A blog for Wesleyan’s Project to Increase Mastery of Mathematics and Science
Nov. 14, 2008 by PIMMS
Dr. McAlear’s PowerPoint presentations from the fourth (11/1/2008) week of the Life Science Course are available by clicking on the links below:
Click here for the Chapter 16 PowerPoint:
Oct. 30, 2008 by PIMMS
Dr. McAlear’s PowerPoint presentations from the third (10/4/2008) week of the Life Science Course are available by clicking on the links below:
Click here for the Chapter 13 PowerPoint:
Sep. 26, 2008 by PIMMS
Dr. McAlear’s PowerPoint presentations from the second (9/20/2008) week of the Life Science Course are available by clicking on the links below:
Click here for the Chapter 6 PowerPoint:
Click here for the Chapter 51 PowerPoint:
Click here for the Chapter 52 PowerPoint:
Sep. 10, 2008 by PIMMS
Dr. McAlear’s PowerPoint presentations from the first week of the Life Science Course are available by clicking on the links below:
Click here for the Chapter 1 PowerPoint:
Watch this space for Dr. Bob’s (Dr. Robert A. Rosenbaum’s) reflections and thoughts on various topics in mathematics, education, and his career
Aug. 19, 2008 by PIMMS
Musings on Factoring of Polynomials
Bob Rosenbaum
The factoring of polynomials (1) is a topic in algebra about which students have vastly different feelings:
· for some, factoring is a prime example of a technique for which the most appropriate response is, “When are we ever gonna use this?”
· for some others, factoring provides an enjoyable puzzle, akin, perhaps, to diagramming sentences in an English class.
I should be explicit about the difference between factoring a polynomial, such as
x2 – 5x +6 =(x – 2)(x – 3) and
factoring an integer, such as 629 = 17 • 37.
In the first example, the equals sign means that, for every x, the value of the polynomial, x2 – 5x – 6, for any number x, equals the product of the numbers, x – 2 and x – 3, for that number x, and so there are infinitely many numerical equalities contained in the single algebraic equation; while, in the second example, we are told that the number, 629, equals (or can be expressed as, or can be factored into) the product of the two numbers, 17 and 37.
Few students see any significance in factoring, and many teachers join students in disdain or distaste for factoring. Sandie Coelho, PIMMS’ former Associate Director for Mathematics, showed me a sheaf of questions and answers about what’s factoring good for? or why teach factoring?—the teacher-discussants were seriously trying to find justification for their teaching of a topic that they feared has no significance. In that sheaf, not one person could provide a reason for learning how to factor polynomials! Indeed, one frustrated respondent said that, if asked by a student, “What good is it to know how to factor x2 – 5x – 6?”, he would answer, “Factor this expression or I’ll pull the trigger of this loaded pistol that I’m holding to your temple.” This mean Dickensian teacher isn’t much worse than the sarcastic Euclidean mentor who tells his assistant to give a dime to the student “since he needs to have some reason to study.”
If I am asked, “Should students in a high school algebra class spend substantial time to learn factoring of polynomials?”, I respond with a clear-cut “NO and YES.” Let me explain: Continue Reading »