This month’s featured resources discuss culture-building. What will you do in those first few days to help students understand what it means to do math together? As teachers work on engaging students in productive struggle, eliciting student thinking, facilitating discourse, and using multiple representations, students need support to understand that in this class, math means trying out new processes, talking about ideas, listening to others’ ideas, and trying to understand what is the same and what is different across ideas. We are focusing on routines that you can begin early in the year and on tasks that will help you diagnose your students’ skills in working together, sharing ideas, and listening productively and drawing on experiences that will help students think about what it really means to do math.
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From the first day of school, many primary students engage in a calendar routine focused on mathematics. How does your calendar routine support students to share ideas, notice patterns, and make and test conjectures? First-grade teacher Zoe Donahue shares parts of her calendar routine focused on patterns, skip-counting, and odd and even numbers in the Teaching Children Mathematics article,
“Opening the World of Mathematics: The Daily Math Discussion.” She uses these mathematical routines to support all students to understand that they have important ideas about math and to build a culture of listening to one another’s ideas, testing conjectures, and explaining our reasoning.
How can you begin the conversation with your students about the importance of listening to others’ ideas? Have your students experienced someone else holding the “missing piece” and whose explanation allowed them to gain a complete understanding? Have they experienced the difference between offering help and taking over someone else’s thinking?
The Quiet Game, sometimes also called Broken Squares, was invented by Alex Bavas in 1973 and has been used ever since by teachers to help students reflect on how to learn effectively in cooperative groups. Math teacher Suzanne Alejandre blogged for NCTM about how she facilitates the Quiet Game and the reflective conversations she leads with students after they have played.
Alejandre's post includes links to the rules of the game and multiple templates for playing the game with students at different levels.
“Establishing Standards for Mathematical Practice,” former middle school teacher and current mathematics education professor Michelle L. Stephan describes the ratio and proportion task that she used to help establish the standards for mathematical practice with her students from the first day of math class. Using strategies from
5 Practices for Orchestrating Productive Mathematics Discussions
, Stephan describes how she purposefully selects a student to share experiences about a task, knowing that other students might be confused and need to ask questions. She establishes the norms that as other students share their thinking, the job of the audience is to understand the strategy well enough to say it in their own words. The article provides snippets of dialogue to model how to coach students through formulating a question about what they do not understand. The task could be used at multiple grade levels in middle school. The strategies and norms described in the article are important to establish early in the school year.
“Mathematical Conversations to Transform Algebra Class” describes three very different conversations that teachers can introduce to students early in the year to help assess students’ understanding of big ideas about what it means to do algebra. Students consider the meaning of the equals sign, the role of mathematical representation, and how precision in mathematical language differs from precision in everyday language. For each prompt, the author provides samples of student conversations, as well as an explanation of why these prompts help students consider what it means to think algebraically. Any one of these prompts could be an interesting conversation starter early in the year.
How might you assess your students’ understanding and use of the mathematical practices at the beginning of the year? How can you ascertain students’ levels of perseverance, how they look for structure, their repeated reasoning, or how they use tools strategically? In the article,
"The Handshake Problem and Preassessing Practice Standard Skills," math teacher Masha Albrecht uses the Handshake problem on the first day of school to assess her students on the Standards for Mathematical Practice (SMPs) as well as how they engage with mathematics and as members of a group. The Handshake problem arises naturally on the first day of school as Albrecht introduces herself to her students and provides a context, where possible, to assess all eight SMPs.
“Conversations to Transform Geometry Class” describes three very different conversations that teachers can introduce to students early in the year to help assess students’ understanding of big ideas about what it means to do geometry. Students consider whether geometric shapes exist in the real world, the role of definitions in geometry, and the relationship between examples and proof. For each prompt, the author provides samples of student conversations, as well as an explanation of why these prompts help students consider what it means to think algebraically. Any one of these prompts could be an interesting conversation starter early in the year.
“Engaging Students in Survey Design and Data Collection,” a Mathematics Teacher article by Marla A. Sole, focuses on the context of texting while driving. In addition to being an engaging topic, this could also be a life-saving discussion. The article focuses both on designing an unbiased, informative survey question and designing a series of experiments. Students get a chance to grapple with what makes a good survey question and revise questions until they can generate useful data. Then they get a chance to consider what other data they might want to collect about texting and driving and refine an experimental process. This could be a lesson assigned over several days or returned to during the year. The data that students collect on texting and driving could also tie into other topics.
Be sure to also check out these additional resources and tools for your classroom.
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