Prealgebra for Two-Year Colleges/To the instructor

This is a prealgebra text for adult students at a two-year college. This text is meant to facilitate teaching via the Socratic method. The book also endeavors to connect topics through themes that are useful to adults, as opposed to covering fractions, decimals, and percents in three separate chapters, as if they were unconnected concepts.

Target Audience

This is a prealgebra text for adult students at a two-year college. Most of these students have passed a prealgebra class (or higher) in the past, but do not remember enough of it to accurately solve linear equations in one variable that contain fractions and decimals, without the aid of a calculator.

These students remember many mathematical procedures and rules, but they do not remember them correctly, or they do not know when to use which procedure. For example, these students remember that "two negatives make a positive," so they will tell you that (-3) + (-5) = +8. Also, they will tell you that

${1 \over 3}+{5 \over 8}={6 \over 11}$,

because they are misapplying the rule

${1 \over 3}\times {5 \over 8}={1\times 5 \over 3\times 8}$.

When asked to draw a circle and shade in two fifths, these students are likely to draw one of the pictures below.

or

Socratic workbook

This text is meant to facilitate teaching via the Socratic method. Our premise is that use of the Socratic method will help students understand the reasons behind the procedures and rules. Students will then be able to figure out which rule to use, or (if they have forgotten the rule altogether) they will be able to reason their way to an answer.

In order to facilitate the Socratic method, this text is in the style of a workbook. There is a teacher's edition, with both halves of the Socratic dialogue (suggestions for teacher's half are in red italics). The student edition has white space for the student's work in place of the italic font.

Scope

This book includes the content of the traditional prealgebra curriculum, but emphasizes themes that are useful to adults.

Content

Expository material explaining procedures and rules is relegated to the appendices. Students have already seen the exposition. The expository material includes

• procedures for adding, subtracting, multiplying, and dividing rational numbers represented both as fractions and as decimals;
• procedures for solving linear equations in one variable, where the coefficients and constant terms may be rational numbers represented both as fractions and as decimals
• geometrical formulas for
  • perimeter of a polygon and circumference of a circle
  • area of triangles, rectangles, and circles
  • volumes of cuboids, right circular cylinders, and right triangular prisms.
  • metric system, U.S. customary units, and unit conversion

Themes

• Problem solving, following the approach of George Polya
• Estimation
• Explaining one's reasoning clearly, accurately, and logically
• Flexibility in shifting between representations of a number
  • decimal
  • fraction
  • percent
  • number line
  • area
  • words
• Flexibility in shifting between representations of a binary operation (viz., addition, subtraction, multiplication, division, exponentiation)
  • pictures
  • formula
  • verbal descriptions
• Flexibility in shifting between representations of a function
  • input-output table
  • Cartesian graph
  • formula
  • verbal input-output rule