Writing in Mathematics

1. Writing in Mathematics Carlos Rodriguez Area 11 Curriculum & Instructional Coach Spring 2011

2. Objectives • Why math journaling? • Key essentials? • Establish a routine • Choose a focus • Model the process and expectations • Models and anchor charts • Establish a feedback protocol • Implementation Strategy Scaffold • Open end response (opinion, reflection, questions…) • Review and introduce math skills/concepts • Problem solving (extended response)

3. Why use Math Journals? Math journals are an effective way for teachers to understand a child’s mathematical thinking, processes, strategic knowledge, and/or proficiency with skills and concepts. Journaling within the math class should reflect a gradual progression that include but are not limited to the following: • Response to Open-ended Prompts • Solving Daily Math Problems • Skills Review/Scaffolding • Extended Response Problem Solving

4. Start by… • Determine how and when to use the math journals: • Select several uses and discuss each with the students: Ex. Daily problem solving, open response, exit slips, selected writing prompts, etc. MODEL, MODEL, MODEL! • Determine when journals will be incorporated into the math lesson: Ex. During the Warm-Up, during the wrap up, “x” number of days per week, etc. • Develop a protocol for how journals will be assessed and shared: Ex. Develop a schedule for feedback/assessment, encourage students to write with the intention to share with their classmates, create a rubric for assessment, etc. • Determine how journals should be organized: storage in the classroom, how they will be distributed when it’s time to use them, whether they are organized by unit, quarterly or a continuation of the whole year, etc. • Support students writing by building anchor charts for concepts, creating math word walls, posting math problem solving strategies, etc. • Increase the classroom discourse during math instruction: students who are able to articulate their thinking will find it easier to translate their thoughts into writing. • Encourage students to focus on their thought processes, not the “right answer”

5. Implementation Strategies:Open-Ended Response • Begin implementation of journals with affective, open ended questions regarding the students feelings about a particular experience, concept, lesson and/or problem. This will give the teacher greater insight regarding how to develop each individual student and diagnose misconceptions and or areas of difficulty immediately: • Example #1: Reflect on your participation in class today and complete the following statements: I learned that …… I was surprised that…. I’m not sure about…. I noticed that..... • Example #2: Have students write a paragraph about their math experiences in and out of school: When you were younger, what didn’t you like about math? What did you like? Did you have any tricks to help you remember certain concepts? Who was your favorite math teacher? What did he/she do to keep your interest? Can you remember a time when you learned something about math in school and then was able to use it outside of school? How did that make you feel? What is your earliest memory of being taught Mathematics?

6. Implementation Strategies:Reviewing Math Concepts and Scaffolding New Concepts • Once students are comfortable with writing their attitudes and feelings about mathematics, they are ready to write about simple and familiar concepts . Students should not be asked to write about a skill that is unfamiliar to them, it reduces their confidence which will have a negative impact on their attitude towards writing and mathematics. Instead, they should be asked, at this point, to write about a skill/concept that you are reviewing and/or a skill that was addressed during the lesson: • Examples: Explain in your own words what subtraction means. How would you define a fraction to someone that you were teaching? Tell two ways to solve a division problem. When is it appropriate to use an estimate rather than the actual number? Draw your favorite shape and give the attributes of the shape. Describe some objects in your environment that have a measurement of less than 6 centimeters. Explain inverse operations and provide an example of how it works. Compare solving single-step equations to solving two-step equations, how are they alike and/or different? How are fractions, decimals and percents related? Which type of graph would be best to show change over time? Are there more than one?

7. Implementation Strategies:Problem Solving • By this time, students should be accustomed to writing, students will now be asked to write solutions to math problems. They should be able to write about the solution they got as well as how they arrived at that solution. This will translate into higher scores for Math Extended Response as well as help teachers diagnose where the misconceptions or “break down” took place in the students thinking. When selecting problems for students to solve and write solutions, consider the following: Selected Problems should: • Pin point a confusing or easily misunderstood concept or mathematical idea: Example: Write 0.2 and 0.020 as a fraction. Are they equal? Explain your answer; • Have several solution strategies: Example: The Chicago Bulls won 8 out of 10 games. The Boston Celtics won 15 out of 18 games. Whose team won a greater fraction of games? Explain your answer. • Encourage students to compare or debate two different solutions to the same problem: Example: Who is correct? The problem: Which fraction is greater? 1/3 or 2/5? Jason’s solution: 2/5 is bigger because 15 is the LCD and 1/3 equals 5/15. 2/5 equals 6/15. So 2/5 is greater. Blake’s solution: I used the calculator, I made them decimals and then compared the decimals. For 1.3, I divided 1 into 3 and got 3.0. Then I divided 2 into 5 and got 2.2. 3.0 is bigger than 2.2 , so 1/3 is greater. • Use logical reasoning in determining if their answers or thoughts are appropriate for the question: Examples: Ms. James wants to treat her students to some cupcakes for their behavior. There are 30 students in the class. The cupcakes are sold in packages of 7 cupcakes per box. What is the least number of boxes Ms. James needs to purchase? • Elicit students to think beyond applying procedures, but focus on contextual application: Examples: include situational problems that allow students to use background knowledge and experience to make the problem relative.

8. Creative Writing • Creative Writing allows students to broaden their view of mathematics and incorporate their own individual interest into mathematics instruction. One way to begin the implementation of creative writing in math is by reading math stories aloud (ex. Marilyn Burns), writing a math story together, using Math Mad-Libs (funny stories), and incorporating poetry. • Examples of creative writing prompts: If you were a centimeter high, what would you be able to do? Using magazine pictures and clips, write a problem or short story that the pictures could represent. Create your own shape, what would you name it and what are it’s attributes? Create a menu for your favorite restaurant, write a story detailing what you ordered, how much it costs, how much change was left, etc. Write a children's book explaining place value to a younger student. What would you do if you won $100, $1,000, $100, 000, and $1,000,000? What if the number system did not contain “0”, how would that effect people? What’s your favorite number, why? Create a Math Superhero or Math Fairy Tale character and write a story (be sure to include numbers, math symbols, vocabulary, etc.)

9. Creative Writing Continued… • Examples of Math Poetry: Math Haiku: the season has come the days are getting longer minutes and hours Math Acrostics: A.N.G.L.E.S- Acute less than 90°; None are less than 0; Greater than 90° are called obtuse; Lines that are 180° are called straight angles; Equivalent angles measure the same; Supplementary angles add up to 180° Math Limericks: There was a young student from Rye, Who worked out the value of π. "It happens," said he, "That it's just over 3, Though I'd rather you don't ask me why."

10. Real World Connections: • Students must be able to connect their learning by understanding conceptually how the mathematics will be applied in a real world context. Teachers should make these connections daily (when new concepts are introduced) as well as through writing: • Examples: Take students on “math walk” throughout the building or neighborhood to take photographs of mathematics (street signs, benches with parallel lines, obtuse angles created by branches of trees, slope of sliding board at the playground, etc.) Have students write a story or series of problems related to their observations and create a class book. Have students respond to the following types of prompts weekly, bi-weekly or monthly: List all of the ways that you used math this week Write about something mathematical that you saw on television Name at least 10 things that you can do in a second, a minute, an hour, a day… Make a graph and chart of how you spend your day. Write a narrative explaining the data.

11. Helpful Reminders: • Talk to students regarding the purpose of their writing. Motivate students to write with positive praise, modeling and feedback! • Consider allowing students to personalize their journals with stickers, pictures, etc. Make the process engaging and exciting for students, not laborious and tedious. • Keep journals in the classroom, do not send home for homework. • Set a timer for journal entries to focus students. • Decide on a system for identifying journal entries, do not spend time having students write the prompt each time. Use a numbering system, print prompts on strips of paper to staple to their journal pages, etc. • Do not focus heavily on grammar and spelling initially, build up to improvement in their overall writing • Periodically allow for peer collaboration such as brainstorming ideas and providing collaborative feedback. • Regularly allow students to share entries with the class • Respond to students writing, personalized responses will encourage students to want to improve. • Allow students to suggest prompt ideas • Use students responses to evaluate your instruction • Begin the year writing EVERYDAY in math, once students are accustomed to the various types of entries, 2 to 3 times a week is sufficient.

12. Conclusion: • A comprehensive student math journal will display samples from each of the fore mentioned writing styles; it will also display a progression of improved content throughout the year. As with any new concept, journal writing is a skill that will require patience for proper implementation, so focus on quality, not quantity!

13. Additional Resources for Math Writing Prompts • http://www.myteacherpages.com/webpages/jgriffin/journal.cfm • http://www.superteacherworksheets.com/journal-prompts.html • http://www.quincy.k12.mi.us/qms/PDF_2009_2010/ • http://letsplaymath.net/2007/08/21/writing-to-learn-math/ • http://www.mathpower.com/funstuff.htm • http://www.mathlibs.com/ • http://www.teach-nology.com/worksheets/language_arts/madlibs/