Monthly Archives: December 2011

The Best Way to Factor Trinomials

Warning to all beginning algebra students: The answers you get using this method will not be the same as those in your text nor what your math instructor expects to see, but they will be correct and more useful.  You … Continue reading

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Grading with Red Pens

Nick Chura in a comment to this post cited this paper, The pen is mightier than the word: Objective priming of evaluative standards by A.M. Rutchick, M.L.Slepian, and B.D. Ferris (RSF).  As I read the pit there are two issues.  … Continue reading

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Solving Equations as Proofs

On a test, a student wrote for this problem: . I gave him a little bit of credit since that was the correct answer.  I assumed that he had guessed the answer and checked it mentally.  If he had shown … Continue reading

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Fast Algebra Techniques

At some point a math student needs to move from learning algebra to doing algebra.  Many techniques that students learn are designed to facilitate a person’s understanding and remembrance of algebraic processes and are not optimized for efficiency or speed.  … Continue reading

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Grading Tests – Ego Depletion (Mental Energy)

I am on page 43 of Kahneman’s book. He states there that high levels of concentration by what he calls System 2 of the brain causes ego depletion and actually drains a body’s physical resources (glucose).  Some researchers studied eight … Continue reading

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I Calculate the Digits of Pi – Very Slowly – Reprise

This post somehow got lost a year ago.  I am reposting it here. Years ago I wrote an assembly language routine that drew circles with  a pen plotter.  This entailed approximating the arc of a circle with a series of … Continue reading

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Resemblance Heuristics and Bayesian Analysis

I have just started reading Daniel Kahneman’s book  Thinking, Fast and Slow.  In the introduction he gives this example (my précis).   Steve is neat and orderly and good with detail.  Is he more likely to be a farmer or … Continue reading

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An Ancient Problem

I ran across this problem on page 90 in Mathematics in Historical Context by Jeff Suzuki: Find the length of the side of a equilateral pentagon inscribed in a square with one vertex coinciding with a corner of the square.  … Continue reading

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What We Test For

Almost all exams in mathematics courses up through the calculus sequence are composed of a series of problems for students to work.  These questions are generally much less problems than exercises.  The idea is for our students to demonstrate that … Continue reading

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