An Overview of the Communications Standard for School Mathematics? 1

2 Instructional programs from prekindergarten through grade 12 should enable all students to— Communications Standard organize and consolidate their mathematical thinking through communication; communicate their mathematical thinking coherently and clearly to peers, teachers, and others; analyze and evaluate the mathematical thinking and strategies of others; use the language of mathematics to express mathematical ideas precisely.

3 Communications Standard Students who have opportunities, encouragement, and support for speaking, writing, reading, and listening in mathematics classes reap duel benefits: they communicate to learn mathematics, and they learn to communicate mathematically.

4 Communications Standard for Grades 6 – 8.

5 What should communications look like in grades 6 through 8?  When students are required to communicate their thinking orally and in writing it is more challenging to think and reason mathematically.  When students in grades 6-8 explain their thinking, they can be held to higher standards that are more stringent than would be likely for younger students.  Teachers should build a sense of community so students feel free to express their ideas honestly and openly, without fear of ridicule.

6 What should be the teacher’s role in developing communications in grades 6 through 8? Communication should focus on worthwhile mathematical tasks. Task that -  Are accessible to multiple methods of solution;  Relate to important mathematical ideas;  Allow multiple representations;  Afford students opportunities to interpret, justify, and conjecture.

7 What should be the teacher’s role in developing communications in grades 6 through 8? Teachers can use communications in mathematics to give students opportunities to -  Formulate explanations;  Think through problems;  Try out new vocabulary or notation;  Experiment with forms of argumentation;  Justify conjectures;  Critique justifications;  Reflect on their own understanding and on the ideas of others.

8 Communication Standard for Grades 9 – 12.

9 What should communication look like in grades 9 through 12?  Students should formulate mathematical definitions and express generalizations discovered through investigations;  Students should express mathematical ideas orally and in writing;  Students should read written presentations of mathematics with understanding;  Students should ask clarifying and extending questions related to mathematics they have read or heard about.

10 What should be the teacher’s role in developing communication in grades 9 through 12?  Appropriate symbolism an vocabulary should be used in all material presented to students, the the clear expectation of appropriate use by students.  Techniques used in teaching writing – brainstorming, clarifying, and revision can be effectively used in teaching mathematics.  Students can be encouraged to use journals describing their mathematical experiences.  The use of calculators and computers require students to use and understand accurate, concise mathematical language.

11 Working in three groups (7-8, 9-10 and 11-12), develop a lesson for students in that band width that will illustrate at least one of the bullets in the communication standard. We will leave time at the end of the period to present your ideas. Only develop the mathematics of the lesson. Do not worry about the mechanics of the lesson plan. Pick a topic and develop the way in which you will present it so that at least one of the bullets is used. Bonus points if you use bullets from one of the curriculum standards.

12 Assignment Read: NCTM Principles and Standards p 64-66, , and