**MATH 115, Mathematics through Its History**

is an activity-based elementary mathematics
history course I designed and taught with mathematics majors, the majority of
whom intended to become mathematics teachers.
The somewhat ungrammatical title of the course is intended to carry two
meanings; we attempt to study mathematics throughout its (early) history and we
study mathematics by approaching it via its early history. Although the course could and will be taught
during a traditional academic term, it so far has been offered during our
Interim (January) term, which means it has met for 3 hours per day, 4 days per
week during a 4-week term. A typical class session begins with a
(usually) short quiz, followed by worksheet activities, followed by a
combination of interactive lectures and hands-on activities, such as learning
to use an abacus, learning to use a Chinese counting board, exploring
Pythagorean figurate numbers with "pebbles" (candy), doing puzzle
proofs of the Pythagorean Theorem, doing straightedge and compass constructions,
and constructing the Platonic solids to discover Euler's formula. In general, activities are designed so that
students discover results rather than simply review or practice them. Students also have nightly reading and
homework.

The
course covers the historical development of counting, number systems,
arithmetic, geometry, and algebra---that is, school
mathematics---along with some fun topics like Fibonacci numbers, perspective
drawing, Pascal’s Triangle, the Konigsberg Bridge Problem, and the Four Color
Theorem. It has followed a different
schedule and included different topics each time it has been offered, but is
organized roughly into units on:

very early mathematical artifacts;

counting and number systems in various (early)
civilizations;

algorithms for elementary arithmetic from various
times and places;

mathematics of ancient

the Pythagorean Theorem in various cultures;

circles and p in various
cultures;

and newer developments.

The
majority of my co-teachers have been prospective high school mathematics
teachers; all have studied mathematics history with me previously in a
sophomore-level mathematics history course for mathematics majors. We initially designed and prepared the course
during summer sessions for which students were paid and during fall sessions
for which students earned academic credit.
Pairs of students prepared and presented individual units of their
choosing, and continue to do so.

MATH 115 has been popular with
students, who seem to find it challenging but enjoyable. The course has been even more rewarding for my
mathematics major co-teachers, several of whom have gone on to teach high
school mathematics or to serve as graduate TAs in mathematics masters and PhD
programs. Several have returned as guest
presenters after graduating from the

**Schedule:**

Day 1

Day 4 and Pythagorean Theorem problems

Day 5 and mathematics autobiography guidelines

Day 7 and reading on early history of length, area, and volume measurement

Days 9 and 10 and Classical Greece timeline

Days
13 (Assignment #12), 14, 15, and 16

Resources for
activities, homework, readings

Sample
activities:

Ratio of
Circumference to Diameter

Quizzes

Student co-instructors and funding