Our work investigated how six primary school students used a non-traditional method for adding and subtracting: the ABN method, a Spanish acronym for Open (method) Based on Numbers. Commognitive theory [Sfard, A. 2008. "Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing." New York: Cambridge…

This manuscript reports the results of an investigation of the simultaneous prompting procedure to teach a five-step algorithm for solving three addition basic facts. Four preschool students receiving Tier 1 services in their school's multi-tier system of supports (MTSS) framework participated. A multiple probe across participants single case…

This observational study used data from 270 second-grade students to investigate the association between students' strategy use for multidigit addition and subtraction and their mathematics achievement. Based on strategies they used during a mathematics interview, students were classified into the following strategy groups: (a) standard algorithm,…

The purpose of this study was to find out what difficulties Nicaraguan children encounter in doing addition and subtraction exercises. The results were used in the design of radio lessons in mathematics for elementary school. The performance on addition exercises is analyzed with a view toward identifying the distinct skills that are required by…

Eighteen college students solved addition problems using the Hutchings Low Fatigue Addition Algorithm, which requires a written record of running sums, and the standard algorithm, which does not. Students using the Hutchings algorithm had significantly higher reaction times to a tone, indicating that the Hutchings method requires less cognitive…

Analyzes a didactical sequence for the teaching of addition and subtraction procedures and algorithms. Uses didactical procedures by children in problem solving activities in order to gain a better understanding of the interaction between numbers, numeration, and operations knowledge which are involved in the construction of addition and…

Fifty Brazilian children aged seven-13 were individually given addition and subtraction exercises. Counting was the preferred procedure, with use of school-taught algorithms limited. Some children decomposed numbers into tens and units and then worked at both levels. They rarely referred to previous results when doing related exercises. (MNS)

Describes the success, the methods (mental, informal written, standard algorithm) and the strategies of informal written arithmetic to be observed when 300 elementary students worked on six addition and six subtraction problems with three-digit numbers. (Author/MM)

Fourth graders' (n=117) solutions to addition problems were analyzed in terms of standard or idiosyncratic written algorithms. Students had not previously been taught pencil-and-paper algorithms. Preference for horizontal layout, working from left to right, and a wide variety of written algorithms were found. (Contains 48 references.) (Author/MKR)

This paper presents the results of three experiments studying routine problem-solving tasks in simple addition and subtraction. Indications are that children tend to solve such problems by internalized counting procedures which may be learned independently as a consequence of practice in problem solving. Brief descriptions of exploratory studies…

Five reports from a 2-year study are presented. Frequencies and descriptions of systematic errors in the four algorithms in arithmetic were studied in upper-middle income, regular, and special education classrooms involving 744 children. Children were screened for adequate knowledge of basic facts and for receiving prior instruction on the…

The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to…

Refinements of work with calculator algorithms previously conducted by the author are reported. Work with "chaining" and the doing/undoing property in addition and subtraction was tested with 24 third-grade students. Results indicated the need for further instruction with both ideas. Students were able to manipulate the calculator keyboard, but…

This paper discusses an approach to the study of algorithms which values students' construction of nonstandard algorithms but also emphasizes the essential roles of the teacher and instructional activities in supporting the development of students' numerical reasoning. Episodes are presented from a 3rd grade classroom in which a 9-week teaching…

Coordinates anthropological and cognitive perspectives on one child's learning of the standard addition algorithm in second and third grade. Analysis showed that the student abandoned his self-generated computational algorithms in favor of less understood conventional procedures. (25 references) (Author/MKR)