If we walked into 100 classrooms where students were learning about graphing lines in slope-intercept form, we'd find more than our fair share of lessons where some sort of direct instruction is happening. We'd likely hear academic vocabulary, see a formula for finding slope and probably even a general equation like y = mx + b.
I'm not against those things. However, I'm for giving students an experience that can be precisely described by knowing those things. Activities like Marbleslides do this.
The activity isn't enough.
Here are four different students who are all engaged in the same activity. Consider the following questions:
What do you notice?
What questions would you ask this student?
What could you have offered this student prior to starting this activity?
Here's what I see.
Student 1 is WAGging like crazy. These are just random guesses. No adjusting or learning from feedback. If this student achieves success, it'd be like a blind squirrel finding an acorn.
Student 2 is an answer chaser. I mean literally, look at the guesses. Once this student sees which part of the equation to adjust and the line moving in the right direction, the adjustments are incremental.
Student 3 is a strategic thinker. Slope? Nah, don't need it. y-intercept? Yeah, that's the stuff. Let's trap the answer and close in on it.
Student 4 is engaged, believe it or not. This student is paralyzed by options. Just waiting for the correct answer to pop into the brain.
So, how do you respond to each student?