Differentiating Math Chapter 5: Differentiating for Elementary Word Problem Solving February 11, 2008
Posted by mirish in Math Instruction.trackback
This chapter covered strategies to improve a student’s metacognition which means “thinking about thinking”; it is also defined as planning and monitoring how one performs a task.
In metacognitive instruction, students are taught to specifically plan their thinking and subsequently monitor their own performance of those steps. If math teachers can teach the steps that a student must engage in to complete a math problem, that student will be better able to plan the stops in the problem and to monitor his or her progress in that problem. This will lead to higher math achievement.
Bender explained once again that students with learning disabilities will struggle in math. They will struggle with metacognition because they have difficulty with organization and planning tasks. Thus, specification of these steps for the student allows the student to “think about his or her thinking” in solving the problem and in monitoring his or her performance.
Bender presented a few strategies that could be used:
1. RIDD
Read the Problem
Imagine the Problem
Decide What to Do
Do the Work
2. STAR Learning Tactic
Search the Word Problem
Translate the words into an equation in picture form
Answer the problem
Review the solution
3. SQRQCQ Tactic: A student’s reading skills can directly hinder his or her achievement in mathematics. Therefore, teachers of mathematics must also teach reading, and one way to do this is to provide students with a graphic organizer that will assist them in seeing concepts and operations in the problem.
a. Survey: Read the problem quickly to get a general understanding of it
b. Question: Ask what information the problem requires.
c. Read: Reread the problem to identify relevant information, facts, and details needed to solve it.
d. Question: Ask what must be done to solve the problem: “What operations must be performed and in what order?”
e. Compute: Do the computations and compute a solution.
f. Question: Ask whether the solution process seems correct and the answer reasonable.
4. Schema-Based Instruction: Pages 101-106 discuss the use of schemas. Students are provided schematic diagrams, and their task is to “fill them in” during their reading and solving of a word problem.
Page 107 gave a very good idea for an activity that could be planned for a tear out group. Students act out word problems in a short play.
I think teaching students to “think about thinking” is a extremely valuable skill, but I don’t feel that is something we do a lot of. I know strategies are being taught for problem solving, but they seem to be more problem specific strategies. “If you encounter this type of problem, use this stategy.” The problem I see is, outside of the math lesson, students don’t know what type of problem they are trying to solve. I think teaching students to “think about thinking” would give students strategies to follow to figure out what type of problem they are trying to solve. They could then use their problem specific strategies to solve the problem. In school, I felt math was one of my strengths, but I was not always able to earn an ‘A’ because my instructors required me to solve the problem in a certain way. I could solve the problem, but I could not always explain how I solved it. I think that if I had been more aware of the way I thought about and solved problems, I might have been able to explain my answers.
I think it is so interesting to see how brain research has shown that students use different parts of their brain to monitor their own steps toward problem completion than they use when actually doing the math problem. “Planning” the steps takes place in the forebrain, but the actual calculations are done in other areas of the brain. This explains clearly why it is important to help children conceptualize the problem.
* I like the idea on page 95. The Simon-Says game can integrate movement when helping students associate various distance measurements. When drilled, the students will know quickly how far the specific words represent.
* I can imagine using the various schemas to help children categorize problems with similar features. When they can identify the like features, this will lead them to the correct choice of operation. I would do many examples and categorize in class, clearly defining the features and what they indicate. Page 102-105 was very helpful.
“Thinking about thinking” is an essential mindset before teaching word problem solving. Plan and monitor for success! Makes sense!
Although this chapter talked mostly about using metzcognition in story problems, metacognition also applies to any other area. In music, students may be asked to organize the notes into measures – we talk about the steps involved, much like a math problem – before we do it. Students are also asked at various times throughout the year to compose/create their own music, using concepts we’ve learned earlier, or to compare or evaluate music performances, again using concepts we’ve explored individually.