptic Curves: Study of Curves Defined by Cubic Equations
• Hyperelliptic Curves: Study of Curves Defined by Higher-Degree Equations
• Modular Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Number Theory
• Zeta Functions: Analytic Functions with Special Properties
• Analytic Number Theory: Study of Number Theoretic Functions Using Analysis
• Dirichlet Series: Analytic Functions Represented by Infinite Series
• Euler Products: Product Representations of Analytic Functions
• Arithmetic Dynamics: Study of Iterative Processes on Algebraic Structures
• Dynamics of Rational Maps: Study of Dynamical Systems Defined by Rational Functions
• Julia Sets: Fractal Sets Associated with Dynamical Systems
• Mandelbrot Set: Fractal Set Associated with Iterations of Complex Quadratic Polynomials
• Arithmetic Geometry: Study of Algebraic Geometry Over Number Fields
• Diophantine Geometry: Study of Solutions of Diophantine Equations Using Geometry
• Arithmetic of Elliptic Curves: Study of Elliptic Curves Over Number Fields
• Rational Points on Curves: Study of Rational Solutions of Algebraic Equations
• Galois Representations: Study of Representations of Galois Groups
• Automorphic Forms: Analytic Functions with Certain Transformation Properties
• L-functions: Analytic Functions Associated with Automorphic Forms
• Selberg Trace Formula: Tool for Studying Spectral Theory and Automorphic Forms
• Langlands Program: Program to Unify Number Theory and Representation Theory
• Hodge Theory: Study of Harmonic Forms on Complex Manifolds
• Riemann Surfaces: One-dimensional Complex Manifolds
• Shimura Varieties: Algebraic Varieties Associated with Automorphic Forms
• Modular Curves: Algebraic Curves Associated with Modular Forms
• Hyperbolic Manifolds: Manifolds with Constant Negative Curvature
• Teichmüller Theory: Study of Moduli Spaces of Riemann Surfaces
• Mirror Symmetry: Duality Between Calabi-Yau Manifolds
• Kähler Geometry: Study of Hermitian Manifolds with Special Symmetries
• Algebraic Groups: Linear Algebraic Groups and Their Representations
• Lie Algebras: Study of Algebraic Structures Arising from Lie Groups
• Representation Theory of Lie Algebras: Study of Representations of Lie Algebras
• Quantum Groups: Deformation of Lie Groups and Lie Algebras
• Algebraic Topology: Study of Topological Spaces Using Algebraic Methods
• Homotopy Theory: Study of Continuous Deformations of Spaces
• Homology Theory: Study of Algebraic Invariants of Topological Spaces
• Cohomology Theory: Study of Dual Concepts to Homology Theory
• Singular Homology: Homology Theory Defined Using Simplicial Complexes
• Sheaf Theory: Study of Sheaves and Their Cohomology
• Differential Forms: Study of Multilinear Differential Forms
• De Rham Cohomology: Cohomology Theory Defined Using Differential Forms
• Morse Theory: Study of Critical Points of Smooth Functions
• Symplectic Geometry: Study of Symplectic Manifolds and Their Geometry
• Floer Homology: Study of Symplectic Manifolds Using Pseudoholomorphic Curves
• Gromov-Witten Invariants: Invariants of Symplectic Manifolds Associated with Pseudoholomorphic Curves
• Mirror Symmetry: Duality Between Symplectic and Complex Geometry
• Calabi-Yau Manifolds: Ricci-Flat Complex Manifolds
• Moduli Spaces: Spaces Parameterizing Geometric Objects
• Donaldson-Thomas Invariants: Invariants Counting Sheaves on Calabi-Yau Manifolds
• Algebraic K-Theory: Study of Algebraic Invariants of Rings and Modules
• Homological Algebra: Study of Homology and Cohomology of Algebraic Structures
• Derived Categories: Categories Arising from Homological Algebra
• Stable Homotopy Theory: Homotopy Theory with Stable Homotopy Groups
• Model Categories: Categories with Certain Homotopical Properties
• Higher Category Theory: Study of Higher Categories and Homotopy Theory
• Higher Topos Theory: Study of Higher Categorical Structures
• Higher Algebra: Study of Higher Categorical Structures in Algebra
• Higher Algebraic Geometry: Study of Higher Categorical Structures in Algebraic Geometry
• Higher Representation Theory: Study of Higher Categorical Structures in Representation Theory
• Higher Category Theory: Study of Higher Categorical Structures
• Homotopical Algebra: Study of Algebraic Structures in Homotopy Theory
• Homotopical Groups: Study of Groups with Homotopical Structure
• Homotopical Categories: Study of Categories with Homotopical Structure
• Homotopy Groups: Algebraic Invariants of Topological Spaces
• Homotopy Type Theory: Study of Foundations of Mathematics Using Homotopy Theory

In conclusion, the world of mathematics is vast and multifaceted, offering endless opportunities for exploration and discovery. Whether delving into the abstract realms of pure mathematics or applying mathematical principles to solve real-world problems, mathematicians play a vital role in advancing human knowledge and shaping the future of our world.

By embracing diverse math research topics and interdisciplinary collaborations, we can unlock new possibilities and harness the power of mathematics to address the challenges of today and tomorrow. So, let’s embark on this journey together as we unravel the mysteries of numbers and explore the boundless horizons of mathematical inquiry.

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Research Topics & Ideas: Education

170+ Research Ideas To Fast-Track Your Project

If you’re just starting out exploring education-related topics for your dissertation, thesis or research project, you’ve come to the right place. In this post, we’ll help kickstart your research topic ideation process by providing a hearty list of research topics and ideas , including examples from actual dissertations and theses..

PS – This is just the start…

We know it’s exciting to run through a list of research topics, but please keep in mind that this list is just a starting point . To develop a suitable education-related research topic, you’ll need to identify a clear and convincing research gap , and a viable plan of action to fill that gap.

If this sounds foreign to you, check out our free research topic webinar that explores how to find and refine a high-quality research topic, from scratch. Alternatively, if you’d like hands-on help, consider our 1-on-1 coaching service .

Overview: Education Research Topics

• How to find a research topic (video)
• List of 50+ education-related research topics/ideas
• List of 120+ level-specific research topics 
• Examples of actual dissertation topics in education
• Tips to fast-track your topic ideation (video)
• Free Webinar : Topic Ideation 101
• Where to get extra help

Education-Related Research Topics & Ideas

Below you’ll find a list of education-related research topics and idea kickstarters. These are fairly broad and flexible to various contexts, so keep in mind that you will need to refine them a little. Nevertheless, they should inspire some ideas for your project.

• The impact of school funding on student achievement
• The effects of social and emotional learning on student well-being
• The effects of parental involvement on student behaviour
• The impact of teacher training on student learning
• The impact of classroom design on student learning
• The impact of poverty on education
• The use of student data to inform instruction
• The role of parental involvement in education
• The effects of mindfulness practices in the classroom
• The use of technology in the classroom
• The role of critical thinking in education
• The use of formative and summative assessments in the classroom
• The use of differentiated instruction in the classroom
• The use of gamification in education
• The effects of teacher burnout on student learning
• The impact of school leadership on student achievement
• The effects of teacher diversity on student outcomes
• The role of teacher collaboration in improving student outcomes
• The implementation of blended and online learning
• The effects of teacher accountability on student achievement
• The effects of standardized testing on student learning
• The effects of classroom management on student behaviour
• The effects of school culture on student achievement
• The use of student-centred learning in the classroom
• The impact of teacher-student relationships on student outcomes
• The achievement gap in minority and low-income students
• The use of culturally responsive teaching in the classroom
• The impact of teacher professional development on student learning
• The use of project-based learning in the classroom
• The effects of teacher expectations on student achievement
• The use of adaptive learning technology in the classroom
• The impact of teacher turnover on student learning
• The effects of teacher recruitment and retention on student learning
• The impact of early childhood education on later academic success
• The impact of parental involvement on student engagement
• The use of positive reinforcement in education
• The impact of school climate on student engagement
• The role of STEM education in preparing students for the workforce
• The effects of school choice on student achievement
• The use of technology in the form of online tutoring

Level-Specific Research Topics

Looking for research topics for a specific level of education? We’ve got you covered. Below you can find research topic ideas for primary, secondary and tertiary-level education contexts. Click the relevant level to view the respective list.

Research Topics: Pick An Education Level

Primary education.

• Investigating the effects of peer tutoring on academic achievement in primary school
• Exploring the benefits of mindfulness practices in primary school classrooms
• Examining the effects of different teaching strategies on primary school students’ problem-solving skills
• The use of storytelling as a teaching strategy in primary school literacy instruction
• The role of cultural diversity in promoting tolerance and understanding in primary schools
• The impact of character education programs on moral development in primary school students
• Investigating the use of technology in enhancing primary school mathematics education
• The impact of inclusive curriculum on promoting equity and diversity in primary schools
• The impact of outdoor education programs on environmental awareness in primary school students
• The influence of school climate on student motivation and engagement in primary schools
• Investigating the effects of early literacy interventions on reading comprehension in primary school students
• The impact of parental involvement in school decision-making processes on student achievement in primary schools
• Exploring the benefits of inclusive education for students with special needs in primary schools
• Investigating the effects of teacher-student feedback on academic motivation in primary schools
• The role of technology in developing digital literacy skills in primary school students
• Effective strategies for fostering a growth mindset in primary school students
• Investigating the role of parental support in reducing academic stress in primary school children
• The role of arts education in fostering creativity and self-expression in primary school students
• Examining the effects of early childhood education programs on primary school readiness
• Examining the effects of homework on primary school students’ academic performance
• The role of formative assessment in improving learning outcomes in primary school classrooms
• The impact of teacher-student relationships on academic outcomes in primary school
• Investigating the effects of classroom environment on student behavior and learning outcomes in primary schools
• Investigating the role of creativity and imagination in primary school curriculum
• The impact of nutrition and healthy eating programs on academic performance in primary schools
• The impact of social-emotional learning programs on primary school students’ well-being and academic performance
• The role of parental involvement in academic achievement of primary school children
• Examining the effects of classroom management strategies on student behavior in primary school
• The role of school leadership in creating a positive school climate Exploring the benefits of bilingual education in primary schools
• The effectiveness of project-based learning in developing critical thinking skills in primary school students
• The role of inquiry-based learning in fostering curiosity and critical thinking in primary school students
• The effects of class size on student engagement and achievement in primary schools
• Investigating the effects of recess and physical activity breaks on attention and learning in primary school
• Exploring the benefits of outdoor play in developing gross motor skills in primary school children
• The effects of educational field trips on knowledge retention in primary school students
• Examining the effects of inclusive classroom practices on students’ attitudes towards diversity in primary schools
• The impact of parental involvement in homework on primary school students’ academic achievement
• Investigating the effectiveness of different assessment methods in primary school classrooms
• The influence of physical activity and exercise on cognitive development in primary school children
• Exploring the benefits of cooperative learning in promoting social skills in primary school students

Secondary Education

• Investigating the effects of school discipline policies on student behavior and academic success in secondary education
• The role of social media in enhancing communication and collaboration among secondary school students
• The impact of school leadership on teacher effectiveness and student outcomes in secondary schools
• Investigating the effects of technology integration on teaching and learning in secondary education
• Exploring the benefits of interdisciplinary instruction in promoting critical thinking skills in secondary schools
• The impact of arts education on creativity and self-expression in secondary school students
• The effectiveness of flipped classrooms in promoting student learning in secondary education
• The role of career guidance programs in preparing secondary school students for future employment
• Investigating the effects of student-centered learning approaches on student autonomy and academic success in secondary schools
• The impact of socio-economic factors on educational attainment in secondary education
• Investigating the impact of project-based learning on student engagement and academic achievement in secondary schools
• Investigating the effects of multicultural education on cultural understanding and tolerance in secondary schools
• The influence of standardized testing on teaching practices and student learning in secondary education
• Investigating the effects of classroom management strategies on student behavior and academic engagement in secondary education
• The influence of teacher professional development on instructional practices and student outcomes in secondary schools
• The role of extracurricular activities in promoting holistic development and well-roundedness in secondary school students
• Investigating the effects of blended learning models on student engagement and achievement in secondary education
• The role of physical education in promoting physical health and well-being among secondary school students
• Investigating the effects of gender on academic achievement and career aspirations in secondary education
• Exploring the benefits of multicultural literature in promoting cultural awareness and empathy among secondary school students
• The impact of school counseling services on student mental health and well-being in secondary schools
• Exploring the benefits of vocational education and training in preparing secondary school students for the workforce
• The role of digital literacy in preparing secondary school students for the digital age
• The influence of parental involvement on academic success and well-being of secondary school students
• The impact of social-emotional learning programs on secondary school students’ well-being and academic success
• The role of character education in fostering ethical and responsible behavior in secondary school students
• Examining the effects of digital citizenship education on responsible and ethical technology use among secondary school students
• The impact of parental involvement in school decision-making processes on student outcomes in secondary schools
• The role of educational technology in promoting personalized learning experiences in secondary schools
• The impact of inclusive education on the social and academic outcomes of students with disabilities in secondary schools
• The influence of parental support on academic motivation and achievement in secondary education
• The role of school climate in promoting positive behavior and well-being among secondary school students
• Examining the effects of peer mentoring programs on academic achievement and social-emotional development in secondary schools
• Examining the effects of teacher-student relationships on student motivation and achievement in secondary schools
• Exploring the benefits of service-learning programs in promoting civic engagement among secondary school students
• The impact of educational policies on educational equity and access in secondary education
• Examining the effects of homework on academic achievement and student well-being in secondary education
• Investigating the effects of different assessment methods on student performance in secondary schools
• Examining the effects of single-sex education on academic performance and gender stereotypes in secondary schools
• The role of mentoring programs in supporting the transition from secondary to post-secondary education

Tertiary Education

• The role of student support services in promoting academic success and well-being in higher education
• The impact of internationalization initiatives on students’ intercultural competence and global perspectives in tertiary education
• Investigating the effects of active learning classrooms and learning spaces on student engagement and learning outcomes in tertiary education
• Exploring the benefits of service-learning experiences in fostering civic engagement and social responsibility in higher education
• The influence of learning communities and collaborative learning environments on student academic and social integration in higher education
• Exploring the benefits of undergraduate research experiences in fostering critical thinking and scientific inquiry skills
• Investigating the effects of academic advising and mentoring on student retention and degree completion in higher education
• The role of student engagement and involvement in co-curricular activities on holistic student development in higher education
• The impact of multicultural education on fostering cultural competence and diversity appreciation in higher education
• The role of internships and work-integrated learning experiences in enhancing students’ employability and career outcomes
• Examining the effects of assessment and feedback practices on student learning and academic achievement in tertiary education
• The influence of faculty professional development on instructional practices and student outcomes in tertiary education
• The influence of faculty-student relationships on student success and well-being in tertiary education
• The impact of college transition programs on students’ academic and social adjustment to higher education
• The impact of online learning platforms on student learning outcomes in higher education
• The impact of financial aid and scholarships on access and persistence in higher education
• The influence of student leadership and involvement in extracurricular activities on personal development and campus engagement
• Exploring the benefits of competency-based education in developing job-specific skills in tertiary students
• Examining the effects of flipped classroom models on student learning and retention in higher education
• Exploring the benefits of online collaboration and virtual team projects in developing teamwork skills in tertiary students
• Investigating the effects of diversity and inclusion initiatives on campus climate and student experiences in tertiary education
• The influence of study abroad programs on intercultural competence and global perspectives of college students
• Investigating the effects of peer mentoring and tutoring programs on student retention and academic performance in tertiary education
• Investigating the effectiveness of active learning strategies in promoting student engagement and achievement in tertiary education
• Investigating the effects of blended learning models and hybrid courses on student learning and satisfaction in higher education
• The role of digital literacy and information literacy skills in supporting student success in the digital age
• Investigating the effects of experiential learning opportunities on career readiness and employability of college students
• The impact of e-portfolios on student reflection, self-assessment, and showcasing of learning in higher education
• The role of technology in enhancing collaborative learning experiences in tertiary classrooms
• The impact of research opportunities on undergraduate student engagement and pursuit of advanced degrees
• Examining the effects of competency-based assessment on measuring student learning and achievement in tertiary education
• Examining the effects of interdisciplinary programs and courses on critical thinking and problem-solving skills in college students
• The role of inclusive education and accessibility in promoting equitable learning experiences for diverse student populations
• The role of career counseling and guidance in supporting students’ career decision-making in tertiary education
• The influence of faculty diversity and representation on student success and inclusive learning environments in higher education

Education-Related Dissertations & Theses

While the ideas we’ve presented above are a decent starting point for finding a research topic in education, they are fairly generic and non-specific. So, it helps to look at actual dissertations and theses in the education space to see how this all comes together in practice.

Below, we’ve included a selection of education-related research projects to help refine your thinking. These are actual dissertations and theses, written as part of Master’s and PhD-level programs, so they can provide some useful insight as to what a research topic looks like in practice.

• From Rural to Urban: Education Conditions of Migrant Children in China (Wang, 2019)
• Energy Renovation While Learning English: A Guidebook for Elementary ESL Teachers (Yang, 2019)
• A Reanalyses of Intercorrelational Matrices of Visual and Verbal Learners’ Abilities, Cognitive Styles, and Learning Preferences (Fox, 2020)
• A study of the elementary math program utilized by a mid-Missouri school district (Barabas, 2020)
• Instructor formative assessment practices in virtual learning environments : a posthumanist sociomaterial perspective (Burcks, 2019)
• Higher education students services: a qualitative study of two mid-size universities’ direct exchange programs (Kinde, 2020)
• Exploring editorial leadership : a qualitative study of scholastic journalism advisers teaching leadership in Missouri secondary schools (Lewis, 2020)
• Selling the virtual university: a multimodal discourse analysis of marketing for online learning (Ludwig, 2020)
• Advocacy and accountability in school counselling: assessing the use of data as related to professional self-efficacy (Matthews, 2020)
• The use of an application screening assessment as a predictor of teaching retention at a midwestern, K-12, public school district (Scarbrough, 2020)
• Core values driving sustained elite performance cultures (Beiner, 2020)
• Educative features of upper elementary Eureka math curriculum (Dwiggins, 2020)
• How female principals nurture adult learning opportunities in successful high schools with challenging student demographics (Woodward, 2020)
• The disproportionality of Black Males in Special Education: A Case Study Analysis of Educator Perceptions in a Southeastern Urban High School (McCrae, 2021)

As you can see, these research topics are a lot more focused than the generic topic ideas we presented earlier. So, in order for you to develop a high-quality research topic, you’ll need to get specific and laser-focused on a specific context with specific variables of interest.  In the video below, we explore some other important things you’ll need to consider when crafting your research topic.

Get 1-On-1 Help

If you’re still unsure about how to find a quality research topic within education, check out our Research Topic Kickstarter service, which is the perfect starting point for developing a unique, well-justified research topic.

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55 Comments

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You can find our list of nursing-related research topic ideas here: https://gradcoach.com/research-topics-nursing/

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Kindly help me with the research questions on the topic” Effects of workplace conflict on the employees’ job performance”. The effects can be applicable in every institution,enterprise or organisation.

Greetings, I am a student majoring in Sociology and minoring in Public Administration. I’m considering any recommended research topic in the field of Sociology.

I’m a student pursuing Mphil in Basic education and I’m considering any recommended research proposal topic in my field of study

Kindly help me with a research topic in educational psychology. Ph.D level. Thank you.

Project-based learning is a teaching/learning type,if well applied in a classroom setting will yield serious positive impact. What can a teacher do to implement this in a disadvantaged zone like “North West Region of Cameroon ( hinterland) where war has brought about prolonged and untold sufferings on the indegins?

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Look at British Library as they keep a copy of all PhDs in the UK Core.ac.uk to access Open University and 6 other university e-archives, pdf downloads mostly available, all free.

May I also ask for a topic based on mathematics education for college teaching, please?

Please I am a masters student of the department of Teacher Education, Faculty of Education Please I am in need of proposed project topics to help with my final year thesis

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Greetings and Regards I am a doctoral student in the field of philosophy of education. I am looking for a new topic for my thesis. Because of my work in the elementary school, I am looking for a topic that is from the field of elementary education and is related to the philosophy of education.

Masters student in the field of curriculum, any ideas of a research topic on low achiever students

In the field of curriculum any ideas of a research topic on deconalization in contextualization of digital teaching and learning through in higher education

Amazing guidelines

I am a graduate with two masters. 1) Master of arts in religious studies and 2) Master in education in foundations of education. I intend to do a Ph.D. on my second master’s, however, I need to bring both masters together through my Ph.D. research. can I do something like, ” The contribution of Philosophy of education for a quality religion education in Kenya”? kindly, assist and be free to suggest a similar topic that will bring together the two masters. thanks in advance

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• Relationship between learners’ proficiency in common and algebraic fractions : a case of grade 10 learners at a Limpopo high school  Mangwende, Lina ( 2021-06 ) In Mathematics, the topic of fractions is one of the most difficult topics for both teachers and learners. The primary focus of the study was to examine how pedagogical strategies could be used in the teaching of common ...
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Posing Researchable Questions in Mathematics and Science Education: Purposefully Questioning the Questions for Investigation

• Published: 07 April 2020
• Volume 18 , pages 1–7, ( 2020 )

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• Jinfa Cai 1 &
• Rachel Mamlok-Naaman 2  

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Perhaps the most obvious example is the set of 23 influential mathematical problems posed by David Hilbert that inspired a great deal of progress in the discipline of mathematics (Hilbert, 1901 -1902). Einstein and Infeld ( 1938 ) claimed that “to raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science” (p. 95). Both Cantor and Klamkin recommended that, in mathematics, the art of posing a question be held as high or higher in value than solving it. Similarly, in the history of science, formulating precise, answerable questions not only advances new discoveries but also gives scientists intellectual excitement (Kennedy, 2005 ; Mosteller, 1980 ).

In research related to mathematics and science education, there is no shortage of evidence for the impact of posing important and researchable questions: Posing new, researchable questions marks real advances in mathematics and science education (Cai et al., 2019a ). Although research in mathematics and science education begins with researchable questions, only recently have researchers begun to purposefully and systematically discuss the nature of researchable questions. To conduct research, we must have researchable questions, but what defines a researchable question? What are the sources of researchable questions? How can we purposefully discuss researchable questions?

This special issue marks effort for the field’s discussion of researchable questions. As the field of mathematics and science education matures, it is necessary to reflect on the field at such a metalevel (Inglis & Foster, 2018 ). Although the authors in this special issue discuss researchable questions from different angles, they all refer to researchable questions as those that can be investigated empirically. For any empirical study, one can discuss its design, its conduct, and how it can be written up for publication. Therefore, researchable questions in mathematics and science education can be discussed with respect to study design, the conduct of research, and the dissemination of that research.

Even though there are many lines of inquiry that we can explore with respect to researchable questions, each exploring the topic from a different angle, we have decided to focus on the following three aspects to introduce this special issue: (1) criteria for selecting researchable questions, (2) sources of researchable questions, and (3) alignment of researchable questions with the conceptual framework as well as appropriate research methods.

Criteria for Selecting Researchable Questions

It is clear that not all researchable questions are worth the effort to investigate. According to Cai et al. ( 2020 ), of all researchable questions in mathematics and science education, priority is given to those that are significant. Research questions are significant if they can advance the fields’ knowledge and understanding about the teaching and learning of science and mathematics. Through an analysis of peer reviews for a research journal, Cai et al. ( 2020 ) provide a window into the field’s frontiers related to significant researchable questions. In an earlier article, Cai et al. ( 2019a ) argued that

The significance of a research question cannot be determined just by reading it. Rather, its significance stands in relation to the knowledge of the field. The justification for the research question itself—why it is a significant question to investigate—must therefore be made clear through an explicit argument that ties the research question to what is and is not already known. (p. 118)

In their analysis, Cai et al. ( 2020 ) provide evidence that many reviews that highlighted issues with the research questions in rejected manuscripts specifically called for authors to make an argument to motivate the research questions, whereas none of the manuscripts that were ultimately accepted (pending revisions) received this kind of comment. Cai et al. ( 2020 ) provide a framework not only for analyzing peer reviews about research questions but also for how to communicate researchable questions in journal manuscript preparations.

Whereas Cai and his colleagues, as editors of a journal, discuss significant research questions from the perspective of peer review and publication, King, Ochsendorf, Solomon, and Sloane ( 2020 ), as program directors at the Directorate for Education and Human Resources at the U.S. National Science Foundation (NSF), discuss fundable research questions for research in mathematics and science education. King et al. ( 2020 ) situate their discussion of fundable research questions in the context of writing successful educational research grant proposals. For them, fundable research questions must be transformative and significant with specific and clear constructs. In addition, they present examples of STEM education research questions from different types of research (Institute of Education Sciences [IES] & NSF, 2013 ) and how the questions themselves direct specific design choices, methodologies, measures, study samples, and analytical models as well as how they can reflect the disciplinary orientations of the researchers.

Hjalmarson and Baker ( 2020 ) take a quite different approach to discussing researchable questions for teacher professional development. They argue for the need to include mathematics specialists (e.g. mathematics coaches or mathematics teacher leaders) for studying teacher learning and development. To Hjalmarson and Baker ( 2020 ), researchable questions related to teacher professional learning should be selected by including mathematics specialists because of their role in connecting research and practice.

Sanchez ( 2020 ) discuss, in particular, the importance of replication studies in mathematics and the kinds of researchable questions that would be productive to explore within this category. With the increased acknowledgement of the importance of replication studies (Cai et al., 2018 ), Sanchez Aguilar has provided a useful typology of fundamental questions that can guide a replication study in mathematics (and science) education.

Schoenfeld ( 2020 ) is very direct in suggesting that researchable questions must advance the field and that these research questions must be meaningful and generative: “What is meant by meaningful is that the answer to the questions posed should matter to either practice or theory in some important way. What is meant by generative is that working on the problem, whether it is ‘solved’ or not, is likely to provide valuable insights” (pp. XX). Schoenfeld calls for researchers to establish research programs—that is, one not only selects meaningful research questions to investigate but also continues in that area of research to produce ongoing insights and further meaningful questions.

Stylianides and Stylianides ( 2020 ) argue that, collectively, researchers can and need to pose new researchable questions. The new researchable questions are worth investigating if they reflect the field’s growing understanding of the web of potentially influential factors surrounding the investigation of a particular area. The argument that Stylianides and Stylianides ( 2020 ) use is very similar to Schoenfeld’s ( 2020 ) generative criteria, but Stylianides and Stylianides ( 2020 ) explicitly emphasize the collective nature of the field’s growing understanding of a particular phenomenon.

Sources of Researchable Questions

Research questions in science and mathematics education arise from multiple sources, including problems of practice, extensions of theory, and lacunae in existing areas of research. Therefore, through a research question’s connections to prior research, it should be clear how answering the question extends the field’s knowledge (Cai et al., 2019a ). Across the papers in this special issue lies a common theme that researchable questions arise from understanding the area under study. Cai et al. ( 2020 ) take the position that the significance of researchable questions must be justified in the context of prior research. In particular, reviewers of manuscripts submitted for publication will evaluate if the study is adequately motivated. In fact, posing significant researchable questions is an iterative process beginning with some broader, general sense of an idea which is potentially fruitful and leading, eventually, to a well-specified, stated research question (Cai et al., 2019a ). Similarly, King et al. ( 2020 ) argue that fundable research questions should be grounded in prior research and make explicit connections to what is known or not known in the given area of study.

Sanchez ( 2020 ) suggest that it is time for the field of mathematics and science education research to seriously consider replication studies. Researchable questions related to replication studies might arise from the examination of the following two questions: (1) Do the results of the original study hold true beyond the context in which it was developed? (2) Are there alternative ways to study and explain an identified phenomenon or finding? Similarly, Hjalmarson and Baker ( 2020 ) specifically suggest two needs related to mathematics specialists in studies of professional development that drive researchable questions: (1) defining practices and hidden players involved in systematic school change and (2) identifying the unit of analysis and scaling up professional development.

Schoenfeld ( 2020 ) uses various examples to illustrate the origin of researchable questions. One of his (perhaps most familiar) examples is his decade-long research on mathematical problem solving. He elaborates on how answering one specific research question leads to another and another. In the context of research on mathematical proof, Stylianides and Stylianides ( 2020 ) also illustrate how researchable questions arise from existing research in the area leading to new researchable questions in the dynamic process of educational research. The arguments and examples in both Schoenfeld ( 2020 ) and Stylianides and Stylianides ( 2020 ) are quite powerful in the sense that this source of researchable questions facilitates the accumulation of knowledge for the given areas of study.

A related source of researchable questions is not discussed in this set of papers—unexpected findings. A potentially powerful source of research questions is the discovery of an unexpected finding when conducting research (Cai et al., 2019b ). Many important advances in scientific research have their origins in serendipitous, unexpected findings. Researchers are often faced with unexpected and perhaps surprising results, even when they have developed a carefully crafted theoretical framework, posed research questions tightly connected to this framework, presented hypotheses about expected outcomes, and selected methods that should help answer the research questions. Indeed, unexpected findings can be the most interesting and valuable products of the study and a source of further researchable questions (Cai et al., 2019b ).

Of course, researchable questions can also arise from established scholars in a given field—those who are most familiar with the scope of the research that has been done. For example, in 2005, in celebrating the 125th anniversary of the publication of Science ’s first issue, the journal invited researchers from around the world to propose the 125 most important research questions in the scientific enterprise (Kennedy, 2005 ). A list of unanswered questions like this is a great source for researchable questions in science, just as the 23 great questions in mathematics by Hilbert ( 1901 -1902) spurred the field for decades. In mathematics and science education, one can look to research handbooks and compendiums. These volumes often include lists of unanswered research questions in the hopes of prompting further research in various areas (e.g. Cai, 2017 ; Clements, Bishop, Keitel, Kilpatrick, & Leung, 2013 ; Talbot-Smith, 2013 ).

Alignment of Researchable Questions with the Conceptual Framework and Appropriate Research Methods

Cai et al. ( 2020 ) and King et al. ( 2020 ) explicitly discuss the alignment of researchable questions with the conceptual framework and appropriate research methods. In writing journal publications or grant proposals, it is extremely important to justify the significance of the researchable questions based on the chosen theoretical framework and then determine robust methods to answer the research questions. According to Cai et al. ( 2019a ), justification for the significance of the research questions depends on a theoretical framework: “The theoretical framework shapes the researcher’s conception of the phenomenon of interest, provides insight into it, and defines the kinds of questions that can be asked about it” (p. 119). It is true that the notion of a theoretical framework can remain somewhat mysterious and confusing for researchers. However, it is clear that the theoretical framework links research questions to existing knowledge, thus helping to establish their significance; provides guidance and justification for methodological choices; and provides support for the coherence that is needed between research questions, methods, results, and interpretations of findings (Cai & Hwang, 2019 ; Cai et al., 2019c ).

Analyzing reviews for a research journal in mathematics education, Cai et al. ( 2020 ) found that the reviewers wanted manuscripts to be explicit about how the research questions, the theoretical framework, the methods, and the findings were connected. Even for manuscripts that were accepted (pending revisions), making explicit connections across all parts of the manuscript was a challenging proposition. Thus, in preparing manuscripts for publication, it is essential to communicate the significance of a study by developing a coherent chain of justification connecting researchable questions, the theoretical framework, and the research methods chosen to address the research questions.

The Long Journey Has Just Begun with a First Step

As the field of mathematics and science education matures, there is a need to take a step back and reflect on what has been done so that the field can continue to grow. This special issue represents a first step by reflecting on the posing of significant researchable questions to advance research in mathematics and science education. Such reflection is useful and necessary not only for the design of studies but also for the writing of research reports for publication. Most importantly, working on significant researchable questions cannot only contribute to theory generation about the teaching and learning of mathematics and science but also contribute to improving the impact of research on practice in mathematics and science classrooms.

To conclude, we want to draw readers’ attention to a parallel between this reflection on research in our field and a line of research that investigates the development of school students’ problem-posing and questioning skills in mathematics and science (Blonder, Rapp, Mamlok-Naaman, & Hofstein, 2015 ; Cai, Hwang, Jiang, & Silber, 2015 ; Cuccio-Schirripa & Steiner, 2000 ; Hofstein, Navon, Kipnis, & Mamlok-Naaman, 2005 ; Silver, 1994 ; Singer, Ellerton, & Cai, 2015 ). Posing researchable questions is critical for advancing research in mathematics and science education. Similarly, providing students opportunities to pose problems is critical for the development of their thinking and learning. With the first step in this journey made, perhaps we can dream of something bigger further on down the road.

Change history

15 may 2020.

The original version of this article unfortunately contains correction.

Blonder, R., Rapp, S., Mamlok-Naaman, R., & Hofstein, A. (2015). Questioning behavior of students in the inquiry chemistry laboratory: Differences between sectors and genders in the Israeli context. International Journal of Science and Mathematics Education, 13 (4), 705–732.

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Cai, J., Mamlok-Naaman, R. Posing Researchable Questions in Mathematics and Science Education: Purposefully Questioning the Questions for Investigation. Int J of Sci and Math Educ 18 (Suppl 1), 1–7 (2020). https://doi.org/10.1007/s10763-020-10079-5

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Exploring research trends of technology use in mathematics education: A scoping review using topic modeling

Sunghwan hwang.

1 Department of Mathematics Education, Chuncheon National University of Education, 126 Gongji-ro, Chuncheon, Gangwon-do, South Korea

Eunhye Flavin

2 Department of Education Studies, Stonehill College, 320 Washington St, North Easton, MA 02357 USA

3 Department of Teacher Development and Educational Studies, Oakland University, Rochester, MI USA

Associated Data

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

This study performed a scoping review of the literature concerning the use of technology in mathematics education published between January 1981 and March 2022 to explore research trends. After the defined filtering process, we retrieved 2,433 articles from Web of Science , ERIC , and PsycInfo databases and employed Latent Dirichlet Allocation (LDA) topic modeling to extract key terms and topics from the selected articles. The analysis focused on the four aspects: (a) evolution of research trends of technology use in mathematics education, (b) frequently used words, (c) latent research topics, and (d) research trends for particular topics. The findings revealed a steady increase in research interest, and the combination of frequently used words in the article abstracts suggests popular research topics that have been studied during the set period. The results of LDA identified seven research topics that were not precisely aligned with those identified in prior studies on mathematics education or educational technology. This implied technology integration into mathematics education as a distinctive research area. Over time, the seven topics showed different research trends (stable, fluctuating, increasing, and decreasing). We discussed plausible reasons for these varied patterns and proposed implications based on the research findings.

Introduction

Human life and society have changed as a result of technological development. Technological devices and apps have affected how people learn, communicate, work, and interact with each other (Chen et al., 2020 ; Kenski, 2008 ). In addition to these societal changes, especially the increase in distance education due to the COVID-19 pandemic, it would be safe to say that the use of technology in education is no longer a choice but an essential tool for suitable educational development (Kimmons, 2020 ). The introduction and expansion of technology in education have tremendously changed the educational environment. It has transformed not only curricula, educational resources, textbooks, and classroom environment but also teacher instructional practices and student learning styles (Akapame et al., 2019 ; Chen et al., 2020 ; Clements et al., 2013 ; Hoyles, 2018 ; Ozyurt & Ayaz, 2022 ; Roschelle et al., 2017 ), which led to different student achievement, motivation, and attitudes (Bicer & Capraro, 2016 ; Higgins et al., 2019 ).

Mathematics education is not an exception. In 1980, The National Council of Teachers of Mathematics (NCTM) proposed an agenda for the development of mathematics education and highlighted the importance of using technological tools (e.g., calculators and computers) in mathematics teaching and learning at all grade levels. Moreover, NCTM ( 2014 ) reported that the use of technology could improve teachers’ instructional quality and student mathematics learning, which assists in achieving educational equity. In this perspective, researchers in mathematics education have conducted various studies to examine features, opportunities, challenges, methods, resources, implementation, and outcomes of technology use in mathematics education. For example, the Third International Handbook of Mathematics Education (Clements et al., 2013 ) extensively explained how the use of technology influences mathematics curriculum, teaching, learning (e.g., modeling, reasoning, and algebra), and assessment. Such efforts have changed the entire landscape of mathematics education (Hoyles, 2018 ; Roschelle et al., 2017 ).

In response to the popularity and importance of technology use, diverse literature reviews were conducted in mathematics education. The topics covered both general educational technology, such as artificial intelligence (Hwang & Tu, 2021 ), educational robotics (Zhong & Xia, 2020 ), tablets (Svela et al., 2019 ), and mathematics-specific technology, such as GeoGebra (Yohannes & Chen, 2021 ) and graphing calculators. Furthermore, researchers have reviewed mathematics teachers’ technological pedagogical and content knowledge (TPACK; Zou et al., 2022 ) and the effectiveness of technology use in mathematics achievement (Cheung & Slavin, 2013 ).

These studies provided information on the current status of technology use in mathematics education and directions for future studies. However, most review studies have examined research trends on a particular topic. Thus, we still have limited information on overall research topics on technology use in mathematics education and how they have evolved. Previous studies have analyzed less than 100 articles with manual coding methods to synthesize previous studies, which might lead to inaccurate outcomes due to a prolonged process and an insufficient number of articles (Chen et al., 2020 ; Yin & Yuan, 2022 ). Kimmons ( 2020 ) emphasized the importance of reliable review studies revealing research trends of technology in education. However, only a few studies have extensively examined what research topics have been examined and how they evolved regarding technology use in mathematics education.

This study aims to fill this gap and synthesize relevant studies on the use of technology in mathematics education published in the last four decades (1981–2022) after the publication of the NCTM’s ( 1980 ) document. We employed topic modeling to automatically analyze a large corpus of text data to efficiently examine a large volume of articles (Blei, 2012 ). The findings of this study could provide information on past and present research trends of technology use in mathematics education and directions for future studies.

Literature review

To enlighten readers about what mathematics educators have researched, we first provided the research trends in mathematical education. Then, we discussed research trends of overall educational technology, which might provide insight regarding the research trends of technology use in mathematics education. Additionally, we reviewed literature that utilized topic modeling that informed the data analysis approach in our study.

Research trends in mathematics education

Researchers have synthesized peer-reviewed articles to identify research trends in mathematics education (e.g., Foster & Inglis, 2019 ; Gökçe & Güner, 2021 ; Inglis & Foster, 2018 ). These studies have found several domains consisting of dozens of topics. For example, Inglis and Foster ( 2018 ) examined articles published in two leading mathematics education journals ( Educational Studies in Mathematics and Journal for Research in Mathematics Education ) between 1968 and 2015 and employed topic modeling. They identified 28 topics across four domains. The domains included mathematical content (e.g., algebra and geometry), mathematical process (e.g., proof and argument), teaching and learning environments (e.g., teachers’ knowledge and beliefs, reform curriculum, and novel assessment), and hard cores and heuristics (e.g., research theory and methods). They reported that topics about algebra, proof and argumentation, teachers’ knowledge and beliefs, reform curriculum, classroom discussion, and sociocultural theory had received increasing attention. In contrast, the interest in geometry, constructivism, and experimental design topics has declined over time. Later, Foster and Inglis ( 2019 ) analyzed two mathematics education journals in the UK (Mathematics Teaching and Mathematics in School ). They again reported similar findings.

Similarly, Gökçe and Güner ( 2021 ) examined 1,021 mathematics education articles published between 1980 and 2019. They found the following four research domains: foundation (e.g., theory, perspective, and standard), implementation (e.g., effect, performance, and intervention), association (e.g., science, technology, and grade), and evaluation (e.g., success, policy, and program). They also reported that the research focus has shifted from individual student learning and generalization to curriculum and teacher-related factors, equity, and cognitive and affective skills (e.g., motivation, attitude, and self-efficacy).

These research trends can be explained by a paradigm shift in mathematics education (Bray & Tangney, 2017 ; Gökçe & Güner, 2021 ; Stinson & Bullock, 2012 ). In the early stage, mathematics education researchers focused on examining the effect of a certain program in predicting student achievement with quasi-experimental methods. However, with the demise of the process–product movement, researchers have paid more attention to examining individual students’ problem-solving. Various studies have been conducted to understand how students construct new knowledge and reorganize the existing knowledge (Bray & Tangney, 2017 ; Inglis & Foster, 2018 ). Moreover, with the effect of sociocultural theory (Vygotsky, 1986 ), researchers have examined the effects of sociocultural factors and classroom environments on mathematics teaching and learning processes (Inglis & Foster, 2018 ). The topic included classroom discourse and norms (Yackel & Cobb, 1996 ), curriculum materials (Remillard, 2005 ), teacher knowledge (Ball et al., 2008 ), student background and identity (Hand & Gresalfi, 2015 ), and technology (Drijvers, 2015 ).

The reform movement in mathematics education has also affected the research trends. The reform movement asked mathematics teachers to shift from traditional teacher-centered instructional practices into student-centered ones (Munter et al., 2015 ; Schoenfeld, 2004 ). Drills and exercises based on behaviorism were deemphasized in mathematics classrooms, whereas student autonomy, conceptual understanding, investigations, discussion, and cooperation were emphasized (Munter et al., 2015 ; NCTM, 2014 ; Schoenfeld, 2004 ). Therefore, teachers are expected to teach mathematical content and processes (e.g., problem-solving, reasoning and proof, communication, connections, and representations), which improve students’ mathematical competencies (NCTM, 2014 ). In this process, educational technologies were extensively introduced in mathematics education to support mathematics teaching and learning (Hoyles, 2018 ). For example, dynamic geometry software (e.g., Cabri and Sketchpad) and mathematical apps could support students’ investigation and help them examine and compare various mathematical ideas (Drijvers, 2015 ).

The roles of technology use in mathematics education

Mathematics educators have highlighted that mathematical technology should be integrated into mathematics education (Association of Mathematics Teacher Educators [AMTE], 2022 ; NCTM, 2014 ). Trends in International Mathematics and Science Study researchers have emphasized using various types of technology for mathematics teaching and learning, such as interactive whiteboards, internet, apps, calculators, computers, and smart tables (Mullis & Martin, 2017 ). Moreover, from a practical perspective, researchers in OECD countries ( 2019 ) reported that technology should be stressed in school mathematics as most workplaces are required to use technological tools.

The introduction of technology in mathematics education transforms mathematics teaching and learning environments (Clements et al., 2013 ; Roschelle et al., 2017 ). Students could investigate conceptual knowledge, practice problems, justify mathematical ideas, and communicate with their peers and teachers using various technology tools (Higgins et al., 2019 ; Roschelle et al., 2017 ). Thus, Cullen et al. ( 2020 ) proposed four roles of technology use in mathematics education, including supporting proof, presenting, and relating representations, enhancing reasoning, and working as a tutee.

Similarly, Drijverse ( 2015 ) examined student learning and proposed the following three didactical functions of technology use in mathematics education: doing mathematics, practicing skills, and developing conceptual understanding. Doing mathematics indicates using technology to outsource works that could be done by hand (e.g., drawing a figure and doing simple computation). The technology for practicing mathematics refers to using technology to improve speed, accuracy, and proficiency of mathematical skills and providing instructions and feedback to support mathematics learning (e.g., online-tutoring system). The technology for developing conceptual understanding provides students with more autonomy and flexibility in the construction of mathematical knowledge. Examples of this type of technology are dynamic geometry software, such as Cabri, Desmos, Geogebra, and Sketchpad. Later, Roschelle et al. ( 2017 ) proposed another category regarding the roles of technology in mathematics education: the context for interest-driven mathematics. This technology is designed to enhance students’ motivation and interest in mathematics learning, such as 3D printers, games, and Lego Mindstorms. However, using technology in the mathematics classroom is affected by technology type and knowledge, beliefs, and curriculum (Akapame et al., 2019 ; Gökçe & Güner, 2021 ; NCTM, 2014 ). Thus, researchers have also examined how those factors facilitate or hinder using technology in mathematics education (e.g., Hu et al., 2020 ; Radmehr & Goodchild, 2022 ).

Research trends in educational technology

The research trends of educational technology have shown a shift from studies on individual student learning and assessment to studies on collaboration and new learning strategies with emerging technology. Zawacki-Richter and Latchem ( 2018 ) examined articles published in  Computers and Education between 1976 and 2016. They reported that the research trends have changed across four stages: computer-assisted teaching, stand-alone multimedia learning, network computer use for collaboration, and online learning. Chen et al. ( 2020 ) examined the 50 years (1971–2018) of research trends in  the British Journal of Educational Technology (BJET) with topic modeling. They found that topics related to student collaboration (e.g., online social communication and socialized e-learning) and emerging technologies (e.g., mobile-assisted language learning and game-based learning) have received increasing attention over time.

Tatnall and Fluck ( 2022 ) examined articles published in  Education and the Information Technologies (EAIT). They reported the following research trends: evaluation and software (1996–2000), case study and pedagogy (2001–2005), collaboration and learning efficacy (2006–2010), the emergence of e‐learning (2011–2015), and mobile and blended learning (2015–2020). Similarly, Ozyurt and Ayaz ( 2022 ) analyzed research trends in the EAIT journal and reported that technology acceptance and social network-based learning were the most studied topics during the past 25 years. Additionally, the gamification topic showed the highest acceleration rate in popularity.

Unlike studies examining research trends in a journal, Kimmons ( 2020 ) analyzed 7,708 educational technology articles published between 2015 and 2019. Kimmons found that current studies have focused on three topics: (a) learning environments as modalities (e.g., mobile, flipped, and online learning), (b) achieving learning goals of school subjects (e.g., language learning and mathematics), and (c) using emerging technology for educational purposes (e.g., augmented reality [AR] and virtual reality [VR]). Similarly, Dağhan and Gündüz ( 2022 ) examined 10,386 articles in educational technology journals published during 2000–2018 and reported that interactive learning environments were the most frequently used keywords, followed by teaching/learning strategies, higher education, online learning, and e-learning. Moreover, flipped classroom, social media, and game-based learning keywords showed a considerable increase over time.

Topic modeling

Topic modeling is one of the analytical methods in text mining methodology. Computer scientists created this natural language processing technique, and social scientists have used topic models to understand certain phenomena in the world through the text people have written (Ramage et al., 2009 ). Topic modeling is a statistical model where topics are treated as latent variables. Each document includes multiple sets of words that have underlying topics. The topic modeling provides a set of words that frequently co-occur with each topic, and a topic represents a recurring pattern in which the words co-occur (Blei, 2012 ; Yin and Yuan, 2022 ). While topic modeling is an automated process, researchers label the topic names based on the results of data analysis. Thus, topic modeling is an amalgam of objective data analysis and subjective data labeling processes (Hwang & Cho,  2021 ). Latent Dirichlet Allocation (LDA) is one of the widely used methods for exploring topic models because LDA is a powerful method for generating a probabilistic model to discover a topic from the corpus (Blei, 2012 ; Yin & Yuan, 2022 ).

A scheme of the LDA algorithm with mathematical notations can be addressed as follows. First, creating a topic starts with choosing the collection of documents (i.e., corpus D ) to be analyzed. Each document ( d ) consists of words ( N ). The observed n th word in document d can be detected ( W d , n ). The LDA algorithms set two hyperparameters (α and η) that act as a prior to the posterior calculation. The α parameter is a Dirichlet parameter for a document-topic density specifying prior beliefs about topic uniformity and sparsity within documents. The η parameter is a representative of topic-word density. This parameter specifies prior beliefs about word uniformity and sparsity within topics. This LDA algorithm assumes that each document displays the topics in different proportions ( θ d ). Each word in the document is chosen from one of the topics ( Z d , n ) . After repeating this topic generation in each document, researchers obtain document-topic probability distributions ( β k ) and topic-per-word probability distributions ( θ d ). While these processes provide a probabilistic model, researchers need to determine how many numbers of topics are optimal to represent the dataset. Thus, researchers should decide the optimal number of topics ( k-number ) based on the perplexity value. The lower perplexity value indicates a better model fit (Blei, 2012 ; Nikita, 2020 ).

The current study

Several review studies have been conducted to examine the research trends of technology use in mathematics education (e.g., Zhong & Xia, 2020 ). However, these studies have examined the research trends of limited topics with a small number of articles. Therefore, as a scoping review, this study collected articles regarding the use of technology in mathematics education after the publication of the NCTM ( 1980 ) document and synthesized them. Scoping reviews refer to exploratory research that aims to “determine the scope or coverage of a body of literature on a given topic and give clear indications of the volume of literature and studies available” (Munn et al., 2018 , p. 2). Thus, scoping reviews address broad research questions and are helpful in systematically analyzing a wide range of extant work to assess the extent of the available evidence and highlight gaps (Arksey & O'Malley, 2005 ; Major et al., 2018 ; Munn et al., 2018 ). Arksey and O'Malley ( 2005 ) proposed a framework to conduct scoping reviews: (1) identifying research questions, (2) identifying related literature, (3) collecting studies, (4) charting the collected data, and (5) synthesizing, summarizing, and reporting the findings. Following this framework, the sections below describe how we collected, analyzed, charted, and synthesized data and what the major findings of this study were. Moreover, this study used topic modeling which helps us to identify latent research topics and examine how they evolve, which might not have been discussed in previous studies (Blei, 2012 ; Chen et al., 2020 ; Yin & Yuan, 2022 ). The research questions of this study are as follows:

• Q1. How did overall research trends of technology use in mathematics education evolve?
• Q2. Which words were frequently used in previous studies?
• Q3. What were the latent research topics?
• Q4. What were the research trends for individual topics?

Methodology

Data collection and retrieving process.

We implemented four steps to collect articles on technology use in mathematics education (Fig.  1 ). First, we used three research databases, Web of Science, ERIC, and PsycInfo, to search for relevant articles and selected articles containing “mathematics or math” and “technology or technologies” in the abstract and “education” in any field of the document. Second, we excluded dissertations and theses and only included peer-reviewed articles to ensure scholarly quality (Hwang & Cho, 2021 ). In addition, we excluded non-English written articles. As NCTM’s ( 1980 ) document that emphasizes technology use in mathematics education was first published in 1980, we only included articles published after 1980 (January 1981– March 2022). After this process, we obtained 13,886 research articles ( Web of Science: 4,861 , ERIC: 5,482, and PsycInfo: 3,543). Third, the EndNote 20 software was used to import articles obtained. After deleting the duplicated articles, we obtained 5,687 articles. Fourth, the titles, abstracts, and full texts of each article were reviewed, and the articles that were irrelevant to technology use in mathematics education (e.g., technology use in engineering education) were excluded. A total of 2,433 articles were retrieved through this filtering process.

Data retrieving process following the guidelines of the PRISMA group (Moher et al., 2009 ). Note. The data that support the findings of this study are available on request from the authors

Data analysis

Pre-processing.

We adopted the programming language R and conducted two pre-processing steps: stop words removal and stemming (Yin & Yuan, 2022 ). We first eliminated stop words (e.g., pronouns, conjunctions, and prepositions) that do not represent the topic of the research articles. We also eliminated the terms usually included in an abstract but contain low information about the article, such as ‘‘study,’’ ‘‘database,’’ ‘‘journal,’’ ‘‘paper,’’ and ‘‘author.’’ Second, we conducted a stemming process where it reduced a word to its word stem (e.g., the term “technologies” is transformed into “technology.”). This text normalization technique is necessary for the use of the LDA algorithm to enhance the efficiency and accuracy of the data analysis. Words such as “teacher” and “teachers” will be reduced to the word “teacher.” Figs.  3 , ​ ,5, 5 , and Table ​ Table3 3 technically show the word stems that were undertaken in the stemming process. For the stemming technique, we used a SnowballC package in R . Through these pre-processing steps, we retrieved 136,262 words.

A word cloud of topic 5 with the fifty highest term-topic probability words. Note . The bigger and bolder the word stem appears, the higher the word stem's term-topic probability

Frequently used words in the abstract. Note. The words shown in Fig. 5 are technically word stems. For example, ‘includ’ is a word stem of include, includes, included, and including that reduces the suffixes

Word Clouds of Each Topic with the Fifty Highest Term-Topic Probability Words

Note . The bigger and bolder the word stem appears, the higher the word stem's term-topic probability.

Perplexity analysis

To determine the optimal number of topics ( k ), we used a ldatuning package in R , which provides model fitness scores for the given topics (Nikita, 2020 ). We calculated a model fitness score using CaoJuan2009 , which provided the information on the optimal topic number. Cao et al. ( 2009 ) validated that the best k number of LDA is correlated with the distances between topics. This metric uses the average cosine distance between every pair of topics to measure the stability of the topic structure. A smaller average distance represents that the topic structure is more stable. Therefore, in the CaoJuan2009 metric, the lower value represents a better model fit. Figure  2 depicts that a line level falls off (the lowest value) when the number of topics is 7. This shows that the study data at hand had the best generalization performance with seven topics. Thus, we decided to categorize the collected articles into seven topics.

Perplexity of topic model

Determining research topic name

We used three types of information to determine the name of each topic: (a) top 15 characteristic words, (b) word clouds, and (c) top 20 representative articles. We first examined each topic’s top 15 characteristic words to initiate our idea around the possible topic names. The top 15 characteristic words refer to the words with the highest term-topic probability words ( β k ), which were frequently revealed in the abstract. Second, we created a word cloud of each topic with the top 50 words. The size of a term in a word cloud reflects the value of a term-topic probability, and a larger term indicates a higher term-topic probability. This visualization made it easier to see which terms (or research areas) are more representative than other terms within the topic. Third, we read the top 20 articles ( θ d ) with the highest proportion of words. This process helped us understand the narratives of each topic (e.g., research purpose and findings) and determine the research topic name.

For example, topic 5 was named “teacher instruction and TPACK” for the following reasons. First, the top 15 terms obtained by the LDA algorithm were ‘‘teacher,’’ ‘‘teach,’’ ‘‘integrate,’’ ‘‘classroom,’’ ‘‘practice,’’ ‘‘knowledge,’’ ‘‘preservice,’’ ‘‘content,’’ ‘‘lesson,’’ ‘‘pedagogy,’’ ‘‘participate,’’ ‘‘pd [professional development],’’ ‘‘train,’’ and ‘‘instruct.’’ The combination of these terms would be the name of the topic. Second, the word cloud analysis (see Fig.  3 ) revealed that ‘teacher’ took the larger proportion, followed by ‘‘teach,’’ ‘‘integrate,’’ ‘‘classroom,’’ ‘‘practice,’’ ‘‘knowledge,’’ ‘‘preservice,’’ and ‘‘content.’’ Third, the articles with the highest topic-article probability examined teachers’ technology use for mathematics instructions and their TPACK (e.g., Akapame et al., 2019 ).

Overall research trends and word frequency

This study examined 2,433 articles published between January 1981 and March 2022. Table ​ Table1 1 and Fig.  4 show the number of articles by 10-year period and a year. As the table and figure show, the number of articles has gradually increased over time, indicating the popularity of this field. In the 1980s, only 26 articles (1.1%) examined technology use in mathematics education. However, since 2009, more than 100 articles have been published every year. For example, in the 2010s, 1,408 articles were published (57.8%). These results were aligned with previous studies reporting that since the 1980s, educational technology has facilitated integration in mathematics education (Bray & Tangney, 2017 ; Roschelle et al., 2017 ).

The Number of Articles Over a 10-Year Period

The number of articles by a year

We also examined the most frequently used words in the collected data. Figure  5 depicts the words with more than 500 frequencies in abstracts. There were 53 words found, such as ‘‘student,’’ ‘‘teacher,’’ ‘‘learn,’’ ‘‘teach,’’ ‘‘school,’’ ‘‘develop,’’ ‘‘classroom,’’ ‘‘effect,’’ ‘‘design,’’ and ‘instruct.’’ Note that while ‘‘technology’’ and ‘‘mathematics’’ were not included in Fig.  5 , all articles included the two terms as we only selected articles that included them in abstracts. The combination of these words allowed us to build an idea of what research topics might have been studied. The words ‘‘student,’’ ‘‘classroom,’’ ‘‘effect,’’ and ‘‘learning’’ might represent a topic that examines the effect of technology use on student mathematics learning (e.g., Bicer & Capraro, 2016 ).

Determining research topics names

Tables ​ Tables2 2 and ​ and3 3 show the information on seven topics derived from the LDA algorithm. Table ​ Table2 2 presents topic names, top 15 words, and a sample representative article of each topic. Table ​ Table3 3 provides word clouds that visualized each topic with the top 50 frequently used words. Topic 1 (T1) was named “using technology to support mathematics learning.” The articles in T1 were concerned with using technology to foster student engagement, interaction, and investigations in mathematics learning (e.g., Cheng-Huan et al., 2017 ). Topic 2 (T2) was labeled “technology in K-12 curriculum.” The articles in T2 examined how technology resources in curriculum materials related to teacher instruction and student learning (e.g., Hu et al., 2020 ). Topic 3 (T3) was labeled as “computers and ICT (information and communication technology) use at school.” Articles in T3 examined mathematics students’ or teachers’ attitudes, perceptions, readiness of using computers and ICT, and factors affecting them (e.g., Birgin et al., 2020 ).

Topic Names, Characteristic Words, and a Sample Representative Article of Each Topic

Topic 4 (T4) was named “technology use at higher education.’’ The representative studies primarily concerned technology use in college and university environments, which utilized online mediation techniques or computer-assisted methods for teaching and learning mathematics (e.g., Radmehr & Goodchild, 2022 ). Topic 5 (T5) was labeled as “teacher instruction and TPACK.” Articles on this topic examined in-service and pre-service mathematics teachers’ instructional practices with technology and their TPACK (e.g., Akapame et al., 2019 ).

Topic 6 (T6) was named “using technology for conceptual understanding.” This topic discussed the use of technology for teaching and learning mathematical content and process, which improve students' conceptual understanding of solving mathematical tasks (e.g., Urban-Woldron, 2015 ). Topic 7 (T7) was labeled “examining the effect of technology on cognitive and affective development.” This topic mainly examined the effect of technology use on students' cognitive and affective development (e.g., Bicer & Capraro, 2016 ).

Research trend analysis

We analyzed the proportion of each topic by a 10-Year Period to understand the research trend (see Table ​ Table4 4 and Fig.  6 ). The greater topic proportion showed that the topic had received more attention from researchers in that period. According to the 2010s data, the difference between the highest (T5 and T6, 14.7%) and the lowest (T3, 13.7%) topic proportion was negligible (1%). However, different patterns were observed when we analyzed the topic proportion between January 1981 and March 2022. For example, the topic proportions of T5 have slightly decreased over time. In the 1980s, T5 took 16.5% of the total publication. However, in the 2010s and 2020–2022 March, T5 took 14.7% and 14.0%, respectively. Moreover, while the topic proportion of T6 has steadily increased over time (9.6% in the 1980s and 15.4% in 2020–2022 March), T2, T3, and T7 showed fluctuation patterns. For example, T7 took 13.3% in the 1980s, followed by 17.7% in the 1990s and 14.0% in the 2010s. The analysis of research trends of each topic by a year also revealed similar patterns (see Table ​ Table5). 5 ). Except for outliers, two topics (T1 and T4), showed a relatively stable change over time. However, other topics revealed decreasing (T5), increasing (T6), or fluctuating (T2, T3, and T7) patterns.

Topic Proportion by a 10-Year Period

Research trends of each topic by a 10-year period

Research Trends of Each Topic by a Year

To understand the research trends more closely, we calculated the Pearson correlation between the topics using the R package psych . Table ​ Table6 6 shows that T1 and T4 (0.36*, stable pattern) and T3 and T7 (0.39*, fluctuating pattern) had positive relationships, showing that they had similar research trends. However, T2 was negatively associated with T1 (-0.37*), T3 (-0.34*), T4 (-0.61***), and T7 (-0.38*), while T1 and T6 (-0.41**), and T5 and T7 (-0.51***) were negatively related, indicating opposite research interests over time.

The Correlation Between Research Topics

* p  < .05. ** p  < .01. *** p  < .001

Overall, the research trends analysis showed different emphases over time (see Fig.  6 ). In the 1980s, T2 and T5 were the most popular topics. However, during the 1990s and 2000s, T7 was the most popular topic while the trendline gradually decreased over time and interest diminished in the 2010s. In addition, T1 and T3 have received increasing attention in the 2000s. Since the 2010s, T2 and T6 have received increasing attention. In particular, the research interest on T6 has grown steadily from the 1980s until March 2022.

The study aimed to analyze research trends of technology use in mathematics education from 1981 to March 2022. The study has the following four research questions: (1) How did overall research trends of technology use in mathematics education evolve? (2) Which words were frequently used in previous studies? (3) What were the latent research topics? (4) What were the research trends for individual topics? To solve the research questions, we retrieved relevant articles from Web of Science, ERIC, and PsycInfo databases and selected 2,433 peer-review English-written articles published between January 1981 and March 2022. Then, we examined their abstracts using topic modeling (Blei, 2012 ).

The findings of the first research question revealed that research interest in technology use in mathematics education has steadily increased. During the 1980s, only 26 articles examined using technology in mathematics education, whereas more than 100 articles have been published yearly since 2007. These increasing research trends aligned with the arguments of NCTM ( 1980 , 2014 ) and the Programme for International Student Assessment (OECD, 2019 ) documents emphasizing the importance of technology use in mathematics education. This could be because researchers have found new opportunities and positive effects of technology use on teacher instruction (Hoyles, 2018 ; Hu et al., 2020 ) and student learning outcomes (Higgins et al., 2019 ). Consequently, other relevant studies, such as mathematics teachers’ perception of ICT (Birgin et al., 2020 ), professional development (Bicer & Capraro, 2016 ), TPACK (Akapame et al., 2019 ), and online teaching and learning (Radmehr & Goodchild, 2022 ), have been conducted.

To delve into the second research question, we identified 53 frequently used words with more than 500 frequencies. The words included ‘‘student,’’ ‘‘teacher,’’ ‘‘learn,’’ ‘‘teach,’’ ‘‘school,’’ ‘‘develop,’’ ‘‘classroom,’’ ‘‘effect,’’ ‘‘design,’’ and ‘‘instruct.’’ The combination of these words (e.g., the effects of teacher instruction with technology on student learning) can represent important research topics on technology use in mathematics education.

As for the third research question, we examined the major research topics and found seven topics: “Using technology to support mathematics learning” (T1), “technology in K-12 curriculum” (T2), “computers and ICT use in schools” (T3), “technology use in higher education” (T4), “teacher instruction and TPACK” (T5), “using technology for conceptual understanding” (T6), and “examining the effect of technology on cognitive and affective development” (T7). However, these topic classifications were not neatly aligned with the previous topic classification of mathematics education research (e.g., Gökçe & Güner, 2021 ; Inglis & Foster, 2018 ). Inglis and Foster ( 2018 ) classified research on mathematics education into the following four domains: mathematical content, mathematical process, teaching and learning environments, and hard cores and heuristics. However, our analysis did not show topics related to hard cores and heuristics examining research theories and methods. Moreover, some topics were linked to more than two domains. For example, T4 included calculus (mathematical content), discussion and communication (mathematical process), and course and online (teaching and learning environments) as top characteristic words (see Tables ​ Tables2 2 and ​ and3). 3 ). This result may stem from the difference in the scope of data used for the study. Our study includes articles examining technology use in mathematics education, while Inglis and Foster ( 2018 ) examined articles in two mathematics education journals only.

The seven topics found in this study were not aligned with previous literature reviews on educational technology (e.g., Chen et al., 2020 ; Ozyurt & Ayaz, 2022 ; Tatnall & Fluck, 2022 ). In a study examining research trends of BJET , Chen et al. ( 2020 ) identified 15 topics relating to a teacher (e.g., teacher education), learning strategies (e.g., problem-based learning, game-based learning, mobile-assisted language learning, socialized e-learning), learning environment (e.g., online social communities), evaluation (assessment and feedback), and other areas (e.g., early childhood education in the digital age and review studies). However, their analysis could not find topics related to conceptual understanding (T6) and K-12 curriculum (T2). Additionally, early childhood education, review studies, and learning strategies with emerging technologies were not identified in this study.

These differences are not unplausible because individual studies have analyzed different datasets according to different research purposes. However, these differences also indicate that research on technology use in mathematics education has distinctive research topics. While there are amalgams between mathematics education and educational technology, researchers have developed their distinctive research areas to enhance mathematics teaching and learning with technology use. Thus, researchers who are interested in technology use in mathematics education need to study mathematics education and educational technology and the integration of technology into mathematics education as a distinctive research area.

To delve into the fourth research question, we examined the number of publications on each topic over a year and a 10-year period. The findings revealed four different patterns, including stable (T1 and T4), decreasing (T5), increasing (T6), and fluctuating (T2, T3, and T7) patterns. The popular topics have changed from T2 and T5 (the 1980s) to T1, T3, and T7 (between the 1990s and the 2000s) to T2 and T6 (between the 2010s and March 2022). Interestingly, T6, the least studied topic in the 1980s, has received steadily increasing attention over four decades. Additionally, T2 has received the most research interest in the early (1980s) and later periods (since 2010).

These results are plausible. Since 1980, researchers have paid much more attention to enhancing student conceptual understanding by developing the reform-based curriculum and improving teacher instructional skills and knowledge (Bray & Tangney, 2017 ; Inglis & Foster, 2018 ). In this process, technological resources presented in mathematics curriculum (T2) and teachers’ technology use in mathematics classrooms and their TPACK (T5), which could facilitate or hinder the development of students’ conceptual understanding, were extensively analyzed. According to Remillard ( 2005 ), the curriculum included formal curriculum (e.g., printed documents) and teachers’ intended (e.g., teaching goals) and enacted curriculum (i.e., actually teaching in the classroom). Furthermore, mathematics teachers’ instruction and pedagogical content knowledge were related to teachers’ knowledge of curriculum (Ball et al., 2008 ). In sum, the similar research trends of T2 and T5 between the 1980s and 1990s were reasonable.

However, T2 and T5 have shown different research trends since the 2000s. T2 has revealed increasing research attention (13.3% in the 2000s, 14.3% 2010s, and 15.6% in 2020 – March 2022), whereas the research interest in T5 showed minimal change (14.6% in the 2000s and 14.7% 2010s) or slightly decreased (14.7% in 2010s and 14.0% in 2020–2022 March). Consequently, T2 and T5 showed a fluctuating and decreasing pattern. The revival of research attention on T2 might be affected by the publishment of curriculum documents. The curriculum documents emphasizing technology use in mathematics education have been steadily published. For example, NCTM published curriculum documents and standards emphasizing technology integration in mathematics education (AMTE, 2022 ; NCTM, 1980 , 2014 ). Similarly, Common Core State Standards for Mathematics highlighted technology's roles in mathematics education (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010 ). However, these documents were published by US mathematics educators. Therefore, further studies are needed to understand the research trends of T2 and T5.

The limited research attention on T6 before the 2000s implied that while researchers had focused on enhancing student conceptual understanding using technology, they were more concerned about examining technology integration into curriculum and teacher instruction than the direct relationship between technology use and students’ conceptual understanding. However, since the 2000s, researchers have paid more attention to the direct relationship between them, which indicated a steady increase in T6 over time (9.6% in the 1980s, 12.3% in the 2000s, and 15.4% in 2020–2022 March).

The popularity of T1, T3, and T7 between the 1990s and 2000s showed that researchers were interested in examining the effect of technology at school on student mathematics achievement, motivation, and overall learning experiences. These research trends were aligned with research trends in mathematics education and educational technology. In the early stage, mathematics researchers focused on examining student mathematics achievement using quasi-experimental methods (Bray & Tangney, 2017 ; Stinson & Bullock, 2012 ). They aimed to understand individual student learning processes and generalize teacher instructions (Gökçe & Güner, 2021 ; Inglis & Foster, 2018 ). Similarly, researchers examining educational technology have focused on evaluation and assessment at the early stage of research (Chen et al., 2020 ; Tatnall & Fluck, 2022 ).

However, there were some lags in research trends on the use of technology in mathematics education. Since 1990, as the sociocultural theory has grown in popularity, mathematics educators have placed more emphasis on student collaboration, teacher-student interactions, classroom environments, and student backgrounds than on evaluating student mathematics achievement (Inglis & Foster, 2018 ). As Table ​ Table4 4 shows, T7 was one of the most popular topics before the 2010s.

Since 2000, researchers studying educational technologies have become more concerned with new learning strategies with emerging technologies that could enhance student collaboration and autonomy, such as e-learning, mobile and blended learning, and social network-based learning (Ozyurt & Ayaz, 2022 ; Tatnall & Fluck, 2022 ). These topics, however, were not identified in our study. This implies that the research on technology use in mathematics education is relatively slow in adopting new theories and technologies than research on mathematics education and educational technology.

This study has four limitations. First, we retrieved the articles from three research databases ( Web of Science, ERIC, and PsycInfo ). Also, we included English-written articles published in peer-reviewed journals and excluded dissertations, theses, and non-English written articles. If we had included the excluded articles, our findings might be different. Second, we searched articles containing “mathematics or math” and “technology or technologies” in the abstract. Thus, articles that did not contain those words in abstracts were excluded from this study. For example, a study examining the calculator use for algebra learning might not be included in our data due to our search criteria. Readers should be cautious when interpreting our findings. Third, we only examined the articles’ abstracts. While examining abstracts to understand research trends is a common method (e.g., Chen et al., 2020 ), other important information presented in the different sections, such as findings and conclusions, was excluded during the data analysis process.

Fourth, labeling the topic names was a relatively subjective process. The LDA method is an entirely automatic, unsupervised algorithm (Blei, 2012 ). However, the topic names should be determined by researchers based on the information of the data, such as the most frequently occurring words and the articles with a high proportion on the topic. While this information enabled us to validate the topic names, other researchers might use different names even when analyzing the same data. Given the limitations of the present study, future studies may employ other research databases, including dissertations, theses, and non-English papers, and examine full texts of articles to verify the findings of this study.

Implications and conclusion

The development of technology has changed mathematics teaching and learning environments. Considering the expansion of technology use in mathematics education, this study synthesized previous studies published between January 1981 and March 2022 and examined research trends in the field using topic modeling.

We proposed three implications based on the research findings. First, it would be valuable to examine teaching and learning strategies with emerging technology in mathematics education. This study did not identify topics pertaining to utilizing new technology (e.g., AR, VR, and mobile, game-based, blended, and flipped learning). However, several researchers have emphasized the importance of using new technology in education (Kimmons, 2020 ; Tatnall & Fluck, 2022 ), where teachers serve as facilitators and students take the lead in their mathematical learning as investigators. Therefore, further studies on mathematics teachers' and students' use of emerging technology are needed. We can, for instance, examine mathematics teachers’ instructional strategies in the virtual environment (e.g., Hu et al., 2020 ) and AI-based mathematics learning systems (Hwang & Tu, 2021 ).

Second, it is suggested that researchers consider examining further studies based on sociocultural theory. This study identified topics focusing on individual student mathematics learning, such as examining cognitive and affective development (T7) and conceptual understanding (T6). While these topics are critical issues, it would be productive to examine how technology use affects social interaction in actual and virtual mathematics classrooms (e.g., student collaboration, classroom discourse and norms, and teacher-student interactions). Moreover, it would be innovative to analyze the effect of technology use on the construction of student mathematical identity. Researchers (Hand & Gresalfi, 2015 ; Yackel & Cobb, 1996 ) have documented that classroom activities, resources, and culture affect both student cognitive and affective development and their mathematical identity (i.e., how a student acts, engage, position, and interact in mathematics learning). Given that student mathematical identity affects their educational aspirations and future careers (Black et al., 2010 ), it is valuable to analyze how technology use in mathematics classrooms affects student mathematical identity. Therefore, further studies may examine such issues.

Third, it is important to investigate the relationship between technology use and equity and access in mathematics education. The United Nations (United Nations General Assembly, 2015 ) suggested quality education as one of the agendas for sustainable development of our society and emphasized the importance of accessing quality education, regardless of student background (e.g., race, gender, and socioeconomic status). Technology can help achieve these goals because all students could be provided opportunities to investigate mathematics problems, present ideas, learn needed instructions, and communicate with peers in technological learning environments (AMTE, 2022 ; Clements et al., 2013 ; Higgins et al., 2019 ; NCTM, 2014 ). For example, Crawford ( 2013 ) validated that a supplementary online mathematics curriculum improved the mathematics achievement of English language learners considerably. Crawford ( 2013 ) explained that because students could learn mathematics at their own pace with a web-based curriculum, they could accurately understand mathematical concepts and practice mathematical skills, which enhanced access and equity in mathematics education. Even though this study did not find equity-related topics, the relationship between access, equity, and technology use in mathematics education should be more thoroughly studied to achieve sustainable development.

This study has theoretical and practical significance. Theoretically, this study made a scientific contribution in two ways. First, it provided researchers with overall research trends of technology use in mathematics education. Second, it identified topics that did not precisely align with those identified in previous studies on mathematics education or educational technology (e.g., Chen et al., 2020 ; Inglis & Foster, 2018 ). Practically, the study findings have guided further studies and practices to increase the effects of technology use in mathematics teaching and learning.

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181 Mathematics Research Topics From PhD Experts

If you are reading this blog post, it means you are looking for some exceptional math research topics. You want them to be original, unique even. If you manage to find topics like this, you can be sure your professor will give you a top grade (if you write a decent paper, that is). The good news is that you have arrived at just the right place – at the right time. We have just finished updating our list of topics, so you will find plenty of original ideas right on this page. All our topics are 100 percent free to use as you see fit. You can reword them and you don’t need to give us any credit.

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Our Newest Research Topics in Math

We know you probably want the best and most recent research topics in math. You want your paper to stand out from all the rest. After all, this is the best way to get some bonus points from your professor. On top of this, finding some great topics for your next paper makes it easier for you to write the essay. As long as you know at least something about the topic, you’ll find that writing a great paper or buy phd thesis isn’t as difficult as you previously thought.

So, without further ado, here are the 181 brand new topics for your next math research paper:

Cool Math Topics to Research

Are you looking for some cool math topics to research? We have a list of original topics for your right here. Pick the one you like and start writing now:

• Roll two dice and calculate a probability
• Discuss ancient Greek mathematics
• Is math really important in school?
• Discuss the binomial theorem
• The math behind encryption
• Game theory and its real-life applications
• Analyze the Bernoulli scheme
• What are holomorphic functions and how do they work?
• Describe big numbers
• Solving the Tower of Hanoi problem

Undergraduate Math Research Topics

If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics:

• Methods to count discrete objects
• The origins of Greek symbols in mathematics
• Methods to solve simultaneous equations
• Real-world applications of the theorem of Pythagoras
• Discuss the limits of diffusion
• Use math to analyze the abortion data in the UK over the last 100 years
• Discuss the Knot theory
• Analyze predictive models (take meteorology as an example)
• In-depth analysis of the Monte Carlo methods for inverse problems
• Squares vs. rectangles (compare and contrast)

Number Theory Topics to Research

Interested in writing about number theory? It is not an easy subject to discuss, we know. However, we are sure you will appreciate these number theory topics:

• Discuss the greatest common divisor
• Explain the extended Euclidean algorithm
• What are RSA numbers?
• Discuss Bézout’s lemma
• In-depth analysis of the square-free polynomial
• Discuss the Stern-Brocot tree
• Analyze Fermat’s little theorem
• What is a discrete logarithm?
• Gauss’s lemma in number theory
• Analyze the Pentagonal number theorem

Math Research Topics for High School

High school students shouldn’t be too worried about their math papers because we have some unique, and quite interesting, math research topics for high school right here:

• Discuss Brun’s constant
• An in-depth look at the Brahmagupta–Fibonacci identity
• What is derivative algebra?
• Describe the Symmetric Boolean function
• Discuss orders of approximation in limits
• Solving Regiomontanus’ angle maximization problem
• What is a Quadratic integral?
• Define and describe complementary angles
• Analyze the incircle and excircles of a triangle
• Analyze the Bolyai–Gerwien theorem in geometry
• Math in our everyday life

Complex Math Topics

If you want to give some complex math topics a try, we have the best examples below. Remember, these topics should only be attempted by students who are proficient in mathematics:

• Mathematics and its appliance in Artificial Intelligence
• Try to solve an unsolved problem in math
• Discuss Kolmogorov’s zero-one law
• What is a discrete random variable?
• Analyze the Hewitt–Savage zero-one law
• What is a transferable belief model?
• Discuss 3 major mathematical theorems
• Describe and analyze the Dempster-Shafer theory
• An in-depth analysis of a continuous stochastic process
• Identify and analyze Gauss-Markov processes

Easy Math Research Paper Topics

Perhaps you don’t want to spend too much time working on your next research paper. Who can blame you? Check out these easy math research paper topics:

• Define the hyperbola
• Do we need to use a calculator during math class?
• The binomial theorem and its real-world applications
• What is a parabola in geometry?
• How do you calculate the slope of a curve?
• Define the Jacobian matrix
• Solving matrix problems effectively
• Why do we need differential equations?
• Should math be mandatory in all schools?
• What is a Hessian matrix?

Logic Topics to Research

We have some interesting logical topics for research papers. These are perfect for students interested in writing about math logic. Pick one right now:

• Discuss the reductio ad absurdum approach
• Discuss Boolean algebra
• What is consistency proof?
• Analyze Trakhtenbrot’s theorem (the finite model theory)
• Discuss the Gödel completeness theorem
• An in-depth analysis of Morley’s categoricity theorem
• How does the Back-and-forth method work?
• Discuss the Ehrenfeucht–Fraïssé game technique
• Discuss Aleph numbers (Aleph-null and Aleph-one)
• Solving the Suslin problem

Algebra Topics for a Research Paper

Would you like to write about an algebra topic? No problem, our seasoned writers have compiled a list of the best algebra topics for a research paper:

• Discuss the differential equation
• Analyze the Jacobson density theorem
• The 4 properties of a binary operation in algebra
• Analyze the unary operator in depth
• Analyze the Abel–Ruffini theorem
• Epimorphisms vs. monomorphisms: compare and contrast
• Discuss the Morita duality in algebraic structures
• Idempotent vs. nilpotent in Ring theory
• Discuss the Artin-Wedderburn theorem
• What is a commutative ring in algebra?
• Analyze and describe the Noetherian ring

Math Education Research Topics

There is nothing wrong with writing about math education, especially if your professor did not give you writing prompts. Here are some very nice math education research topics:

• What are the goals a mathematics professor should have?
• What is math anxiety in the classroom?
• Teaching math in UK schools: the difficulties
• Computer programming or math in high school?
• Is math education in Europe at a high enough level?
• Common Core Standards and their effects on math education
• Culture and math education in Africa
• What is dyscalculia and how does it manifest itself?
• When was algebra first thought in schools?
• Math education in the United States versus the United Kingdom

Computability Theory Topics to Research

Writing about computability theory can be a very interesting adventure. Give it a try! Here are some of our most interesting computability theory topics to research:

• What is a multiplication table?
• Analyze the Scholz conjecture
• Explain exponentiating by squaring
• Analyze the Myhill-Nerode theorem
• What is a tree automaton?
• Compare and contrast the Pushdown automaton and the Büchi automaton
• Discuss the Markov algorithm
• What is a Turing machine?
• Analyze the post correspondence problem
• Discuss the linear speedup theorem
• Discuss the Boolean satisfiability problem

Interesting Math Research Topics

We know you want topics that are interesting and relatively easy to write about. This is why we have a separate list of our most interesting math research topics:

• What is two-element Boolean algebra?
• The life of Gauss
• The life of Isaac Newton
• What is an orthodiagonal quadrilateral?
• Tessellation in Euclidean plane geometry
• Describe a hyperboloid in 3D geometry
• What is a sphericon?
• Discuss the peculiarities of Borel’s paradox
• Analyze the De Finetti theorem in statistics
• What are Martingales?
• The basics of stochastic calculus

Applied Math Research Topics

Interested in writing about applied mathematics? Our team managed to create a list of awesome applied math research topics from scratch for you:

• Discuss Newton’s laws of motion
• Analyze the perpendicular axes rule
• How is a Galilean transformation done?
• The conservation of energy and its applications
• Discuss Liouville’s theorem in Hamiltonian mechanics
• Analyze the quantum field theory
• Discuss the main components of the Lorentz symmetry
• An in-depth look at the uncertainty principle

Geometry Topics for a Research Paper

Geometry can be a very captivating subject, especially when you know plenty about it. Check out our list of geometry topics for a research paper and pick the best one today:

• Most useful trigonometry functions in math
• The life of Archimedes and his achievements
• Trigonometry in computer graphics
• Using Vincenty’s formulae in geodesy
• Define and describe the Heronian tetrahedron
• The math behind the parabolic microphone
• Discuss the Japanese theorem for concyclic polygons
• Analyze Euler’s theorem in geometry

Math Research Topics for Middle School

Yes, even middle school children can write about mathematics. We have some original math research topics for middle school right here:

• Finding critical points in a graph
• The basics of calculus
• What makes a graph ultrahomogeneous?
• How do you calculate the area of different shapes?
• What contributions did Euclid have to the field of mathematics?
• What is Diophantine geometry?
• What makes a graph regular?
• Analyze a full binary tree

Math Research Topics for College Students

As you’ve probably already figured out, college students should pick topics that are a bit more complex. We have some of the best math research topics for college students right here:

• What are extremal problems and how do you solve them?
• Discuss an unsolvable math problem
• How can supercomputers solve complex mathematical problems?
• An in-depth analysis of fractals
• Discuss the Boruvka’s algorithm (related to the minimum spanning tree)
• Discuss the Lorentz–FitzGerald contraction hypothesis in relativity
• An in-depth look at Einstein’s field equation
• The math behind computer vision and object recognition

Calculus Topics for a Research Paper

Let’s face it: calculus is not a very difficult field. So, why don’t you pick one of our excellent calculus topics for a research paper and start writing your essay right away:

• When do we need to apply the L’Hôpital rule?
• Discuss the Leibniz integral rule
• Calculus in ancient Egypt
• Discuss and analyze linear approximations
• The applications of calculus in real life
• The many uses of Stokes’ theorem
• Discuss the Borel regular measure
• An in-depth analysis of Lebesgue’s monotone convergence theorem

Simple Math Research Paper Topics for High School

This is the place where you can find some pretty simple topics if you are a high school student. Check out our simple math research paper topics for high school:

• The life and work of the famous Pierre de Fermat
• What are limits and why are they useful in calculus?
• Explain the concept of congruency
• The life and work of the famous Jakob Bernoulli
• Analyze the rhombicosidodecahedron and its applications
• Calculus and the Egyptian pyramids
• The life and work of the famous Jean d’Alembert
• Discuss the hyperplane arrangement in combinatorial computational geometry
• The smallest enclosing sphere method in combinatorics

Business Math Topics

If you want to surprise your professor, why don’t you write about business math? We have some exceptional topics that nobody has thought about right here:

• Is paying a loan with another loan a good approach?
• Discuss the major causes of a stock market crash
• Best debt amortization methods in the US
• How do bank loans work in the UK?
• Calculating interest rates the easy way
• Discuss the pros and cons of annuities
• Basic business math skills everyone should possess
• Business math in United States schools
• Analyze the discount factor

Probability and Statistics Topics for Research

Probability and statistics are not easy fields. However, you can impress your professor with one of our unique probability and statistics topics for research:

• What is the autoregressive conditional duration?
• Applying the ANOVA method to ranks
• Discuss the practical applications of the Bates distribution
• Explain the principle of maximum entropy
• Discuss Skorokhod’s representation theorem in random variables
• What is the Factorial moment in the Theory of Probability?
• Compare and contrast Cochran’s C test and his Q test
• Analyze the De Moivre-Laplace theorem
• What is a negative probability?

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