Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Part D

Course Overview
  The Syllabus


It is convenient to have a course overview that you can use for reference. Here is a one-page syllabus that summarizes much of the material you have just read. If you are working in a workshop or group learning setting, it is appropriate to print this page out and provide it to the participants when beginning the course.

Overview of the Course

The Teaching Math online courses provide pre-service and in-service teachers an overview and exploration of the National Council of Teachers of Mathematics process standards. There are three key goals for the courses:

  • To increase familiarity with and understanding of the NCTM process standards
  • To provide direct examples of effective ways to apply the process standards in the classroom and integrate their use with content goals
  • To help teachers develop habits and practices that improve their teaching and strengthen their students' mathematical process and content skills

There are four courses, one each for the four NCTM grade bands, pre-kindergarten-2, 3-5, 6-8, and 9-12.

Each course consists of sessions, a one-hour introduction, and five four-hour content sessions. Within each session, text, illustrations, animations, video, and interactive activities are used to present the material. Course participants are frequently prompted to reflect on their learning through questions and journal entries. The course may be used in various scenarios; for instance, as a self-paced course, in a facilitated online mode, or in a face-to-face course or workshop.

As the NCTM process standards are the same for all grade bands, the following session-by-session summary applies to all four courses.

Session 1, Introduction

In this session we introduce the course content and structure, providing examples of all the activities in the course. The five part structure of each session, Observe-Explore-Define-Apply-Evaluate, is explained in detail.

Session 2, Communication

Discover the role that communication plays in your teaching and in your students' learning. Topics covered include effective questioning, helping students understand and use precise language, and using writing assignments and presentations to help students clarify and deepen their thinking. The session also includes content and activities designed to help teachers better assess their personal formal and informal mathematics communication.

Session 3, Problem Solving

Explore problem solving as a key means to introducing new material and building conceptual understanding in your students. Topics include problem selection and how to help all students develop a problem-solving disposition. A range of approaches and strategies to problem solving is introduced, as is advice on helping students identify and solve problems in contexts beyond the mathematics classroom.

Session 4, Reasoning and Proof

Investigate how reasoning and proof provide the foundations of mathematics, at all levels and in a broad context. Topics include ways to integrate the concept of deductive proof and reasoning into instruction, particularly in subjects beyond geometry. Help students understand how mathematical arguments work and the meaning of concepts such as deduction, induction, validity, and conjecture. This session also introduces types of reasoning and how mathematical proof relates to other elements of the subject.

Session 5, Representation

Discover how mathematical representations connect concepts and prompt problem solving and communication. Topics include how to help students understand and move fluently among representations, refining informal models, and understanding when and why to move to standard representations. Activities which demonstrate how to use mathematical representations to model real-life phenomena are included as well.

Session 6, Connections

Explore the interrelated nature of mathematics in this session. Topics include information on how to connect concepts within mathematics to related science, engineering, technology topics, and non-technical topics. The session includes exercises designed to help the participant see how mathematics builds as a coherent, connected whole, both from grade to grade and across subject areas.

For a detailed listing of course contents, please see the site map.

Next  The Role of Questions in the Course

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