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History of mathematics
Who takes the course?
Why do they take the course?
What purpose could/should the course serve for pre-service teachers?
Focus on pre-service teachers
Committee on Undergraduate Programs in Mathematics (2004) Curriculum Guide.
• Prospective secondary mathematics teachers need to know the history of the subjects they will teach. It gives them a better appreciation for the struggle that goes into mathematical advances. It enables them to identify conceptual difficulties and to see how they were overcome. And it enriches their own understanding of the mathematics they will teach and the role it has played in human history. (p. 56)
Overview of presentation
Information about the course
Modifications to meet the needs of pre-service teachers.– Teaching (presentation) component– Inquiry-based learning– Lesson plan option
Discussion of how this may apply to other courses
Purpose of the course
To help students develop their own historical perspectives on the development of mathematics so that they gain increased understanding of how mathematics has come to play such a prominent role in our lives.
History of mathematics
History of Mathematics– Burton (6th Edition)
Fall 2008– 20 students– Engineering, Physics, Computer Science, Mathematics,
Mathematics Education majors– Required only for Mathematics Education
Taught in an inquiry-based manner
Daily “schedule”
Class overview and updates
Group presentations of readings
Group problem solving of related historical mathematics problems
Course projects
Two summaries of readings
Final paper on new topic
Group presentations
Students were asked to “teach” the reading material to the class
– Done in small groups
– Few guidelines at the beginning of the semester
Group presentations
Beginning of the semester– The students who were presenting would read aloud their
summary notes.
– The problems were written on the board and “told” to the class.
– The rest of the class would listen quietly.
Do you see a problem here?
Resolution
Let students present in this manner for about 4-6 weeks with hopes that they would modify their method themselves
Intervention– Had a discussion with students on how the presentations
were going– Students came up with their own plan to modify their
“teaching” of the summaries
New ways of presenting
Games– Jeopardy– Dot game– Mathematics Pictionary– Who Wants to be a Mathematician?
Cross-word puzzles
Word searches
Summaries: Option for pre-service teachers Original
– Short papers summarizing big ideas
Alternate– Lesson plan option
• Integrate history of mathematics into secondary lesson plan
Napier Rods Activity
– Brief history on John Napier.Napier’s mathematical writing was focused on
practicalities of computation.Napier first introduced his “rods” (or “bones”) in his
book Rabdologiae, published in 1617. The rods provided a mechanical way of multiplying two numbers. The rods consisted of 10 rectangular blocks that resembled a multiplication table. Each rod was divided into nine squares, where a digit was engraved in the top square, and the remaining squares contained multiples of the digit from 2 through 9. Napier’s rods essentially reduced multiplication to addition.
Napier Rods Activity
Have students partner up for the activity and hand out one Napier’s Rods Table to each group of two.
Begin completing the table containing Napier’s rods to show the students exactly how to fill it in.
Then let the students complete the table.
After the students have completely filled in the table have them cut it apart into columns.
Napier Rods Activity
Go through an example of how to multiply two numbers.
Explain to the students how you add the numbers in each diagonal, where each diagonal stands for the unit values: in this case the unit values are 1000, 100, 10, and 1.
Explain to the students that you need to account for the place value of each partial product when adding the two together at the end.
Other lessons
Egyptian numbers
Estimating the area of a circle
Probability games
Final paper: Option for pre-service teachers Original
– Choose a famous mathematician or a significant problem. The problem you choose should have particular interest to you depending on your major/mathematical interests. You will need to justify this interest/connection in your paper.
Modification– Teachers were encouraged to select something related to
the history of school mathematics
How could these ideas be used in other courses?
Questions, comments, etc.
