Erin E. Reid

Kindergarten Predictors of Mathematical Growth in the Primary Grades: An Investigation Using the Early Childhood Longitudinal Study--Kindergarten Cohort.

This study examined longitudinal predictive relationships between young childrens classroom behaviors and their growth in mathematics skills during the primary grades. Using the Early Childhood Longitudinal Study--Kindergarten cohort, the authors tested a longitudinal model featuring positive (interpersonal skills and approaches to learning) and negative (internalizing and externalizing) behaviors at kindergarten entry as predictors of growth in mathematics achievement through 3rd grade. Results indicated that negative behaviors demonstrate negligible relationships with early development of mathematics skills. Interpersonal skills demonstrated a small negative relationship with mathematics growth when other positive behaviors were included as predictors in the model. In contrast, approaches to learning (goal-directed behavior, persistence, organization) demonstrated small positive relationships with growth in mathematical skills and may represent a skill domain for educators to consider in designing their instructional practices.

Can Computer-Assisted Discovery Learning Foster First Graders’ Fluency With the Most Basic Addition Combinations?

In a 9-month training experiment, 64 first graders with a risk factor were randomly assigned to computer-assisted structured discovery of the add-1 rule (e.g., the sum of 7 + 1 is the number after “seven” when we count), unstructured discovery learning of this regularity, or an active-control group. Planned contrasts revealed that the add-1 conditions were more effective than regular instruction/practice in promoting the learning of the add-1 rule. Contrary to the conclusions of Alfieri, Brooks, Aldrich, and Tenenbaum (2011) and Kirschner, Sweller, and Clark (2006), participants in the structured add-1 condition did not outperform those in the unstructured add-1 group on practiced and unpracticed n + 1 and 1 + n items at the posttests. The control participants did not exhibit evidence of learning a general near-doubles reasoning strategy (if 4 + 4 is 8 and 4 + 5 = 4 + 4 + 1, then the sum of 4 + 5 must be 9). The add-1, but not the active-control, participants achieved success, including transfer, because the former had mastered the developmental prerequisites for add-1 rule and the latter had not mastered the prerequisites for the near-doubles strategy.

Fostering At-Risk Kindergarten Children's Number Sense

A 9-month training experiment evaluated whether computer-assisted discovery learning of arithmetic regularities can facilitate kindergartners’ fluency with the easiest sums. After a pretest, kindergartners with at least one risk factor (n = 28) were randomly assigned to either a structured add-0/1 training condition, which focused on recognizing the n + 0/0 + n = n and the n + 1/1 + n = the number-after-n rules, or an active control group. Using pretest fluency as the covariate, ANCOVAs revealed that the structured add-0/1 group significantly outperformed the control group on both practiced and unpracticed (transfer) n + 0/0 + n and n + 1/1 + n items at the delayed posttest and had significantly larger gains in mathematics achievement. Key instructional implications include: Early intervention that targets discovering rules for adding with 0 and 1 and family-specific developmental prerequisites is feasible and more effective than typical classroom instruction in promoting fluency with such basic sums. Such rules may be a critically important bridge between informal and formal mathematics.

Using a Brief Preschool Early Numeracy Skills Screener to Identify Young Children With Mathematics Difficulties

Abstract. A critical component in enhancing academic success is identifying children at risk of later academic difficulties. Although significant efforts have been devoted to design effective assessment processes in elementary school, fewer efforts (particularly for mathematics) have been made for preschool. The focus of this study was to design and evaluate a brief early numeracy skills screening tool. Measure development and validation occurred in a two-stage process with diverse and distinct samples. In the first stage, 393 preschool children were assessed on a battery of early numeracy tasks. By use of an item response theory framework, 24 items that spanned the ability continuum were selected for inclusion in the brief measure. In the second stage, 129 preschool children were assessed on the brief measure, the Test of Early Mathematics Ability–Third Edition, and two literacy measures. The data resulted in acceptable psychometric properties and strong diagnostic accuracy. Theoretical and practical implications are discussed.

Fostering First Graders’ Fluency With Basic Subtraction and Larger Addition Combinations Via Computer-Assisted Instruction

Achieving fluency with basic subtraction and add-with-8 or -9 combinations is difficult for primary grade children. A 9-month training experiment entailed evaluating the efficacy of software designed to promote such fluency via guided learning of reasoning strategies. Seventy-five eligible first graders were randomly assigned to one of three conditions: guided subtraction (e.g., If 5 + 3 = 8, then 8 – 3 is 5), guided use-a-10 (e.g., If 10 + 7 = 17, then 9 + 7 is 16), or an unguided-practice condition for 30-minute sessions twice a week for 12 weeks. An ANCOVA revealed that at the delayed posttest, the guided-subtraction group outperformed both comparison groups on unpracticed subtraction combinations. Analyses of gains in slow but appropriate use of reasoning and decreases in inefficient strategy use indicated that both types of guided training promoted the learning of a targeted reasoning strategy.

Assessing Young Children's Number Magnitude Representation: A Comparison Between Novel and Conventional Tasks

Previously, researchers have relied on asking young children to plot a given number on a 0-to-10 number line to assess their mental representation of numbers 1 to 9. However, such a (“conventional”) number-to-position (N-P) task may underestimate the accuracy of young childrens magnitude estimates and misrepresent the nature of their number representation. The purpose of this study was to compare young childrens performance on the conventional N-P task and a “modified” N-P task that is more consistent with a discrete-quantity view of number and with measures of theoretically related mathematical competencies. Participants (n = 45), ranging in age from 4;0 to 6;0, were administered both versions of the N-P task twice during 4 sessions in 1 of 2 randomly assigned and counterbalanced orders. Between and within conditions, children were significantly more accurate on the modified version than on the conventional task. The results indicate that the conventional task, in particular, may be confusing and that several simple modifications can make it more understandable for young children. However, when performance on theoretically related number tasks is taken into account, both the conventional and the modified N-P tasks appeared to underestimate competence.

Fostering First Graders’ Reasoning Strategies with Basic Sums: The Value of Guided Instruction

An intervention experiment served to evaluate the efficacy of highly guided discovery learning of relations underlying add-1 and doubles combination families and to compare the impact of such instruction with minimally guided instruction. After a pretest, 78 first graders were randomly assigned to one of three intervention conditions: highly guided add-1, highly guided doubles, or minimally guided add-1 and doubles practice-only. Each highly guided intervention served as an active control for the other. The practice-only intervention served to control for the effects of extra practice. For both the add-1 and the doubles strategies, the highly guided intervention, but not the practice-only control, was more successful (as indicated by effect size) than the active control in promoting meaningful transfer to unpracticed but related combinations. The highly guided doubles intervention, but not the highly guided add-1 intervention, produced greater transfer than the minimally guided practice-only intervention.