The paper discusses the interaction between intuitive biases of probabilistic thinking and mathematical knowledge. It would appear that students may answer numerical problems correctly but falter on simple descriptive solutions. Students appear to relinquish formal knowledge for simpler heuristics when attempting to describe the outcome of an…

Semantic retrieval (SR) and executive-procedural (EP), but not visuospatial (VS) skills, have been found to be uniquely predictive of mathematical calculation skills in a sample of clinically referred college students. This study set out to cross-validate these results in an independent sample of clinically referred college students (N = 337) as…

How does artificial gravity affect the path of a thrown ball? This paper contrasts ball trajectories on the Little Prince's asteroid planet B-612 and Arthur C. Clarke's rotating-drum spacecraft of 2001, and demonstrates curve balls with multiple loops in the latter environment.

For a long time, the medieval university maintained relative consistency throughout Europe in teaching topics and methods. But between 1550 and 1650 this came to an end. The evolution concerned the content of the courses and, to a lesser extent, the way the field was taught. The impact of these changes varied greatly from place to place, and new…

An experimental two-track intermediate algebra course was offered at Saddleback College, Mission Viejo, CA, between the Fall, 2002 and Fall, 2005 semesters. One track was modeled after the existing traditional California community college intermediate algebra course and the other track was a less rigorous intermediate algebra course in which the…

External performance assessments for teachers of mathematics have traditionally been accomplished through reviews of student comments as well as through formal evaluations by superiors. Additionally, evaluating lecture-based teaching (as opposed to more active learning environments) focuses primarily on classroom performance, curriculum planning,…

The present study aims to explore the use of assessment in mathematics content courses for future elementary school teachers. Analysis of self assessment data on mathematical understanding and peer assessment data on oral mathematical presentation showed that pre-service teachers had a balanced understanding of procedural knowledge and problem…

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

Interesting problems sometimes have surprising sources. In this paper we take an innocent looking problem from a calculus book and rediscover the radical axis of classical geometry. For intersecting circles the radical axis is the line through the two points of intersection. For nonintersecting, nonconcentric circles, the radical axis still…

This paper examines the elasticity of demand, and shows that geometrically, it may be interpreted as the ratio of two simple distances along the tangent line: the distance from the point on the curve to the x-intercept to the distance from the point on the curve to the y-intercept. It also shows that total revenue is maximized at the transition…

Confidence intervals are beginning to play an increasing role in the reporting of research findings within the social and behavioral sciences and, consequently, are becoming more prevalent in beginning classes in statistics and research methods. Confidence intervals are an attractive means of conveying experimental results, as they contain a…

The Bologna Declaration brought reforms into higher education that imply changes in teaching methods, didactic materials and textbooks, infrastructures and laboratories, etc. Statistics and mathematics are disciplines that traditionally have the worst success rates, particularly in non-mathematics core curricula courses. This research project,…

This paper is a comparison of three major elementary mathematics textbooks. Although the scope of this investigation is not directly related to college level mathematics, it does address a portion of the oft asked college level question, "How have my students been taught in public school?" The study looks at the strengths and weaknesses of the…

Mathematics can be perceived as being a difficult subject to learn due to the conceptual leaps required to understand particular mathematical topics. In some areas of mathematics, part of the difficulty may be associated with applying sufficient imagination to visualize a particular mathematical concept, and applying sufficient visio-spatial…

The impact of developmental mathematics programs on student success in college-level mathematics has been a controversial topic in higher education. One limitation of the current research is that scholars have been unable to isolate the causal impact of such participation on the student's success in college-level mathematics because it is…