Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and…

This article investigates some of the specific features involved in accommodating the idea of actual infinity as it appears in set theory. It focuses on the conceptions of two individuals with sophisticated mathematics background, as manifested in their engagement with variations of a well-known paradox: the ping-pong ball conundrum. The APOS…

The research study this article is based on aims to implement research knowledge to teaching, that is, the concept of critical aspects and dimensions of variation used in the variation theory. To do this, the researchers worked with willing teachers to explore how to make mathematics teaching more effective. This paper illustrates how teachers…

Building on the claim that teachers need to know how innovative instructional approaches work to be able to adapt them to their own classrooms, design research is presented as a research method that aims to offer exactly that kind of information. We elaborate design research that aims to develop a local instruction theory--a theory about the…

What is meant by "normal science" is described, the first three steps in the "route to normal science" are outlined, and an example is given in which the trend toward research consensus is apparent. This involves current work on learning addition and subtraction. (MNS)

A process for helping students in the elementary grades develop their own algorithms for subtraction with carrying is described. Pupils choose their own times and ways to move from manipulative materials to written notation. (MP)

This study illustrates a process for selecting a preferred model in the validation of hierarchical learning scales. The test performance of 100 8-to 11-year-old children on subtraction tasks involving variations in borrowing are examined. Goodman's response scaling technique is illustrated. (Author/GDC)

The complexity hypothesis suggests that the hierarchical arrangement of learning tasks is related to the complexity of the task. Using a definition of complexity based on an analysis of the rules governing performance on a task, the present study lent support to the hypothesis. (Author/GDC)

Presents a first-semester course in mathematics for 6-year-old children by formulating certain general requirements for the curriculum and the instructional methods with the aim of leading children to form their initial mathematical concepts. (ASK)

It is noted that defining subtraction independently of addition through use of physical objects can help one to illustrate the non-commutativity of this operation. Lack of awareness of the importance of the order of the digits may be a primary cause of errors in compound subtraction. (MP)

Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…

Research on structural learning theory is reviewed as a base for designing computer-assisted instruction programs. An intelligent "Rule Tutor" emphasizing diagnosis and remediation for whole number concepts is described. (MNS)

Analyzes instructional theory requirements and suggests that structural learning theories meet these requirements. Essentials of such theories are illustrated in the context of designing an instructional unit on subtraction. Structural learning theories are then described more generally and contrasted with cognitive theories. Implications for…

Defines "skill-to-meaning" instruction. Describes research designed to determine the effectiveness of skill-to-meaning mathematics instruction for educable mentally handicapped children. Discusses educational implications of the study results and notes the benefits of meaning for handicapped children. (SB)

The object of this study was to specify the relationship between logical and numerical structures by examining the processes used by operational and preoperational children in solving simple addition and subtraction problems. (MP)