#INspirEDmath
November 2020, Volume 26
Valuing Student Voice Through Math Talks
"Children want to think mathematically."
10 Tips for Math Talk
Talk Moves
Revoicing - "So you're saying..." "Do I have that right?"
Repeating - "Can you repeat what he/she/they said in your own words?"
Reasoning - "Do you agree/disagree? Why?"
Adding on - "Add something more to this." "What do you think about that?"
Waiting - "Take your time, we'll share out in a bit."
Questioning
- How did you reach that conclusion?
- Does that make sense? Why?
- Can you show me a model?
- Does that always work?
- Is that true for every problem?
- What would happen if...?
- Do you see a pattern?
- What is your prediction?
- How does this relate to...?
- What have you learned that you can use again?
Asking Questions
- Require more than simple recall, fact-checking, or skill reproduction
- Have more than one correct answer or pathway to the answer
- Allow student learning to happen throughout the process
- Provide insight to you about how the student thinks, what they know, and connections they've made
- Be accessible including language, tools, and entry point
- Encourage students to notice and wonder
Student Thinking
Discourse Rich Environment
Visual Cues
The Teacher's Role
- Anticipate student responses to challenging mathematical tasks.
- Monitor students' engagement and work on the tasks.
- Select particular students to present their mathematical work.
- Sequence the student responses that will be displayed in specific order.
- Connect different students' responses to key mathematical ideas.
Whole Group Math Talk
Solve and Discuss - Have four students each solve a problem using any method they choose. The rest of the class can also work on the same problem. Ask the four students to explain their method. The rest of class can then ask those students questions to develop their understanding of the problem and solution.
Step-by-Step - Have different students complete different parts of a task and describe their method as they solve. The rest of class can work through the problem step-by-step while asking questions to deepen their understanding.
Student Pairs - Pairs of students work together to solve a problem and explain their solution. The pair can then present their method to the whole class as they ask clarifying questions. If you're interested in seeing student pairs in action, check out this video.
Small Group Math Talk
Practice, Practice, Practice
Resources for Math Talk
Secondary Number Talks
If you are new to number talks this blog is a great place to start. Convincing arguments, real examples, easy to follow steps. There is no reason NOT to try! Click here to get started today! "Number Talks are an issue of equity and access for all students. Every, yes every, 6-12 Math Teacher should be doing Number Talks regularly in the core mathematics classes they teach. If a secondary teacher wants all students to make growth in their classrooms then Number Talks MUST be a part of what they are doing in their classrooms." - Sara Van Der Werf
101 Questions
Number Talk Images
Math Language Routines
Design Principle 1: Support sense-making
All learners can and should engage in grade-level content that is appropriately scaffolded to reinforce language so students can make their own meaning. Teachers should consider amplifying their use of disciplinary language rather than simplifying it. This requires teachers to anticipate where students will need support and providing opportunities to access the content and vocabulary. Clearly organizing information, providing visuals, models, and tools, modeling problem solving and think-alouds, creating connections, and layering meaning can all amplify language to supports students in their active mathematical sense-making.
Design Principle 2: Optimize output
Students need many opportunities to communicate their ideas and this can and should come in a variety of ways including oral, written, visual, and non-verbal. Supporting these opportunities will help students communicate their mathematical thinking to others. Students need repeated practice to strengthen this skill as they make their ideas clearer and utilize more precise languages and models. Making claims, justifying with evidence, making conjectures, communicating reasoning, and critiquing the reasoning of others are all necessary skills to increase the quantity and quality of students effectively communicating mathematically.
Design Principle 3: Cultivate conversation
Conversations are a great natural scaffold to help strengthen students communication skills. Conversations require students to develop language while making meaning and expressing ideas. Meaningful, authentic conversations will ensure if the teachers uses instructional opportunities to build a classroom culture that values communication.
Design Principle 4: Maximize linguistic and cognitive meta-awareness
Students must have opportunities to communicate their mathematical understanding to others. Language helps students organize their experiences, ideas, and learning to connect new content to what they know. Some examples of metacognitive questions are, "How does yesterday's method connect with the method we are learning today?" and "What ideas are still confusing to you?"
These four principles can help guide teaching and learning and how to structure opportunities for students to strengthen their mathematical language and learning but how do we put the principles into action? Stanford went further to develop mathematical language routines to be used in any lesson in any grade or subject. A math language routine is "a structured but adaptable format for amplifying, assessing, and developing students' language." These routines offer students opportunities to clarify their mathematical understanding as they organize, communicate, refine, and revise their ideas.
- Stronger and Clearer - provides a structured and interactive opportunity for students to revise and refine bother their ideas and their verbal and written output
- Collect and Display - captures students' oral words and phrases into a stable, collective reference
- Critique, Correct, and Clarify - gives students a piece of mathematical writing that is not their own to analyze, reflect on, and develop
- Information Gap - creates a need for students to communicate
- Co-Craft Questions and Problems - allows students to get inside of a context before feeling pressure to produce answers, creates space for students to produce language of mathematical questions themselves, and provides opportunities for students to analyze how different mathematical forms can represent different situations
- Three Reads - ensures that students know what they are being asked to do, creates opportunities for students to reflect on the ways mathematical questions are presented, and equips students with tools used to negotiate meaning
- Compare and Connect - fosters students' meta-awareness as they identify, compare, and contrast different mathematical approaches, representations, concepts, examples, and language
- Discussion Supports - supports rich and inclusive discussions about mathematical ideas, representations, contexts, and strategies
Learn more about the four design principles and math language routines with examples here.
Video of the Month
Problem of the Month
Elementary
Some tips for implementation:
- Modeling: This may be a students first time with the freedom to explore their reasoning. Model this process and your own thinking behind the prompt to help students understand one approach to the prompt.
- Clear expectations: The whole objective of math talk is to provide students with opportunities to share their ideas and collaborate to clarify their understanding so don't make the mistake of having students complete these independently. Consider providing groups with a set of objectives to be accomplished by the tasks end. \
- Prompt Moderation: Consider implementing "Would You Rather Wednesday" or similar concept to keep this task interesting and engaging so students look forward to this kind of task. Everything is better in moderation, right?
- Student Ownership: Justification is a crucial math skill often overlooked. Use Would You Rather Math tasks to elicit math talk among peers and provide all students with time to think and be heard.
Check out Would You Rather Math here.
Secondary
How? Start by simply by using a visual pattern for your next warm up. There are over 400 to choose from at visualpatterns.org.
- Display a visual pattern for students to see as they enter the classroom.
- When the bell rings, set a timer for two to five minutes, depending on the complexity of the pattern.
- When the timer goes off, set it again for one minute for students to share their thinking with a peer.
- Randomly call on three students to share how they saw the pattern. Take it a step further and ask if they have an equation for it!
- Ask anyone else to contribute a different strategy than what was already shared.
Click here for additional resources, prompts, implementation ideas, and extensions!
Opportunities for the Field
Global Math Department
Women in Steam
Virtual Math Summit
Save the Date
Upcoming Chats:
November 18 - Student Takeover from Bring Change 2 Mind
December 2 - Best Ways to Serve Homeless/Unhoused Students
Follow #INedchat to be a part of the discussion!
News From IDOE
Tools for Teachers Lesson of the Month: Making It Perfect!
Educator Spotlight
Kali Wheeler - Avon Community Schools
Kali earned her undergraduate degree in Elementary Education at Utah State University, in 2008. She has over 10 years of experience in pre-K through first grade and is currently teaching and leading a virtual first-grade classroom in Avon Community Schools. She has finished her coursework and is graduating this December from Purdue University with a Masters in Curriculum and Instruction with an emphasis in mathematics instruction. Kali's future goals are to continue to improve and support mathematics instruction in her classroom, school, and district.
Check out what Kali has to say about helping students develop strong number sense, math talk, and collaboration skills.
"One of my favorite shifts in mathematics instruction is moving towards a more collaborative culture and an increase in dialogue. Of course, there are times in mathematics where we work alone when we need time to think and to work through a problem, but a major part of mathematics does and should involve working with other mathematicians, at all levels.
Over the years, there are several small tweaks I have made in my mathematics teaching that have increased math talk and collaboration in my classroom. These shifts have made a significant difference in how well my students comprehend and understand mathematics.
- Implementing thinking partnerships: Strategies such as Think-Pair-Share are an easy and quick way to increase student interaction and provide all students a chance to think, talk, and reason together. It is also a great way to increase participation and gain insight into how your students are thinking mathematically.
- Purposeful questioning: At the end of one school year, she received a sweet poster from one of her students where they answered questions about his/her teacher. This question said, "My teacher always says ________." He filled it in with "how do you know?" And he's right! I ask that all day every day, no matter the content area. Asking our mathematicians to justify and explain their strategies daily is so important not only for exploring their own thinking but for sharing that thinking with others which leads to this amazing cross-pollination of ideas.
- Peer feedback: As a teacher, being careful in your tone and facial features to mask whether a student's answer is correct or not, can be a great way to give your students an opportunity to agree, disagree, and provide peer feedback.
- Building math talk into everyday mathematics tasks: I am purposeful in not only modeling and expecting my students to talk about their thinking with me in whole or small group instruction, but I build "math talk" into our games and work as an essential step in the process of playing or completing the work. I teach my students to ask each other, "How do you know?" and it's now a normal and expected feature of a mathematician in our classroom.
Finally, I think it is important to keep in mind, that if we want to have a mathematics classroom that is conducive to these and other productive mathematical interactions, we need to be very purposeful to model and teach students how, why, and when to interact with each other, not just socially and not just at the beginning of the school year, but daily within our content areas and learning as well."
Your IDOE Mathematics Team
Robin Conti
Email: rconti@doe.in.gov
Website: doe.in.gov
Location: Indiana Department of Education
Phone: (317)-233-6098
Twitter: @RobinLConti
Emily Bruning
Email: ebruning@doe.in.gov
Website: doe.in.gov
Location: Indiana Department of Education, West Washington Street, Indianapolis, IN, USA
Phone: (317)-232-9142
Twitter: @MrsBruning