Department of Mathematics Generic Syllabus
Boise State University Updated Fri Jan 12 09:52:28 MST 2001

MATH 25
Elementary Algebra
0 semester credits (3 credit equivalent)

Catalog Description

MATH 25 ELEMENTARY ALGEBRA (3-0-0). Brief review of arithmetic operations and their properties. Positive integer exponents, variables, algebraic expressions, solution of linear equations, definition of absolute value. Expansion of the product of two binomials, factorization of quadratics, solution of quadratic equations by factoring. Two-dimensional Cartesian coordinate systems, slope, equations of lines, solution of 2×2 linear systems. Simple ``word problems''.

Prerequisites

MATH 25 is a remedial course for students whose arithmetic skills are adequate, but whose algebraic skills make them unable to attain a 70th-percentile score on the ACT or SAT. The COMPASS placement exam also recommends MATH 25 for students who don't seem ready for MATH 157, MATH 108, MATH 124, or MATH 130.

Jurisdiction

This course is controlled by a departmental committee, whose members may or may not be teaching the course. All sections use the same text, which is chosen by the committee. The committee also writes a syllabus detailing which sections should be covered and how much time should be allotted to each. Exams, homework, and grading system are left to the instructor.

Objectives

The objectives of MATH 25 reflect all four of the Department's teaching goals:

  1. Appreciation of mathematical patterns:

    A main theme of MATH 25 is the graphing-algebra pattern.

  2. Awareness of applications:

    MATH 25 presents use of one- and two-variable linear equations to solve simple story problems having to do with finance, geometry, mixtures, and graphs.

  3. Mastery of some mathematical tools:

    1. graphing,
    2. expansion of algebraic expressions,
    3. factoring,
    4. interpretation of algebraic expressions,
    5. translations between prose and geometry, between prose and algebra, and between geometry and algebra.

  4. Mathematics as a language:

    1. algebraic grammar;
    2. algebraic language and its geometric consequences;
    3. geometric language and its algebraic consequences.

Upon completion of this course, students should:

  1. Show proficiency with order of operations.
  2. Use the various field axioms in solution of simple equations.
  3. Be able to add, subtract, multiply, divide, and factor simple polynomials.
  4. Be able to solve elementary equations that are linear or quadratic in nature.
  5. Be able to translate expressions and statements back and forth between English phraseology and mathematical notation or geometric depiction.
  6. Be able to solve elementary story problems including mixture problems, uniform rate problems involving distance and work, and geometric problems involving area and circumference of circles, triangles, and rectangles.
  7. Be able to manipulate integer exponents, and be able to translate between radicals and fractional exponents.
  8. Be able to graph lines in the plane, find equations of lines, and solve problems involving lines.

Assessment of Learning Objectives

These objectives are periodically assessed via input from instructors in MATH 25 and subsequent courses. The order of presentaion of topics recently moved away from the traditional order in favor of a treatment constantly emphasizing graphing and story problems.

Assessment of Student Progress

Students will be assessed by evaluating their ability to do problems based on the learning objectives. The problems will occur in several contexts:

Topics and Approximate Timeline

The following table is based on a typical semester schedule-45 class meetings of 50 minutes each. The order of topics reflects that of the current text. The actual amount of time spent on each topic will vary slightly from semester to semester and instructor to instructor.

Number of
Topic Meetings
Expressions and coordinate graphs 5
Real-number operations and exponents 6
Solving equations via graphs, tables, and factoring 7
Ratios, rates, similarity, and proportions 4
Polynomial operations, exponents, and scientific notation 6
Squares, square roots, Pythagoras, and quadratic equations 4
Rational expressions 6
Exams/Review 7

Text

Elementary Algebra (3rd edition); by Dugopolski; McGraw-Hill;

Format, Student Activities, and Grades

The individual instructors choose the format that seems most effective. The lecture format is still the dominant method, although when class sizes are small, group activities are used by some instructors. Instructors are encouraged to collect homework on a regular basis and to give quizzes. The instructor chooses the exact grading scheme, but a typical distribution of points would be:

Homework (scaled to) 200
4 Exams 400
Quizzes 100
Final Exam 200
Total 900

Letter grades are usually based on a standard scale in which 90% of the total possible points guarantees an A , 80% a B, 70% a C, and 60% a D.

In assigning an MATH 25 student a final grade, the instructor needs to consider whether this student is ready to embark upon credit-bearing mathematics courses, and grade (or at least make some recommendation to the student) accordingly. MATH 25 is, after all, a remedial course.

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