This article reflects critically on the guidance offered to South African teachers in two canonical texts: the Curriculum and Assessment Policy Statements (CAPS) and Mathematics teaching and learning framework for South Africa: Teaching mathematics for understanding (TMU). I make explicit my philosophical orientation, and how 'teaching mathematics…

In the domain of "Operations & Algebraic Thinking," Common Core State Standards indicate that in kindergarten, first grade, and second grade, children should demonstrate and expand their ability to understand, represent, and solve problems using the operations of addition and subtraction, laying the foundation for operations using…

Do your students have the incorrect idea that addition "makes numbers bigger" and subtraction "makes numbers smaller"? Do they believe that subtraction is always "taking away"? What tasks can you offer--what questions can you ask--to determine what your students know or don't know--and move them forward in their…

Developmental changes in 5- to 7-year-old children's mental representation of addition and subtraction events were examined by means of the response times required to answer more or less questions. (Author/JMB)

Two studies involving 110 and 91 children aged 5 to 7 years show that children's knowledge of counting and addition facilitated their acquisition of a concept not taught in school, that every number has a natural successor (Successor Principle). Even the oldest children could not rank order correctly numbers that contained fractional notations.…

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…

Interviewed 70 children learning multidigit addition and subtraction in 2 different learning environments. Found that understanding and skill were closely related for tasks in which students had received no instruction and on more difficult tasks even after instruction. The alternative instruction, which encouraged students to develop their own…

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…

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…

This paper documents the achievement monitoring component of a three-year study on the acquisition of addition-subtraction problem-solving skills by young children. A set of performance objectives contained in or ancillary to ten instructional units on sentence-writing for verbal problems and algorithms specified test content. Tests measuring…

Compares two experimental programs for teaching mental addition and subtraction in the Dutch second grade (N=275). Discusses realistic program design (RPD) and gradual program design (GPD). Concludes that RPD pupils show a more varied use of solution procedures than GPD pupils. Contains 46 references. (Author/ASK)

Presents a three-year longitudinal study investigating the development of children's (n=82) understanding of multidigit number concepts and operations in grades one through three by using interview processes. Provides an existence proof that children can invent strategies for adding and subtracting and illustrates both what that invention affords…