In the work that I’m doing at the Math Forum I’m often in middle school or upper elementary classrooms and I have the Mathematical Practices on my mind. Also recently I’ve been at New York’s state mathematics conference (AMTNYS) and Pennsylvania’s (PCTM) and one of California’s (CMC-North) and the presentations and conversations have centered around the Common Core and, in particular, the Standards for Mathematical Practice. It’s occurred to me that one small detail is easily lost –> the goal is for the students to develop these practices.
What does it mean to have students “Make sense of problems and persevere in solving them.”?
Both parts of that practice require quite a shift from the practices that have become popular in classrooms feeling pressure from NCLB and the standardized tests that have been used to measure students’ success.
In classrooms where the teacher shows how to do the problem and then the students practice what was shown to them, it is the teacher who is making sense of the problem and not the students.
In classrooms where the focus is on the student making sense of problems, we should hear phrases like:
How do you know?
Can you tell me more?
What did you do?
Does that make sense?
Why do that?
Why did she say that?
If we only have to focus on one person’s practice (our own as the teacher) we have a much easier to control job than if we have to focus on each students’ practice! This change requires a major shift in our classroom environment.
Similarly, the second half of the practice “… and persevere in solving them.” also needs to shift from the teacher demanding that students persevere (or suffer the consequences) to where the students have a “practice” of persevering because they are involved in problem solving as a process.
- engage in a problem over time,
- talk about their ideas,
- use a variety of representations,
- write their ideas and receive feedback,
- reflect on their ideas and revise
… and more …
Establishing the expectation, believing in the students and helping them learn the routines to complete the process of problem solving is the role of the teacher. Those teachers will be helping their students develop ”The Standards for Mathematical Practice.”