This field experiment tested whether a special type of worked-out examples (i.e., heuristic examples) helps learners develop better conceptual knowledge about mathematical proving and proving skills than a control condition focussing on mathematical contents. Additionally, we analysed the benefits of self-explanation prompts and completion…

To achieve the vision of mathematics set forth in "Crossroads" ("AMATYC," 1995), students must experience mathematics as a sensemaking endeavor that informs their world. Embedding the study of mathematics into the real world is a challenge, particularly because it was not the way that many of us learned mathematics in the first place. This article…

We review recently published papers that have contributed to our understanding of how the preverbal infant represents number, area and time. We review evidence that infants rely on two distinct systems to represent number nonverbally and highlight the similarities in the ratio-dependent discrimination of number, time and area. Contrary to earlier…

The revolution of technology in education has heralded a new wave of learning styles and in some cases total dependence on technology. Yet, statistics reveal no significant improvement in student performance in Mathematics and a downward trend in basic algebra skills. The major impediment in the learning process is lack of understanding of the…

Previous research indicates that, prior to entering kindergarten, most children are exposed to some type of formal or direct mathematics instruction. However, the type of mathematical language and the frequency of its use vary greatly in terms of its emphasis on academic content. This study investigated the types and frequency of mathematical…

Although Imre Lakatos described the work published in his book "Proofs and Refutations" as a study of mathematical methodology, work which has been responded to and criticized by philosophers and historians of mathematics more on its own terms, a significant body of writing in the 30 years since its appearance has used it as a pertinent cognate…

We use the Implicit Function Theorem to establish a result of non-existence of limit to a certain class of functions of several variables. We consider functions given by quotients such that both the numerator and denominator functions are null at the limit point. We show that the non-existence of the limit of such function is related with the…

This article describes investigative calculus projects in which students explore a question or problem of their own construction. Three exemplary pieces of student work are showcased. Investigative calculus projects are an excellent way to foster student understanding and interest in calculus. (Contains 4 figures.)

This paper reports a study on the use of ICT to teach parabolic functions to secondary school students. The project was informed by the need to find better ways of presenting parabolic functions to secondary school students in order to improve their learning of the concepts and improve their interest and performance in mathematics. The study was…

Trying to develop new perspectives of teaching is never easy, but trying to cultivate ownership and initiative among teacher education students is a still greater aspiration that is infrequently realized. This article addresses each of these highly valued goals for teacher educators as a case study reveals the impact of involving teacher…

This dissertation presents two studies designed to examine the topic of fraction division in selected Chinese and US curricula. By comparing the structure and content of the Chinese and "Everyday Mathematics" textbooks and teacher's guides, Study 1 revealed many different features presented in the selected curricula. Major differences…

There is a great potential opportunity to use portable physical activity monitoring devices as data collection tools for educational purposes. Using one such device, we designed and implemented a weeklong workshop with high school students to test the utility of such technology. During that intervention, students performed data investigations of…

This article presents an overview of some issues that were confronted when delivering an online second Linear Algebra course (assuming a previous Introductory Linear Algebra course) to graduate students enrolled in a Secondary Mathematics Education program. The focus is on performance in one particular aspect of the course: "change of basis" and…

This study develops virtual manipulative, polyominoes kits for junior high school students to explore polyominoes. The current work conducts a non-equivalent group pretest-post-test quasi-experimental design to compare the performance difference between using physical manipulatives and virtual manipulatives in finding the number of polyominoes.…

Districts face increasing pressure to improve students' mastery of curriculum in the fields of science, technology, engineering and mathematics (STEM). Yet the number of students enrolling in science and math courses drops dramatically in middle and high school. At Sylvester Middle School, Chinook Middle School and Cascade Middle School of the…