COMMUNICATING ABOUT MATHEMATICS WRITING IN THE MATH CLASSROOM Constructed by Professor Susan Stuart Posted with permission because she is forever a teacher! Writing is a key component of the communication component of math teaching and learning.

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 Writing about what they have learned encourages learners to reflect on their learning, ask further questions and check themselves for understanding. Writing in math class provides opportunity for encouraging students to summarize and explain. “When we have to explain it to others, we truely understand”. Recent brain researh indicates that 70-90%

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. Here are two examples fo questions that students in the junior grades could write about. Notice that they focus on understanding of “big ideas” or concepts.

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. What knowledge is being assessed in each of the examples? Why might it be important to encourage students to use WORDS, NUMBERS and PICTURES?

Types of Writing Activities Reflective writing Problem solving Explaining ideas Explaining processes Creative writing Definitions There are many types of writing activities for the classroom. These are among the most common.

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?

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.

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?

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?

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.

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.

Writing prompts Open questions Direct instructions 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.

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…

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

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.