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.
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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