This paper aims to broaden the scope of the construct concept image by addressing the mathematically oriented notion of "solution of an algebraic equation." The notion solution of an algebraic equation is not mathematical per se, but it is most prevalent in mathematical communications and in mathematics education. The paper describes…

A newspaper article about the availability of guns in Chicago, presented at a mathematics education conference in that city in 1998, is linked to a tragic shooting near that city in 2022. The article was used in Australia for many years in research with teachers and students to assess statistical literacy in relation to sampling, until ethics…

Participation in society is increasingly dependent on educational achievement. Accordingly, society as a whole is committing more resources to education to prevent the adverse outcome of students moving through the school system only to emerge without the knowledge and skills that they might be expected to attain. In this paper, we explore the…

Learning Disabilities in Mathematics (LDM) or dyscalculia are a frequent and disruptive problem within schools. Nevertheless, this problem has received little attention from researchers and practitioners, if compared with the number of studies published on disabilities in reading. Therefore, teachers do not have enough guidance to help children…

Complex error propagation is reduced to formula and data entry into a Mathcad worksheet or an Excel spreadsheet. The Mathcad routine uses both symbolic calculus analysis and Monte Carlo methods to propagate errors in a formula of up to four variables. Graphical output is used to clarify the contributions to the final error of each of the…

Vieta's famous product using factors that are nested radicals is the oldest infinite product as well as the first non-iterative method for finding [pi]. In this paper a simple geometric construction intimately related to this product is described. The construction provides the same approximations to [pi] as are given by partial products from…

Mathematics and science are important for success in school, but learning mathematics and science can be a difficult task to some students. Efforts to improve students' learning of school mathematics and science have led to reform efforts in curriculum and instruction over the past decades (e.g., National Council of Teachers of Mathematics [NCTM],…

Nonroutine problem-solving, too, involves elements of routine. Often, elementary routines such as solving for a variable are not carried out without error. In this paper, we use new findings from neuroscientific research to explain why even excellent students make mistakes in elementary routines. [For complete proceedings, see ED489597.]

Fourth-grade students in Title I mathematics took 40-problem tests to determine types of persistent errors made in addition and subtraction. Tests, administered to 117 students (addition) and 104 students (subtraction), were analyzed for basic fact, random, or procedural errors. Findings are reported and discussed, and recommendations for…

This paper reports on the first stage of a research project still in progress aiming at identifying undergraduate students' difficulties and errors in solving linear algebra problems. Some students' difficulties related to very basic notions of vector space theory are shown and discussed with respect to both Balacheff's theory of conceptions and…

The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…

Examples of answers college students studying to be elementary teachers gave to sample student errors and questions in mathematics are presented. The bulk of the prospective answers are judged to have serious flaws. The analysis of such "poor" answers is suggested as a useful vehicle in teacher training programs. (MP)

Presents a selection of solutions of the "Three Hungry Men" problem from grade three to college students with three different strategies used: backward, forward, and forward/backward strategies. Provides error patterns in each strategy. Discusses some implications for teaching of problem solving. (YP)

Advances the idea that performance errors should contribute positively to the process of learning. Argues that errors do not occur randomly and that instructional theory should not condemn errors, but seek them. (PK)