Problem Solving - Not Learned by Discovery
Many State education agencies annual standardized math tests stress word problems in lieu of pure computation problems as they did 30 years ago. Discrete grade level math skills are often combined to create a simple math word problem. For example, here is a typical fifth grade math word problem:
Brendan made a goal to run a total of 50 kilometers in one week. He
ran 7 kilometers each night for 6 days. On the 7th night, he ran until he
met his goal. How many kilometers did Brendan run on the last night?
As expected, when students consistently practice word problems or anything else for that matter, they get better and better – assuming the school curriculum has an effective and accountable numeracy based skills program and the teacher implements efficient and effective daily routines and classroom management.
But, how are children taught to solve math word problems?
Elementary aged children are between eight and eleven years old when they are assessed on standardized tests. Like learning at all ages, a consistent set process is extremely helpful. It should not be done by discovery where each child is doing their own thing. A structured methodology in solving math word problems greatly reduces students' anxiety of solving developmentally difficult problems.
A replicable word problem solving method is needed
Over the years, I have visited many Title 1 urban and rural schools that chose not to adopt a word problem solving structure, and their results are more than evident of their lack of a system. The school’s standardized math scores are as depressed as their children’s problem solving prowess. Fortunately, most elementary teachers provide their students specific instruction in a problem solving methodology. A relatively common method is the following:
1.) Understand the problem. 2.) Make a plan 3.) Work the Problem 4.) Look back and check.
This plan is logical, but I believe it is too general. It does not focus the child’s attention on what they are trying to find in the word problem. I prefer a more specific plan/procedure. For example, the acronym ‘RACE’ problem solving methodology is shown below.
Read the problem and underline the last sentence – circling key word(s)
All needed numbers circled. Extraneous data crossed out.
Calculate a solution showing all work – neatly and organized
Evaluate – Does the solution make sense? – reasonableness
This process should appear on an anchor of support on the classroom wall in easy view of all students. The children should also write ‘RACE’ above each problem – checking off each letter as they complete that step. It is highly beneficial if the problem solving methodology is standardized both horizontally on the grade level and vertical between grades. Once students learn the methodology in one grade level, they readily apply it in the next.
With a daily regimen of structure in this process, students’ methodologies are consistent, predictable and errors are easily corrected. In a relatively short time, students are very successful at solving word problems – again, assuming they possess mastery of grade level numeracy skills and there is effective classroom management procedures in place.
There are other effective methodologies that provide similar specificity and effectiveness, and as long as students are consistent each time, all students in the classroom become adept problem solvers. As children ingrain a structured learning process, their self-confidence is heightened, and they eventually develop creative ways to consistently and successfully solve word problems. Simply put, the process is not a randomized problem solving methodology – the knowledgeable, effective classroom teacher guides their students to success!
Finally, the teacher should implement high levels of accountability when checking student work to ensure the methodology is followed, or students will not be consistent and commit the process to long-term memory.