The Problem with Problem Solving
How do we make it simpler?
There is a lot of know about problem solving, there is looking at the problem and defining it, exploring it and gathering information on it. We need students to use precision, tools (when necessary), communicate what they know, and reason abstractly and quantitatively. Then circumstances can add to the problem solving, how is the classroom set up, are there resources and adequate instruction and time, what are the students emotions around math and what affects does their background knowledge and experiences have on their answers. But the effects of problem solving are great, they do better in other subjects as well as math, their life skills are heightened and they can perform better in many different extracurricular activities.
Let's first look at circumstances. How is the working space set up for students? Do they have an environment where they have the necessary tools and time? Is it a positive place to learn? Are your emotions about math positive?
Next the problem, have we prepared them for looking at the problem. Read and define the problem. Ask the “what” questions; What do I need to find out? What do I know from the problem? Explore the problem; use strategies like guess and check, work backwards, look for patterns, use logic and reasoning. Gather information; draw a picture, make a list, solve a simpler question you might know. These questions may seem hard to teach but if you have incorporated games, pictures, and manipulatives to help students learn, the ability for students to explore these problems becomes enjoyable and less intimidating.
Once they have learned to look at the problem we can move to coming up with the solution. Communication is the key to helping students solve a problem, using accurate vocabulary, listening and asking question. Reasoning, using viable arguments and critiquing the work of others is something that can easily be incorporated through games. Think of a game like Clue by Hasbro, students have to reason and justify answers. They communicate all the time in the game while playing it. This kind of questioning can easily be brought into math lessons. “I think Marcus as the correct answer because …?”. Opening up math so that it isn’t so worksheet, independent work driven makes problem solving so much easier.
Finally, once you start breaking down the parts of problem solving into enjoyable games and activities then positive results happen. Students are better able to apply their math skills of problem solving to other subjects like reading, science and history. They are can apply the skills to sports, music and other afterschool activities. A recent study of 20,000 Kindergarteners showed that if teachers spent more time on mathematics then both reading and social skills increase. I think it is worth the effort.