March Madness in Math Class
MCTM Region 1 Director
K-12 Math Specialist District 241 – Albert Lea
I don’t know about you, but the term “March Madness” is a relevant term in Minnesota Education. When March rolls around I start to think about how far we have gotten addressing the content, and how much further do we need to go. How are we going to get it all done? As the math specialist for our district, I want our students to “understand math” so what does that mean. For me it is focusing on helping students to develop a confidence, perseverance and willingness to tackle problems that they do not automatically know the answer too. I know many of you might be saying ok Christine, really something that big takes time, years. Yes, you’re right it does. That is why it is so important for us as educators to work collaboratively. Focusing on a mathematical instructional paradigm shift where we focus on “HOW” concepts are taught, not only “What” is taught. We need to:
- Challenge students to make sense of what they are doing to solve mathematics problems
- Pose questions that stimulate student’s thinking, asking them to justify their conclusions, strategies, and procedures,
- Have students evaluate and explain the work of others, and compare and contrast different solution methods for the same problem
- Ask students to represent the same ideas in multiple ways (symbolically, pictorially or with manipulatives)
So how do we tame the madness? Especially at the middle school level, where as one of our teachers told me, “I can get them to talk about anything but math.” A small but mighty step is to keep focused on allowing students to explain their thinking. By having students explain their mathematical reasoning on how they came up with their answer, we are able to know what they know. We can then use this information to drive our instruction, being aware that those students who volunteer to share do not always have the “right” answer. Think about it, when we go to colleagues and ask for help it is not because we have the right answer it is because something is not working. We need to think things through, find our error and use the feedback we receive to guide us to a better outcome. For those of us that work in a PLC (professional learning community) atmosphere, it is driving us toward answering critical question number two: “How will we know…” with a focus on knowing how students came up with their answers. What process did they use? Will that process work if the numbers are changed? Can they prove how they came up with their answer using tools, drawings or manipulatives? When students are asked to explain their thinking, they have to be able to put their thoughts into some type of organization. “First I did, and then I did…” We often have students do this back at our desk one to one when they have gotten too many problems wrong. But, what if we do this as a whole class or small group lessons where students work as teams and share their strategies for the solution. “But what if they solve it different ways?” is a question I hear too often. GREAT! Celebrate! There should be more than one way to solve problems. We as teachers should be thinking ahead about those different ways so we can support and facilitate the conversations as students explain their strategies. Think of the impact on the students, their self-confidence, their willingness to communicate/participate, the learning from each other not just the teacher just to name a few.
No, this does not happen overnight. Yes, there will be messy situations in which you the teacher are going to have to discuss with your math team what the child was attempting to do, but isn’t that ok? Isn’t it about the learning? Our student’s and ours. So as you keep going through this “March Madness” try to work in some opportunities for students to share their math reasoning. It will open many doors to many great math opportunities in your classroom. To help you get going here are five practices from the NCTM publication 5 Practices for Orchestrating Productive Mathematic Discussions, which help to have a meaningful discussion, not just a show and tell of math ideas or procedures.
- Anticipate student responses prior to the lesson
- Monitoring students’ work on and engagement with the tasks
- Selecting particular students to present their mathematical work
- Sequencing students responses in a specific order for discussion
- Connecting different students’ responses and connecting the responses to key mathematical ideas.
Some additional resources on this subject are:
Principles to Actions Ensuring Mathematical Success for All (2014) NCTM Executive Summary https://www.nctm.org/uploadedFiles/Standards_and_Positions/PtAExecutiveSummary.pdf Continuing its tradition of mathematics education leadership, NCTM has undertaken a major initiative to define and describe the principles and actions, including specific teaching practices, that are essential for a high-quality mathematics education for all students.
Reinhart, S. (2000). Never say anything a kid can say. Mathematics Teaching in the Middle School, 5(8), 478–483.
Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.
Have a great spring!