Lesson Plan
Math Out Loud!
Heard the word? Talking and writing about math boosts understanding in a big way
By
Robyn Silbey
- Grades: PreK–K, 1–2, 3–5, 6–8
Ensure your students are comprehending their math lessons--talking in the classroom helps ensure math retention in a big way!
Allan had been in the United States for less than a year. A nonnative speaker, he was hesitant to speak up in my math class, although his math abilities were good. While Allan knew the basics of working through a problem, he was unable to explain how he had done so.
For all students, a key to deepening math understanding lies in communication. Talking one's way through a problem, listening to others' solutions, and writing about the steps one took to solve the problem can help students to organize and consolidate their math thinking. Communication is, in fact, one of the five important NCTM process standards in mathematics.
Allan first listened to his classmates talk their way through a solution. As they shared their writing about math, he compared their problem-solving strategies with his own. Finally, using his classmates' verbal and written thought processes as a model, Allan was able to express his own mathematical thinking on paper. As a result, his math understanding grew, and I was better able to assess his progress.
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.
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.
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.
• 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.
- Subjects:Expository Writing, Logic and Problem Solving, Communication and Language Development, Educational Standards, Teacher Tips and Strategies
