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 cop-out 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 K-12 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 grown-ups 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 student-proposed 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 under-appreciated.

Wow!  Writing a top ten list is hard.

 

This entry was posted in Issues in Higher Education, K-12 Mathematics, Math Education, people in math, women in math. Bookmark the permalink.

Topics in Mathematics

Mathematics Education

  • ACDCA 5th Summer Academy Proceedings
    ADD. KEYWORDS: Conference Proceedings, Computer Algebra, Using TI-92 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, E-mail 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, Problem-based 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
  • CAS-CAT 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: TI-85 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, Hard-of-Hearing
  • 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 Microcomputer-Based 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
  • Inter-American 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: CD-ROM, 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 K-8
  • 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 Pencil-and-Paper Arithmetic
    Article, Back to basics, Mental Arithmetic
  • Long Island Consortium for Interconnected Learning in Quantitative Disciplines
    On-Line Projects, News & Reports, Discussion Groups, Educational Technology, Calculus Reform, Precalculus Reform, Underrepresented Groups, Teacher Training
  • Maryland Collaborative for Teacher Preparation
    Pre-Service 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, Math-related 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, non-speech 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, K-12, 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; Computer-based 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 6-12 Mathematics Education: Vertically-Integrated, Inquiry-Based 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, Essay-Writing 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, PCMI-UFP 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, TI-86, TI-92, 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 Two-Year 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 Forum-like Conferencing for Teaching Mathematics?
  • Wisconsin Center for Education Research
    ADD. KEYWORDS: Projects

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