Why Teachers Let Students Use Multiple Methods To Solve Problems.

 

I tend to check a few websites to see the latest in math news and I found an article explaining why teachers allow students to use a variety of methods to solve problems on Physics.org website.  It begins by discussing the change from telling students how to solve problems to letting them explore and use multiple ways to solve problems. 

There has been a change from using the exact same resources and assessments to providing a variety of resources and assessments to see what they've learned.  Furthermore, most of the methods used to teach in the past were based on the group in charge so in the past, teachers showed their way of solving problems as the only way but not everyone see's math in the same way. This sometimes put students at a disadvantage. 

There may also be cultural differences in what method is chosen to teach students. For instance, in Japan, students learn to multiply using times tables while in the Philippines, students use finger multiplication.  I remember in upper elementary/middle school, they had a method for multiplication that I just couldn't get so my father taught me the way he learned and to me, that made so much more sense. 

When teachers draw on the student's prior knowledge, it helps them determine the best way to present the material to them. In addition, the use of collaboration is considered a good tool because it allows students to have their individual voices heard when they work with others.  

Overall, the focus is on a classroom that allows equitable experiences for all students.  It includes what one should look for in an equitable classroom, what it sounds like, and what it feels like.  Some of the ideas include focusing on how students get the answer rather than focusing on the "right" answer, instructional time happens only after students are engaged, teachers ask students what they are thinking about, and they wait till the students ask for help rather than offering it.  

I enjoyed the article as it made me think.  Let me know what you think. Have a great day.

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.