Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students' numerical magnitude understanding: number type…

This paper reports on concept images of 38 secondary school mathematics prospective teachers, regarding the evenness of numbers. Written assignments, individual interviews, and lesson transcripts uncover salient, erroneous concept images of even numbers as numbers that are two times "something" (i.e., "2i" is an even number),…

This research aimed to determine the difficulties that the students experience in inequality solutions that contain inequality in general and rational (proportional) expressions, and to solve these difficulties with an activity. Totally 108 students, who were enrolled in the Department of Mathematics and Science Education, consisted respectively…

We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the…

In this study we set out to investigate the errors made by students in logarithms. A test with 16 items was administered to 89 Secondary three students (Year 9). The errors made by the students were categorized using four categories from a framework by Movshovitz-Hadar, Zaslavsky, and Inbar (1987). It was found that students in the top third were…

Number Concepts; Measurement; Geometry; Probability; Statistics; and Patterns, Functions and Algebra. Procedural Errors were further categorized into the following content categories: Computation; Measurement; Statistics; and Patterns, Functions, and Algebra. The results of the analysis showed the main sources of error for 6th, 7th, and 8th…

The purpose of this report is to make a tentative contribution to the knowledge of students' understanding of the significance of numerical information. The article relates to a study made by the author. (Author/MK)

Common mistakes pupils make when adding fractions are categorized and analyzed. (MP)

Three theorems for Pythagorean triples are presented, with discussion of how students can amend their ideas about such numbers. (MNS)

Some limitations of computing with calculators and computers are described, with particular reference to typical computations which might be performed by senior secondary school students. Types of errors, the laws of number, and intermediate round-offs are each illustrated, with conclusions and implications. (MNS)

Ten examples of when the sequences of key presses given in calculator instruction booklets are either inefficient or lead to an incorrect answer are given. (MNS)

Numerical inaccuracies, which occur in many ordinary computations, can create serious problems and render answers meaningless. Cancellation and accumulation errors are described, and suggestions for experimentation are discussed. (MNS)

Helping students understand the round-off error is the focus. A computer program for Fibonacci numbers illustrates the point, which is then described mathematically. (MNS)

We present a summary of a study carried out with students of the first year of Bachillerato (the first of two pre-university non-obligatory secondary education courses in Spain) to determine and analyse some of their errors and difficulties in learning inequalities with the aim of improving the teaching-learning process of this topic. The study…