Building block toys can be used to illustrate various concepts connected with functions including graphs and rates of change of linear and exponential functions, piecewise functions, and composition of functions. Five brief activities suitable for a pre-calculus course are described.

In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…

The goal of this study was to develop a self-report inventory that measures individual differences in the perceived value of mathematical literacy for general education students. The Mathematics Value Inventory (MVI) is grounded in the Eccles et al. model of achievement-related choices and surveys students' beliefs in four areas: interest, general…

This study measured the amounts of different types of metacognitive statements made by students enrolled in Elementary Algebra courses at a community college in California. A total of 17 students were interviewed three times during the course of a semester. All interviews were coded for types of metacognitive statements that fell into one of three…

Visit with any university math faculty member throughout the United States, and you will soon hear how the freshman students are not prepared to be successful in introductory college algebra classes. The opinions are varied regarding why the students are unsuccessful; however, the concern and frustration is universal. According to American College…

This article reports on an innovative approach to teaching Calculus I which was initiated in a two-semester course designed for students at risk of failing Calculus I. The treatment consisted of voluntary oral assessments offered before every written examination. Analyses showed that the treatment students did significantly better than the control…

According to a 2000 community college study by Miami Dade College (FL) President Emeritus Robert McCabe, 41 percent of students entering community colleges are underprepared in at least one basic skill area. A three-year study of community college students, published in 2009 by the National Center for Education Statistics, reported that 41 percent…

Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively for, or even construct, mathematical knowledge…

The research literature concerning traditionally aged college mathematics students' who require remediation, in beginning Algebra topics, states that these students lack confidence in their mathematical skills, have experienced failure and frustration in the past, have low self confidence issues with respect to mathematics and often lack…

The fact that students have difficulties in constructing proofs is well documented. However, some of these difficulties may be lessened if instructors and students have access to a common evaluation framework. Operating in the theoretical tradition of heuristic inquiry, a proof error evaluation tool (PEET) is constructed that may be used by…

Procedural and conceptual learning are two types of learning, related to two types of knowledge, which are often referred to in mathematics education. Procedural learning involves only memorizing operations with no understanding of underlying meanings. Conceptual learning involves understanding and interpreting concepts and the relations between…

This research compared the effectiveness, in terms of mathematical achievement, of online homework to textbook homework over an entire semester for 145 students enrolled in multiple sections of college algebra at a large community college. A quasi-experimental, posttest design was used to analyze the effect on mathematical achievement, as measured…

This paper reports findings of a post test experimental control group design conducted to investigate the role of modified Moore learning approach on improving students' mathematical understanding and proving abilities. Subjects of study were 56 undergraduate students of one state university in Bandung, who took advanced abstract algebra course.…

The National Council of Teachers of Mathematics has set ambitious goals for the teaching and learning of mathematics that include preparing students for both the workplace and higher education. While this suggests that it is important for students to develop strong mathematical competencies by the end of high school, there is evidence to indicate…

A problem given in the Australian Mathematics Competition for the Westpac Awards was stated as follows: With how many zeros does 2008! end? In this article, the author solves this problem, and provides further discussion on the related problems. These problems form a good model that helps students develop a logical thinking process toward problem…