When I was teaching math, I quickly learned there was a set formula to the lessons presented in the textbook.  Even when I moved schools and changed textbooks the formula stayed the same.  At the beginning of the lesson, the book walked a student through how to solve a problem and taught them the formula.  Then there was a page or two of practice questions that used the formula, presented in increasing difficulty.  Finally, there was a small section of word problems presented at the very end of the lesson.

A group of researchers from the Wisconsin Center for Educational Research compared the highly regarded Connected Mathematics curriculum to a curriculum of their own design called Bridging Instruction.  According to their findings, the traditional formula of presenting word problems at the very end of a lesson may not be effective.

Connected Mathematics was designed by a group at Michigan State University and published by Pearson.  They describe the curriculum as being “problem-centered” and inquiry-based. It was designed to implement research that contends students understand math better when the discovery of knowledge is embedded in a problem.  To this end, it makes heavy use of equations, graphs, and word problems and strives to teach students to move fluidly from one to another.

Connected Mathematics was chosen as a comparison because the curriculum has already been proven to increase mathematical ability.  It was also a curriculum that the teachers participating in the study were familiar with and had been using.

According to the study, Bridging Instruction differs from Connected Mathematics in two areas.  First, linear and nonlinear functions were compared and contrasted earlier in Bridging Instruction.  More importantly, though, Bridging Instruction used word problems as a starting point for instruction.  At the beginning of a lesson, teachers were to present a word problem and then elicit from the students their ideas about the problem and their invented solutions and strategies.  Then the teacher would use the students own knowledge, as presented in class, to introduce the new concept.

The study’s authors claim that while both curriculums led to student gains, those that had been taught using the new Bridging Instruction curriculum performed better than students using the other curriculum.  Gains were seen in using graphs, equations, and, most especially, in their ability to solve word problems, while the gains by students using Connected Mathematics were confined to solving linear, symbolic problems.

While this is an initial study with a relatively small group of students, it is quite possible that the singularly key and simple move of introducing a lesson with a word problem helped achieve these gains.

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