Poster #32 - (In)consistent Labeling of Math Strategies and Problems Guides Strategy Choice

• In Event: 2-055 - Poster Session 06
  In Poster Session: PS 06 Section - Cognitive Processes

Integrative Statement

When children encounter a novel math problem, how do they decide how to solve it? We argue that strategy selection can be viewed as a problem of categorization. For instance, a child who categorizes a problem as a subtraction problem may infer that it could be solved using a subtraction strategy. In contrast, a child who categorizes the same problem as a division problem would likely infer that a different strategy would be appropriate.
We hypothesized that labeling could guide categorization and inference about strategy use, based on prior research in other domains that suggests labeling novel objects guides children’s inferences about those items (e.g., Gelman & Markman, 1986). We tested whether labels guide inferences about strategies in the domain of mathematics problem solving using constant change problems, a type of algebraic word problem. These problems describe an event unfolding over time or space in continuous or discrete terms. For instance, the continuous problem in Figure 1 describes a rate changing gradually. In contrast, the discrete problem describes an increase occurring in jumps. Problem framing is associated with different strategy use (Alibali, Bassok, Solomon, & Syc, 1999). People are more likely to use what is known as the average strategy on continuous problems than on discrete problems and more likely to use the summation strategy on discrete problems than on continuous problems.
In the current study, 120 seventh and eighth graders completed a pretest, lesson, and posttest. At pretest, participants solved one constant change problem. In the lesson, participants read a continuous problem with an example showing how to solve it with the average strategy and a discrete problem with an example showing how to solve it with the summation strategy. At posttest, participants solved two discrete and two continuous problems. In the labels-matched-continuous condition, the posttest problems and the continuous problem and associated average strategy in the lesson had the same labels. In the labels-matched-discrete condition, the posttest problems and the discrete problem and associated summation strategy in the lesson had the same labels. Thus, for some participants, the labels implied that the posttest problems were like the continuous problem in the lesson and could be solved using the average strategy. For the other half of participants, the labels implied that the posttest problems were like the discrete problem and could be solved using the summation strategy.
Participants were more likely to use the average strategy when the posttest labels matched the label given to the continuous problem in the lesson than when the posttest labels matched the label given to the discrete problem (p < .001, see Figure 2). In addition, the effect of the label condition was stronger for discrete problems than continuous problems (p = .03). These results suggest that labels can guide inferences about appropriate strategy use, but these effects depend on problem features. These results extend the research on labels to a new, educationally relevant domain and provide insights into the process of strategy selection.

Authors

• Sarah A Brown, Boston University
  Presenting Author

• Martha W Alibali, University of Wisconsin-Madison
  Non-Presenting Author