EDCI 788T: Researching Mathematics as Mathematics Educators

Course Instructors: Eden Badertscher and Juliana Belding

Time: TBD

Goals of the course:

In the course of their professional work, mathematics educators need to use mathematical knowledge, whether they are teaching, designing curriculum, examining student learning or issues of teacher knowledge, working with preservice or inservice teachers, or consulting on educational policies. What sort of mathematics knowledge might educators need?

As opposed to a traditional mathematics course, which seeks to impart knowledge of a particular topic, this course seeks to help participants develop a set of strategies to explore mathematics of professional and personal interest to them throughout their lives. Toward this end, the focus of the course is in-depth mathematical investigation of topics related to the K-12 curriculum but that also provide gateways to advanced mathematical topics, giving a chance for participants to experience familiar mathematics in a new way. As in the words of Marcel Proust, “The voyage of discovery is not in seeking new landscapes but in having new eyes.”

The course has two principal components of mathematical investigation. The class as a whole will pursue multi-week explorations designed to stimulate problem-posing and solving, as well as highlight fundamental mathematics ideas. Through these experiences, participants will have the chance to develop understandings of why mathematical results in the K-12 curriculum hold (as in Skemp, 1976) and from what mathematical perspectives they might be deemed important.

The second “investigative” component of the course is a semester-long project, based on a mathematical question of interest to each participant. Participants will be expected to choose/develop a question of interest to them, explore/research their question throughout the semester, present their problem and partial findings to the class periodically, and submit a final write-up of their exploration. Though each project is individual, participants will have the support of the instructors and other class members in defining and pursuing their problem.

Throughout the course, there will be opportunities for reflecting on the nature of mathematical activity and exploration, from how new mathematics is created to how students develop personal relationships with the subject. Such opportunities will include limited readings, weekly journals and class discussions.

Required Text: Brown, S. I., & Walter, M. I. (2005). The art of problem posing. Mahwah, NJ: Lawrence Erlbaum. Available Resources:

To facilitate participants’ research, we will arrange for the following sorts of materials to be available to you. Readings for the course may be drawn from some of these materials and others.

 Calinger - Classics of Mathematics  Courant and Robbins - What is Mathematics?  Cuoco – Connected Geometry  Cuoco, Goldenberg & Mark- Habits of Mind:An Organizing Principle of Mathematics Curricula  Davis & Hersh, The Mathematical Experience  Dunham - Journey Through Genius  Freudenthal - Didactical phenomenology of mathematical structures, and Mathematics as an Educational Task  Hadamard – The Psychology of Invention in the Mathematical Field  Klee and Wagon – Old and New Unsolved Problems  Lakatos - Proofs and Refutations  Lakoff and Nunez – Where Mathematics Comes From  Mazur - Number  Paley- The Boy Who Would be a Helicopter  Polya - How to Solve It as well as Mathematics and Plausible Reasoning  Sinclair- The Roles of the Aesthetic in Mathematical Inquiry  SMSG New Mathematics Library Materials  Swetz - Five Fingers to Infinity  Thurston- On Proof and Progress in Mathematics  Usiskin et al – Mathematics for High School Teachers: An Advanced Perspective