maria zack point loma nazarene university. my education plnu as an institution department of...
TRANSCRIPT
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A Layman’s Experience with Using Original Texts in the Classroom
Maria Zack Point Loma Nazarene University
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Background
My education PLNU as an institution Department of Mathematical,
Information and Computer Sciences New Mexico State University Project
and David Pengelley
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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?
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Classes Involved
Linear Algebra Number Theory with Proofs History of Mathematics Special Topics: Mathematics, Art and
Architecture Study Abroad Trip
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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
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Linear Algebra Next Steps
Have students learn about determinants from original sources
Hunting for the right sourcesAny good ideas?
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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.
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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
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Scaffolding and Intermediate Steps
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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.
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Modern Notation
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History of Mathematics
Sums of Numerical Powers in Discrete Mathematics: Archimedes Sums Squares in the Sand
David Pengelley (NMSU PI)
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Cuisenaire Rod Approach
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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……..
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Drawing and Understanding
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Mathematics, Art and Architecture
Book One and Book Two: On Painting Leo Battista Alberti Vanishing points and perspective
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Tiling a Floor
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General Principles
Give the students the text in advance
Have them work in groups Provide “hooks” and scaffolding Have them process the information
kinesthetically