CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
Implementing in the classroom:
Through this practice students are learning to support their thinking and strategies with evidence. As mathematicians they can justify their solutions and communicate their thinking process to others. To become proficient with this practice students need a sufficient amount of time observing teacher modeling, rehearsing and talking with other mathematicians. Teachers can use the 5 Talk Moves below to initiate and model student conversations.
5 Talk Moves for TEACHERS
These 5 Talk Moves can be used by the teacher to start student-centered conversations around mathematics. Teachers use these talk moves throughout a daily lesson. While in the "launch" section of the lesson the teacher should be having students clarify with one another what a problem is asking. Throughout the "explore" section, the teacher is observing students and using these talk moves to deepen their thinking. During the "share" section the teachers again, is using the talk moves to clarify, explain and justify student response and conversation.
1. Re-voice
"So you-re saying that it's an odd number?"
This talk move allows teachers and students to interact with a student who may be unclear.
2. Restate
"Can you repeat what he/she just said in your own words?"
This talk move will extend the responsibility to all students in the classroom. We can teach them the significance of learning from one another.
3. Agree/Disagree
"Do you agree or disagree and why?"
This talk move encourages students to apply their own reasoning to someone else and pushing students to support their ideas with evidence.
4. Add On
"Would someone like to add on?"
This talk move increases conversation amongst students and goes beyond the agree/disagree discussion.
5. Wait Time
(10 seconds)
This talk move is all about giving every student the chance to think about their ideas and apply them.
5 Talk Moves for TEACHERS
These 5 Talk Moves can be used by the teacher to start student-centered conversations around mathematics. Teachers use these talk moves throughout a daily lesson. While in the "launch" section of the lesson the teacher should be having students clarify with one another what a problem is asking. Throughout the "explore" section, the teacher is observing students and using these talk moves to deepen their thinking. During the "share" section the teachers again, is using the talk moves to clarify, explain and justify student response and conversation.
1. Re-voice
"So you-re saying that it's an odd number?"
This talk move allows teachers and students to interact with a student who may be unclear.
2. Restate
"Can you repeat what he/she just said in your own words?"
This talk move will extend the responsibility to all students in the classroom. We can teach them the significance of learning from one another.
3. Agree/Disagree
"Do you agree or disagree and why?"
This talk move encourages students to apply their own reasoning to someone else and pushing students to support their ideas with evidence.
4. Add On
"Would someone like to add on?"
This talk move increases conversation amongst students and goes beyond the agree/disagree discussion.
5. Wait Time
(10 seconds)
This talk move is all about giving every student the chance to think about their ideas and apply them.
The following document, explaining the 5 Talk Moves, can be printed for teacher use.
Student "Talk Moves"
Alongside the 5 Talk Moves for teachers, as educators we need to guide students to deepen their conversations with one another. The structured tiers of the Hierarchy of Talk scaffold student discussions. The document below shows the scaffolding format that can be used for student discussion within the classroom.
Student talking stems are another tools for student mathematicians.
Classroom Connection
Click on the image above to view the lesson example.
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Liz O'Neill works with her first grade students engaging them in composing and decomposing numbers within twenty. Using sentence frames, students shared with their partner responses to two warm-up activities engaging them with the content. A variety of solving strategies were discussed as a whole group after everyone had a chance to share with their partner. Her students then were given a bag with 10 cubes, a paper plate, and the "How Many Are Hiding Recording Sheet." In addition, sentence frames were posted on the board so students could produce academic language using structured student talk and convince their partners with oral justification. During the game, one partner takes some of the cubes and "hides" them under the plate. The remaining are placed on the top. The second partner uses sentence frames to answer the questions "What number do you see?", "How many are hiding?", "How do you know __ are hiding"? In addition, the answers are recorded. Roles are then reversed. The partner game gives students practice in composing and decomposing numbers within ten.
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