The 8 Standards of Mathematical PracticeIn the discipline of mathematics, there are certain desirable practices that promote productive reasoning and lead to success in problem-solving. The California math standards specifically call out eight of them:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
Students' learning experiences in mathematics should include intentional training in these practices and frequent encounters with problem-solving tasks to help them develop into capable and confident mathematical thinkers.
A key practice that Wolf Canyon teachers will be integrating with math problem-solving is feedback. In fact, feedback practices are likely going to be employed in every subject across the curriculum!
So, what is feedback anyway? Feedback is an objective description of a learner's performance that is intended to guide future performance. It is not an evaluation or judgment of the learner's performance. For example, avoid making judgmental comments such as, "This work is wrong. You added incorrectly. Don't you remember how to this?" Instead, offer more objective statements that guide the learner toward improvement such as, "You did not line up the place value of your addends. Keep this in mind as you give it another try."
Teachers provide their students with feedback on a regular basis, and parents can also provide support by incorporating feedback practices at home.
Feedback is the process of helping students:
- Assess how successfully they completed a task. ("For this task, I was able/not able to ___.")
- Identify areas where they are on target. (I did ___ very well by ___.")
- Know what they can do in the future to improve. ("To do even better next time, I will ___.")
The language frames in parentheses show that an important goal of feedback is to help each student develop a "Productive Internal Dialogue" that draws him/her toward excellence. Successful students "talk to themselves" all the time about what they need to do to achieve excellence in every task they undertake.