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Inés Gallego-Sánchez; Verónica Martín-Molina; Isabel Caro-Torró; José María Gavilán-Izquierdo – Education 3-13, 2025
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…
Descriptors: Foreign Countries, Elementary School Students, Addition, Subtraction
Samuel B. Allan; Peter K. Dunn; Robert G. McDougall – International Journal of Mathematical Education in Science and Technology, 2024
In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…
Descriptors: Mathematics Instruction, Teaching Methods, Multiplication, Addition
Karen C. Fuson; Shannon Kiebler; Robyn Decker – Mathematics Teacher: Learning and Teaching PK-12, 2024
The authors have found that having students learn accessible standard algorithms by explaining them using mathematics drawings increases students' sense of place--value numbers and enables students to articulate their understanding of what is actually happening with the numbers and why. In this article, they will discuss three standard algorithms…
Descriptors: Mathematics Instruction, Multilingualism, Teaching Methods, Teacher Student Relationship
Nesrin Sahin; Juli K. Dixon; Robert C. Schoen – Grantee Submission, 2020
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,…
Descriptors: Mathematics Achievement, Comparative Analysis, Grade 2, Elementary School Students

Carraher, Terezinha Nunes; Schliemann, Analucia Dias – Journal for Research in Mathematics Education, 1985
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)
Descriptors: Addition, Algorithms, Cognitive Processes, Educational Research

Friedlander, Richard J. – School Science and Mathematics, 1981
This report illustrates a simple, short, yet relatively little known partial check on addition that elementary school pupils can be lead to discover, and later taught to understand. The process can also be used for subtraction and is viewed as more useful than the traditional check of casting out nines. (MP)
Descriptors: Addition, Algorithms, Elementary Education, Elementary School Mathematics

Gutstein, Eric; Romberg, Thomas A. – Journal of Mathematical Behavior, 1995
Reviews research using diagrams, number sentences, and algorithms to help students learn to add and subtract; poses questions on the relationship of instruction to children's knowledge construction; and proposes a research agenda in this area. (86 references) (MKR)
Descriptors: Addition, Algorithms, Arithmetic, Cognitive Processes

Thompson, Ian – Educational Studies in Mathematics, 1994
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)
Descriptors: Addition, Algorithms, Arithmetic, Computation

Idle, Marion – Mathematics in School, 1979
The importance of place value is discussed. Examples illustrating place value in addition and subtraction are given. (MK)
Descriptors: Addition, Algorithms, Elementary Education, Elementary School Mathematics

Musser, Gary L. – Arithmetic Teacher, 1982
Two mental algorithms, one for addition and one for subtraction, are described. It is felt such algorithms should be taught explicitly. The usual process taught for paper and pencil is seen to inhibit mental arithmetic, and a need to include mental algorithms in the regular mathematics curriculum is promoted. (MP)
Descriptors: Addition, Algorithms, Computation, Elementary Education
Dennis, Sue Shirah – 1984
Use of low-stress algorithms to reduce the cognitive load on students is advocated. The low-stress algorithm for addition developed by Hutchings is detailed first. Then a variation on the usual algorithm is proposed: adding from left to right, writing the partial sum for each stage. Next, a "quick addition" method for adding fractions proposed by…
Descriptors: Addition, Algorithms, Cognitive Processes, Computation
McClain, Kay; Cobb, Paul; Bowers, Janet – 1998
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…
Descriptors: Addition, Algorithms, Arithmetic, Computation

Madell, Rob – Arithmetic Teacher, 1985
The author argues that children not only can but should create their own computational algorithms and that the teacher's role is "merely" to help. How children in grades K-3 add and subtract is the focus of this article. Grouping, directionality, and exchange are highlighted. (MNS)
Descriptors: Addition, Algorithms, Cognitive Processes, Computation

Spence, Lawrence E.; Eynden, Charles Vanden – Mathematics Teacher, 1984
Programing a microcomputer to solve problems in whole-number arithmetic, rather than using the built-in operations of the computer, is described. Not only useful, it also enhances important mathematical concepts and is adaptable to a range of student abilities. (MNS)
Descriptors: Addition, Algorithms, Arithmetic, Computation

Thompson, Charles S.; Van de Walle, John – Arithmetic Teacher, 1980
A method is presented for helping children make a smooth transition from using manipulative materials to using symbols only in solving multidigit addition problems. (MP)
Descriptors: Addition, Algorithms, Educational Games, Elementary Education
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