## What Should Our Math Ed Majors Know When They Graduate?

## What Should Our Core Math Majors Know When They Graduate?

## J. J. Price, David Moore, Carl Cowen

Background: Document prepared for the North Central Accreditation of Purdue, Fall 1999: Department of Mathematics Assessment Document (text file) School of Science Assessment Document (in PDF format) From the discussion of October 12: When our Math Ed Majors Graduate, we want them to: 1) have deep understanding of elementary mathematics. (Question remaining: what is elementary mathematics?) 2) understand the nature of proofs and axiom systems and formal mathematical arguments. 3) be able to write down correct proofs, in paragraph form, of theorems from mathematical subjects that they know (for example, from Euclidean geometry). 4) know how to solve problems using the mathematics they know. Question remaining: What should Math Ed Majors know about Statistics when they graduate?## Mathematical Association of America (Draft) Documents

The Committee on the Undergraduate Program in Mathematics (CUPM) of the MAA is working now on a revision of their recommendations to Departments. This week an interesting document has become available: it addresses the issue of the mathematical education of future high school teachers. CUPM (Draft) Document on Education of Teachers (in PDF format) The (Draft) Preface addresses the larger question of what we want students to know. CUPM (Draft) Document Preface (in PDF format)

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From gottlieb@math.purdue.edu Fri Nov 3 11:26:33 2000 X-UIDL: a34058f6b62d7052035ba3a5b3a4249c Return-Path:Received: from peano.math.purdue.edu (gottlieb@peano.math.purdue.edu [128.210.3.244]) by newton.math.purdue.edu (8.10.1/8.10.1/PURDUE_MATH-4.0) with ESMTP id eA3GQRL18600 for ; Fri, 3 Nov 2000 11:26:27 -0500 (EST) Received: (from gottlieb@localhost) by peano.math.purdue.edu (8.9.3/8.9.3/PURDUE_MATH-3.2) id LAA12591 for cowen; Fri, 3 Nov 2000 11:26:26 -0500 (EST) Date: Fri, 3 Nov 2000 11:26:26 -0500 (EST) From: "Daniel H. Gottlieb" Message-Id: <200011031626.LAA12591@peano.math.purdue.edu> To: cowen@math.purdue.edu Status: RO Content-Length: 1434 WHAT OUR STUDENT'S SHOULD KNOW Dan Gottlieb Our TEACHING students should learn: Rigor comparable to 300 BC Arithmatic from about 1610 AD Algebra from about 1637 AD Calculus from about 1710 AD Linear Algebra Probability History of Elementary Mathematics Our HONORS students should know: All of the above with the exception of the history Abstract Algebra Elementary Topology and Set Theory Geometry of surfaces Fourier Analysis Vector Calculus Differential Equations Combinatorics In addition they should know any THING for which the following statement is true: I would hire someone who has studied Calculus and knows THING over someone who has all of the above courses and doesn't know THING. Examples of THINGS: Know there is more than one way to solve a problem Know what Hypotheses, Conclusions, Theorems, and Definitions are and the role they play in mathematics. Know how to negate a proposition, state its converse and contrapositive, Know how to write well, using words like hence, therefore, let, assume correctly. Know how to read well, in the sense that thet can read a textbook on a subject they have studied at their level which was written in the seventies or early eighties. Know how to construct simple examples and counter examples. Know how to choose a coordinate system appropriate for some simple problem.