Catalog Description

MATH 257 GEOMETRY AND PROBABILITY FOR TEACHERS (3-2-4)(F,S)(AREA III). Probability, geometric concepts and principles, measurement, and topics selected from graphing and computing. The course includes a laboratory. PREREQ: MATH 157.

Prerequisites

The formal prerequisite is MATH 157. Students really need high school geometry and skills in basic algebra, which are prerequisites for MATH 157.

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.

Learning Objectives

MATH 257 is a content course and not a methods course. Our goals are that students learn the mathematical content necessary to teach mathematics in grades K-8, with emphasis on the geometric, probabilistic, and statistical topics frequently found in the middle grades.

Upon completing MATH 257 students should be able to:

• Use various systems of measurement, including the English system, the Metric system and nonstandard systems which they develop.

• Provide derivations of basic area, volume and surface area formulae.

• Categorize geometric objects both in 2 and 3 dimensions and explain the relevant characteristics of each object.

• Represent and solve problems using geometric models and Euclidean constructions.

• Systematically collect, organize and describe data.

• Evaluate and construct arguments based on the analysis of data presented in various forms.

• Determine probabilities by carrying out experiments or simulations.

• Construct a sample space and compute probabilities for an experiment.

• Explain the importance of probability and statistical information in decision making.

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.

Core Outcomes

After successfully completing MATH 257, students will be able to demonstrate the following competencies in order to fulfill specific requirements set by the Core Philosophy and Goals statement:

1. Critical Thinking/Problem Solving Skills

   Clearly identify and analyze a problem, identify possible solutions and give the rationale for a preferred solution

   Students will be asked to identify, analyze, solve and justify their solutions to problems as a normal part of the group work in the course. The areas of statistics and probability give them experience with devising and carrying out simulations. They are also expected to use geometric models to solve problems.

2. Communication Skills

   Employ speaking, listening, and interpersonal communication skills appropriate to various rhetorical situations.

   Students must learn to communicate their mathematical ideas clearly to the other members of their group. Group work also involves using interpersonal communication skills. In traditional mathematics classes often the teacher is the only one who ``speaks math''. The way that MATH 257is taught requires that all students be able to communicate mathematical ideas both written and orally. Students must also be able to write solutions to problems using correct mathematical notation and grammar.

3. Cultural Perspective

   Recognize and understand the choices and responsibilities of involved citizenship

   The sections of the course involving Statistics and Probability result in students becoming more aware of how data is collected and used to make decisions that affect everyone in society. Studying Geometry provides opportunities to discuss mathematics from historical and cultural perspectives.

4. Breadth of Knowledge and Intellectual Perspective

   Apply appropriate critical thinking/problem solving skills and communication skills in discipline-specific contexts.

   Students are given many opportunities to develop and use their problem solving skills and to communicate their solutions throughout the course. Their individual problem solving skills are assessed during exams and other individual work.

Topics and Approximate Time line

The following table is based on a typical semester schedule-75 class meetings of 50 minutes each. The actual amount of time spent on each topic and the order in which the topics are covered will vary slightly from semester to semester and instructor to instructor.

Text

A Problem Solving Approach to Mathematics for Elementary Teachers ,by Billstein, Libeskind and Lott, Seventh Edition, Addison Wesley Longman, (2001)

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.