After evaluating a proposal by Jon Star (2005) that mathematics educators reconceptualize the construct of procedural knowledge, we offer an alternative reconceptualization based on an extension and amalgamation of his and other conceptualizations of procedural knowledge and conceptual knowledge. We then propose some implications for research…

Eleven retarded children with mental ages (MA) less than 4.5 years were examined to evaluate whether there is a critical MA for learning basic counting principles and how an understanding of counting develops. Results are discussed in terms of individual needs. (MNS)

Kindergartners appeared to differ in their readiness to use a concrete counting strategy for addition. Many persisted in counting with objects. Mental counting strategies were sequenced. (MNS)

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…

A model of subtraction development and the computing difficulties and research issues suggested by the model are outlined. Demands of simultaneous processes, difficulties with informal subtraction, and the impact on the counting-up procedure are discussed. (MNS)

Four three-year-old girls were studied in seven sessions during a three-month period for their performance on rote and object counting tasks. Two exhibited behavior consistent with underlying stable-order and uniqueness principles. (MNS)

Use of the commutativity, addition-subtraction complement, and N+1 progression principles was studied by interviewing 54 capable pupils in grades 1-3. Commutativity was used extensively at each grade, while the addition-subtraction principle to solve subtraction varied across grades, and the N+1 pattern was seldom used. (MNS)

Explored is young children's ability to estimate set sizes and use reference points such as 10. Results indicated that many children could accurately place sets somewhat smaller than a reference point but had difficulty placing sets somewhat larger than a reference point. (CW)

Reviewed is an integrated approach to teaching place-value concepts. A semi-integrated approach is proposed which may provide a more effective implementation of the technique. (CW)

Analyzes error patterns of kindergartners' mental addition task. Eight weeks of computational practice affected the errors of unpracticed combinations on a retest. Seven of 10 children mastered previously unknown combinations involving zero by learning a relationship rather than the practice and memorization of individual facts. (Author/YP)

A study with 29 preschoolers showed that a statistically significant number of them successfully reassigned tags in counting (ordinality) but failed to predict that differently ordered counts would produce the same outcome (cardinality). Results indicated that children may not entirely understand implications of their counting actions. (Contains…