Maria Zack Point Loma Nazarene University. My education PLNU as an institution Department of Mathematical, Information and Computer Sciences New Mexico.

A Layman’s Experience with Using Original Texts in the Classroom

Maria Zack Point Loma Nazarene University

Background

My education PLNU as an institution Department of Mathematical,

Information and Computer Sciences New Mexico State University Project

and David Pengelley

Teaching Students to “Read”

Parker Palmer’s To Know as We are Known

How well do our students read the mathematics texts that we give them?

How do we teach them to read?

Classes Involved

Linear Algebra Number Theory with Proofs History of Mathematics Special Topics: Mathematics, Art and

Architecture Study Abroad Trip

Linear Algebra

Sophomore year encounter with texts

Read a short biography of Cramer(http://www-history.mcs.st-and.ac.uk/history/index.html)

Read a contemporary definition of “Cramer’s Rule”

Work through exercises in groups to apply the rule

Write up their findings

Linear Algebra Next Steps

Have students learn about determinants from original sources

Hunting for the right sourcesAny good ideas?

Number Theory with Proofs

Proposition ITwo unequal numbers being set out, and the less being continually subtracted in turn from the greater, if the number which is left never measures the one before it until a unit is left, the original numbers will be prime to one another.

Number Theory with Proofs

Euclid’s Algorithm for the Greatest Common Divisor

Desh Ranjan (NMSU project team) Background and context Preliminary “warm up” exercises to

provide scaffolding and motivation

Scaffolding and Intermediate Steps

History of Mathematics

Theorem:If any number of magnitudes be given, which exceed one another by an equal amount equal to the least, and also other magnitudes, equal in number to the former, but each equal in quantity to the greatest, all the magnitudes each of which is equal to the greatest, plus the greatest will be the duplicate of those exceeding one another by an equal amount.

Modern Notation

History of Mathematics

Sums of Numerical Powers in Discrete Mathematics: Archimedes Sums Squares in the Sand

David Pengelley (NMSU PI)

Cuisenaire Rod Approach

Mathematics, Art and Architecture

I inscribe a quadrangle of right angles, as large as I wish, which is considered to be an open window through which I see what I want to paint…..Then within the quadrangle, where it seems best to me, I make a point which occupies the place where the central ray strikes. This point is properly placed when it is no higher from the base line of the quadrangle than the height of the man that I have to paint there……..

Drawing and Understanding

Mathematics, Art and Architecture

Book One and Book Two: On Painting Leo Battista Alberti Vanishing points and perspective

Tiling a Floor

General Principles

Give the students the text in advance

Have them work in groups Provide “hooks” and scaffolding Have them process the information

kinesthetically