Many teachers still approach problem-solving as if it is a standalone topic to be taught in isolation. There are classrooms with Problem Solving Friday, for example. Doesn’t that send the message that we don’t do problem-solving on Monday through Thursday? And certainly not on the weekends!
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We can and should incorporate problem-solving into our daily math instruction. One excellent way to do that is to allow students to struggle and figure out ideas on their own, rather than explicitly teaching a concept. In other words, let them do the work instead of you!
Here’s an example. Knowing all the combinations for 10 is a critical Kindergarten/1st Grade skill, so we want to frame that as a problem to be solved.
Suzie’s mom is going to let her eat 10 pieces of candy. She can choose between candy pumpkins and candy corn. What are all the combinations of candy pumpkins and candy corn that she can eat?
The first step in solving a problem is to understand it, so read the problem together and discuss what it’s asking them to do. Do the students understand what is meant by all the combinations for example? If they don’t, you might show them 1 pumpkin and 9 pieces of candy corn on the ten-frame and explain that that is one combination.
Give students 10 candy pumpkins, 10 pieces of candy corn, and a ten frame and let them work with a partner to find a solution. Resist the urge to “show” them how to find the combinations! After students have had some time to work on the problem, start a class chart to record the combinations the students found. Initially, just call on pairs and record their responses by listing them. In other words, don’t organize them yet.
After you have listed all the combinations the students came up with, pose the question I wonder if this is all the combinations? Here’s where you do a little teaching. This is a great problem to use the Make an Organized List problem-solving strategy. Do a think-aloud and explain that maybe organizing the list might help us determine if we have all the combinations. Then, rewrite the list in an organized format:
Give students a chance to work with their partner to decide if they think we have all the possible combinations. They may add more, but they still might be missing some. Explain that organized lists are helpful because they often show patterns that help us out. Ask them to look at the list again and see if they notice any patterns.
Do you see how you’re just slightly shifting the teaching workload to the students and allowing them to discover the answer on their own? You still have a plan, and you know what you want to teach, but you’re just pulling it all together at the end–filling in the gaps, so to speak.