Math 5001: Introductory Mathematical Concepts I

Math 5001: Introductory MathematicalConcepts I

An Overview

The discipline of mathematics involves: searching for patterns and structure in quantitative and spatial situations; finding solutions to novel problems; posing and testing conjectures; convincing others of the validity of results; extending problems and situations by posing new questions; generalizing from individual problems and situations to classes of problems or situations.

In this course, middle school mathematics teachers will do mathematics. They will—working alone, in small groups, and as a whole class—solve a series of rich, challenging problems that tap the big ideas in Colorado’s Model Content Standards for Mathematics. By doing mathematics, these teachers will deepen and broaden their conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition—their mathematical proficiency.

Part I: Introductory Problems

This course will begin by placing students in random groups of 3 or 4 to work on a set of 3 problems. Once all groups have made good progress on all problems, we hold the first set of whole-class discussions. At the end of this part of the course, students complete their first Collected an Assessed Problem (CAP). The problems, and the ways in which instructors orchestrate student engagement, are designed to establish norms and expectations for this course as well as its sequel, Introductory Mathematical Concepts II.

Part II: Patterns

Identifying and using patterns to solve problems forms the foundation for algebraic thinking. In addition, gathering information and searching for patterns is an essential problem-solving tool. In Part II of this course, students will work through 18 problems designed to build their capacity to find and use patterns.

Part III: Geometry and Measurement

In this sequence of 17 problems and activities, students re-visit important ideas in geometry and measurement - angle, dimensions, area, π and the Pythagorean Theorem - with emphasis on the connections among these ideas and their conceptual foundation.

Part IV: Counting and Number Sense

The last part of the course has 2 foci: we pose 10 problems that involve counting (using the Multiplication Principle and the notions typically called “permutations” and “combinations”); and 4 problems that ask students to make sense of rational numbers.

Assessments

The course will offer 2 types of assessment items:

• Collected and Assessed Problems (CAPs) which are extended problems to be completed in writing outside of class.
• A variety of problems will be used for in-class assessments and on the final exam.

QuickTime Videos

In addition, a digital video archive of 8 QuickTime movies that illustrate important issues for instructors will be used.