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:

 

University Studies:  Oral Communication Flag

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.

 

University Studies:  Oral Communication Flag

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