Influences of Different Instructional Approaches on First-Graders’ Manipulative Use

• In Event: Poster Session 09
  In Poster Session: PS 09 Topic - Cognitive Processes

Abstract

Elementary teachers often rely on concrete objects, called manipulatives, to help their students understand abstract mathematical ideas (McNeil & Jarvin, 2007). Some research suggests that teachers should make explicit links between the representations and their intended referents to optimize student learning (Carbonneau et al., 2013). Other research contends that children benefit from constructing their own understanding of representations (Brown et al., 2009), which may help them transfer knowledge to different contexts and be more flexible in their manipulative use (Martin & Schwartz, 2005). No previous research has compared these instructional approaches directly in the context of children’s manipulative use in mathematics.

In the present study, we compared the outcomes of explicitly telling children the quantitative referents for manipulatives to encouraging exploration with the objects in more open problem-solving environments. After instruction, we assessed their use of manipulatives and problem-solving accuracy as a function of instructional approach. Sixty-five (N = 65) first-graders used novel manipulatives called “pollies” to represent specific quantities. Children were randomly assigned to one of three instructional conditions: (1) Direct Instruction (DI), where children were explicitly told that the referent for each polly was 2; (2) Guided Exploration (GE), where the researcher first let the children explore and decide on a referent for each polly before constraining the task with prompts that led children to “discover” that the referent was 2; (3) Control, where children were permitted to attribute the referent of their choice to the pollies with no feedback.

Children completed a symbolic flexibility task requiring them to use the pollies to solve n x 3 and n x 5 multiplication word problems (n being the number of groups, and 3 and 5 being the number in each group). The task evaluated the degree to which children could assign a new quantitative referent (i.e., 3 or 5) to the pollies. Students were categorized into profiles based on their manipulative use (Figure 1). Children who received direct instruction were the only ones who gave a referent of 2 only to all items. Relative to the other conditions, a greater proportion of students in the GE condition demonstrated a higher level of symbolic flexibility by either using both referents 1 and 2 for the pollies or using referents other than 1 or 2.

We examined accuracy on the symbolic flexibility task as a function of condition and referent use. A 2 (condition: DI, GE) x 4 (referent profile) ANOVA revealed that items solved by children in the GE condition were more accurate than items solved by children in the DI condition when referents of 2 only were used and when referents other than 1 or 2 were used (Figure 2).

In sum, explicit instruction on how to use the pollies prevented some children from using them in flexible ways. The greater flexibility of those who learned through guided exploration might account for the greater accuracy in problem-solving performance. For stronger generalizations about symbolic flexibility, more research remains to determine the robustness of the findings across tasks and manipulative types.

Authors

• Emmanuelle Adrien, Concordia University
  Presenting Author

• Helena Patricia Osana, Concordia University
  Non-Presenting Author

• David H. Uttal, Northwestern University
  Non-Presenting Author