Essential Component of an Effective Math Lesson

As an elementary math coach, one very important part of my job is to be in the classroom noticing all the small good things students are doing or saying, as well as the different teaching moves that shift students’ thinking about how they approach a math problem.

I usually send an email to the teacher right after my visit, highlighting these positive moments, as we all know that feedback is crucial for students and also for teachers. As teachers we are always learning, and believe in continuous improvement. Feedback helps teachers make their best even better!

I have been in a variety of classrooms from Kindergarten to Grade 5 for the past few weeks noticing and highlighting the great things happening during the SHARE OUT part of the math lesson.

Elementary teachers make a dozen decisions a minute, sometimes the lesson runs longer, or a small group needs more time, or they have a guest speaker coming in, so there are days where the last part of the math lesson has to be very short, or moved to the next day.

However, this is the most essential component of a math lesson because it is where “students listen to other students’ ideas, they come to see a variety of approaches in how problems can be solved and see mathematics as something they can do.” (Teaching Student-Centered Mathematics, John A. Van de Walle)

Student explaining her model and strategy to solve this problem. First I ……. , then I thought ……., lastly I figured out ……..

I saw different teaching moves while facilitating the share out, some teachers ask “Who would like to share how they solved their problem?”  Students like having this choice, however there is the risk that it is always the same students sharing, or the 2 or 3 students sharing the same strategy. You could miss the opportunity of a teaching point right here.

Who Shares?

Something the teacher could try is to choose who will share that day. While students are solving the problem of the day, the teacher is walking around asking questions, and noticing the different strategies students are using.

Then they choose ahead of time the 2 or 3 students that will be sharing. It is good to ask them first “Would you like to share your strategy/ideas at the end?” Students usually say yes.

When the teacher chooses who shares, they can make sure to fit in a teaching point for the day. For example, students could discuss which of the strategies they saw is the most efficient. This is essential in problem solving, as students tend to use a strategy that they are comfortable with, even though sometimes it is not the most efficient. Decomposing for example, is an efficient strategy when adding two digits by 2 digits, but partial sums becomes a more efficient strategy as the students solve with multi-digit numbers.

Ask students to discuss which strategy is more efficient for this problem and why.

Be intentional about the order in which students share their strategies and solutions; for example, select 2 strategies or models that could be connected, ask students to notice the similarities in the 2 strategies/models. This is an essential move to move students from a concrete or pictorial model into a more abstract strategy.

This is a concrete area model next to a pictorial area model. Ask students to make connections between both strategies.

I saw a 5th grade teacher show one student work but covered the name, then he asked “If you look at this work, can you understand how this person solved?” Students had some great feedback about missing labels and how that could help understand what each part of the model represented. One student said “I can see the answer, but no idea how he/she thought about it.” As you can imagine, this was a perfect teaching moment for that teacher to emphasize how to best show how you solve.

When students are used to share their work and explain how they solve, they make sure to have clear models that help their audience understand their work.

How Much to Tell and Not to Tell

When students are sharing their strategies, pay special attention to not take over their thinking. Even if they are struggling to explain, it is important to only ask questions, giving them time to think and elaborate their sentence. Having some sentence starters could help.

Taking over students thinking by talking for them, sends the idea that you do not believe they can explain it themselves, and that can inhibit the discourse you are trying to encourage.

Students show their work and explain how they figured out a solution.

Telling too much eliminates that productive struggle that is key to conceptual understanding. Telling too little can leave students confused.

If an efficient strategy did not emerge from the students, this is the chance to share “another way” to solve, not the only way to solve, but a different way.

Let’s always remember that the person doing the talking, is the person doing the learning.

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