Cognitive Strategy Instruction on Math Problem Solving
As he drew each circle, I could hear him counting in fours: 4, 18, 12, 16, 20, 24, 28 .... and as he approached 36, he slowed down with his drawing. Of course, if my son was already fluent with division, he could have just simply written the following:
Teaching students how proficient word problem solvers approach and solve math questions is a cognitive strategy instruction. An example is the Solve It! intervention.
|Above copied from Solve It! (Montague 2003)|
Mr. Wright: Watch me say everything I am thinking and doing as I solve this problem.
Mr. Swanson needs 12 gallons of brown paint at $9.95 a gallon. He needs to buy three brushes at $2.45 each. How much does he spend in total?
First, I am going to read the problem for understanding.
SAY: Read the problem. Okay, I will do that. (Mr. Wright reads the problem.) If I don’t understand it, I will read it again. Hm, I think I need to read it again. (He reads the problem again.)
ASK: Have I read and understood the problem? I think so.
CHECK: For understanding as I solve the problem. Okay, I understand it.
Next, I am going to paraphrase by putting the problem into my own words. SAY: Put the problem into my own words.
This guy is buying 12 cans of paint and three brushes. Paint is $9.95 and brushes are $2.45 each. How much altogether?
Underline the important information. I will underline 12 gallons and $9.95 a gallon and three brushes and $2.45 each.
ASK: Have I underlined the important information? Let’s see, yes I did.
What is the question? The question is “how much did he spend in total?” What am I looking for? I am looking for the total amount of money for the paint and brushes.The complete sample lesson can be obtained here.
The observed effect size of Solve It! as an intervention is quite large (0.88). This is almost one standard deviation of improvement. Shown as a graph, applying the Solve It! intervention in a grade 7 class leads to a faster growth trajectory in math word problem solving:
|Above copied from Montague et al. Journal of Educational Psychology, 2014, Vol. 106, No.2, 469-481|