Math word problems were difficult for me when I was a kid. At the end of thirty or so skill base computation problems on the exercise page in the math book lurked several word problems – the nemesis of my childhood elementary math experience – and I fared not much better during middle school. For example, the word problems involving two trains departing stations from different locations at different times confused me so much when I was doing my homework one afternoon that I considered calling a travel agent to assist me. So, why were word problems so difficult for me?
What was the cause of my dread and downfall with math word problems as a kid?
At an early age, I liked and was quite respectable at math. After high school, I earned a civil engineering degree from the University of Texas at Austin with high marks. However, when I quit my senior design structural engineering job and began teaching fifth graders in an elementary school twenty five years ago, I discovered the primary reason I struggled with math word problems when I was my students’ age. And, the answer was simple: My classmates and I did not practice working word problems when I was the same age as my fifth grade students. We were exceedingly good at skill base computation problems because we worked so many of them. But, we worked so few word problems each day that we never developed high levels of competency. Mystery solved.
A solution to developing better problem solving math student is not confined to the fact that students simply require more practice. Of course, it is one of the keys. But, the other issue is ensuring students have high skill level proficiency, numeracy levels in both math fact operations and general math skills (i.e. place value, fractions, algorithm – computations, decimals, etc.). It is these two important factors in combination that successfully ready young students in a word problem solving environment.
What does the successful problem solving math class look like?
There are three (3) general parts of a daily math lesson apart from a daily differentiated numeracy program. First, a quick daily review (spaced repetition instruction) prior to the daily core lesson on previously taught math skills providing sufficient math skill repetitions that ensure student mastery. Second, the core lesson should be sequential, interactive and fundamentally designed initiating with concrete math models and transitioning to abstract paper-pencil learning.
Finally, each day, students require a steady diet of 4 to 8 grade level word problems. The word problems may be either teacher generated or purchased from a commercial vendor. Regardless of the source of the Bridge Resource (i.e. a daily set of application word problems combining discrete math skills), the word problems must be representative of a Standards-based grade level mathematics curriculum.
Ideally, the word problems in a daily Bridge Resource should closely follow the skill base portion of the daily core lessons. If the word problems are randomly sequenced from a commercial product, there are a couple of options. The teacher can cut and paste word problems from the vendor resource and align the sequencing order to that of presented skill lessons in their classroom. Another option is for students to collectively work the non-sequential problem with the teacher as guided practice. Then, the classroom teacher may prepare similar problems on subsequent days with only the numbers changed from the original word problems until students are capable to work the problem independently via drawing and labeling a picture of their solution, as needed. In only six (6) to ten (10) repetitions of a new problem/concept type, perimeter or area, for example, students invariably demonstrate high levels of proficiency.
Whenever a task or endeavor is consistently practiced with good habits, competence will follow in a relatively short period of time. Put simply, consistent daily practice is required to attain proficiency. Math word problems are not an exception to this thinking.