Problem-Solving or Solving Problems?
By Carolyn Marchetti
In both math and science, problem-solving is a critical skill. It is a process that students will use throughout their schooling, work life, and beyond. By developing problem-solving skills, our students not only learn how to tackle a math or science problem but also how to logically work their way through any types of problems that they face. Our textbooks include word problems after every lesson – so this incorporates problem-solving skills, right? Not necessarily.
I was at a conference over 10 years ago and heard a presenter say, “Problem-solving is what you do when you don’t know how to solve a problem”. Solving problems, like the typical word problems found in our texts, on the other hand, is applying a known method to a problem that has already been solved before.
Here’s an example of how the majority of textbooks phrase a lesson — “Today we are going to learn how to multiply fractions. Here are the steps to multiplying 2 fractions. Here are some non-contextual examples to hone your skill”. Then most follow with ‘real-life’ word problems which, more times than not, involve fractions that require multiplication. This is a routine of practicing skills. I’m not saying that this isn’t important, just that problem solving is much more than this.
As teachers, we need to know the differences between the 21st-century skill of problem-solving and the traditional way of solving problems, and we especially need to learn how to recognize and even create true problem-solving experiences for our students.
I would like to give some tips on creating a problem-solving classroom by using an example of a task that I used when doing professional development with math teachers. The task is called The McDonald’s Claim Problem. There are several versions of this task on the internet, but basically, it goes like this:
- Wikipedia reports that 8% of all Americans eat at McDonald’s every day.
- There are 310 million Americans and 12,800 McDonald’s in the United States.
- Do you believe the Wikipedia report to be true? Create a mathematical argument to justify your position.
Tips on creating a problem-solving classroom:
- Engage students in real-world problems that students can relate to and have a prior understanding of. For McDonald’s, it was an interesting problem because it engaged students in prior learning – they’ve all been to McDonald’s and have all used Wikipedia. For other tasks, videos can be used to spark interest. For example, Dan Meyer’s 3 Act Tasks are one way to spark interest. Another suggestion is to use a career video like the Defined STEM videos that are included with each performance task. These videos grab students interest by answering the question of “When will I ever use this?”.
- Use group work for problem-solving. Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. By discussing the problem, students will start to realize that problems have multiple solution strategies, and some may be more effective than others. For the McDonald’s problem, I would have teachers work in groups of 4-5. There would be many discussions among the members before even starting the task. Discussions around what does “eat at” mean? Does the drive-through count? Does the question mean the same 8% eat there every day? These questions and discussions had teachers brainstorming ideas before deciding on a course of action to solve the problem.
- There should not be a direct path to the solution. Even better if there is not one right answer, like the McDonald’s problem, but these are harder to find. Monitor student progress and solutions. When they get stuck, answer their questions with other probing questions. When the math teachers would ask me questions regarding the McDonald’s problem, I would always come back with “What does your group think?”, to encourage them to collaborate and come to a consensus.
- Have students share their solutions. When everyone is finished, have groups present their solution to the others, especially the ones that went about the problem in different or unique ways. Having the groups share their solutions and justifications is very important for others to see various ways of problem-solving. For the McDonald’s problem, even though groups often used calculations to solve the problem and would get the same numbers, many had a different answer of “yes or no” depending on their reasoning. Hearing the different reasons from other groups can be very enlightening. I heard a lot of “I never thought of it that way”, which is a powerful aspect of problem-solving.
There are many other tips I can give, which I will continue in a later post. For now, I would like to leave you with a quote from a colleague: “It is better to answer 1 problem 5 different ways than to answer 5 different problems”. In one short sentence, that is the difference between problem-solving and solving problems.