Developing Numerical Magnitude Knowledge through Measurement Activities

• In Event: 2-024 - From the Lab to the Field: Using Early Math Development Research to Improve Educational Practice

Integrative Statement

One key objective of early math instruction is to help children develop an understanding of numerical magnitude, which provides a foundation for subsequent mathematics learning. Theories of numerical cognition propose that numerical magnitude is represented spatially along a mental number line (Siegler & Lortie-Forgues, 2014). This mental representation of magnitude is formed gradually over the first years of school. At the outset of schooling, children demonstrate substantial variability in numerical magnitude knowledge, and the level of this knowledge in kindergarten predicts math achievement through high school (Geary, 2011).

The present study aimed to improve kindergartners’ numerical magnitude understanding. It tested an intervention designed to do so by leveraging a complementary area of mathematics – measurement. Measurement provides a unique arena in which spatial and numeric reasoning intersect and abstract numeric relations can be demonstrated concretely. The intervention tested in the present study contained a sequence of measurement activities that were hypothesized to promote measurement skills, as well as children’s understanding of numerical magnitude.

Participants were 88 children from six kindergarten classrooms in Moscow, Russia. Within classrooms, participants were randomly assigned to condition. In the experimental condition, instruction focused on key measurement concepts, such as the importance of equal intervals (units). In the control condition, children practiced math tasks similar to those taught in their regular class (solving simple arithmetic problems and learning geometric shapes). Each condition included ten 30-minute small-group (4-6 children) instructional sessions conducted by researchers.

Learning was assessed by examining pre-to-posttest changes on two number magnitude tasks. Numeric Magnitude Comparison (dyads) task included 24 single-digit (SD) number pairs and 48 double-digit (DD) pairs; children were told to cross out the bigger number in each pair. The other task, Numeric Distance Comparison (triads), included 8 SD and 16 DD items that depicted a target number and two answer choices; children were told to cross out the number closest to the target.

Results for the dyads task are illustrated in Figure 1. On SD items, children showed high accuracy at pretest; on DD items, pretest accuracy was below 50%. A 2(Condition)x2(TestTime) ANOVA with DD accuracy as dependent variable revealed main effect of Condition, qualified by TestTime*Condition interaction, F(1,82)=8.707, p=.004, 2=.096. Simple-effects test showed that the conditions varied at posttest, but not at pretest.

Results for the triads task are illustrated in Figure 2. Accuracy on SD items was higher than on DD items, but did not approach ceiling at pretest. A 2(Condition)x2(NumberType)x2(TestTime) ANOVA revealed main effects of NumberType and Condition, qualified by TestTime*Condition interaction, F(1,82)=14.417, p<.001, 2=.15. Simple-effects tests showed conditions varied at posttest for both number types, but did not vary at pretest for either.

Findings confirmed that measurement instruction facilitates numeric magnitude understanding, affecting children’s performance on non-spatial tasks assessing symbolic number knowledge. These findings have implications for educational practice. They suggest that elementary math instruction may benefit from an earlier introduction of measurement activities focused on conceptual understanding of units than currently outline in Common Core, because this approach promotes numerical magnitude knowledge critical for subsequent math learning.

Authors

• Marina Vasilyeva, Boston College
  Presenting Author

• Elida V. Laski, Boston College
  Non-Presenting Author

• Aleksander Veraska, Moscow State University
  Non-Presenting Author

• Darya Bukhalenkova, Moscow State University
  Non-Presenting Author