Math is Thinking

Yesterday, I had the opportunity to attend a professional development day with the 8th grade teachers in our district. The day was run by a woman, Carrie, from Math in Focus, which is the textbook that the math classes in the district use. It’s based on Singapore Math, which strives to teach students mathematical concepts deeply and with meaning.

We began our day discussing the successes and challenges thus far in using the Math in Focus text, as this is the first year the district is implementing it. The successes included the notion that ALL students, top and bottom and everything in between, were rising up in ability, the visualizations in the text made it easier to teach topics, connections were made between ideas, parents were able to learn alongside their children, etc. Challenges included the requirement of critical thinking, pacing due to snow days and other interruptions, the high difficulty level of topics and problems, and the frequent use of story problems. We addressed each of these issues and discussed how the challenges might be alleviated and the successes continued. 

Next, we focused on the four instructional strategies that Math in Focus is based on–gradual release, math is thinking, concrete-pictorial-abstract pedagogy, and visualization. All the teachers in the district were unanimous on which they were most comfortable with (gradual release) and which they were struggling with (math is thinking.) Math is Thinking is focused on critical thinking strategies to problem solve. The teachers were having issues with this due to a lack of time, a lack of focus from students, and the students’ uneasiness to attack problems that involved critical thinking. Carrie wants teachers to explicitly note to students that they don’t care what they say, as long as they’re thinking. Answers can be wrong. Questions can be “dumb.” But, students must be thinking about the math involved. Some questions that Carrie uses in teaching to encourage this are: “what is different?,” “what is the same?,” “where’s your entry point with this problem?,” “what do you notice?,” and “where’s your thinking at right now?” Each of these questions give students the opportunity to think critically about the problem at hand and make connections with their prior knowledge. 

Following this, we were to watch Carrie give a demonstration lesson to one of my CT’s classes about functions and their multiple representations. We all constructed a three-columned paper with the headings: Student Action and Thinking, Teacher Action and Thinking, and I Wonder… We were to use this to take notes during the lesson and guide our observations about specific student and teacher actions, focusing on the four instructional strategies mentioned earlier. Some of my main takeaways are listed below: 

  • Use partnered discussion for students to talkabout their thinking. Ensure that everyone is participating. Carrie used phrases like “what are you supposed to be doing right now?” or “this is your job, to figure out what a function is from a friend.”
  • Ensure that students are using visualization. Use phrases like “can you picture it?” when students give an answer. “Can you picture a function passing the vertical line test, what does it look like?” 
  • Students often say “I think I know the answer.” Get them in the habit of saying “I know the answer.” 
  • Giving students choices can increase engagement and motivation. Even if it’s as simple as choosing between guided practice problem one or two, students will enjoy the choice. 
  • Highlight same and different aspects for students between previous day’s problems, warm-up, modeled problem, guided practice, and homework. Ask them for the same and different parts to help them make connections. 
  • Use self-check often. Have students give a thumbs up or down on how confident they are with the material being presented. In this way, they evaluate themselves and you get an assessment of their progress. 
  • Make sure that independent practice is done completely alone. They don’t get help from other students or you. They need to practice their individual ability with this material. 
  • Only give homework if you’re completely confident they can complete it independently. If the class is struggling, think about giving homework on the previous day’s material or no homework instead. 
  • Make sure students clarify what they are saying. Don’t assume that they mean what you think they’re trying to say. Get them to say it.
  • Conduct a reflection or closure piece in every lesson. Make sure students grasp the main ideas and feel like the lesson has been completed.
  • Image

    My notes from during the lesson


One thought on “Math is Thinking

  1. Cassie, your list of takeaways from the PD and demo lesson had me saying “yes” over and over again as I read through it. I have heard many of those bits of wisdom in piecemeal fashion over the course of my 13 years as an educator. How exciting that you got to hear so many of them through a single PD event — and kudos to you for blogging about it for the rest of us to benefit from. Thanks for sharing!

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