Approved by
University Studies Sub-Committee 1/22/02

Approved
by Faculty Senate 2/10/03

University
Studies Course Approval Proposal

** **

Oral
Communication Flag

The
Department of Mathematics and Statistics proposes the following course for inclusion in
University Studies courses satisfying the Oral Communication Flag requirement at Winona
State University. This was approved by the
full department on Thursday, November 7, 2002.

**Course:** History
of Mathematics (MATH 410), 3 s.h.

**Catalog Description:** General view of the historical development of the
elementary branches of mathematics. This is a University Studies course satisfying the
Oral Communication Flag requirement. **Prerequisites:** MATH 160 and MATH 210. **Offered:** every
Spring semester

This is an existing course, previously
approved by A2C2.

Department Contact Person for this course:

Steven D. Leonhardi, Department of Mathematics and Statistics

Email sleonhardi@winona.edu

General Discussion of University Studies
– Oral Communication Flag in relation to MATH 410:

The purpose of the
Oral Communication Flag requirement is to complete the process of providing graduates of
Winona State University with the knowledge and experience required to enable them to
become highly competent communicators by the time they graduate.

Courses can merit
the Oral Communication Flag by demonstrating that they allow for clear guidance, criteria,
and feedback for the speaking assignments; that the course requires a significant amount
of speaking; that speaking assignments comprise a significant portion of the final course
grade; and that students will have opportunities to obtain student and faculty critiques
of their speaking.

These courses must
include requirements and learning activities that promote students’ abilities
to…

**a. ****Earn significant
course credit through extemporaneous oral presentations;**

Typically, students
will be required to give at least three oral presentations to the class: one
“major” presentation of an expository research paper, and at least two
“minor” presentations either summarizing a short (5-10 page) section of the
text, or explaining the solution to a mathematical problem based on a historical topic of
study. These presentations will be worth
roughly 15% to 25% of the student’s final grade, although this varies somewhat
depending upon the instructor and year. Typically,
a full week of the semester is used for oral presentations of the “major”
student projects.

** **

**b. ****Understand the
features and types of speaking in their disciplines;**

Students in this
course are required to learn and perform four different types of speaking in this course: (1) the discussion necessary for a group of 2 to 4
students to solve mathematical problems; (2) presenting solutions to the class; (3)
presenting brief summaries of historical topics taken from the text; and (4) presenting
the results of a major expository research project to the class.

The
four types of speaking about mathematics listed above reflect four primary types of
speaking needed by mathematicians and mathematics teachers.
The first type, discussion among peers about mathematical concepts, examples, and
arguments, is the primary means of progress in mathematical research, and is also a highly
effective means of helping students at any level construct their own mathematical
knowledge. Even to mathematics majors, mathematics is essentially a foreign language. This
course is intended to help students learn to use and communicate mathematical terminology
and arguments correctly and at a level of rigor and following the stylistic standards
appropriate to the discipline.

The
second type of speaking, presenting a solution to an audience, corresponds to the type of
presentation that a teacher would give to a class after they have had time to work on a
problem, or a presentation that a mathematician might give at a specialized conference. The audience is assumed to already know a
significant amount of background and terminology, but a complete, step-by-step explanation
of the specific claim must be given. This
type of speaking requires the highest level of rigor out of the four types. This type of speaking is especially useful for
preservice teachers, who constitute the majority of the students who are enrolled in
History of Mathematics.

The
third and fourth types of speaking, presenting the results of a minor or major research
project, correspond to the type of talk one would give for a more general audience that is
presumed to have some general background knowledge but no specialized knowledge of the
topic. In this type of speaking, a large
amount of information is condensed and summarized to an introduction to the main themes of
a topic.

** **

**c. ****Adapt their speaking
to field-specific audiences;**

Students
in History of Mathematics learn to adapt their speaking to communicate effectively with
(1) “collaborators,” i.e., students working together on the same problems, (2)
“experts,” i.e., students in the same class working on different problems who
have read or skimmed the background info but still need to hear details of the
speaker’s specific work or topic, and (3) “non-experts” with only minimal
background in the topic, as described in item **b.**
above.

** **

**d. ****Receive appropriate
feedback from teachers and peers, including suggestions for improvement;**

Students
receive immediate feedback from peers during discussion done in groups. The instructor circulates throughout the class
during this group work, confirming when terminology and arguments are appropriate, and
offering corrections, hints, and suggestions for improvement.

The
instructor also comments orally after problem solutions and section summaries are
presented to the class, and students receive written grades with feedback, evaluation, and
suggestions for improvements on various aspects of their presentations.

For
the major expository project and presentation, the instructor offers comments on a
preliminary outline, then comments on a first draft, with suggestions for improvement and
suggestions on the oral presentation, and comments on the final presentation.

** **

**e. ****Make use of the
technologies used for research and speaking in the fields; and**

**
**

Students
typically use the blackboard and chalk to present solutions to homework problems; some use
overhead slides or printed handouts to supplement their explanations. They often use a graphing calculator or a computer
algebra system (such as Mathematica) to help them solve the problems and present
solutions. For their major project
presentations, many students use Power Point (sometimes with audio supplements), some
students use overhead slides, some use printed handouts, and some use the blackboard-- in
approximately the same proportions as would be represented at a professional conference
for mathematicians or mathematics teachers.

** **

**f. ****Learn the
conventions of evidence, format, usage, and documentation in their fields.**

Students must learn not only the current
conventions and internationally held standards of evidence, format, usage, and
documentation in the field of mathematics, but also how those conventions have evolved
over the course of time and in different contexts and cultures.

In reading about different mathematical
topics in history and solving mathematical problems, students must learn how to move
through the process of communicating their informal intuitions based on concrete examples,
to developing formal, rigorous proofs, and then finally to explaining their proofs in ways
that others can understand. That is, the type
of speaking that is most effective for “discovering” a theorem and/or its proof
is very different from the type of speaking that is required for presenting a formal
statement of a theorem and its proof. Students
must learn how to carry out both types of speaking, and learn to recognize which type of
speaking (namely, what level of formality in terms of evidence and usage) is appropriate
in different situations.

Students also must learn how notation,
terminology, and standards of rigor have evolved over time and in different cultures as
mathematical concepts are further developed.

**COURSE OUTLINE—History of Mathematics
(MATH 410)**

** **

**WINONA STATE UNIVERSITY**

**COLLEGE OF SCIENCE AND ENGINEERING**

**DEPARTMENT OF MATHEMATICS AND
STATISTICS**

**Course Title: **History of Mathematics (MATH 410)
**Number of Credits: **3 s.h.

**Prerequisite: **MATH 160 and MATH 210
**Frequency:** Offered each spring semester.

**Course
Description: **General view of the historical development of the elementary branches of
mathematics. This is a University Studies
course satisfying the Oral Communication Flag requirement.

The purpose of the
Oral Communication Flag requirement is to complete the process of providing graduates of
Winona State University with the knowledge and experience required to enable them to
become highly competent communicators by the time they graduate.

Courses can merit
the Oral Communication Flag by demonstrating that they allow for clear guidance, criteria,
and feedback for the speaking assignments; that the course requires a significant amount
of speaking; that speaking assignments comprise a significant portion of the final course
grade; and that students will have opportunities to obtain student and faculty critiques
of their speaking.

These courses must
include requirements and learning activities that promote students’ abilities
to…

a. Earn significant course credit through
extemporaneous oral presentations;

b. Understand the features and types of speaking in
their disciplines;

c. Adapt their speaking to field-specific audiences;

d.
Receive appropriate feedback from teachers and peers, including suggestions for
improvement;

e.
Make use of the technologies used for research and speaking in the fields; and

f. Learn the conventions of evidence, format, usage,
and documentation in their fields.

Requirements and
learning activities **(a)-(f)** are included as part of the satisfaction of every
course objective listed below, due to the pervasiveness of the speaking requirements and
the interrelatedness of these course objectives.

**Statement of major focus and objectives of the course:**

The major focus
of this course is to provide students with

a) knowledge of the historical development of
mathematics;

b) the ability to connect mathematics to
other disciplines and to learn of the physical problems which gave rise to important
mathematical topics; and

c) understanding of the role of axiomatics
and proof in mathematics.

Note that a
focus of this course will be to prepare students to develop the competencies outlined in
the following Minnesota Standards of Effective Teaching Practice for Beginning Teachers:
Standard 1—Subject Matter;

Objectives: To develop within the future teacher…

a) an understanding of the interrelationships
within mathematics;

b) the ability to connect mathematics to
other disciplines and real-world situations;

c) an understanding of the role of axiomatics
systems in different branches of mathematics, such as algebra and geometry;

d) the ability to use mathematical modeling
to solve problems from fields such as natural sciences, social sciences, business and
engineering;

e) an understanding of the major concepts of
both Euclidean and non-Euclidean geometries;

f) knowledge of the historical development of
mathematics that includes the contributions of underrepresented groups and diverse
cultures.

**Topics Covered:**

I. Ancient Mathematics

II. The Beginnings of Mathematics in Greece

III. Archimedes and Apollonius

IV. Mathematical Methods in Hellenistic Times

V. The Final Chapters of Greek Mathematics:
Number Theory and Analysis

VI. Medieval
China and India

VII.
The Mathematics of
Islam

VIII.
The Mathematics of
Medieval Europe

IX. Mathematics
Around the World

X. Algebra
in the Renaissance

XI. Mathematical
Methods in the Renaissance

XII.
Geometry, Algebra, and
Probability in the Seventeenth Century

XIII.
Beginnings of Calculus

XIV.
Analysis in the
Eighteenth Century
*(optional)*

XV.
Probability, Algebra
and Geometry in the Eighteenth Century
*(optional)*

XVI.
Algebra, Analysis, and
Geometry in the Nineteenth Century *(optional)*

XVII. Aspects of the Twentieth Century
*(optional)*

XVIII. Mathematics in the Twenty-first Century
*(optional)*

**Method
of Instruction: **(some or all of the following)

Lecture-instructor presentations

Student presentations

Discussion, question/answer sessions

Individual and group work on problems and
projects

**Evaluation: **Students will be evaluated
using oral presentations and a final exam. Other measures of performance usually include
some or all of the following: written
projects, quizzes, homework, midterm examinations, attendance and participation in group
activities, and other assignments as specified in the instructor’s syllabus.

**Possible Texts:**

Boyer, C., __A History of Mathematics__

__ __

Burton, D., __The History of Mathematics:
An Introduction__

Eves, H., __An Introduction to the
History of Mathematics__

Katz, V., __A History of Mathematics, An
Introduction__

**Course
Requirements: **No specific mathematical software is required.

Revised November 2002, by Steven D.
Leonhardi

**Approval/Disapproval
Recommendations**

** **

Department
Recommendation:
Approved __
__ Disapproved __ __
Date __ __

Chairperson Signature __
__ Date __
__

Dean's
Recommendation:
Approved __
__ Disapproved __ __
Date __ __

Dean's Signature __
__ Date __
__

*In the case of a Dean's recommendation to
disapprove a proposal, a written rationale for the recommendation to disapprove shall be
provided to USS.

USS
Recommendation:
Approved __
__ Disapproved __ __
Date __ __

University Studies Director's Signature __
__ Date __
__

** **

A2C2
Recommendation:
Approved __
__ Disapproved __ __
Date __ __

A2C2 Chairperson Signature __
__ Date __
__

** **

Faculty
Senate Recommendation:
Approved __
__ Disapproved __ __
Date __ __

FA President's Signature __
__ Date __
__

** **

Academic
VP's Recommendation:
Approved __
__ Disapproved __ __
Date __ __

VP's Signature __
__ Date __
__

** **

President's
Decision:
Approved __
__ Disapproved __ __
Date __ __

President's Signature __
__ Date __
__