Catalog Description

MATH 157 STRUCTURE OF ARITHMETIC FOR TEACHERS (3-2-4)(F,S). The study of number systems from whole numbers through the reals; numeration, number operation, algorithms, and properties. The course includes an integrated laboratory component which makes use of physical models appropriate to the content of the course. PREREQ: MATH 108 or a satisfactory score on mathematics placement examination.

Prerequisites

MATH 108 Intermediate Algebra or a satisfactory score on the mathematics placement examination.

Jurisdiction

This course is controlled by the Elementary Mathematics Education Committee which selects the book and prepares the syllabus. Individual instructors are responsible for deciding the order of the presentation of the material, exams, homework, and grading systems.

Learning Objectives

The objectives of MATH 157 include components of all of the Department's teaching goals: that students be able to express mathematics through the study of patterns, be able to model mathematical ideas, be able to use problem solving skills and strategies, be able to select suitable mathematical tools, and be able to communicate mathematically. These goals parallel those supported by the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics. Upon completion of this course, students should be able to:

Use problem-solving approaches to investigate and explain mathematical concepts and to solve both simple and nonroutine multistep problems.

Communicate mathematical ideas to one another by using oral, written, concrete, pictorial, graphical, and algebraic methods.

Recognize and apply mathematics to support conjectures by using inductive and deductive reasoning processes.

Represent and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, and scientific notation) in real world and mathematical problem situations.

Apply ratios, proportions, and percents in a wide variety of situations.

Demonstrate number sense for whole numbers, fractions, decimals, integers, rational, and irrational numbers

Apply number theory concepts (eg. sets, primes, factors, and multiples) in real-world and mathematical problem situations.

Develop, analyze, and explain procedures for computation and techniques for estimation in both base ten and bases other than ten.

Assessment of Learning Objectives

The exact forms of assessment that are used will be chosen by each instructor for the course. Examples of the kinds of assessment used include the following.

• Group work may be evaluated either informally or formally as it is in progress or it may result in written work which is collected and evaluated. Group work plays a significant role in the course and a student's participation in group work will be evaluated throughout the course.

• Students are also assigned individual tasks such as problems or writing assignments. These may be collected, discussed in groups, and/or discussed in class. Some instructors may give short quizzes based on the problems and activities that students have worked on instead of or in addition to collecting and grading individual assignments.

• Students will also be given periodic exams which are used to see if students can demonstrate an acceptable level of mastery of the material. Most exams also provide an opportunity to see if students can apply what they have learned to new situations.

Topics and Approximate Time line

The following table is based on a typical semester schedule-77 class meetings of 50 minutes each. The actual amount of time spent on each topic will vary slightly from semester to semester and instructor to instructor.

Text

A problem Solving Approach to Mathematics For Elementary School Teachers, Billstein, Libeskind and Lott (2001) 7th edition

Format, Student Activities, and Grades

The course is taught using cooperative learning methods so most class periods are spent with students working together on activities in small groups. The amount of time spent lecturing depends on the individual instructor and the topic being studied, but most instructors lecture less than 1 hour per week. Students are expected to come to class prepared to participate in each day's activities. Because so much of the work is done in small groups attendance is very important. The choice of activities to be graded and the exact weight of these activities varies from one instructor to another. One possible grading scheme is given below.