In my last blog post I talked about how reading the research on student adaptive pedagogy has given me a new lens in which to facilitate productive struggle with students. It has been so exciting to see the great effort that students will naturally put forth when a math task is in their zone of potential construction (ZPC). I like to call their zone of potential construction their math sweet spot. It is that place that students can be reflective and learn. I used to think my students had “learned” if they were able to get the right answer. My new lens has given me tools to be able to see if the students actually learned, or if they are simply mimicking me or a peer. To illustrate, I want to tell you a story about Diego.
When I was teaching 1st grade last semester, I interviewed all of my students with a research-based instrument that we developed and are currently refining. This research has allowed me to chart the progression of the math of students that I can use while observing students. The math interview is similar to a reading inventory teachers give at the beginning of the year to know their students’ reading level.
When I interviewed Diego, I noticed that he recognized spatial patterns, which left me curious if he could use these patterns while adding two numbers. Using a pattern in an addition scenario was a potential next step for him based on his progression. The video below shows his productive struggle and how my suggestion to imagine the dots fostered his use of a spatial pattern during the addition task. This suggestion had worked in the past with students and facilitated the creation of a mental image of the pattern they could use in an addition task. Below is a picture of the cards I used for the task.
When he attempted to imagine the dots, he counted past six and then corrected himself. This self correction is another cue that I was in his math sweet spot, and that he was hooked into the problem. You may have also noticed in the video that he moved around a lot and appeared unfocused. Movement in young children can also be a cue that they are deep in thought. Students may have to correct themselves multiple times before they can reflect and construct or use that mental material. Constructing imagined items was an appropriate next step for Diego based on his math. Two tasks I presented which fostered productive struggle for Diego were:
* Promoting imagining patterns: showing and hiding two patterns he recognized and asking how many altogether. (If you don’t have dots, you can use anything to make the spatial pattern. Be creative!)
* Promoting imagining counting: Counting one collection into one cup and another collection into a second cup. Then asking how many altogether in both cups. (A prompt I may use: “Can you tap out each number?”)
Productive struggle is something I feel I am getting better at fostering in my students. In my next blog post, I’ll write about my journey working with different students and how I used their math to inform my decisions.