The terms conceptual knowledge and procedural knowledge are often used by teachers and never more so than when discussing how teachers teach, and children learn mathematics. This paper will look at literature regarding conceptual and procedural knowledge and their place in the classroom, to offer teachers and teacher educators' advice on some of…

According to National Council of Teachers of Mathematics (NCTM), students must develop a conceptual understanding of place value by second grade to understand that mathematics processes are more than a set of procedural steps. Yet, students with learning disabilities in mathematics typically struggle to understand place value in a deeper,…

A study was conducted to explore the beliefs and practices of 49 New South Wales (NSW) primary school teachers regarding their beliefs and practices concerning the use of concrete materials in the learning and teaching of Number and Algebra. This paper reports on elements of the study regarding why and how teachers use concrete materials. Not only…

The objective of this paper is to apply Formal Concept Analysis (FCA) to identify the best open source Learning Management System (LMS) for an E-learning environment. FCA is a mathematical framework that represents knowledge derived from a formal context. In constructing the formal context, LMSs are treated as objects and their features as…

With our conceptualization of Harre and van Langenhove's (1999) positioning theory, we draw attention to immanent experience and read transcendent discursive practices through the moment of interaction. We use a series of spatial images as metaphors to analyze the way positioning is conceptualized in current mathematics education literature and…

The research objectives were to identify the middle level mathematics teachers' conceptions of mathematics teaching and learning and ascertain changes in their conceptions and instructional behavior at the end of a three-year professional development (PD) project. These changes were studied through the qualitative analysis of their reflective…

Describes a number of ways in which the adoption of the metric system in the United States will increase the effectiveness of mathematics teaching. It provides a concrete model for many concepts commonly taught in grades K-12, and thus provides a means by which confusion can be alleviated. (JR)

A didactic principle of operative concept formation is described and explained. It is argued that this principle meets current demands for practical geometric activities with concrete forms and for the exploration of the primordial relation between geometry and reality. (MK)

A collaborative research study was designed to facilitate, at the local school level, a mathematics teacher's development of a "constructivist" pedagogy. This paper discusses the nature and influence of the teacher's professional beliefs on his attempts to create a classroom learning environment congruent with the principles of a constructivist…

This essay clarifies what it means to know mathematics by examining ways of knowing multiplication and explores what those ways of knowing imply for the teaching and learning of mathematics in schools. It reviews the perennial argument about whether computational skill or conceptual understanding should guide the school curriculum. A mathematical…

This paper describes the implications of constructivism both for what to teach and for how to teach. The first part discusses three approaches on what to teach: (1) relating mathematical knowledge to other knowledge; (2) checking for self-consistency; and (3) putting thinking before facts. The second part is on how to teach based on…

Students come to the classroom with theories that they have actively constructed from their everyday experiences. However, some of these theories are incomplete half-truths. Although such misconceptions interfere with new learning, students are often emotionally and intellectually attached to them. Some common mathematical misconceptions involve:…

Analyzes multiplication word problems to identify the origin of children's difficulty. Emphasis is given to problems involving the concept of combination. (JN)

This book presents the findings of 12 years of research. The data gathered and analyzed from almost 700 samples of children's' graphics show how powerful patterns of cognition (schema) in the early years of development gradually evolves into recognizable forms of writing and mathematics. The goal was to chart the progress of children's thinking…

Examines the development of students' understandings about fractions during six weeks of instruction. Reports that all students possessed informal knowledge disconnected from their knowledge of fraction symbols and procedures and that knowledge of rote procedures often interfered with students' attempts to build on their informal knowledge.…