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, Pascalís 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 Egypt, Mesopotamia, China, and Greece;

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 University of Redlands.

 

More detailed lists of topics

 

Course syllabus

Schedule:
Day 1

Day 2

Day 3

Day 4 and Pythagorean Theorem problems

Day 5 and mathematics autobiography guidelines

Day 6

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

Day 8

Days 9 and 10 and Classical Greece timeline

Day 11 (Assignment #10)

Day 12 (Assignment #11)

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