Research Paper Topics In Mathematics Education
What are your “top ten”? Sue VanHattum, a full time faculty member at Contra Costa College inspired me with her wonderful top ten list .
Below are my top ten Issues in Mathematics Education. While this is my opinion, I do highly encourage you to check our Ms. VanHattum’s post as well as her blog Math Mamma writes…
10) Math IS, by its very nature, FUN! A coworker of mine told me “I am never bored”. He did not mean to say that he was constantly entertained. The copout statement “Math is boring” or the equally ridiculous “Let’s MAKE math fun!” betray a general trend in society to dismiss what we don’t understand as simply being unappealing. I was tempted to write about this earlier this year when the NY Times article “Who Says Math Has to be Boring?” and response piece in Slate “Math Has to Be at Least a Little Boring“came out, but I didn’t want to bore my readership.
9) Discovering and uncovering content should take precedence over covering and recovering content. A quote from RL Moore “He who is taught the least learns the most.” Or from Paul Halmos “The best way to learn is do; the worst way to teach is talk.” Also see a great recent post from Grant Wiggins concerning when/if lecturing is an effective a teaching technique.
If you know you want to shut up more, but you have trouble (like me) not filling the dead space with your own voice sometimes, try Bob Kaplan’s advice for becoming invisible . Read about how to help students become “productively stuck” at Math For Love. Or for more information on Inquiry Based Learning, check the IBL blog. Lastly, I’ll share what I told an administrator who told me to “cover” more material while I was teaching High School. I pointed to my desk (which was COVERED in student work) and I told him that the textbook was under there already!
8) Underrepresented groups in mathematics will remain underrepresented (especially in academia) unless measures are taken to recruit and retain them. I am familiar with programs like EDGE, SK Days, Women in Number Theory, MSRI Connections for Women, etc, exist, but many women don’t know about them or aren’t actively encouraged by their departments to get involved in the mathematical community. We can bring new perspectives into our field by providing role models for those who are traditionally underrepresented in our field, making the academic workplace more family friendly, and by breaking down stereotypes. See Adriana Salerno’s recent post in PhD+Epsilon on the subtle ways in which women can be discriminated against.
7) Mathematics Educators deserve respect and more autonomy. Without the freedom to teach as they see fit, educators cannot be experimental and take risks in their approaches. Departments and school systems should reward creative teaching styles by having regular teaching observations of junior faculty by qualified individuals who can supply meaningful feedback. These observations should be formal, made regularly by a small group of individuals, and play a greater role in advancement than test scores and/or student reviews. As a postdoc, I would have loved more observations of my classroom. If some courses need to have uniformity in curriculum, the instructors should be given a concise outline (such as the Common Core) of ideas to be studied.
6) Mathematics Educators deserve opportunities to further their own content knowledge for teaching. Opportunities for ongoing professional development that truly connects research in education to implementation in the classroom are scant. Both university and K12 teachers tend to model their teaching after what they experienced as students regardless of whether it was truly effective. Having reading groups on math ed papers is an activity done at some universities like the University of Arizona.
5) Mathematics (not the instructor) IS the Authority – this one is stolen directly from Ms. VanHattum’s list. Part of the beauty of mathematics is that `proof by intimidation’ is not a valid method of proof.
4) All students can be trusted to learn mathematics, there is no Math Gene, and math courses should NOT be mandatory. This does not mean that teachers should stop trying to inspire and excite students, but it does bear repeating that everyone can do math. Many teachers unknowingly perpetuate the Math Gene myth by saying things like “Well, you COULD subtract ‘x’ from both sides… but that wouldn’t be very smart now would it?”. Along this line of reasoning, we should trust students to take relevant courses. They are grownups and eventually they will figure out (perhaps with some advice) what skills they need to succeed in their area of interest. I’m sure many people will disagree with this last point.
3) Students don’t realize that Math is fiddling around, turning your drawing upside down, looking at it through the paper, being befuddled, being sure that you are a genius….being sure that you are a moron, waking up and realizing that you didn’t actually prove the Beal Conjecture in your sleep, waking up and realizing that that lemma you thought was wrong in your thesis is actually right! In other words, mathematics is joyful and unexpected. See Math With Bad Drawings and Math Ed Matters “Be Predictably Unpredicatble”. Share your own mathematical learning experiences with students.
2) Students don’t know thatMath comes in many flavors. It’s hard to stay abreast of all the developments in your own field, much less others, but being curious is leading by example. If you go to a colloquium that isn’t in your area it may pay off. I’m often surprised at the number of ways there are to look at one problem like linear regression: as a machine learning problem where the data is a training set, as a geometric problem to be solved using singular value decomposition, as a parameter estimation problem involving Fisher’s matrix, as a classical minimization problem. Help students explore one toy problem from many perspectives.
1) Teachers should ask deep questions about basic ideas and be ready for questions or answers that might be better or different from what was anticipated. Sometimes when I go where students take me, it doesn’t align with my initial ideas. This is both vexing and exciting! It requires careful thought about definitions, purpose, and motivation behind concepts, not just examples and theorems. Anyway, in the blog Math for Love, Dan Finkel talks about the rewards in pursuing a studentproposed problem:“A dollar that cost a dollar”. I imagine that the ultimate goal in being an adviser is to have a PhD student who was “depending on you” become one who just totally blows you away with his/her conjectures and proofs. Of course, this has the potential for being simultaneously invigorating (“Yay! I’m an awesome mentor”) and depressing (“Was I ever that creative?”). So I put this at number one because I think that it is the item on this list that is potentially the most challenging and underappreciated.
Wow! Writing a top ten list is hard.
This entry was posted in Issues in Higher Education, K12 Mathematics, Math Education, people in math, women in math. Bookmark the permalink.

 ACDCA 5th Summer Academy Proceedings
ADD. KEYWORDS: Conference Proceedings, Computer Algebra, Using TI92 in a "Traditional" Calculus and Differential Equations Course, Exponential Growth, Black Boxes and Teaching Mathematics, Analytical Mechanics Problems with DERIVE, etc.
SOURCE: Austrian Center for Didactics of Computer Algebra
TECHNOLOGY: Adobe's Acrobat Reader  Advanced Mathematical Thinking
Psychology of AMT, AMT Literature, Papers & Reports, Email Discussion Group  AMTE 2000 Conference Proceedings
ADD. KEYWORDS: Conference Proceedings, Tutoring Field Experience, (Inter)Active Geometry, Formative and Summative Portfolio Assessment, Individualized Instruction, Number/Algebra Course for Preservice Middle Grades Teachers of Mathematics, Mathematics Discourse, Electronic Discussion Forum, Problem Solving
SOURCE: Association of Mathematics Teacher Educators
TECHNOLOGY: Adobe's Acrobat Reader  ARUME Math Ed Paper Database
ADD. KEYWORDS: Searchable database
SOURCE: ARUME, Better File Cabinet, Eric Hsu, Joan Garfield  Asian Technology Conference in Mathematics
Conference Proceedings, Distance learning, Multimedia, Numerical integration and differentiation, Computer algebra, Theorem proving, Applications of Computer Algebra Systems (CAS), Graphing calculators  Australian Catholic University, Mathematics Teaching and Learning Centre Research Reports
ADD. KEYWORDS: Problem Solving, Mathematical Writing, Problembased mathematics curriculum, Performance assessment  Austrian Center for Didactics of Computer Algebra
ADD. KEYWORDS: Projects, Conferences / Events, Proceedings, Paper
TECHNOLOGY: Adobe's Acrobat Reader  Canadian Mathematics Education Study Group
Society, Meetings  CASCAT Project  Computer Algebra Systems in Schools  Curriculum, Assessment and Teaching Project
 CASE  Computer Algebra Systems in Education Newsletter
 CBMS Mathematical Education of Teachers Project
 Classroom Compass
Online Magazine for Teachers  COMET  California Online Mathematics Education Times
ADD. KEYWORDS: Online newsletter
SOURCE: California Curriculum Correlating Council  Comparative Technology: TI85 with MAPLE  A work book approach
Elementary calculations, Floating point versus exact arithmetic, Elementary number theory, Roots of polynomials, Graphing, Sojourn into Calculus, Matrix manipulation, Drawing in LOGO, Programming in LOGO, Recursion in LOGO  Computer Algebra Systems in Calculus Reform
ADD. KEYWORDS: Article  Computers in Teaching Initiative (CTI)
ADD. KEYWORDS: Pedagogy, Software  Connected Mathematics
Modelling, Complexity, Software, StarlogoT, Probability, Papers  DeLibertions  Mathematics Section
ADD. KEYWORDS: Pedagogy  Developing a Digital National Library for Undergraduate Science, Mathematics, Engineering, and Technology Education
ADD. KEYWORDS: Report of a Workshop  Developing Multimedia Case Studies for Preservice Teacher Education
SOURCE: Janet Bowers, San Diego State University
TECHNOLOGY: Adobe PDF reader  Discovery Learning Project
 DOCUMENTA MATHEMATICA  Extra Volume ICM 1998  Section: 18. Teaching and Popularization of Mathematics
Articles
DOCUMENTA MATHEMATICA, Proceedings of the International Congress of Mathematicians
Postscript and DVI readers  Dynamic Geometry
ADD. KEYWORDS: NSF Project, Interview Data, Project Papers  EASI  Equal Access to Software and Information  Science and Math
ADD. KEYWORDS: Online workshop, Teaching Math To Visually Impaired Students, Spoken and Braille Access to Math, Tactile Graphics, Learning Disabilities, HardofHearing  Educational Studies in Mathematics
ADD. KEYWORDS: Printed Journal  ERIC  Mathematics Education Resources
ADD. KEYWORDS: Articles, Standards, Assessment, Reform, Homogeneous Groupings, Multicultural Mathematics  Essays on Education
 European Research in Mathematics Education
ADD. KEYWORDS: Conference Proceedings, Nature of Mathematics, New Technologies, Teaching Practices, Social Interactions, Cognition, School Algebra, Methodologies, Teacher Education
SOURCE: European Society for Research in Mathematics Education
TECHNOLOGY: Adobe Acrobat reader  EXTEND  Perspectives on Mathematics Education
ADD. KEYWORDS: Reports, Position Papers, Reader Commentary  FACHBIBLIOTHEK DIDAKTIK DER MATHEMATIK  Zeitschriften
ADD. KEYWORDS: List of periodicals  For the Learning of Mathematics
ADD. KEYWORDS: Published journal
SOURCE: Faculty of Education, Queen's University  Gateways to Advanced Mathematical Thinking
ADD. KEYWORDS: Empirical Research, Curriculum Development, Theoretical Research, Project Papers  Graphing Misinterpretations and MicrocomputerBased Laboratory Instruction, with Emphasis on Kinematics
ADD. KEYWORDS: Article  Great Expectations
ADD. KEYWORDS: Task Force Report to address what students need to make the transition from high school to college mathematics.  The Handbook of Mathematical Discourse
ADD. KEYWORDS: Mathematical Language, Usage of words, Behaviors and Attitudes  High School Mathematics at Work: Essays and Examples for the Education of all Students
 History and Pedagogy of Mathematics Newsletter
 The IASE Statistical Education Research Group
ADD. KEYWORDS: Newsletters  ICMI  International Commission on Mathematical Instruction
ADD. KEYWORDS: International Congress on Mathematical Education, ICMI Studies, Meetings  INPUT  Innovative Programs using Technology
ADD. KEYWORDS: Developmental Math, Quantitative Literacy, Precalculus, Business Math, Introductory Statistics, Competition, Technological and Innovative Reform in Mathematics Service Courses  InterAmerican Committee on Mathematics Education
ADD. KEYWORDS: History, Conferences  InterMath
ADD. KEYWORDS: Professional Development, Lesson Plans, Algebra, Geometry, Data Analysis, Number Concepts
SOURCE: James W. Wilson, University of Georgia  International Journal for Mathematics Teaching and Learning
ADD. KEYWORDS: Electronic Journal
SOURCE: Centre for Innovation in Mathematics Teaching at Exeter University, UK and the Mathematics Department at Bessenyei College, Nyiregyháza, Hungary
TECHNOLOGY: Adobe Acrobat reader  The International Journal of Computer Algebra in Mathematics Education
ADD. KEYWORDS: Published Journal  International Journal of Computers for Mathematical Learning
ADD. KEYWORDS: Published Journal  International Journal of Computers for Mathematical Learning
ADD. KEYWORDS: Published Journal  International Study Group for research on learning Probability and Statistics
ADD. KEYWORDS: Newsletter  Investigations in Teaching Geometry
ADD. KEYWORDS: CDROM, Iintegrated media case
SOURCE: Elizabeth Goldman, Vanderbilt University et al.  Issues in the Undergraduate Mathematics Preparation of School Teachers
ADD. KEYWORDS: Journal, Discussion Group, Technology  Italian Research in Mathematics Education 1988  1995
ADD. KEYWORDS: Essays, Teaching and Learning of Aritmetics, Algebra, Geometry, Logic, and Calculus, Technology and Mathematics, Mathematical Problem Solving, Models of Teaching and Learning Processes in Mathematics  Journal of Computers in Mathematics and Science Teaching
Journal  The Journal of Mathematics and Science: Collaborative Explorations
Journal, Preparation of Prospective Teachers of Mathematics and Science in Grades K8  Learning and Mathematics: Research in Math Education
Bibliographies, Newsgroups  LDOnline  Math Skills
Learning disabilities, Articles, Dyscalculia  Legacy of R. L. Moore
Discovery Learning  Let's Abolish PencilandPaper Arithmetic
Article, Back to basics, Mental Arithmetic  Long Island Consortium for Interconnected Learning in Quantitative Disciplines
OnLine Projects, News & Reports, Discussion Groups, Educational Technology, Calculus Reform, Precalculus Reform, Underrepresented Groups, Teacher Training  Maryland Collaborative for Teacher Preparation
PreService Program to Prepare Special Teachers for Elementary and Middle School Science and Mathematics, Research, Papers, Essays on constructivism and education, Technology  MATC  Mathematics and Its Applications Throughout the Curriculum
 Math Page
Math Learning Differences, Dyscalculia, Mathrelated Learning Disabilities  Mathematica Based Math Teaching
Mathematica, Quadratic Equations, Application in Sports  Mathematicians and Education Reform (MER) Forum
 Mathematics Anxiety
ADD. KEYWORDS: Mathematics Anxiety Rating Scale (MARS)
SOURCE: Ronald D. Ferguson, San Antonio College  Mathematics Education Bibliography
 Mathematics Education  International Directory
People, Centers, Journals, Projects, Newsgroups, Societies, Meetings  The Mathematics Initiative  Education Development Center
Research, curriculum, and professional development in mathematics and mathematics education  The Mathematics Teacher Education Resource Place
Forum, Syllabi, Articles, Print and Video Resources, Technology Resources  MATHS  Mathematical Access for TecHnology and Science for Visually Disabled People
blindness, visual disability, visual impairment, speech, nonspeech sounds, braille, SGML  MathSkills Discipline Network
Articles, Meetings, People, Newsgroup, Teaching Inovations  MAVIS  Mathematics Accessible to Visually Impaired Students
Students with Disabilities  MEME  Meaning Enguiry in Mathematics Education
Glossary, Frames, Ideography, Protases, People  The Mathematical Miseducation Of America's Youth
Article, Reform  Multiplayer Activities that Develop Mathematical Coordination
Article, Computer supported collaborative learning, Mathematics education, Mathematical Coordination, Multiple mice, Color matching, Curve fitting, Chord matching, Cooperative learning  National Center for Education Statistics (NCES)  Mathematics
Publications, K12, Assessment, Achievement, Mathematics Report Card  Newsletter of the International Study Group for Research on Learning Probability and Statistics
 North American Chapter of the International Group for the Psychology of Mathematics Education  Working Group on Representations and Mathematics Visualization
ADD. KEYWORDS: Articles, Working Group on Representations and Mathematics Visualization PMENA XX (North Carolina, 1998); The Use of Technology as a Means to Explore Mathematics; Rethinking Representations; On Visualization and Generalization in Mathematics; Some Remarks on Conventions and Representations; Representation, Interpretation, and Signification: A Peircean Perspective; Figures' Representational Function in Geometry and Figure's Multiple and Parallel Entries; Computer Mediated Learning: An Example of an Approach; Geometric Representations in the Transition from Arithmetic to Algebra; Students’ Approaches to the Use of Technology in Mathematical Problem Solving; Construction of Mathematical Concepts and Internal Cognitive Frames; Computerbased Tools for Data Analysis: Support for Statical Understanding; Graduate Students’ Visualization in Twu Rate of Change Problems; Using Concept Representations for the Construction of Frameworks for Research, Curriculum Design, Instruction, and Student Refection; Implications of Shift from Isolated, Expensive Technology to Connected, Inexpensive, Diverse and Ubiquitous Tecnologies; Coordinating Representations through Programing Activities: An Example Using Logo
SOURCE: Center for Research and Advanced Studies (Cinvestav), Mexico
TECHNOLOGY: Adobe Acrobat reader  Notices of the American Mathematical Society  Math Education Items
Bibliography  On the Teaching and Learning of Mathematics at University Level
 Online Exercises
ADD. KEYWORDS: Exercises, Tutorials, Interactive Pages  Overcoming Math Anxiety
ADD. KEYWORDS: Meta Learning, Learning Styles, Multiple Intelligences, Memory, Brain Growth and Enrichment, Brain Gym, Multimedia, Brain Research
SOURCE: Mathematics Department, Diablo Valley College  Parrot Math
ADD. KEYWORDS: Article, Reform  Philosophy of Mathematics Education Journal
ADD. KEYWORDS: Electronic Journal  Preparing the Ground and Planting the Seeds: Initial Knowledge States and Early Concept Development in Introductory Calculus Students
ADD. KEYWORDS: Article  Preuve Proof Prueba
ADD. KEYWORDS: Newsletter, Bibliography, Pedagogy  Primus  Problems, Resource, and Issues in Undergraduate Mathematics Studies
ADD. KEYWORDS: Journal, Pedagogy, Teaching of Undergraduate Mathematics  Problem Solving In Mathematics
SOURCE: Chuck Peterson, Pine Eagle High School  A Project to Transform 612 Mathematics Education: VerticallyIntegrated, InquiryBased Geometry
ADD. KEYWORDS: NSF Teacher Enhancement project, Teaching Scenarios
SOURCE: Richard Allen, et al., St. Olaf College  PROMPT  Professors Rethinking Options in Mathematics for Prospective Teachers
ADD. KEYWORDS: Newsletters, Courses, Class room activities
SOURCE: Humboldt State University Mathematics Department  Psychology of Mathematics Education
ADD. KEYWORDS: Society, Newsletter, Meetings  Reconceptualizing Mathematics: Courseware for Elementary and Middle Grade Teachers
SOURCE: Center for Research in Mathematics & Science Education, San Diego State University  Reform in Mathematics
ADD. KEYWORDS: Articles
SOURCE: Eisenhower National Clearinghouse  Reform in Mathematics and Science
ADD. KEYWORDS: Articles
SOURCE: Eisenhower National Clearinghouse  Research in Undergraduate Mathematics Education  RUME  ARUME
ADD. KEYWORDS: Special Interest Group of the MAA, Organizations, Online Research Resources,
Columns and Newsletters, Individuals, Specific Articles
SOURCE: Mathematical Association of America  Research on Logo: Effects and Efficacy by Douglas H. Clements and Julie S. Meredith
 Resources for Teachers of Developmental Mathematics
Bibliography, Programs, Discussion Group  Roles of Calculators in the Classroom
Conference Papers  To Sum It Up: Case Studies of Education in Germany, Japan, and the United States
Third International Mathematics and Science Study (TIMSS), International comparative studies of achievement in mathematics and science  School Mathematics Journal
ADD. KEYWORDS: Electronic Journal, Pedagogy  Selected Papers from the Annual Conference of Didactics of Mathematics
ADD. KEYWORDS: Articles, Teachers and Computers, EssayWriting in Mathematics, Conception of Numbers, Spatial Geometry and Spatial Ability, Computer Algebra, etc.  The SIAM Report on Mathematics in Industry
 Supporting Discovery Learning in Mathematics: Design and Analysis of an Exploration Environment and Inquiry Activities
ADD. KEYWORDS: Article, Discovery learning, Microworlds, Exploration, Inquiry  TALUM  Teaching and Learning Undergraduate Mathematics
ADD. KEYWORDS: Electronic Newsletter  Teaching Linear Algebra: Issues and Resources
ADD. KEYWORDS: Article, PCMIUFP Reports, Curriculum Issues, Connections with Secondary Mathematics, Research on How Students Learn, Ideas from Physics Education, Technology.
SOURCE: Jane M. Day, San Jose State University, and Dan Kalman, American University
TECHNOLOGY: Adobe Acrobat reader, Maple, Matlab  Technology in Math
ADD. KEYWORDS: Course Materials
SOURCE: Gene Fiorini, Shippensburg University
TECHNOLOGY: TI Calc, Spreadsheets, Geometer Sketchpad, The Internet  Technology in the Mathematics Classroom
ADD. KEYWORDS: Lesson Plans, Data and analysis about the use of technology in the Secondary Math Classrooms in Missouri, Compound Interest, Matrices Echelon, Compound Interest, Combinations, Proportionality theorem, Multiplying Binomials, Using FOIL, Conversion Units, Regression, Inscribed angles in circles, Median and Mean, Using the ideas of Galileo, Analyzing Data, Regular Polygons, Binomial Theorem, Quadratic Inequalities, A Circle through 2 points, Graph Translations, Introduction to circles, etc.
SOURCE: Susan LaGrassa, Truman State University
TECHNOLOGY: Adobe Acrobat reader, TI86, TI92, Geometer's Sketchpad, PowerPoint, Excel  Teaching Mathematics and Its Applications
Journal  Teaching Math to Visually Impaired Students
 Teaching With Original Historical Sources in Mathematics
Class Materials, Books, Articles, Bibliography
Reinhard Laubenbacher and David Pengelley, New Mexico State University  Teaching With Original Sources
 Technology in Mathematics Education  TiME
Newsletter, Report on Usage of Technology in TwoYear Colleges
AMATYC  Technology in Mathematics Education Committee  Ted's cooperative learning and WAC web site
Electronic Books, Cooperative Learning, Writing across the curriculum  Undergraduate Mathematics Education Needs Your Critical Concern by Ed Dubinsky
 Uses of Java Applets in Mathematics Education
Article  Why use Forumlike Conferencing for Teaching Mathematics?
 Wisconsin Center for Education Research
ADD. KEYWORDS: Projects
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