"I just don't get it!" - Habit 1 Monitor and Repair

I've been contemplating Pearse and Walton's first habit to improve mathematical thinking.  This habit is borrowed from elementary reading instruction, good readers know repair strategies.  They monitor their reading to be sure they are comprehending and know strategies to "fix-up" their comprehension as needed.

In order for math students to monitor their understanding, they have to interact with the math.  Too often students gather the numbers from a problem and apply whatever rule they have been learning.  And then when they get answers, they don't know if those answers make sense.

First students must be aware of the work they are doing, engaged with the problem situation, reading for comprehension.  Even in a raw equation, students should be noting the type of equation, how many expected solutions, and noting the possibility of extraneous solutions. In problem scenarios, students need to visualize what the problem represents, even sketch out that representation.  They need to be able to determine what type of equation, graph, or table is needed to solve the problem. After completing procedures, they need to determine if the solution makes sense in the scenario.  And all math teachers utter, "Duh!'  Yet, often students are not able to complete all of these steps.  And if you ask them at what point they get stuck, they can't answer.  "I just don't get any of it."  This is where we must teach the concept of monitoring comprehension.  Students need to be aware of their thinking process enough to determine at what point they no longer comprehend.  And it is at that point we can offer "fix-up" strategies!

It's important to note here that if students say they don't get any of it, teachers should not give answers or even tell students what to do next.  Instead, teachers should take students back through the problem solving process.  Reread the problem.  Tell me what it is asking.  What do you know about this type of question?  What would a sketch of this problem reveal?  Coaching by asking questions allows students to own the learning and models for them a way to repair understanding.

Repair or "fix-up" strategies to assist in comprehension that we might use in a secondary math class

include:

For raw problems:

1. What type of equation or problem am I solving? If related to a function, what function? (ex. linear? quadratic? square root?  exponential? absolute value?)
• If related to a function, visualize the graph.
2. Ask yourself questions.  
• Is there a pattern to consider? 
• How many solutions should I expect? 
• What are legal moves, operations, that I can apply to both sides of the equation?
3. At what point in the solving am I having difficulty?
• Review the notes on this unit.
• Ask a classmate to talk you through the problem.
• Watch a review video or read the textbook for additional examples.

For problem scenarios:

1. Re-read the problem pausing at the end of each sentence to think about what it is saying.
2. Try to picture what is happening in the problem.
3. Ask yourself questions as you read and pause.
4. Determine at what point the problem is alluding you.
• Review notes given in the unit that might apply to this problem.
• Talk with a classmate about what the problem is asking.
• Watch a review video or read the textbook for additional examples.

What are other repair strategies that you suggest to your students?

I plan to create an anchor chart this year on monitoring and repairing comprehension.  I'll post my version in the blog later this summer.

Pearse, M., & Walton, K. (2011). Habit 1: Monitor and Repair Understanding. In Teaching numeracy: 9 critical habits to ignite mathematical thinking. Thousand Oaks, Calif.: Corwin Press.