Reasoning and Proof for the P-6 Classroom

General

Prefix

STEM

Course Number

451

Course Level

Undergraduate

Department/Unit(s)

Stem Education

College/School

College of Science and Engineering

Description

Problem solving, conjecture, generalization, and proof in effective teaching of STEM. Mathematical reasoning as an iterative process of conjecturing, generalizing, and investigating. Topics are drawn from set theory, logic, arithmetic, algebra, geometry and STEM fields.

Credits

Credit Hours

Min

Max

Repeatable

Goals and Diversity

MN Goal Course

Cultural Diversity

Learning Outcomes

Outcome

Formulate and interpret statements presented in Boolean logic. Reformulate statements from common language to formal logic. Apply truth tables and the rules of propositional and predicate calculus.

Outcome

Write and interpret mathematical notation and mathematical definitions.

Outcome

Demonstrate a mathematical proof of a stated algebraic relation using any of the following techniques: direct proof, indirect proof, contradiction, mathematical induction.

Outcome

Demonstrate the use of mathematical reasoning by justifying and generalizing patterns and relationships.

Outcome

Write solutions to problems and proofs of theorems that meet rigorous standards based on content, organization and coherence, argument and support, and style and mechanics.

Outcome

Identify and use current standards (state, national, and NCTM), both content and process, for the P-6 mathematics curriculum.

Outcome

Analyze research on the teaching and learning of problem solving, conjecture, generalization and proof in the P-6 mathematics curriculum.

Outcome

Identify technologies as an instruction tool in the P-6 or special education classroom.

Outcome

Use problem solving approaches to solve and justify solutions of various types of problems drawn from the STEM fields.

Outcome

Develop lessons for the P-6 or special education classroom using recent research on the teaching and learning of problem solving, conjecture, generalization, and proof.

Course Outline

Inductive and deductive reasoning. 15% Problem-solving approaches. 15% Numbers and numeration systems. 10% Logic. 10% Set theory. 10% Current trends in teaching mathematics in the P-6 and special education classrooms. 10% Instructional strategies and material selection for teaching proof, conjecture, and generalization in the P-6 and special education classroom. 15% Number theory. 5% Geometry. 5% Topic chosen by instructor. 5%

Dependencies

Programs

STEM451 is a completion requirement for: