Maria Zack Point Loma Nazarene University A Layman’s Experience with Using Original Texts in the Classroom
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 sources • Any good ideas?
Number Theory with Proofs Proposition I Two 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 • DeshRanjan (NMSU project team) • Background and context • Preliminary “warm up” exercises to provide scaffolding and motivation
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.
History of Mathematics • Sums of Numerical Powers in Discrete Mathematics: Archimedes Sums Squares in the Sand • David Pengelley (NMSU PI)
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……..
Mathematics, Art and Architecture • Book One and Book Two: On Painting • Leo Battista Alberti • Vanishing points and perspective
General Principles • Give the students the text in advance • Have them work in groups • Provide “hooks” and scaffolding • Have them process the information kinesthetically