Issues With Teaching Problem Solving.

  Unfortunately, problem solving in the past has often been ignored in favor of having students learn algorithms and processes needed to solve equations.  If problem solving was taught, it was taught using a standard technique such as identify key words, underline the important information, choose one method, and solve.

There are several reasons why problem solving is not taught in the lower grades in a way that helps students become comfortable with the experience.

First, many teachers are uncomfortable teaching problem solving skills because they do not have the skills themselves, or they are not comfortable with mathematics in the first place.  Some teachers believe they need to take a class on teaching problem solving because they have not learned it.  In addition, teachers often do not want to admit they don't know if a student's explanation is valid and rather than saying something like "Let me check it out and get back to you.", they don't teach it.

Furthermore, students are often uncomfortable with open ended questions because they are used to primarily solving equations with one answer rather than multiple possibilities. Their insecurity can cause them to shut down and refuse to do the problem.

Sometimes teachers feel that teaching problem solving skills take too much time away from covering the material in the curriculum so they ignore it. What they ignore is that many problems are designed to have students recognize patterns which translate to mathematics in general.  Once students are able to see patterns, it speeds up their learning.  Problem solving also allows students to take ownership and acquire greater understanding of the material.

In addition, it is often felt that lower ability students, students who struggle with reading or mathematics should not attempt problem solving but this is incorrect. Since all students should read the problems more than once, it can improve reading ability, and if the teacher has students restate the problem in their own words, it is easy to see if they understood it.

One way to help students with low reading abilities is to have the whole class read the problem together.  If the teacher prepares an audio version of the problem, students can play it and listen to it as many times as needed.

Unfortunately, most problems that require real problem solving such as word problems, tend to use exactly the same methodology as the equations in the section and most word problems have a feel of having been made up to fit the section topic.  In addition, many of the word problems are not complex, even in high school. 

I sometimes think, solving word problems should be compared to solving mysteries.  Let me know what you think, I'd love to hear.