Howe (2014, Three pillars of first grade mathematics, and beyond. In: Li Y. & Lappan G. (eds), Mathematics curriculum in school education, Springer, Dordrecht, pp 183-207) identified three pillars of first grade mathematics and beyond that described central mathematical and sense-making aspects of major Common Core State Standards Math…

Exemplifies a model of a conceptual-support net in the domain of multidigit addition that provides guidance in making curricular and classroom teaching choices about what kinds of conceptual supports to provide in a particular setting. Presents summaries of several different multidigit addition solution methods that indicate how different quantity…

First graders were taught to solve symbolic subtraction combinations by counting up from the smaller number to the larger while keeping track of the number counted up by using one-handed finger patterns. They improved quite considerably on a timed test of the more difficult subtraction combinations. (MNS)

A learning and teaching approach using base-10 blocks to embody the English named-value system of number words and digit cards to embody the positional base-10 system of numeration is described. Examines the students' understanding and arithmetic skills on the multidigit arithmetic. (Author/YP)

This case study of a low-achieving first grader learning to subtract two-digit quantities with several different pedagogical objects demonstrates the complexities of the conceptual shift from the tens part of a number to the ones part. An appendix contains interview transcripts. Contains 52 references. (Author/MKR)

Analyzed conceptual and linguistic complexities of matching situation word problems. Found a four-level progression in conceptualizing and solving these problems: Relational ("who had more/less" but not "how much more/less"); Language Cue (equalizing or compare language); Understand Matching Situations (difference between two…

Examined Korean second and third graders' understanding of multidigit addition and subtraction. Korean children showed exceptional competence in multidigit addition and subtraction, and their solutions were based on quantitative understanding of multidigit numbers. Results are compared to the literature on the performance and conceptual structures…

The grade placement of topics in addition and subtraction was compared across the five countries through analysis of textbooks. "Remarkable" uniformity in grade placement was noted for Japan, China, the Soviet Union, and Taiwan, but the United States differed substantially. (MNS)

Reviewed is research regarding multidigit addition and subtraction which may be used to question the organization and placement of topics in curriculum materials. Discussed are issues surrounding multidigit addition and subtraction, and the linguistic and cultural disadvantages in constructing units of 10 experienced by children in the United…

Report provides new data concerning children's accuracy as measured by previous studies and clarifies progress of first graders during entire year on difficult single-digit addition and subtraction problems. Discussion focuses on advantages of an adding on interpretation of subtraction and the importance of emphasizing conceptual understanding…

Two classes of second graders (24 high and 19 average math ability students) were taught to use differing schematic drawings to represent differing categories of addition and subtraction word problems. Results indicate that American textbooks could include many more difficult word problems than is currently the case. (TJH)

Ten teachers successfully taught first- and second-grade children to count up while keeping track with finger patterns. Learning to subtract by counting up greatly improved children's performance on take-away, compare, and equalize word problems, and enabled them to accelerate by as much as three years their learning of subtraction topics. (MNS)

Thirty-six Korean first graders were interviewed to study their ability solving addition problems with sums of 10, single-digit sums between 10 and 18, and subtraction problems with minuends between 10 and 18. Finger methods to show sums over 10 and the regular named-10 Korean number words supported their learning of 3 efficient recomposition…