The subtraction ideas presented are designed for elementary and junior high school children, yet are felt to be flexible enough to offer some challenge for high school students, particularly in algebra. (MP)

A teaching sequence providing a smooth transition from concrete materials to the subtraction algorithm is presented. (MP)

Directions for making a device that parents can use to help children practice basic skills are given. (MK)

Four procedures used by children for deriving answers to unknown subtraction facts are described. They are counting forward, counting backward, derivation, and bridging. (MP)

One teacher's struggle with conveying a concrete realization of the subtraction algorithm to students leads to a discussion of elementary mathematics instruction in general. (MP)

Instructional problems springing from teachers' incorrect use of mathematical models during the initial development of ideas and processes are analyzed. Examples of models for subtraction and division are given, and their appropriate use discussed. (DT)

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…

Investigated whether children who reflected the structure of word problems with their concrete models were successful in learning to symbolically represent problems with structure-based open number sentences. Forty-five first graders were taught to write canonical and noncanonical open number sentences. (Author/YP)

Discusses the geometrical array of the keys on a calculator that can be turned into a problem-solving, problem-posing situation for the upper elementary or middle school classroom. Provides figures showing the arrays, including rows, diagonals, crosses, rhombi, angles, and squares. Lists seven references. (YP)

Discusses developmentally appropriate activities for teaching counting skills for kindergarten and early first-grade programs. Describes four activities: (1) counting on; (2) counting back; (3) auditory patterning; and (4) visual patterning based on the 10-frame. (YP)

Third- and fourth-grade students (n=401) were taught problem solving through structure-plus-writing, heuristics, or no explicit instruction. The structure-plus-writing group outperformed the heuristics group, and the gap widened 10 weeks after the treatment. Includes sample student-authored problems. (MKR)

Seven junior high students with educable mental handicaps were trained to solve four-column subtraction problems involving regrouping. Results in performance favored calculators over pencil and paper, with rehearsal and visual cues influencing performance for only one student. With calculators, subjects' performances were equivalent to a…

Attempted to establish the incidence of using taught algorithms versus invented methods of subtraction in (n=1,370) male secondary school students and to relate the use of invented methods to age, mathematical achievement, and lateral thinking ability. Use of invented algorithms increased with age. (23 references) (MKR)

In two parallel one-year studies, solution strategies for subtraction number facts and achievement patterns of matched groups of first graders in two different instructional programs were examined. Significant differences between groups were found favoring the strategy approach. (Author/CW)

Six elementary-age children with learning disabilities were found to learn subtraction facts more rapidly when a rule teaching and correction strategy was employed, compared to learning facts by rote. A study of generalization of rule usage found that the two children studied did generalize the strategy to an additional problem. (Author/JDD)