In the second half of the math workshop, Mia Buljan works with a student who had a misconception about how to use the ten sticks to represent the quantities in the problem. Mia asks, “how were you counting them?” The student explains that she first used the ten sticks to represent tens, then switched over to using the ten sticks to represent ones.
After the students represent their thinking using tools, Mia asks them to use whiteboards to write down their strategies. She asks a struggling student: “Is this a ‘put-together’ problem or a ‘take-apart’ problem?” and works with the students to articulate their answers aloud.
When they do, several students catch the errors in their own thinking. Once the students move to the whiteboards, they share the drawings that represent their thinking in adding the quantities.
In my work with students, I aim for the “sweet spot” beyond right and wrong answers, when students are understanding their own thinking — moments of “real clarity” along with struggling with their work. In such moments, I intentionally give students an opportunity to continue thinking and working.
It’s easy to fall into the trap of helping them “fix” their thinking to get to a right answer.
But then you’re stealing this chance they have to take their wrong answer all the way, and the act of going all the way into recording and arguing their idea is often the best way for them to catch their own errors.
Sometimes, complexity in students’ lives affects the continuity of their learning in the classroom. In connecting students to each other to extend their thinking, I appreciate having one student who was able to explain her strategy well to others — “you only need one!” — in order for students to start convincing each other.