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Anantharajan, Madhuvanti – Journal for Research in Mathematics Education, 2020
Counting is fundamental to early mathematics. Most studies of teaching counting focus on teachers observing children count. The present study compares mathematical ideas that 12 PK, transitional kindergarten (TK), and kindergarten teachers noticed from observing their own students count during a classroom session of Counting Collections with ideas…
Descriptors: Mathematics Skills, Kindergarten, Preschool Teachers, Preschool Children
Hunt, Jessica; Silva, Juanita – Journal for Research in Mathematics Education, 2020
We investigated the extent to which one elementary school child with working-memory differences made sense of number as a composite unit and advanced her reasoning. Through ongoing and retrospective analysis of eight teaching-experiment sessions, we uncovered four shifts in the child's real-time negotiation of number over time: (a) initial…
Descriptors: Elementary School Students, Short Term Memory, Mathematical Logic, Learning Disabilities
Pérez, Arnulfo – Journal for Research in Mathematics Education, 2018
This theoretical article describes a framework to conceptualize computational thinking (CT) dispositions--"tolerance for ambiguity," "persistence," and "collaboration"--and facilitate integration of CT in mathematics learning. CT offers a powerful epistemic frame that, by foregrounding core dispositions and practices…
Descriptors: Mathematics Education, Thinking Skills, Secondary School Teachers, Mathematics Teachers

Hector, Judith H.; Frandsen, Henry – Journal for Research in Mathematics Education, 1981
Results of this study indicated calculator algorithms can serve as an effective alternative instructional strategy where computational skill is an instructional goal. (MP)
Descriptors: Algorithms, Basic Skills, Calculators, College Mathematics
Murata, Aki; Fuson, Karen – Journal for Research in Mathematics Education, 2006
The framework of Tharp and Gallimore (1988) was adapted to form a ZPD (Zone of Proximal Development) Model of Mathematical Proficiency that identifies two interacting kinds of learning activities: instructional conversations that assist understanding and practice that develops fluency. A Class Learning Path was conceptualized as a classroom path…
Descriptors: Teaching Methods, Grade 1, Computer Assisted Instruction, Asian Culture

Steinberg, Ruth M. – Journal for Research in Mathematics Education, 1985
This study: (1) documented the spontaneous derived facts strategies (DGSs) that second-grade children (N=23) used; (2) investigated how training in use of DFSs influenced the solution strategies children used to solve addition and subtraction problems; and (3) examined the role of DFSs in the transition to recall of number facts. (JN)
Descriptors: Addition, Computation, Elementary School Mathematics, Grade 2

Wachsmuth, Ipke – Journal for Research in Mathematics Education, 1983
This critique discusses Gagne's position that students should understand how to mathematize a concrete situation and validate a solution but need not understand how a solution is derived. Reconciling his views with those of mathematics educators and raising questions are both included. (MNS)
Descriptors: Cognitive Processes, Computation, Educational Theories, Instruction

Gage, Robert M. – Journal for Research in Mathematics Education, 1983
Gagne's reply to critiques by Wachsmuth and by Steffe and Blake notes that their approaches are from different points of view. He urges that mathematics educators examine critically the view that understanding involves some aspects of the structure of mathematics. (MNS)
Descriptors: Cognitive Processes, Computation, Educational Theories, Instruction

Wheatley, Grayson H.; McHugh, Daniel O. – Journal for Research in Mathematics Education, 1977
The authors attempt to determine the effects of the use of direct and "combinations of tens" methods of two column-addition, ability, and grade level as factors in column addition efficiency. (MN)
Descriptors: Addition, Algorithms, Computation, Educational Research

Baroody, Arthur J. – Journal for Research in Mathematics Education, 1985
Mastering the basic number combinations involves discovering, labeling, and internalizing relationships, not merely drill-based memorization. Counting procedures and thinking strategies are components, and it may be that using stored procedures, rules, or principles to quickly construct combinations is cognitively more economical than relying…
Descriptors: Cognitive Processes, Computation, Educational Research, Elementary Education

Ashcraft, Mark H. – Journal for Research in Mathematics Education, 1985
The author first corrects Baroody's description of the network retrieval model for basic number facts, in which facts are stored in memory and retrieved as needed. He then indicates weaknesses in Baroody's argument. (MNS)
Descriptors: Cognitive Processes, Computation, Educational Research, Elementary Education

Fuson, Karen – Journal for Research in Mathematics Education, 1984
Discusses four ways in which subtraction is more difficult than addition: (1) verbal solutions do not always parallel object solutions; (2) methods may interfere with each other; (3) special problems exist with subtraction on the number line; and (4) subtraction has multiple situational interpretations. (MNS)
Descriptors: Cognitive Processes, Computation, Educational Research, Elementary Education

Steffe, Leslie P.; Blake, Rick N. – Journal for Research in Mathematics Education, 1983
This critique focuses on Gagne's attempt to apply information-processing theory to mathematics education, noting that this distorts what it means to learn mathematics. This is discussed with specific illustrations. (MNS)
Descriptors: Cognitive Processes, Computation, Educational Theories, Instruction

Barr, David C. – Journal for Research in Mathematics Education, 1978
This study compares three methods of introducing two-digit numeration. It is concluded that teachers should build on the preschool exposure children have in counting past ten, rather than have children begin by counting out groups of tens and ones and only later in the process use the normal number names. (MN)
Descriptors: Computation, Concept Formation, Educational Research, Elementary School Mathematics

Schoen, Harold L.; And Others – Journal for Research in Mathematics Education, 1981
Two grade 4 classes provided subjects for a study in the teaching of estimation in computation. A second study was conducted with two grade 5 and two grade 6 classes that supported the idea that estimation in whole number computation can be taught in a short period of time. (MP)
Descriptors: Computation, Educational Research, Elementary Education, Elementary School Mathematics
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