Writing About Math
Writing about math can be a very positive and fruitful learning experience. Here's a look at some of the benefits; a variety of writing categories and topics; and suggestions for creating a positive environment for writing about math.
WHY WRITE IN MATH CLASS?
Writing can help students think about ideas in new ways and develop critical thinking skills, while involving students directly in the learning process. When students incorporate personal experiences into their writing, learning becomes more meaningful. Writing opens new lines of communication between student and teacher, and teachers can use students' writing to assess understanding and make instructional decisions. Informal writing can make a topic more appealing and stimulate creativity. Writing about math can be a path to understanding, as students clarify and "take ownership" of concepts and connect math to the real world.
WRITING SUPPORTS NCTM PROCESS STANDARDS
As you read through this partial listing of NCTM Process Standards, reflect on how writing about math can engage students in each.
- solve problems that arise in mathematics and in other contexts
- apply and adapt a variety of appropriate strategies to solve problems
- monitor and reflect on the process of mathematical problem solving
- make and investigate mathematical conjectures
- select and use various types of reasoning and methods of proof
- organize and consolidate mathematical thinking though communication
- communicate 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
- recognize and use connections among mathematical ideas
- recognize and apply mathematics in contexts outside of mathematics
- create and use representations to organize, record, and communicate mathematical ideas
TYPES OF WRITING ABOUT MATH
Writing to explain how a problem was solved is a common and valuable form of mathematical writing, but it's just one of many possible forms. Writing in different genres taps different ways of thinking and keeps assignments fresh. Here's a grab bag of possibilities:
- Math autobiography
This is a good writing category for the start of the year, as you're learning about students' backgrounds and attitudes. "What has been one of your best/worst experiences in math? How did you use math over the summer?"
- Learning log, journal, or blog
A math journal can be kept in a composition book or spiral notebook, or can be recorded in an online blog if students have easy access to computers. It's great when a teacher or classmates write short responses to entries in learning logs or blogs, but not every entry needs a comment if students are writing frequently. Topics can be drawn from any of the categories in this section, or might include
Write rapidly for a short, fixed amount of time to "dump out ideas."
- One-Minute Paper
To gauge understanding or reactions
- Explain mathematical ideas; construct meanings
Examples: What is subtraction? What games involve chance, strategy, or both? Compare different procedures.
- Explain in detail how you solved a math problem
Encourage students to write a clear, concise paragraph, citing the strategy chosen and describing the steps used to implement the strategy.
- Create word problems or test questions.
- Respond to word problems.
- Write to vent (anonymously) or make suggestions.
- Write to ask or answer questions.
Questions can be shared anonymously for more candid input. They can be written on sticky notes placed in a "parking lot" on a large paper on the wall. Classmates can help categorize and answer the questions.
- Write creatively to explore, have fun, and look at math in fresh new ways.
The ideas are endless. Consider:
- Write to inform or teach in the "real world."
- Write to persuade
Using real-life data to support an argument helps students see the power of math in daily life. For example, a persuasive essay on "the greatest baseball hero of all time" or "why we need to be green" or even "why we need a longer lunch period" surely would use data to support the thesis.
- Write a friendly letter
The letter can be to a real or imaginary audience, on a math topic of interest.
- Define vocabulary
- Include words from a word bank in an assignment
- Translate an equation into English
- Reword a teacher's explanation in your own words
- Formal papers, including research papers
- Idea box for students' contributions to writing topics
SET THE STAGE FOR POSITIVE WRITING EXPERIENCES
The following strategies are some you can use to create an environment in which writing about math is a positive learning experience.
Ask good questions worth communicating about, with multiple possible approaches.
Make sure early activities are fairly easy and satisfying for all students. (We don't want to compound a possible bad attitude about math with a bad attitude about writing! We want writing to enhance the experience of learning math.)
Discuss the assignment before writing time begins. Make sure students understand why you are asking them to write.
Begin with verbal explanations as a shared class activity. As students explain orally, ask questions to help them clarify their responses.
Don't just "assign" writing -- facilitate it in many ways; guide students as they learn how to be more effective thinkers and communicators.
Provide writing prompts -- including guidelines, criteria, rubrics, and strategies.
Share models of successful student writing.
Ask students to consider a specific audience Imagine they are explaining to a young child step by step, or write as if they are mathematicians (using proper terminology).
Provide frequent opportunities for cooperative learning: Discuss beforehand in small groups; write in pairs or small groups; respond to writing in small groups.
During writing time, circulate, ask questions, and elicit ideas
- "What do you have to do?"
- "What ideas do you have?"
- "How will you start?"
- "Tell me something you know."
- "Why do you think that?"
Provide plenty of time for writing.
Provide constructive feedback. Respond to the content.
EIGHTEEN WRITING TOPICS OR PROMPTS
- How long do you think it would take you to count to a million by ones? What makes you think that?
- How are the numbers 10 and 100 alike? How are they different?
- What is your favorite shape? it? Why do you like it so much? Write a poem or poster describing why it's so great.
- How many measurements can you think of to describe yourself? (height, weight, shoe size, and so on)
- Is a map a measuring device? Why or why not?
- List five or more kinds of statistics or number facts that are used to talk about baseball and baseball players. How else are numbers used in baseball?
- Explain how you could multiply 6 x 99 in your head.
- Estimate how many students are in the whole school. Explain how you came up with your estimate and how you might check the accuracy of the estimate.
- Write a story problem that cannot be solved because there is not enough information.
- Describe an object from your bedroom or kitchen using as many numbers and math terms as you can.
- How do your parents use math? Interview them about it, and then list all the things they do that involve math.
- What is money? Define it in your own words.
- Think of three activities you could do to teach the concept of decimals to students who don't speak much English.
- Would you rather take a test that has 10 questions worth 10 points each, or one with 20 questions worth 5 points each? Or 25 questions worth 4 points each? Or 50 questions worth 2 points each? Explain your reasoning and estimate where you would score the highest.
- Make up a word problem involving cooking and fractions.
- Write a letter to the school board to convince them that students should be able to use calculators in math class.
- Write the numerals from 1 to 9 and answer these questions about them: Which is most artistic? Most expressive? Most colorful? Most useful? Luckiest? Give reasons for your choices.
- If you could be any number from 1 to 100, which would you be, and why? Which numbers would you choose for friends and family members?
Prompts 1-12 come from Marvelous Math Writing Prompts, by Andrew Kaplan, Scholastic, 2001. Prompts 13-18 come from Standards-Based Math Graphic Organizers, Rubrics, and Writing Prompts for Middle Grade Students, by Imogene Forte & Sandra Schurr, Incentive Publications, 2001.
Article by Wendy Petti
Copyright Â© 2008 Education World
As you know, mathematics is a very complex subject. Learning it requires more than just memorizing sets of facts and examples. If students are not able to process their ideas before, during, and after learning has taken place, they will have trouble really improving their conceptual framework.
This processing can take place orally, through discussion; mentally, through thinking back over the work and learning done; or in writing, by explaining in a narrative form the process they just went through. Ideally, all of these modes are used by a teacher, so that students have multiple opportunities to cement new knowledge, and also so that students who learn in different ways can have their unique learning styles supported.
This might sound funny, but mathematicians don’t just scribble mathematical notations on chalkboards until arriving at a profound new theorem, or answer to a problem. In addition to doing math, mathematicians are also required to write clearly and effectively. How else could they explain their ideas to people who don’t have their specific skill sets—or, in some cases, even to those who do?
In addition to these considerations, mathematicians also need to keep a complete record of their ideas and work, and be in a position where they can communicate their findings to the world. The list below takes a look at some of the strategies that can be used to engage math students in essay writing.
This is a writing strategy that a teacher uses throughout or at the end of a lesson to engage students to develop big and better concepts and ideas. In mathematics, you can use these strategies to foster this kind of engagement.
1. CALLA Strategy.
The Cognitive Academic Language Learning Approach is a strategy designed to provide students with support when it comes to learning content as well as learning how to learn. What the strategy demands is that the students read and record whatever it is that the problem is requesting.
Students are guided throughout the process to a particular solution by asking them to solve, check and explain every step of their work. This process demands that students write about the things that made the problem difficult, or any other strategies that helped them to solve the problem. This strategy will provide support for ESL learners in content and learning strategies, and go ahead to help them get organized. It also gives students a powerful tool for any kind of future learning endeavor, which is the ability to self-reflect and improve their own learning process.
2. Column Notes Strategy
The Column Notes strategy involves the double and at times the triple entry journal as a column graphic organizer. Students are record important and factual information from a lecture and/or text on the left hand side of the column, and the right hand side is normally used by students to record and process their personal responses and information.
The students can use the third column for the triple journal to summarize their understanding of concepts. This strategy is basically used to help students recall information, gives them an opportunity to clarify information, helps them make personal connections with the gathered new information, and encourages them to analyse and question information that is presented.
3. Compare and contrast strategy.
This strategy has students collect information relating to two or more mathematical concepts. The student will then be required to record the key attributes on a two column graphic organizer that will clarify both the similarities and the differences. This strategy ultimately encourages students to examine the systems being compared analytically, and helps them to clarify any information that they provide in a personal manner that will make the most sense to their own unique learning process.
4. Content definition map strategy.
The Concept Definition Map Strategy is basically a visual representation whereby examples, vocabulary terms, and sub-concepts are related to a main topic. This goes to help students make connections that are in existence between the ideas, gives the students amazing opportunities for review, provides them with tools that allows them to reflect on the changes in their understanding, and gives them the opportunity of accessing prior knowledge.
5. The Frayer model of concept development.
In this strategy, students are required to use a variety of modes and methods including: oral, written, and visual content to develop not only a personal but an in-depth understanding of some of the key mathematical concepts and terms as a whole. The strategy was generally developed to help students gain a better understanding of concepts.
The most intriguing aspect about the model is that it relies on a graphic organizer help with the understanding of the concepts. The concepts are explained to you through definitions, characteristics, and examples.
6. The Gist strategy.
The General Interactions between Schemata and Text is a strategy that involves a step by step process of summarizing text materials. This strategy in particular is very useful for students who have difficulties putting what they have read into their own words.
What students are required to do for the GIST Strategy is to restate their main ideas from mathematics texts while at the same time omitting specific examples that have been used to illustrate concepts. This strategy basically helps students gain a better comprehension of mathematics text, allows them to process new information, and establishes connections with their own ideas while providing students with a structure for identifying and remembering some of the key ideas covered.
Any of these strategies can help to engage a math student into writing. You should explore them all, and adopt the one—or ones!—that prove most effective in supporting your students.
You can still combine two or even more of these approaches to enhance your chances of supporting every individual student. But maybe the best way to engage students into writing is rewards—for instance, by offering some kind of prize or reward to those students who participate, or who do well on a given assignment. You can also show students how easily they can earn some extra money by participating in different writing contests and competitions (this has been working with my students!).
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About the Author
Jessica Millis is an educator and freelance blogger. She works as an essay editor and writer at EssayMama.com – a service that connects students and writers all over the world. Follow EssayMama on Facebook, G+ and Twitter!