4 Elementary Problems
It is now time to begin applying some of the general ideas about procedural and conceptual knowledge to word problems. We begin with arithmetic problems that children encounter in the lower elementary grades. These problems are interesting for two reasons. The first is that they provide a valuable source of information regarding the kinds of difficulties young children encounter when they begin working on mathematical problems. For instance, is successful performance at this age constrained by a lack of ability to do addition and subtraction or is successful performance constrained by an inability to understand the problems? The second reason these problems are useful is that it can later be seen whether the analysis of more complex problems builds on the same theoretical ideas used to analyze simple problems. Can the kinds of relations identified in simple problems be combined to form more complex problems, or do we need different kinds of knowledge structures to represent complex problems? This issue is explored in chapter 5 on multistep arithmetic problems and again in chapter 6 on algebra word problems.
Children use a variety of strategies for solving elementary story problems. Here's an example of an exchange between a sixth-grade student named Ann (a pseudonym) and an interviewer (1) based on the problem:
A bag of snack food has 4 vitamins and weighs 228 grams. How many grams of snack food are in 6 bags?