Learning 10ness Horizontally Improves First Graders' Estimation of Numerical Magnitudes

• In Event: 54.018 - Promising Scholarship in Education: Dissertation Fellows and Their Research

Abstract

Recent studies have found that children with a more accurate estimation of numerical magnitude in the first grade exhibited better mathematic skills (Booth & Siegler, 2008). However, children as early as kindergartner differs in their understanding of numerical magnitudes (Booth & Siegler, 2008). Extending this line of work, I examined two different ways that number-line estimations are taught: blocks and bundles. In my study, 58 kindergartner and first-graders from Southern California were randomly assigned to one of the three instructional contexts: blocks, bundles, and control condition. I found that students using an exact combination of base-10 and unit-blocks gained more from the instruction than the other two groups. The study demonstrated that representing numbers of 10ness in a linear fashion proved effective in improving children’s understanding of two-digit number magnitudes. The students in the treatment group gained a higher linearity on their mental number line at posttest (R2= 95% vs. 89%). In addition, only block group transited from logarithmic to linear from pretest to posttest (R2 = 72% vs. 97%). The research question is below:
To what extent do kindergartens and first graders who receive instructional interventions outperform those in the control group on 0  100 mental number line task and base-10 understanding score?
To analyze the research questions, the quasi-experimental design was used to assess the 58 K-1 students’ performance on the mental number line (Siegler & Booth, 2004) and base-10 questions tasks (Miura & Okamoto, 1989). The mental number line task is a closed-end experiment. The students were identified with corresponding number magnitudes ability by placing 10 two-digit numbers on the correct place on the 0-100 number line. The base-10 questions are a battery of numerical questions pertaining to the base-10 and place-value concepts. Twenty-eight K-1 students were assigned to the control group were selected but merely in the regular instruction without receiving any specific interventions. Thirty student were in the treatment groups. Among them 15 were instructed with bundles and other 15 used blocks to learn to construct two-digit numbers. They receive about 1 hour instruction on two-digit number counting and constructing skills. The research assistant taught and correct their mistakes until they fully understand and acquire the skills.
To analyze the research questions, the quasi-experimental design was used to assess the 58 K-1 students’ performance on the mental number line (Siegler & Booth, 2004) and base-10 questions tasks (Miura & Okamoto, 1989). The mental number line task is a closed-end experiment. The students were identified with corresponding number magnitudes ability by placing 10 two-digit numbers on the correct place on the 0-100 number line. The base-10 questions are a battery of numerical questions pertaining to the base-10 and place-value concepts. Twenty-eight K-1 students were assigned to the control group were selected but merely in the regular instruction without receiving any specific interventions. Thirty students were in the treatment groups. Among them, 15 were instructed with bundles and other 15 used blocks to learn to construct two-digit numbers. They receive about 1-hour instruction on two-digit number counting and constructing skills. The research assistant taught and correct their mistakes until they fully understand and acquire the skills.
Significance of the research
Many primary education concerns on numerical understanding are often related to the low efficiency of representation and ineffective instructional approached involved. The fields of cognitive development and numerical understanding deal with the issue of learning difficulties for multidigit number magnitudes both at proximity and a theoretical level. Increasingly educational researchers are turning to cognitive-based intervention as a framework in which to interpret mental representation and to understand possible solutions of number magnitudes understanding (e.g. Dehaene’ book on human mental representation is based on a cultural development analysis for left-to-right mental number line). My research will illustrate the importance of reconciling linear representation and base-10 concept in the K-1 group. The work will provide a new perspective by which to ameliorate the learning effect. In addition, the instructional way recommended has a high profile in educational policy and public awareness on children’s developmental leering. The question of the role of linear representation in the core for the fundamental understanding of child development, especially the relationship of how to teach them and how they learn. Therefore, it is anticipated that this project would generate a great deal of interest, not only among education or, but also among the Prek-3 policy makers and practitioners. 

Author

• Yu Zhang, University of California - Davis