The way mathematics teaching and learning activities are presented to learners can make them hate or like the subject. The question of accomplishing the mathematics education of the learner from primary to post-secondary school levels is one which necessarily tasks, not only the teacher's stock of mathematical knowledge but also his skill, his…

In "MT218" the author looked at the possibility of basing a classroom activity on a simple, though not totally transparent, number-theoretic result. In this article he considers another relatively straightforward idea from number theory that could be used either as a lesson starter or as the basis of a more substantial task, requiring students to…

Two experiments, one measuring eye fixations of 38 undergraduates and the other assessing memory of 37 undergraduates, provide evidence that unsuccessful problem solvers are more likely to comprehend by direct translation and that successful word problem solvers are more likely to build a problem model. (SLD)

Methods used by adults to read numerals were investigated by asking graduate students in education to read and solve mathematics problems. Eye movement studies noted reading patterns. Distinct first reading and rereading phases and two distinct methods of reading numerals were identified. (SLD)

Eye-fixation analysis of 38 undergraduates allowed identification of phases in solution of arithmetic word problems and location of students' difficulties with inconsistent problems within the phases. Results indicate that the locus of the inconsistency effect lies outside the execution phase of problem solving. (SLD)

Eight articles review and report on research involving computers and problem solving skills. Topics discussed include research design; problem solving skills and programing languages, including BASIC and LOGO; computer anxiety; diagnostic programs for arithmetic problems; and relationships between ability and problem solving scores and between…

This paper reports a study that sought to explain student understanding of the concept of linear inequality as presented in a problem-solving setting. In the course of data analysis, the transition from arithmetic to algebra emerged as a critical issue. Therefore, the study examined the differences in the problem-solving activities of solvers who…

This study sought to provide an explanation of (n=13) university students' understanding of the concept of linear inequality as presented in a problem-solving setting. In the course of the analysis of the data, the transition from arithmetic to algebra emerged as a critical issue. Therefore, the study examines the differences in the…

This paper reports on five related studies on upper elementary school students' beliefs about the role of real-world knowledge in solving mathematical word problems, and on possibilities of overcoming their unrealistic mathematical modeling. Findings from the first study of 75 Belgian fifth-grade students showed that as a consequence of current…

Presents three sample problems related to arithmetic and algebra, geometry, and calculus, indicating, in each case, similar problems that could be posed. Includes a discussion of positive benefits which result by asking students "Can you derive the result differently?" (JN)

A description is given of a calculator-oriented arithmetic course given at a community college. Problem solving was the primary objective of the course. (MK)

A few examples, relating specifically to fractions, of the many possible intriguing and substantial ideas to be found in remedial mathematics are given. (MN)

The author discusses Professor Henry A. Bent's presentation regarding the nature of the difficulty that many college and university students have with arithmetic reasoning involving division. (HM)

Analogies between topics in algebra and in arithmetic are noted. It is suggested that algebra teachers should consider how to take advantage of student backgrounds in arithmetic by exploiting these analogies. (MP)

Presented is a proof where special attention is accorded to rigor and detail in proving the lemma that relates ruler-and-compass constructions to arithmetical operations. The idea that some angles cannot be trisected by a ruler and compass is proved using three different cases. (KR)