InsightMath is designed around the belief that meaningful learning happens when students productively struggle with rich tasks and actively engage in discourse around their thinking. Students are encouraged to create or choose their own strategies, develop their own mathematical explanations, and compare, build on, or supportively critique diverse ideas from their peers.
The teacher’s role in these discussions is critical, not only in eliciting multiple voices and creating a supportive mathematics community, but also in making sure that all students reach the mathematical goal of each lesson.
The Slides are Not the Whole Story!
The lesson slides in InsightMath are designed to encourage curiosity, creativity, and active engagement in mathematical thinking from students. However, they are only the first part of the story.
Each lesson is designed to ensure that all students reach specific mathematical skills and understandings–which might not be apparent from the slides–and it’s the work of the teacher to make sure that students get there. If a teacher only uses the lesson slides to support students in responding as they choose, students will still have the opportunity to think flexibly and creatively, but maybe missing many of the content goals that they are expected to reach.
Look Fors Show What Students Should Understand and Be Able to Do
The Look Fors that accompany each lesson slide are designed to help teachers guide students toward the mathematical point of the lesson. These aren’t just suggestions of what students might possibly do, but instead a list of concepts, strategies, and responses that teachers should make sure that the entire class can model, explain, and understand. Below are some key strategies for guiding the class toward the mathematical point.
Teacher Move #1: Observing Students’ Strategies to Plan Student Sharing
While students work, a critical role of the teacher is observing students’ responses to notice which students are using key models and strategies from the Look Fors. Teachers can do this by walking around the class and chatting with students about their work or by using the Data tab at the top of the lesson screen to view the on-screen responses from all students in the class.
From these observations, consider:
- Who is using the key strategies from the Look Fors that we need to demonstrate to reach the mathematical point of the lesson?
- Who is using a less advanced strategy that can be highlighted as strong work?
- Has anyone developed a new and unexpected strategy that could be shared to encourage creativity?
- Is there a key strategy from the Look Fors that no one has utilized? If so, is there an Argumenteer that can be used to model it?
- Did any students make a mistake or demonstrate a misconception that should be discussed? Is there an Argumenteer available to highlight an important misconception?
Plan in advance which students you will choose to share their thoughts and strategies, and the best order to build a strong mathematical progression. The Discussion Planning Tool can support you in this. As you plan a sequence of students to share, consider:
- progressing from less sophisticated to more advanced strategies
- ensuring that all students have opportunities to share their mathematical brilliance
- noting which strategies it would be valuable to show side-by-side for comparison
- identifying misconceptions that are important to discuss (either from the Argumenteers or that arise from student work)
- noting whether there are Argumenteers available to highlight strategies that students have not discovered or attempted on their own
Teacher Move #2: Eliciting and Highlighting Key Concepts and Strategies
While students share, teachers have a central role in making sure that the entire class reaches the mathematical understandings from the Look Fors. Teachers can guide the discussion by first eliciting key ideas from students to help them articulate the concepts on their own, and then highlighting those key ideas by rephrasing them in mathematically accurate terms to repeat to the whole class.
The Discourse Questions are designed to support students in reaching the mathematical point of the lesson. Below are some suggestions for effectively using the Discourse Questions and your own teaching strategies to elicit and highlight key understandings.
- Start by reading the Look Fors to understand where students need to go.
- Use the Discourse Questions to guide students toward the mathematical goals from the Look Fors.
- After students share a key idea, restate it so that everyone can hear the most important information using mathematically accurate language. (e.g., “Makayla just said that the equal sign means that both sides of the equation have the same value. Do you agree?”) Asking students if they agree will encourage active consideration and illuminate any misconceptions.
- Use the Data tab and Share with Class action to bring up student work from up to four students at a time. From there, use the Discourse Questions and your own questions to help students make connections between the different approaches.
- Use the Discourse Questions selectively. If students have already articulated a concept, you don’t need to ask the question again (unless you want to make sure other students can also answer it).
- You can repeat and rephrase the Discourse Questions as necessary to help students reach the mathematical goals in the Look Fors. You may want to ask additional questions on your own to help students get there.
- If students are sharing multiple models or strategies, you may want to ask some of the Discourse Questions for each approach.
Teacher Move #3: Highlighting Misconceptions and Supporting Students in Learning from Mistakes
Making mistakes and learning from them is a critical mathematical practice and a necessary mindset to thinking flexibly and creatively. One of the InsightMath student strengths is “I learn from my mistakes.” Honoring these mistakes in the classroom community helps students to feel comfortable trying new ideas, and even excited and proud when they recognize their mistakes and use them to fuel new learning.
One tool that InsightMath uses to give students practice evaluating and learning from mistakes is Argumenteers. Throughout the lessons, Argumenteers are used to highlight common errors or misconceptions. You can read more about common misconceptions and errors that students may make in the Supporting Students section of each Cluster in the Teaching Guide and digital Planning Guides.
As you plan ways to discuss common misconceptions and errors, consider the following strategies:
- Use Argumenteers to support the practice of identifying common mistakes and provide supportive corrections with “student work” that doesn’t belong to a student in the class. Use the Discourse Questions to help students articulate the mistake.
- Say, “Mistakes are important for being great mathematicians. I want to share a piece of work that highlights an important mistake that can help us learn.” before sharing work.
- Share student work with a mistake anonymously to focus on learning from the mistake instead of who made it.
- Privately ask a student who made a mistake if they’re willing to share it, then let them present the mistake along with their correction. Highlight the student strength, "I learn from my mistakes!"
References
Boerst, Timothy A., et al. “Preparing Teachers to Lead Mathematics Discussions.” Teachers College Record, vol. 113, no. 12, 2011, pp. 2844–77.
Sleep, Laurie. “The Work of Steering Instruction Toward the Mathematical Point: A Decomposition of Teaching Practice.” American Educational Research Journal, vol. 49, 2012, pp. 935–70.
Stein, Mary Kay, et al. “Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move beyond Show and Tell.” Mathematical Thinking and Learning, vol. 10, 2008, pp. 313–40.