Solve It! is a cognitive strategy instruction that works on the framework that successful problem-solving in mathematics is predicated upon a person’s ability to select and utilize appropriate strategies for understanding and solving problems (Montague, 2010). Solve It! teaches students to solve math problems through a seven-step, explicit instruction approach wherein they:
As with any strategy I would recommend, data should always be the primary indicator of whether or not you should use, or continue to use, the program. Therefore, it is important that frequent assessments are utilized. The Solve It! manual provides all of the materials necessary to get started with implementing this program including practice sheets. Therefore, we are going to provide a quick outline of the strategies utilizing an adapted version of the cognitive processes and self-regulation strategies and first lesson.
Cognitive Processes and Self-Regulation Strategies
Read (for understanding)
Say: Read the problem. If I don’t understand, read it again.
Ask: Have I read and understood the problem?
Check: For understanding as I solve the problem.
Paraphrase (your own words)
Say: Underline the important information. Put the problem in my own words.
Ask: Have I underlined the important information? What is the question? What am I looking for?
Check: That the information goes with the question.
Visualize (a picture or a diagram)
Say: Make a drawing or a diagram.
Ask: Does the picture fit the problem?
Check: The picture against the problem information.
Hypothesize (a plan to solve the problem)
Say: Decide how many steps and operations are needed. Write the operations symbols (+, -, x, and /).
Ask: If I do___, what will I get? If I do____, then what do I need to do next? How many steps are needed?
Check: That the plan makes sense. Estimate (predict the answer)
Say: Round the numbers, do the problem in my head, and right the estimate.
Ask: Did I round up or down? Did I write the estimate?
Check: That I used the important information.
Compute (do the arithmetic)
Say: Do the operations of the right order.
Ask: How does my answer compare with my estimate? Does my answer makes sense? Are the decimals or money signs in the right places?
Check: That all the operations were done in the right order (Montague, 2010, pp. 150-151).
Prep. Make folders with a graph for student scores and room for all work. Make class charts for either transparencies or in a PowerPoint, also post them on the wall. Make cue cards out of index cards.
(A crowded classroom in a small town in Kansas. Mr. Losinski is at the head of the class getting ready to teach students all about Solve It! Kids in the class include, Timmy, Levi, and Willow.)
Alright, everyone sit down.
Alright, thank you. So... for the next two weeks I’m gonna be teaching you guys a strategy to help figure out working out word problems. Y’all haven’t been doing a great job with them, so... I figure we’ll try this new thing, Solve It! I know y’all don’t like math, but it’s something you need to learn. So, one of you tell me why you want to improve your math?
(no one responds)
Come on, somebody’s got to tell me something. Willow?
(she doesn’t look up, but shakes her head).
Thank you for responding to me calling your name, Willow. Alright, Timmy why do you want to learn math?
Okay. Pretend that you do and tell me why you would want to learn.
Uh. So, I can figure out how many pieces of pizza to cut when someone orders one?
Losinski jots this down on the board
OK. Sure, cutting pizza takes an understanding of fractions. And sometimes when people order pizza they are gonna tell you all kinds of stuff they want and how much pepperoni to put on 1/3 of it, and then 1/3 with pineapple, etc. Now, Y’all have decent math skills, but again we are going to transfer the skills you already have over to working out these word problems.
(Losinski hands out folders)
Alright, let’s look at the tests you’ve taken. Right now, I want to discuss the graph and what a baseline score is. If you look at the first dot, that’s how you did on the first test, how many correct out of 10 you got. Some of you guys did alright. Some didn’t, but we want everybody to do good on all the problems, all the time. So, for a goal, let’s say we want everybody to get seven problems correct out of 10 on each of the measures for the rest of time. I’m pretty confident that if you guys apply yourselves, you’ll be able to do that.
Any questions? Levi, got anything to ask?
How many people like doing word problems?
(nobody raises hand)
Alright. I get this, most people don’t. But I think it may be because they haven’t been successful at it. If you become a better story problem solver, I think you might change your mind. How do you feel about that Willow?
Thank you for answering me, Willow.
I appreciate you answering again, Willow.
Can we move on please?
Yup. So, everyone, what is our goal?
Alright. First we’re to work on the seven part strategy for Solve It! we’re going to practice the strategy, then take a test, practice a little bit more, take another test... These aren’t really tests, because they’re not going to count for your grade, they’re only to see our improvement. That’s all we’re doing today. Then, the next couple of weeks we’re going to keep doing these tests and track our progress in our folders. Does anyone have any questions? Smashing! Let’s get started.
OK, some people who do good on story problems do a lot of stuff in their heads when they solve these problems. These are called metacognitive processes. Someone raise your hand if you know what a process is.
Timmy raises hand
Read for understanding.
Very good. willow. Next, they paraphrase the problem in their own words. What do they do next?
That’s right paraphrase. Levi, what do they do next?
Oh, right... phrase...
Uh-huh. what does paraphrase mean?
Is it like parasailing? My mom went parasailing once. Said it was awesome.
No. It is not even a little like parasailing, Timmy. It is shortening a long passage into it’s main parts in your own words. What is paraphrasing?
Shortening stuff in your own words.
Shortening stuff in your own words that’s right. Timmy what is paraphrasing?
Making stuff shorter in your own words.
That’s right, good job, Timmy. Next, visualizing. They use objects in some kind of picture or diagram on paper or in their head. What is visualizing?
Making a picture in their head.
That’s right, making a picture in their head. Willow, what is visualizing?
Imagining I am not in this class.
Very good, Willow that is a form of visualizing. Not of a math problem, but still visualizing. Next, they hypothesize. Anybody know what: to hypothesize is?
Is that like those lotions they make so you don’t have to take Benadryl?
That is hypoallergenic. Not hypothesize. Anyone else? A hypothesis is an educated guess. What’s a hypothesis?
An educated guess.
That’s right, an educated guess. Levi what is a hypothesis?
Educated guess. Like, this class is never gonna end.
Very good. An educated guess. So, then people estimate the answer. Raise your hand if you know what an estimate means...
Estimating means making a prediction...
Isn’t that the same thing as a hypothesis?
Essentially, yes. However, the hypothesis in this case it’s more about establishing a plan to solve the problem, where as the estimation is our guess at an answer.
That’s not really what hypothesis means.
I appreciate that you understand the semantic lack of differences between hypothesis and estimation, Willow. However, I think we can move on... People tend to estimate the answer before they even start doing math. Then they do the math get an answer and compare it. So after they estimate they compute, which means doing the math. What does compute mean?
Doing the math.
Doing the math. That’s right. Levi, what is computing?
Getting my math on.
That’s right, Levi. Last, good word problem people check their work. Means checking to make sure That they’ve the right calculations, they have set up their problem right. Sometimes they use reverse operations. so like using subtraction to figure out an addition problem. Why do you check math word problems? To make sure you get it right.
(switch to: say, ask, check)
So, good problem solvers also do stuff in their head. First thing he does is ask himself what to do...
Why does it have to be a guy?
It doesn’t. Thank you for checking me on gender micro-aggressions, Willow. So, the first thing they do is SAY things to tell them what to do. Next, They ASK themselves questions. Finally, they CHECK their work. I put Say, ask, check On These charts. Show metacognitive strategy chart. I also have these cards that’ll help you study. This big chart so you can See what to do. And now I’m going to go through the whole process once.Then, we will read it as a group. Finally, I’ll call on each of you to read it. Perform the explanations as described by Losinski.