Choosing a Task based on the Math of Students (part 1)

In my last blog post, I talked about how Student Adaptive Pedagogy allowed me to meet the diverse needs in my classroom in a way that left my students and me feeling empowered. They were empowered as mathematicians, and I was empowered to use their math to support their academic growth. I mirrored teaching math like I taught my reading groups. I started with an interview and then used the data I gathered to guide how I grouped my students and the tasks I presented them. Today I want to write about some student behavior I noticed in the interview that informed the task(s) I presented to the students. A foundation of student adaptive pedagogy is inherent in the title, which is you adapt your pedagogy (teaching) based on the student.

One of the first behaviors I saw was a fixed finger pattern. A fixed finger pattern is when there is only one way to make a finger pattern for four, six, etc. One of the tasks that elicits this behavior is 6 + 3. After they make their finger pattern for six, they only lift two more fingers to make a finger pattern for three on their second hand. Watch the video below of Sophia as she models this behavior.

This method works well for many of the tasks children encounter. As long as each addend is five or less, they would be accurate. Seeing this behavior allowed me to understand that my students were still wanting to create things they see (their fingers) to be able to count them. They could not imagine counting each addend yet. One of my math groups predominantly used this method.

One of the addition tasks I presented for these students included working with spatial patterns they recognized. I would hide the addend of the recognized pattern for the child, so that they would need to use a mental image to count all of the items. If a child struggles with that, a teacher move would be to flip the spatial pattern over to allow them to count the pattern, and then hide the pattern again. Below is a video of a student who can use their mental image of a spatial pattern to add two numbers.

One math group was able to imagine counting both addends. One of the behaviors I used to understand that was they would reuse some fingers. When students can solve problems like 8 + 5, they have to be able to move beyond their ten fingers. They use their fingers in a more sophisticated way. This can look different in different children. Some will count to eight with one hand and count five more with their second hand. Others might solve it by counting eight fingers sequentially using both hands and then “erase them” and count five more. They know to stop because they recognize a finger pattern for five. Check out this video as an example of a child that can reuse their fingers.

The task I presented to the group of students that could reuse their finger was similar to the 8 + 5\. I would increase the first addend and choose the second addend based on what patterns they know. I used number cards to give them the tasks because they were not ready for the symbolic notation of an expression. See the video below as a demonstration.

Both students are using their fingers, but they are doing so in very different way. Their behavior points to stage in their constructing number as a concept. Have you seen your students use their fingers in these ways? In my next blog I will talk about other tasks I gave students based on their behavior.

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