It is becoming widely recognised that teachers' content knowledge has an important influence on their pedagogical content knowledge, and hence on the learning of students. In secondary schools, function is one of the fundamental concepts of mathematics. This paper considers the understanding of function exhibited by a group of teacher trainees in…

Describes teaching strategies in which children are encouraged to develop computational procedures that are meaningful to them. Authors state that classroom observation reveals most primary students to be capable of developing their own accurate solution procedures for multi-digit addition and subtraction as well as for simple multiplication and…

Inventories of space characteristics and utilization evolved into college space planning guidelines. Several approaches and methods for calculating space needs are described. The guidelines that an institution selects depends on its organization, the availability of the data the models call for, and the amount of work that one wants to do.…

Describes mathematical problems which occur when using the computer as a calculator. Considers errors in BASIC calculation and the order of mathematical operations. Identifies errors in spreadsheet and calculator programs. Comments on sorting programs and provides a source for Mathemagical Black Holes. (MVL)

Illustrates how a computer software symbolic-processing program can be easily incorporated into an advanced undergraduate microeconomics course. Symbolic-processing programs are relatively sophisticated software packages that combine numeric, symbolic, and graphic computation in a single unified computing environment. Includes examples of…

We present the design principles for a new kind of computer system that helps students learn algebra. The fundamental idea is to have a system based on the microworld paradigm that allows students to make their own calculations, as they do with paper and pencil, without being obliged to use commands, and to verify the correctness of these…

A fundamental question in developmental science is how brains with and without language compute numbers. Measuring young children's verbal reactions in Spain and Finland, we show that, although there is a general arithmetic ability for small numbers that is shared by monkeys and preverbal infants, the development of such initial knowledge in…

The wave equation is a classic partial differential equation that one encounters in an introductory course on boundary value problems or mathematical physics, which can be used to describe the vertical displacement of a vibrating string. Using a video camera and Wave-in-Motion software to record displacement data from a vibrating string or spring,…

Mathematics in textbooks and indeed in conventional classrooms is often presented as exercises or worksheets in which the mathematics itself has been processed into a form that is easily digested. This McDonald's version of mathematics ensures that the mathematical skill or technique is laid bare and typically the sole focus of attention. In this…

This article demonstrates how a child's invented algorithm about tens and ones generated "transitional thinking" on the way to the construction of a mathematical understanding of place value. The articles also discusses how two important "best practice" classroom strategies, mathematical discourse, and the role of wait time in that discourse take…

This document is the final report of the Regional Training Workshop for the Development of Materials for Mathematics Education in Asia and the Pacific, using a problem-solving approach. The workshop was committed to identifying materials which are readily available at low cost, in sufficient quantities to be used by children in classrooms in any…

Proposes that teachers should examine the elements of mathematical understandings that precede conservation and one-to-one correspondence and tailor classroom instruction to benefit both conserving and nonconserving students. (PK)

This paper addresses statistical aspects of the No Child Left Behind (NCLB) Act (Bush, 2001), with the following goals: to further the discussion on how gaps in performance might be defined and to offer candidate gap estimators, to evaluate candidate gap estimators with respect to three separate student performance measures, to provide…

The paper initially describes the sources of uncertainty in National Assessment of Educational Progress (NAEP) data and standard errors. As NAEP sample sizes have increased, greater precision has been attained by the program. For this reason, exclusion effects are increasingly important. Two scenarios of revised NAEP results are presented (for New…

Most experts believe that young children possess a substantial amount of informal knowledge about mathematics. The teacher's role is to create a link between children's ability to use informal math and the ability to understand the more formal math taught in elementary school. Teachers must help children construct and elaborate upon what they…