Acquiring abstract Mathematics concepts is often challenging for young children. This study explored young children's use of digital cameras to exhibit their understanding of the addition concept. It investigated how the processes involved in producing the photographs and creating the visual representation that helped to develop the children's…

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…

Although often considered a more advanced area of mathematics, principles of algebra are taught throughout different mathematical concepts, and algebra is often considered gateway mathematical knowledge for more advanced mathematical concepts. For this reason, attention is needed toward making algebraic instruction more accessible to all types of…

Addressed are four key issues regarding concrete instruction: What is concrete? What is a worthwhile concrete experience? How can concrete experiences be used effectively in early childhood mathematics instruction? Is there evidence such experiences work? I argue that concrete experiences are those that build on what is familiar to a child and can…

When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…

The use of two different colored beans or chips to represent positive and negative charges is discussed as a method of demonstrating operations with integers. (MP)

Described are activities using paper plates with dots drawn on them which place a heavy emphasis on matching and ordering sets, on developing mental images of sets, and on perceiving sets of a certain size as composed of smaller subsets. Also suggested are activities involving numerals. (Author/TG)

Investigates issues of conceptual understanding in teaching and learning mathematics provided conceptually based instruction on place value and two-digit addition and subtraction without regrouping in four first grade classrooms. Conventional textbook-based instruction was provided in two first grade classrooms. Experimental-group students scored…

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…