Mathematical Knowledge for Teaching: Ratio, Proportion, and Algebraic Reasoning
EMAT 6130E
3 hours
Mathematical Knowledge for Teaching: Ratio, Proportion, and Algebraic Reasoning
Course Description
Students will examine secondary mathematics topics that include ratio, proportional reasoning, relationships to linear functions, the multiple roles of variable, making sense of equations, and the utility, types, and representations of functions. The course will review research on students’ reasoning and instructional strategies for fostering proportional and algebraic reasoning.
Athena Title
MKT Algebraic Reasoning
Non-Traditional Format
This course will be taught 95% or more online.
Semester Course Offered
Offered summer semester every year.
Grading System
A - F (Traditional)
Student learning Outcomes
Students will understand how to address and investigate basic concepts in secondary pre-algebra and algebra courses, including ratio, proportional reasoning, the different uses of variable, equations and equality, and linear, quadratic, and exponential functions.
Students will understand how to engage in weekly problem-solving activities by solving ratio, proportion, and function problems.
Students will understand how to review and synthesize the research literature on students’ understanding of ratio, proportion, variable, equations, and functions.
Students will understand how to review and synthesize the research literature on effective instruction of ratio, proportion, variable, equations, and functions.
Students will understand how to communicate and reason mathematically, make connections across representations, including tables, functions, and graphs, and develop and present justifications and proofs.
Students will understand how to design and analyze tasks and activities that promote the learning of key concepts related to ratio, proportion, variable, equations, and functions.
Students will understand how to use general tools such as word processing, spreadsheets, and the Internet to facilitate mathematical investigations and to communicate about mathematical investigations.
Students will understand how to explore mathematics using a variety of technologies including online graphing calculators and online geometric and algebraic construction software.
Topical Outline
The use of variables and symbolic representations
Ratios, rates, and proportions and their connections to fractions and linear functions
Equality, equations, and solution techniques for solving equations
Linear, quadratic, and exponential functions
Research on students’ reasoning about ratio, proportion, and algebra
Research on the effective instruction of ratio, proportion, and algebra
Research on the use of representations and manipulatives in supporting mathematical reasoning in ratios, proportion, and algebra
Best practices for enacting graphing, modeling, argumentation, and other current priority topics in the 6-12 pre-algebra and algebra classroom
Connections to precalculus, calculus, and other college-level mathematical ideas
