Writing in the Math Classroom

1. Writing in the Math Classroom Pam Pedigo Dodson Elementary Numeracy Coach Tammy Parsons John Early Middle School Numeracy Coach

3. According to NCTM, students should be able to. . . 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 (NCTM, 2006).

4. In the beginning students typically need. . . a great deal of guidance and support clear understanding of the assignment; a purpose for writing to verbalize their thinking clear structures for writing assignments encouragement

5. Writing in the Mathematics Classroom: Model, Model, Model! Teacher must model the writing , over and over. Do “Think Alouds” and tell students “What good writers do,” as you model. On chart paper, create class examples together with student input, then display in class for student reference.

6. C-R-A Model: Concrete to Representational to Abstract • 1stConcrete-Students will use their prior knowledge to construct concrete representations of math • 2nd Representational-Students must represent their understanding in a reflective &/or symbolic form • 3rdAbstract-One or both forms will be a visual reminder for the understanding of the higher-thinking abstract

7. Quick Writes These are short pieces of writing designed to focus students’ thinking. Teachers can use quick writes to: PreK-4: assess prior knowledge before instruction in order to set the stage for new information (ex. create a list of keywords, a list of questions, 3 things I know/don’t know) give students time to write briefly on the day’s topic before contributing to class discussions. pause in the middle of instruction to check for understanding, or to make connections and predictions. summarize main points, form opinions, or reflect on what was learned after instruction

8. Quick Writes 5th-8th assess prior knowledge before instruction in order to set the stage for new information. Read these “Entrance Slips” anonymously before instruction to set the stage for new ideas. (create a list of keywords, a list of questions, 3 things I know/don’t know) give students time to write briefly on the day’s topic before contributing to class discussions. pause in the middle of instruction to check for understanding, or to make connections and predictions. (paraphrase, ask a question) summarize main points, form opinions, or reflect on what was learned after instruction. (“Exit Slip” 3-Things I Learned, 2- Things I Wonder About, 1- Thing I Could Teach Someone Else)

9. Quick Writes Evaluation tips First, model “incomplete”, “adequate”, and “excellent” responses (check minus, check, check plus). Look for content, quantity, appropriateness, elaboration, etc. Assess as complete/incomplete, correct/incorrect, or trade for peer review. Evaluate content only, never for grammar

10. Creative Writing – Tangram Stories

11. R.A.F.T. R.A.F.T. writing prompts challenge students to assume a Role before writing, to write for an imaginary Audience, to write using a given Format, to write about a certain Topic. This is a simple but powerful technique that will inspire more thoughtful writing from yourself or your students. Enter the RAFT writing assignment. Its sole purpose is to make writing feel more authentic in two ways: 1) students are asked to think and write from a real world person's perspective, and they are asked to shape their ideas to appeal to an audience outside the classroom; 2) because they are considering perspective as they go through the writing process, students are being asked to think at a much deeper level of Bloom's Taxonomy.

12. PROMPT Builder http://www.writingfix.com/WAC/Writing_Across_Curriculum_RAFTS_Math.htm You will write as though you are a . . .FARMER Writing something to be heard by. . .a 6 o’clock newscast audience The writing will take the form of . . a news story And will be about . . . Perimeter Your piece of writing’s purpose will be to . . COMPLAIN about something

15. ORGANIZATION WRITING LEADS (HOOKS) • It might surprise you that… • I would never have believed that… • In order to understand ___________, you need to know… • What I discovered about this problem was… • The strangest thing about this problem was/is… • I expected my answer to be ____________, but it… • If I could summarize my findings in a few words, it would be… • What I learned from this problem was… • Originally, I tried to do the problem like ________________, but then I gave up and did… • This problem is easy/difficult because… • I was surprised to use ____________ to solve this problem. • This problem related to our learning target because… • This problem made me think about… • Did you know…? • Can you imagine…?

16. Problem writing • Have students write math problems using the skill that is being learned in class. Example prompts: • Write an addition problem that has an answer for 465. • Write a math problem to go with a picture. • Write a story problem that involves multiplication and subtraction. • Write and illustrate a story problem for a 2nd grader (McGehe, 1991). • Write a step-by-step explanation of how to solve an equation or graph a function for a student who was absent.

17. Explanations Have students explain how they solved a problem. Have students write a “how to” piece for another student (Burns, 2004; Fortescue, 1994; Brandenburg, 2002; Evans, 1984).

18. Troubleshooting Have students explain their errors

19. Definitions Have students write definitions in their own terms (Evans, 1984). Illustrate your definition. Give examples and non-examples of your definition. Compare and contrast your definition with that which is in the textbook.

20. Word webs Gathering ideas about concepts (definitions, uses, ways to write or express the concepts, how the concept connects to other math skills, feelings about the concept)

22. Make a sentence using the following words WORDS (2): foot yard inch WORDS (3): dividend divisor quotient WORDS (4): ordered pair quadrant WORDS (5): solution round remainder

23. Cubing • A writing strategy that “allows students to examine a problem from six viewpoints.” “Each of the viewpoints is written on one face of a cube. … [T]he prompts can be modified to meet the objectives of many learning situations…” Students write informal responses to share with their classmates. (Pugalee, DiBiase & Wood, 1999) • Describe it (the process, event, features, traits) • Compare and contrast it • Associate it (analogies, makes me think of?) • Analyze it (composed of? Steps? Procedures?) • Apply it (how can it be applied to other situation?) • Argue for or against it (support decision)

24. Math journals / math logs Keep track of what students are doing and feeling in class. You may choose to use prompts to guide student responses summarize newly acquired knowledge. write vocabulary terms in their own words. draw what was most interesting or confusing. create a list of questions. explain math or science problems or terms in writing. make connections (between new info and prior knowledge).

25. Notebook Assessment Flag a piece of work that shows . . . • Something you learned about _________ • Something that shows your writing skills • Something that shows you know how to make observations • Something your learned about data collection • Something that shows you know how to give a good explanation • Something that shows improvement • Something that shows your best work

26. Here are some generic writing assignments that may be able to be modified to fit your curriculum. Remember to always think of your curriculum first and make the assignment meaningful. Remember also that these writing assignments can/should be of various lengths. Some could be a couple of sentences, some paragraph length and even some full papers. Think about having students write a(n): Letter to the editor News article about a current event in math Children’s book teaching a concept Cause-effect paragraph/paper about a math concept Poem about a critical concept Character profile of a famous or little known mathematician Questions that they have about a lesson or critical concept Discussion of ways to use a math concept in the “real world” Justifications or explanations of answers Lab report Summary of a flight plan Stock market report Corporation financial report • Reaction to a lesson • Summary of a lesson • Comparison/contrast between two subjects/types of problems • Answer to an essay question on a test • Definition(s) of a key term or set of terms • Paragraph explaining how to solve a problem • Learning log • Paragraph/paper discussing a career in the field • Documented paragraph/paper • Evaluation of their progress in learning material or completing assignment

27. References http://writingfix.com/WAC/numberfix.htm http://www.math.du.edu/~mkinyon/mathwrite.html http://www2.ups.edu/community/tofu/lev2/journaling/writemath.htm http://www.umassmed.edu/MathGraphicOrganizers.aspx?linkidentifier=id&itemid=49072 http://olc.spsd.sk.ca/DE/PD/instr/strats/raft/ Writing in Math Class, Marilyn Burns