Why Use Multiple Ways To Solve Problems

 

One thing that is emphasized is to show students as many ways as possible to do something, but unfortunately, many teachers and textbooks tend to show only one way to do something rather than exposing students to multiple ways.  For instance, FOIL seems to be the main way students are taught to multiply binomials yet there are so many ways to do it.

I know when I was in school, teachers only taught one way to do any problem including only the FOIL method for multiplying binomials.  It's only since I began teaching that I've learned multiple other methods or rather how to use methods they already knew from earlier situations that could be applied to a situation.  Research indicates when we teach students to solve math problems in only one way, the method taught may not be the "best" way of doing other problems.  We need to focus on having students learn multiple methods so they can choose the method that works best for the situation and for them.

Teaching students multiple strategies to solve problems helps make them more flexible mathematical thinkers. This is because they have multiple methods to choose from to solve any problem and can select the one that works best for the situation rather than trying to figure out how to apply the one method to every single problem. 

In addition, when we teach students multiple strategies to solve problems, we are providing scaffolding so they find a place that has what they need. In addition to finding the strategy they can use, they are exposed to methods that may be beyond them at that point but which they may be ready for later on.  Furthermore, these strategies can be used as they go from one skill to another.  For instance, an elementary teacher taught me how to multiply using the lattice methods.  I saw it and realized I could use the same method with my high school students when they multiply binomials, or trinomials. Many of my students had this teacher in 5th or 6th grade so they knew the method and could easily use it. 

Furthermore, when students feel they can't do math, or don't like math, or don't have that math gene, they often are more willing to try doing problems when they've been taught multiple strategies. Teaching them multiple strategies allows all students to have an entry point  and a way of attacking problems at their level rather than feeling lost because they don't understand or can't do the method taught by the teacher. 

One thing that comes up again and again in research is to teach students how to visually represent the problem no matter what age or level of mathematics students are in. Another thing that show up is one thing that I have not always done.  Research indicates that in addition to teaching at least two ways to do every problem, the teacher should take time to compare and contrast the two methods because it helps build analytical thinking.  I've never done the compare and contrast part and need to start doing that.  It has been found that students benefit when they are expected to use multiple methods to find solutions. 

Once students are used to using multiple methods, teachers can then take time to start looking at why one method might be better for solving certain problems for its easy and efficiency.  In addition, it is suggest that teachers show methods that look like they would work but don't and then take time to lead a discussion on why it happened this way.

Finally, it is important for the teacher to create a culture of problem solving by having discussions where students show the different ways they used to find the solution.  This reinforces the idea that there is not one way to solve a problem.  Let me know what you think, I'd love to hear.  Have a great day.