COMMUNICATING ABOUT MATHEMATICS

1. COMMUNICATING ABOUT MATHEMATICS WRITING IN THE MATH CLASSROOM Constructed by Professor Susan Stuart Posted with permission because she is forever a teacher!

2. Value of writing in mathematics • Writing as a learning tool • Helps learners clarify their understanding • Helps retention of ideas • Writing as an assessment tool • Allows teacher to see if learners ‘got’ the ideas • Allows teacher to assess knowledge of math language

3. Writing as a learning tool • Ask the students to explain how both diagrams below show two-thirds • Ask students to explain why the perimeter of a rectangle with whole-number side lengths is always an even number.

4. Writing as an assessment tool • Would you rather have 4/5 of a pizza or 4/3 of a pizza? Explain your answer using words, numbers and/or pictures. • Describe two situations for which you might use a circle graph instead of a bar graph. Explain why.

5. Types of Writing Activities 6 types:

6. Reflective Writing • What did you learn about using arrays for multiplications? • Describe one thing about fractions that you understand better than you did yesterday. • How well do you feel you worked in your geometry group today?

7. Problem Solving • Use words, pictures and numbers to explain how you arrived at your answer. • Rewrite the problem in your own words. • Describe another way that you might solve the problem.

8. Explaining ideas • Why might the teacher want you to know the average score on a test? • Choose two solids. Explain how you know which has the largest volume. • How do you know that one decimal is greater than another decimal? • What makes a pattern?

9. Explaining processes • Explain what Susan did incorrectly when solving this addition : 5.2 +3.45 3.97 • Explain how to find the area of a triangular garden. • Why do we often place a number above the tens column when we are adding large numbers?

10. Creative Writing • Write a story about “The day that all the numbers disappeared”. • Choose your favourite number. Write a poem to tell why it is important. • Look at this graph. Write a newspaper article telling people about the information in the graph.

11. Definitions • Work with a friend to write a definition for ‘polygon’. Share you definition with the class. • Read the definition of ‘mean’ in the dictionary. Rewrite it in your own words and provide an example. • Keep a class math ‘pictionary’ so it can be referred to by all students.

12. Writing prompts • Open questions • How did you… • Why did you… • In what type of situation would you… • What did you think when you found… • Direct instructions • Write a letter of advice to … • Write a set of instructions for … • Explain how you know the following is incorrect… • Describe the pattern that you see.

13. Writing prompts • Explain the reason for… • Write a story problem for the number sentence… • When, in you daily life, would you… • What I liked the most about … • Explain in your own words the meaning of… • Change the problem so that…

14. Strategies for improving writing • Discuss with the whole class • List key words • Ask several questions to those who are stuck • Write as often as possible • Share examples of good writing • Model useful writing • Provide a purpose and an audience • Use words and ideas from class discussions • Ask students to explain their writing • Have students work in pairs at first writing

15. AN EXAMPLE: Mental Math: Explain two different ways to multiply 4 x 276 in your head. Which way is easier to use? Would you use a different way to multiply 5 x 98? Explain why you would use the same or different methods.