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“Issues” concern features of the US K-12 educational system that impede later preparation for technical careers. Further, there is either no clear way to fix the problem, or there are several...
Teaching Notes are suggestions about how material might be presented to students.
Topics range from abstract learning principles (Separation of tasks) to highlighting problems caused by common...
The AMS Working Group on Preparation for Technical Careers was authorized by the Council of the American Mathematical Society on 21 April 2007. Goals and methods of the group are summarized in...
FOIL is a mnemonic for an algorithm for multiplying two binomials. Students seem to like it and it increases speed and accuracy with this special case.
Unfortunately students taught FOIL often have...
Problem Collections
Mathematics Standards Study Group; Sample Problems, Jerome Dancis, Solomon Friedberg, Bert Fristedt, and Harvey Keynes. 28 page extract from the Proceedings of the Mathematics...
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A diagnostic aid for a problem is information that helps locate and identify errors. The most primitive diagnostic aid is the answer to the problem, and this may be sufficient for short problems....
Mathematicians are painfully aware that fresh knowledge is unreliable and it is necessary to mercilessly hunt down and fix errors before it becomes useful. In contrast, there is very little error...
The use of calculators in the schools has been heavily promoted by the K-12 education community and is specified in many state standards. They are widely used in K-8. The reception at the 9-12...
This note addresses confusions about fractions, decimal numbers, polynomials etc. and is intended for teachers rather than students.
Objective and Overview
As students learn they develop internal...
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We welcome wisdom and insights from anyone. We particularly invite participation by college teachers of math prerequisites for technical careers (math, science and engineering).
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American Math Society
Education Committee http://ams.org/ams/coe-home.html
National Council of Teachers of Mathematics
Standards documents http://standards.nctm.org/
2005 Park City Standards Study...
In Brief
The restriction to problems that can be quickly solved has biased the school math curriculum in ways that cause difficulty in later study. Are there ways to include long problems in the...
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The Preparation for Technical Careers project seeks to address problems in the high-school/college transition in mathematics. The principal aim is to develop a sense of the mathematical community...
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Parentheses are usually absent from early school math. Later in the curriculum they are avoided when possible and treated as though their use is bad form. “Simplify”, for instance, frequently...
Tasks
Find quotient and remainder in problems stated in both fraction and product form. For linear divisors iterate to rewrite as a polynomial in the divisor. This can also be described as finding...
Task
Limited factoring of polynomials; rewriting to reduce order or eliminate terms; using discriminant to count roots of a quadratic.
Basic methods
Quadratic formula; division (when given a...
Task
Predict total degree of a product or degrees in which nonzero terms will appear. Rewrite a product of expressions as a polynomial in a specified variable.
Teaching notes
products of sums,...
Annotated problem sets are the focus of the Preparation for Technical Careers project. Reasons for this focus are described in Objectives; here we explain the problem sets themselves.
In brief,...
The objective is an way to deal with a product of sums, particularly products of polynomials. Much of the difficulty lies in working with the large number of terms resulting from the initial...
Welcome!
If you are a member of this site you are invited to post suggestions for the “Issues” section of the site using this page, or in the forum thread attached to this page.
Welcome!
If you are a member of this site you are invited to post suggestions for the “Key Ideas” section of the site using this page, or in the forum thread attached to this page.
Welcome!
If you are a member of this site you are invited to post problems and annotations using this page, or in the forum thread attached to this page.
Welcome!
If you are a member of this site you are invited to suggestions for the “Teaching Notes” section of the site using this page, or in the forum thread attached to this page.
PROBLEM SETS
Algebra
Polynomial Products
Polynomial Division
Polynomial Factors and Roots
Recently contributed
ISSUES
Focus Issue: Calculators
Other issues
Numerical Error...
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Supplements include annotations for problem sets and resources for users and developers.
Key Ideas
Key Ideas are formulations of mathematical structure that play significant roles in the way a...
Symbolic expressions are typically much more powerful than numbers
The formula for the area of a circle is simpler and more powerful than the approximation and far simpler and more useful than a...
Experience suggests that qualitatively different tasks interfere when they are combined, resulting in higher error rate. Students should be encouraged explicitly and by example to separate such...
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Welcome to the web site of the American Mathematical Society Working Group on Preparation for Technical Careers. Our long-term goal is to improve preparation of high-achieving K-12 students for...
