E. Reid

Erikson Institute, Early Math Collaborative, Assistant Director for Research

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

by E. Reid, Arthur Baroody, and David Purpura

Journal of Cognition and Development, 2015

ABSTRACT Previously, researchers have relied on asking young children to plot a given number on a... more ABSTRACT 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 children’s magnitude estimates and misrepresent the nature of their number representation. The purpose of this study was to compare young children’s 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 years to 6.0 years, were administered both versions of the N-P task twice over four sessions in one of two randomly assigned and counter-balanced 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.

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

by Arthur Baroody, Michael Eiland, E. Reid, and David Purpura

School Psychology Review, 2015

2015). Using a brief preschool early numeracy skills screener to identify young children with mat... more

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The impact of highly and minimally guided discovery instruction on promoting the learning of reasoning strategies for basic add-1 and doubles combinations

by Arthur Baroody, E. Reid, and David Purpura

Early Childhood Research Quarterly, 2015

A 9-month training experiment was conducted to evaluate the efficacy of highly and minimally guid... more A 9-month training experiment was conducted to evaluate the efficacy of highly and minimally guided discovery interventions targeting the add-1 rule (the sum of a number and one is the next number on the mental number list) and doubles relations (e.g., an everyday example of the double 5 + 5 is five fingers on the left hand and five fingers on the right hand make 10 fingers in all) and to compare their impact with regular classroom instruction on adding 1 and the doubles. After pretest, 81 kindergarten to second-grade participants were randomly assigned to one of three training conditions: highly guided add-1 training, highly guided doubles training, or minimally guided add-1 and doubles practice. The highly guided add-1 training served as an active control for the highly guided doubles training and vice versa, and the minimally guided practice condition served to control for the impact of extra practice. ANCOVAs using pretest score and age as covariates indicated that both highly guided and minimally guided interventions were successful in promoting retention and transfer for the relatively salient add-1 rule, but only highly guided training produced transfer for the less-salient doubles relations. The findings indicate that the degree of guidance needed to achieve fluency with different addition reasoning strategies varies.

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Early Childhood Mathematics

by Veena Paliwal, Arthur Baroody, E. Reid, David Purpura, and Neet Priya Bajwa

Oxford Bibliographies Online Datasets, 2000

ABSTRACT Although the term early childhood mathematics education often refers to instruction for ... more ABSTRACT Although the term early childhood mathematics education often refers to instruction for three- to six-year-olds in preschool or kindergarten programs by a teacher or paraprofessional, the present review will focus on the mathematical teaching and learning of children from birth to kindergarten (six years of age). This is because a preschooler’s mathematical learning begins before three years of age, can involve a wide variety of people (e.g., parents, siblings, other relatives or caregivers, peers), and can occur in informal or everyday situations. Indeed, increasingly, the term early childhood mathematics education includes other intentional training by educational media (e.g., educational television programming, computer programs, websites dedicated to math games, or other forms of training). Moreover, although the term sometimes includes primary school (grades one and two) children, this review will not include references that focus on grade one children or those who are older primarily because of limited space. However, some references in which a portion of the sample included those who were as old as eight years are included. Since the 1970s, research has revealed that preschoolers are capable of developing a surprising degree of informal mathematical knowledge. Although scholars continue to debate how children acquire this knowledge, they generally agree that early mathematical knowledge provides an essential foundation for understanding and learning school or formal mathematics. Unfortunately, research has also shown that significant differences in mathematical knowledge emerge before school begins. Consensus has grown in recent years that early intervention programs are important for “leveling the playing field.” Although some agreement exists on what these programs should teach, debate is ongoing on how best to teach mathematics to preschoolers.

COMMENTS ON LEARNING AND TEACHING EARLY AND ELEMENTARY MATHEMATICS

by E. Reid and Arthur Baroody

Instructional Strategies for …, 2011

C l-IAPTER 8 COMMENTS ON LEARNING AND TEACHING EARLY AND ELEMENTARY MATHEMATICS Arthur J. Baroody... more

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

by Arthur Baroody, E. Reid, and David Purpura

Cognition and Instruction, 2014

Achieving fluency with basic subtraction and add-with-8 or -9 combinations is difficult for prima... more 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.

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Fostering At-Risk Kindergarten Children's Number Sense

by Arthur Baroody, E. Reid, and David Purpura

Cognition and Instruction, 2012

ABSTRACT A 9-month training experiment evaluated whether computer-assisted discovery learning of ... more ABSTRACT 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.

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

by Arthur Baroody, E. Reid, and David Purpura

American Educational Research Journal, 2013

ABSTRACT In a 9-month training experiment, 64 first graders with a risk factor were randomly assi... more ABSTRACT 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 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 1 and 1 1 n items at the posttests. The control participants did not exhibit evidence of learning a general near-doubles reasoning strategy (if 4 1 4 is 8 and 4 1 5 = 4 1 4 1 1, then the sum of 4 1 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.

An Example of a Hypothetical Learning Progression: The

by E. Reid, Arthur Baroody, and David Purpura

Some time ago, I asked Nikki, a kindergartner, what she thought the largest number was. The girl ... more Some time ago, I asked Nikki, a kindergartner, what she thought the largest number was. The girl responded, "a million." I then asked what number she thought came after a million. After a moment's thought, Nikki responded, "a million and one." I next asked what she thought came after a million and one. Again the girl thought for a moment and answered, "a million and two." I pressed Nikki further by asking what she thought came after a million and two. After a few moments of thoughtful reflection, she concluded, "there is no largest number."

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