MATH 561, ``The Role of History in the Teaching of Mathematics''

New Mexico State University

Dec. 31, 2001, David Pengelley

Information for students and instructors

**Advance Information for students:**

This course will be valuable to anyone who plans to teach or is already teaching mathematics. The course description is:

An in depth study of selected mathematical topics through examination of their historical development, with special emphasis on studying original sources. Pedagogical aspects of using history and original sources in teaching mathematics. Research and preparation of classroom materials based on original sources.This will be a seminar-style course including individual student investigations, discussion, preparation, and presentation of teaching materials based on historical sources, particularly original sources. The topics of study, and of student projects, will be based largely on the individual interests of students, both mathematically and in terms of teaching level. Much of our focus may be on aspects of nineteenth or twentieth century mathematics relevant to the undergraduate and graduate curricula, including analysis of that relevance. This can include applications to courses individual students have been taking, teaching, or expect to teach. The intent is to shed historical light on what we teach and why we teach it, to enrich the mathematical learning experience itself, and to improve our teaching through the various ways of incorporating history. At the same time, students will learn some history of mathematics in the context of the mathematics they study and work with. Much more information about teaching with original sources is available at our web sitePrerequisite: A good undergraduate mathematics background.

There is a collection in the Mathematics Reading Room of all the original source teaching projects developed by students in this course in past semesters, which you are welcome to look at. You will find it on the top shelf of the curriculum bookcase on the south wall. There is a black-spiral bound blue cover collection from Spring 95, and a manila folder collection inside containing projects from later semesters.

**Advance information for instructors:**

This seminar style course, with discussion format and regular student
presentations, introduces graduate students to the many pedagogical facets
of using history in teaching mathematics worldwide, via numerous resource
materials, with special emphasis on using original historical source material
in the teaching classroom at all levels, from elementary school to graduate
school. Graduate students in the course are expected to learn enough to
be able each to create, write, polish, present, and in some cases publish,
at least one major teaching module for a teaching setting of their choice,
usually based on original historical source material. Many of the course
resources used are provided or referenced at `http://math.nmsu.edu/~history`,
including a list of all the teaching modules developed by students in previous
semesters of MATH 561. The actual teaching modules are archived in the
Mathematics Reading Room (top shelf of teaching bookcase on south wall),
from which they may be copied by students and instructors.

**Instructor's advance preparation for the course:**

Advertise course to mathematics and education graduate students (ask D. Pengelley for his advertising material)

Order books at bookstore: V. Katz, A History of Mathematics, second edition, required text for all students; Carl Boyer & Uta Merzbach, A History of Mathematics, 2nd ed., recommended; R. Calinger, Classics of Mathematics, 2nd ed, recommended; J. Fauvel & J. Gray, The History of Mathematics: A Reader, recommended.

Put things on reserve at the library as needed, e.g. Mathematical Expeditions, Vita Mathematica, Learn from the Masters, History in Mathematics Education, and the recommended books above.

Find out dates for submission for student presentations at NMSU Graduate Research and Arts Symposium.

**Books and resources for course:**

`see web' means available online at `http://math.nmsu.edu/~history`;
especially good is the BSHM website linked here.

Teaching modules developed by students in previous semesters of MATH 561 are in the MRR, with a list at `see web'.

R. Laubenbacher & D. Pengelley, *Some Selected Resources for Using
History in Teaching Mathematics *(see web under A selective bibliography
for using history in teaching mathematics)

J. Fauvel and J. Van Maanen, The ICMI Study discussion document on *The
role of the history of mathematics in the teaching and learning of mathematics
(1997-2000)*, in `http://www.math.rug.nl/~maanen/Maanen.html#dd`,
which led to the book

John Fauvel and Jan van Maanen, editors, *History in mathematics education*,
Kluwer, Dordrecht, Boston, 2000 (in NMSU library).

Cornell University Mathematics Library (see web), *Bibliography of
Collected Works of Mathematicians*

R. Laubenbacher & D. Pengelley, *Mathematical Expeditions: Chronicles
by the Explorers*, Springer, 2000 (see web and NMSU library).

Man-Keung Siu (see web), *The ABCD of using history of mathematics
in the (undergraduate) classroom*

Anna Sfard, *The Development of Algebra: Confronting Historical and
Psychological Perspectives*, J. of Mathematical Behavior **14 **(1995),
15-39 (from D. Pengelley).

Miguel de Guzmán (see web), *Origin and Evolution of Mathematical
Theories: Implications for Mathematical Education*

R. Laubenbacher & D. Pengelley (see web), *Recovering Motivation
in Mathematics: Teaching with Original Sources *UME Trends **6**,
September 1994.

*Critique of Modules Questions for MATH 561 *(from D. Pengelley,
and also at back of bound teaching modules in MRR)

*Instructions for daily diary *(from D. Pengelley)

**Course activities:**

Day 1: Give history of course, goals, current worldwide viewpoint on
using history in teaching mathematics, course combines history/mathematics/education,
introduce everyone, find out backgrounds, interests, make contact info.
sheet for everyone. Explain what we'll do, and that project modules can
be tailored to individual student interests and level. Seminar style: presentations/discussion/written
assignments. Show previous course student modules, and various resource
materials. Hand out various resource materials, or tell students to print
them from the web, especially *Some Selected Resources for Using History
in Teaching Mathematics*. Students should write about their background
in mathematics, history. Students should join the Historia Matematica web
discussion list at `http://chasque.net/jgc/history.htm`. Students
should keep a daily journal (see handout from D. Pengelley).

Weeks 1-2: Each student should read in Katz, pick a topic, read/write/present on it in the next week or two, to get started learning how to read and think about history. Students should discuss together and pick jointly 2-3 of the previous course modules, read and write critiques of them using the critique questions. Explore web and other resources.

Weeks 2-3: Revise Katz and module critiques after class presentation and instructor feedback. Read and write critiques of Guzman and UME Trends articles. Then discuss in class. Students select/write some ideas for topics of first (primary) course project, get instructor feedback. Students read/write on sections of Mathematical Expeditions, class discussion of pedagogical use.

Week 3: Flesh our project ideas further. Read/write on Siu's ABCD article, then discuss in class over the next few weeks.

Week 4: Refine project ideas, make individual timetables for project work and completion.

Week 5: Students report on project progress, discuss. Look at more prior semester modules, discuss.

Week 6: Students report on projects every week from now on. Instructor meets individually with students to help with projects.

Week 7: Read/write on ICMI discussion document, then discuss. Set dates for preliminary project presentations in class, and for rough drafts for everyone to read and critique.

Week 8: Read/write to compare and contrast corresponding material in Katz with Calinger's Contextual History of Mathematics (from David; this is not Calinger's source book). The two books reflect very different approaches to history. Start class presentations based on preliminary project drafts.

Week 9: Continue project presentations, work with students individually, begin to refine drafts. Student projects will go through numerous written draft revisions with instructor feedback. Plan for public presentations of final projects at conference (NMSU Graduate Research and Arts Symposium) or dept. seminar or colloquium.

Week 10: Start reading Sfard article, and discuss over next several weeks. Heavy and lengthy, deep and intellectually rewarding; worth emphasizing for several weeks.

Weeks 11 - end: Continue project revisions, instructor feedback and individual assistance, class presentations, practice for public presentations, continue detailed discussion of Sfard article. Final student projects are copied and added to materials in MRR, with copy to D. Pengelley for further archiving and addition to web list.

**List of student written assignments:**

Students write about their own background in relation to the course

Each student writes critiques of three previous teaching modules using historical sources developed in the course in previous years (see web for listing; actual modules are in Math Reading Room); use developed list of questions to consider in critiquing modules

Each pick a historical thread from Katz and write on it, present and discuss

Write critique of Guzman and UME Trends articles (see web), discuss

Read/write on part of Mathematical Expeditions as teaching material

Individual project ideas due

Write on ABCD article (see web)

Individual project plans due

Each student chooses and critiques three more previous teaching modules developed in the course

Critique ICMI document (this is now evolved to a book *History in
mathematics education*; see NMSU library)

Compare and contrast parts of Calinger and Katz History books (not Calinger's source book)

Critique Sfard article

Oral project presentations

Final semester projects due, after numerous revision cycles, reports, and presentations. These become the final course modules, added to the course materials in the MRR.

Make public presentations of projects, in a seminar or at a conference.

Encourage preparation of some projects for publication.

File translated from T

On 3 Jun 2002, 23:53.