**Nuts and Bolts: Student
Team to Design MATH 115, **

**Mathematics through Its History, Summer 1998**

Using

After I provided the students with
dozens of sample activities, we held a series of joint meetings in order to
hammer out an outline for the course and then to divide up the topics among
two-student teams. After that, I worked
with the students individually or in pairs.
Students prepared from two to four units each, centered around an activity or set of activities; each student ended
up presenting or co-presenting at least one unit in the class. Units and activities were to be designed to
help MATH 115 students discover, explore, and understand the earliest uses of
number systems and counting, arithmetic, fractions, geometry, algebra,
probability, number theory, and infinite sums in civilizations around the
world. For the most part, students
organized the sample activities I had provided for them into a coherent whole,
often following suggestions I made, but they also found resources on the Web
and in books and journals they found on their own. They found the background information they
needed in mathematics history texts borrowed from me and from their local
libraries.

During
the fall semester of 1998, we met weekly to organize and practice our class
presentations. During the first offering
of the course (Interim 1999), I met nightly with my co-instructors to fine-tune
(OK, micro-manage) their presentations.
(Students earned 1 unit of directed study credit for fall preparation
and another unit for Interim preparation and teaching.) During the second offering of the course
(Interim 2000), five student co-instructors participated. I would say that student co-instructors participated
in at least some part of the class session for at least two-thirds of the class
sessions the first year and for at least one-half of the class sessions the
second year.

This was a great experience for the
students involved, and was very rewarding for me as well. Eight of my eleven co-instructors now teach
mathematics in high school or college (the latter as teaching assistants in
their graduate programs). One of the
student instructors prepared and taught a three-week, intensive mathematics
history course for the very bright fifth and sixth grade students in the

See proposal for
funding and invitation to potential student instructors, below.

**PROPOSAL
FOR HEWLETT FUNDS **

**FOR
STUDENT/FACULTY TEAM TO DESIGN AN ACTIVITY-BASED **

**ELEMENTARY
MATHEMATICS HISTORY COURSE**

**Summer,
1998**

**Project
Director: Dr. Janet L. Beery,
Mathematics**

My own
relatively recent interest in mathematics history reflects a healthy and
growing trend in the mathematics community.
At long last, mathematics faculty and students are becoming interested
in the history of their own subject, and are seeking ways to incorporate
historical knowledge and ideas into their mathematics courses and
curriculum. What I hereby propose is
funding for a cadre of students to work with me this summer to design a new
Liberal Arts Foundation (LAF) course featuring the history of mathematics. This course would be an elementary course
open to all students having the basic algebra skills required for admission to
the University, and would be activity-based.

**How project meets departmental objectives**

The project
would meet mathematics department objectives of (1) offering a wider variety of
Liberal Arts Foundation (LAF) mathematics courses for

(1) During the past year, especially, the
mathematics department has had several requests from students for additional
elementary mathematics courses satisfying the "M3" portion of the LAF
Mathematics and Science (MS) requirement.
These requests stem both from students' interest in mathematics and from
the dearth of such courses offered by other

(2) Our very best students participate in
externally funded national summer mathematics programs. However, we have many excellent students,
including many students who are strongly interested in mathematics teaching
careers, who either are not chosen for these programs
or are not interested in them. These
students have chosen a challenging major and career and need all the
preparation, motivation, and encouragement we can give them.

**Expectations for student participants**

Students would
design activities and projects to be used in the mathematics history
course. They would begin by reviewing
samples of activities that I already have collected. They also would spend some time searching for
samples of such exercises at relevant websites and in relevant journals, most
notably the journal of the National Council of Mathematics Teachers (NCTM), *Mathematics Teacher,* a
publication with which students interested in teaching careers should become
familiar! For the most part, though, the
students would design activities based on descriptions of historical
mathematical concepts found in original mathematical sources (some in languages
other than English) and in mathematics history textbooks.

The piece of the
project on which we would work first would make use of the six early arithmetic
texts in our own Armacost Library Rare Book Room and
the two early arithmetic texts in the Heritage Room of the Smiley Library. We would design exercises to guide students
as they themselves examine these locally available early arithmetic (and
algebra) texts. For instance, students
would be led to compare algorithms for the basic arithmetic operations and some
algebraic operations in these texts with present day algorithms.

Other projects
would be designed to help future students discover and understand the earliest
uses of counting, fractions, geometry, algebra, probability, infinite sums,
etc. in civilizations around the world.
Student participants would be encouraged to generate their own ideas for
projects, but also could be assigned activities to write. They would be closely supervised by me; I
would discuss with them frequently the general outline for the course and how
the individual activities fit into or modify this outline.

I would
encourage students to work in pairs and would expect each pair of students to
complete three to five activities/projects, depending on length. Most, if not all, work on activities would
be done on campus so that I could supervise it.
Each student would complete about 50 hours of work, but this could
vary. Since students would have
full-time jobs near their permanent residences, each student would set up a
work schedule with me at the start of the summer. Schedules could include work on several
consecutive weekends, or during one or two weeks at the start of the summer, or
etc.

**Outcomes, including dissemination**

The
student-designed activities would be used in the elementary mathematics history
course, and also could be used in our MATH 100/101, Finite Mathematics /
Mathematics for Liberal Arts (equivalent courses in that students may receive
credit for at most one of the two) and MATH 102, our mathematics course
especially for (and open only to) prospective elementary school teachers
(liberal studies majors). Projects not
only would be used in mathematics courses, but could be disseminated by the
students who designed them at local (and perhaps national) mathematics meetings
and in publications such as *Mathematics
Teacher.* The National Science
Foundation sponsored Institute for the History of Mathematics and its Use in
Teaching, of which I am a member, plans to publish volumes of classroom history
units, so students might have the opportunity to disseminate their work there,
too. Unpublished activities would be
available at my website.

In addition,
students would serve as teaching assistants for the course in which the
activities would be used, so would have the chance to facilitate their own
activities. Since most of the students
currently are sophomores, they would be available to help with the course even
if it were not taught until Fall 1999.
Student participants also would have the opportunity to present and use
their work in the MATH 100/101/102 courses described above.

**Qualifications of project director**

I have taught
our sophomore/junior level mathematics history course for mathematics majors
and minors for two years, and have participated in the National Science
Foundation sponsored Institute for the History of Mathematics and its Use in
Teaching for two years. Last summer, I
worked with a student on various mathematics history projects, most
curriculum-related. Two of these
projects involved early mathematics texts in English and in Spanish; the
current project would make use of this earlier work.

**Qualifications of student participants**

The students who
would work on this project would be sophomore and junior students who

(a) have studied
mathematics history with me, so have a framework on which to build activities,

(b) have a
strong interest in teaching mathematics, usually at the high school level,
after graduation,

(c) have a grade
point average (well) over 3.0 and a demonstrated ability and willingness to
work hard, and

(d) are able to
commute to

I would select
these students from a group of eight students who meet the above criteria and
are interested in the proposed project.
Four of these students applied to participate in national summer
mathematics programs and still are waiting to hear if they are accepted. I could name these students and provide more
information about each one, if you like.

**Budget**

Ideally, six
students would be funded at $400 each, to include stipend, travel, and food,
for a total of $2400. Travel to **Total: $2600**.
Of course, I'll use whatever you are able to give me: funding at a lower level would mean fewer
students and/or a smaller stipend for each student.

A single student
funded under the

**YOU ARE INVITED **

**TO
JOIN A STUDENT TEAM FORMED TO DESIGN **

**AN
ELEMENTARY MATHEMATICS HISTORY COURSE**

**Summer,
1998**

**Project
Director: Dr. Janet L. Beery,
Mathematics**

**OUR GOAL:**
Design a new Liberal Arts Foundation (LAF) course featuring the history
of mathematics. This course would be an
elementary course open to all students having the basic algebra skills required
for admission to the University (meaning, they've passed the Math Placement
Exam), and would have a strong activity component. The course would be at least as mathematical
as it is historical; students would earn M3 LAF credit (rather than, say,
HH). The typical student in the course
probably would be a student who has taken MATH 100 or 101 for M2 and a lab
science for M1, and would prefer to fulfill the M3 requirement with a math
course rather than a science course.

**What would YOU do?**

·
Decide
on an outline for the course---that is, decide what to include in the course. We'd put together a draft outline at the
start, with the understanding that we'd probably modify it a lot as we go. You'd review comprehensive mathematics
history texts in order to put together the draft outline.

·
Design
units of study and especially students activities and
projects to be used in the mathematics history course. Topics might include counting, fractions,
geometry, algebra, probability, infinite sums, and calculus. You would be encouraged to generate your own
ideas for topics and activities, but don't worry: lots of resources for ideas would be
available, such as the following ones.

o
You
could begin by reviewing samples of activities that I already have collected.

o
You
could search for samples of math history exercises at relevant websites and in
relevant journals, most notably the journal of the National Council of
Mathematics Teachers (NCTM), *Mathematics Teacher.*

o
You
could get ideas for activities from descriptions of historical mathematical
concepts found in mathematics history textbooks and in original mathematical
sources (some in languages other than English: Spanish, French, German,
Hawaiian, etc.).

o Some activities (or one big activity)
would make use of the six early arithmetic texts in our own Armacost
Library Rare Book Room and the two early arithmetic texts in the Heritage Room
of the Smiley Library. We would design
exercises to guide students as they themselves examine these locally available
early arithmetic (and algebra) texts.
For instance, students would be led to compare algorithms for the basic arithmetic
operations and some algebraic operations in these texts with present day
algorithms. We also could include
arithmetic algorithms from even earlier European and

When working on teaching units and on
activities/projects, you probably would work in pairs, with each pair
completing three to five units/ activities/projects, depending on length. Most work on activities would be done on
campus, with each student completing about 50 hours of work, but this could
vary. Since students would have
full-time jobs near their summer residences, each student would set up a work
schedule with me at the start of the summer.
Schedules could include work on several consecutive weekends, or during one
or two weeks at the start of the summer, etc., but it would be most effective
for us to choose as many common times as possible.

·
Finally,
you would have the opportunity to serve as a teaching assistant for the math
history course, so would have the chance to teach and/or facilitate your own
units and/or activities. You could earn
work-study money and/or academic credit and/or glory for this experience. You might also have the opportunity to
present your work in the MATH 100/101/102 courses described above.

**When would this course be offered,
anyway?**

As early as next
fall, probably next spring (Spring 1999), possibly the following fall

The activities
you design also might be used in our MATH 100/101, Math for Liberal Arts /
Finite Mathematics courses (equivalent courses in that students may receive
credit for at most one of the two) and MATH 102, our mathematics course
especially for (and open only to) prospective elementary school teachers
(liberal studies majors).

Furthermore, you
might be able to present especially good activities at local mathematics
meetings and/or publish them in teaching magazines.

**Are you qualified?**

The six (6)
students who would work on this project ideally would be sophomore and junior
students who

(a) have studied
mathematics history with me, so have a framework on which to build activities,

(b) have an
interest in teaching mathematics, perhaps at the high school level, after
graduation,

(c) have a grade
point average over 3.0 and a demonstrated ability and willingness to work hard,
and

(d) are able to
commute to

**What would you get out of the project
besides an expanded knowledge of mathematics history, personal satisfaction, and a great entry for
your resume? **

Cold, hard cash,
of course! Now, we're not talking about
a whole lot of cash--- you'd still have to get a summer job---but I should be
able to pay you about $400 each. My
grant would cover special travel to