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Mathodology presents Three-Dimensions to Differentiating Mathematics Lessons

This two-day workshop focuses on how to break down math instruction during and after the lesson to support both struggling and advanced learners. Developing effective instructional strategies that allow teachers to fill in gaps and enrich thinking is key!

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# How can we differentiate instruction without putting more work on our plate?

Teachers do not have time to prepare multiple tasks and lessons to meet the needs of each student in the classroom. The key is giving an anchor task that all students can enter and knowing how to adjust the task based on our observations.

In this class, students were guided to use “Katell’s” method (aka-left to right strategy) to solve the problem 65 – 12. Notice how the student recorded their thinking process.

How can we differentiate with one task?

During the guided structure component of the lesson, teachers are observing and questioning students. This student demonstrates and can explain the left to right strategy. What comes next for this student? During our planning phase, we need to ask ourselves, “What can I do for the student that already knows the answer”? Looking at this student’s work, how can we deepen the mathematical understanding?

After listening to the student explain his thinking, the teacher commented, I can understand your verbal explanation, but your written work is confusing to me. I wonder why I am confused? The teacher then walked away, and the student grappled with the idea of equality. Differentiation is meeting the student where they are at and extending the learning.

Do not try to create more problems for students to practice. Plan your task thinking of what mistakes students typically make and how you can help extend the thinking. Use your observations to go deeper and differentiate!

What are other ways you could take the task 65 – 12 and extending the task? Share your thought below.

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# Is it possible?

Participants were asked at the 2017 Fall Mathodology Institute if it was possible to use the digits 0-6 only once to make a true statement?

Is it possible? Participants worked and worked and did not find a way to solve the problem with the given conditions. The teacher allowed the task to move on without closure for a purpose. When students work to become confident problem solvers we want them stating, “this is not possible, I have exhausted every situation.” Listen to their reasoning, and look for a systematic way to prove it is not possible. All too often we focus on finding the solution, and we can deepen the process and allow for practice when we alter the task.

Try giving a task where it is not possible and see how your students handle it. Follow-up by asking, “if it is not possible, can we change one of the symbols to make it a true statement?”

When we do not provide immediate closure, we allow students to continue to explore. Many participants emailed after the institute because they would not quit until they figured it out. Below are a few of the pictures they sent.

Great perseverance by participants who refused to give up?

This is what we want from students…next question for Shelly…can I change any symbol to make it a true statement? If so is there only one way?

Ok…..I’ve worked literally for hours and I’ve come to the conclusion that this problem is NOT possible. If the lesson was to teach us to let kids struggle so they work harder like a ???? I get it. I’ve done at least 100 fraction problems over the weekend. If you would’ve given us the answer I would’ve never thought about this problem again……but you’ve let us struggle and now it’s just painful. Please tell me it’s not possible

my sanity is at stake.

-Shelley

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# Grade 1 Task- Not enough information

At 2017 Mathodology Fall Institute participants worked on a task from think!Mathematics which required them to use the given shapes to make a composite figure. Figure C posed a problem for many. Is it possible? Participants worked and worked and did not find a way to solve the problem with the given shapes. The teacher allowed the task to move on without closure for a purpose. When students work to become confident problem solvers we want them stating, “Figure C is not possible with the given shapes. I would need an additional… to complete this shape.” We have built perseverance and another way to assess them. Do they know what to ask? “I need two more pieces of one shape.”

When we do not provide immediate closure, we allow students to continue to explore. Many participants emailed after the institute because they would not quit until they figured it out. Below are a few of the pictures they sent.

Try giving a task where there is not enough information and see how your students handle it. Will they be confident to state this is not possible, and know what to ask?

Great perseverance by participants who refused to give up?

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