Strategies for Speaking

In classrooms and on state assessments across the country, students are required to explain their thinking and justify their answers in writing. In order for students to be successful at writing about math, talking about math must be an integral part of the daily program. Rich math discourse requires students to think about their solution strategies and tell why they make sense. These conversations are the prerequisite for articulating thoughts and ideas on paper.
 
It´s relatively simple to get a handful of students to offer solution strategies and ideas — but what about the rest of the class? Students are more apt to contribute when they can compare their responses with those of just a few other classmates. Here are some strategies for getting everyone into the act of speaking mathematically through small-group discussions:
 
• Speakers and listeners: A problem is first discussed in small groups before sharing with the whole class. One student, the speaker, leads the small-group discussion and may not represent the group when it reports back to the whole class. Only listeners share the ideas they heard.
 
• Numbered heads: Students are arranged in groups of four and are numbered from 1 to 4. Groups discuss a solution. To report back to the class, the teacher chooses a random number, such as 2; only the 2s in each group may respond.
 
• Cooperative groups: Each student has a separate task or speaking part that contributes to the answer.
 
For questions that are less open-ended, try these Every Pupil Response strategies:
 
• Choral answers: Pose a problem or ask a question, pause 10 seconds, then say, "Answer, please." The 10-second wait is essential because it opens the field to those students who are able to arrive at the answer, but cannot do it in an instant.
 
• 1, 2, 3, Flash: Students let their fingers do the talking. Pose a problem or ask a question that has three or four possible responses. At the count of "1-2-3-flash," students respond with the number of fingers that reflect their response. Quickly scan the room for results and make adjustments to your instruction, if it seems necessary.

A Process for Writing

Once you´ve gotten students comfortable with sharing their math solutions and ideas verbally, you can begin to take them through the writing process. Here are the steps:
 
1. Present students with a rich word or story problem. For example, fourth-grade students were given the following problem: Alan has $48. Ben has $41. Carrie has $25. How much money must Alan and Ben give Carrie so they all have the same amount?
 
2. After 30 seconds of thinking independently about a solution strategy, students share their strategies in small groups. This five- to seven-minute small-group discussion is about process, but may include finding the solution.
 
3. Small groups report back to the class about the solution and the strategies for finding it. The "listeners" at each table are encouraged to participate. In the sample problem, there were several pathways leading to the solution, and all were received respectfully. These prewriting discussions solidify thinking and are an integral part of the program.
 
4. Students write a first draft, solving the problem and explaining the solution strategy step by step. A rubric is provided so that students have guidelines.
 
5. As students work, circulate to identify responses that are "near perfect." One or more volunteers share their responses with the class. In this case, John´s paper (right) is shared with the class.
 
6. As John reads his paper to the class, students listen and rank his response according to the rubric. If they rank the response as a 2 or less, they are required to tell how John can improve it to become a 3. John may or may not accept his classmates´ suggestions.
 
7. Based on the class discussion around John´s paper, all students are invited to make a second draft of their own papers. John´s first draft reflects an error in thinking, which he corrects in his second draft.

Assess and Reflect

Once you have collected and reviewed the papers individually, reflect upon them in a global sense. Ask yourself questions such as:
 
• What concepts do most students understand fully? These concepts can be used as springboards to new knowledge and require no further class time.
 
• Did students use the most efficient strategy to solve the problem? If not, why not? Students typically use the most efficient strategy with which they feel comfortable. Students who use a less efficient strategy may need additional time to grasp more sophisticated algorithms.
 
• How clearly do they articulate their thoughts and ideas? Clear language, good mechanics, and proper punctuation help students share their ideas so that others can understand their thinking.
 
• How extensively do they use appropriate math terminology? Math terminology helps students communicate clearly about their solutions and thought processes. The written use of these terms will be a natural outgrowth.
 
• What other patterns do I see in the students´ papers? Identify common errors in students´ work. Think about how your instruction should address those misconceptions.
 
• Based on the students´ papers, how should I adjust instruction tomorrow? Use the reflection questions to guide your future lessons in math and writing.

Powerful Tools

Speaking and writing in math offer students an opportunity to synthesize their thinking and articulate it for others to hear, read, and review. Moreover, speaking and writing in math provide teachers with insights into students' thinking that, in some cases, are not otherwise accessible. Taking time to reflect on the writing also maximizes instructional time for you and your students. In short, speaking and writing in math are powerful tools that can be used for assessing student knowledge and informing future instruction.

Robyn Silbey is a school-based math specialist in Montgomery County, Maryland. This article was originally published in the April 2003 issue of Instructor.

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