The purpose of this study was to investigate how the use of TI-Nspire[TM] could enhance the teaching and learning of calculus. A conceptual framework for the use of TI-Nspire[TM] for learning calculus in a mathematics classroom is proposed that describes the interactions among the students, TI-Nspire[TM], and the learning tasks, and how they lead…

The teaching of mathematics in Singapore continues, in most cases, to follow a traditional model. While this traditional approach has many advantages, it does not always adequately prepare students for University-level mathematics, especially applied mathematics. In particular, it does not cultivate the ability to deal with "non-routine…

Earlier quantitative studies in computer-supported collaborative learning identified "Productive Failure" (Kapur, Cognition and Instruction 26(3):379-424, "2008") as a phenomenon in which students experiencing relative failures in their initial problem-solving efforts subsequently performed better than others who were in a condition not involving…

Much research has been conducted to document and sometimes to provide proximate explanations (e.g., Confucianism vs. Western philosophy) for East-West cultural differences. The ultimate evolutionary mechanisms underlying these cross-cultural differences have not been addressed. We propose in this review that East-West cultural differences (e.g.,…

Every semester, the authors encounter students who are attracted to the visual and spatial aspects of geometry. They have other students who consider geometry to be challenging for the very same reasons. Students are confounded not only by the fact that geometry relies on visual interpretations but also because it has a language of its own and…

The purpose of this research was to investigate the effects of using cognitive and metacognitive prompting strategies in a web-based learning environment to engage college students in a complex, ill-structured task. The course context was a freshman/sophomore level Information Sciences and Technology course, and the topic was web design. Four…

The Lithuanian Informatics Olympiads (LitIO) is a problem solving programming contest for students in secondary education. The work of the student to be evaluated is an algorithm designed by the student and implemented as a working program. The current evaluation process involves both automated (for correctness and performance of programs with the…

The current investigation examined the effects of behavioral history on elementary students' preference for making a choice in two studies. Previous research on choice has focused on the arrangement of current contingencies and has not accounted for the effects of behavioral history. Study 1 examined participants' preference for two options (i.e.,…

This study utilized both quantitative and qualitative methods in investigating how a novel science curriculum, geared towards the 21st century student, affected skills and attitudes towards science for tenth grade students. The quantitative portion of the study was a quasi-experimental design since random groups were not possible. This portion of…

This practice guide presents five recommendations intended to help educators improve students' understanding of, and problem-solving success with, fractions. Recommendations progress from proposals for how to build rudimentary understanding of fractions in young children; to ideas for helping older children understand the meaning of fractions and…

This preliminary study described fourth grade students verbally solving a mathematics problem using a think-aloud protocol. Comments in the think aloud were categorized according to type (e.g., paraphrases and elaborations) and facilitative nature (i.e., whether the comments facilitated correct solution of the problem). Amount of the students'…

In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…

In order to understand how students approach multi-variate problems, we report a study on the cues organic chemistry graduate students perceive from mechanism tasks, and the reasoning processes induced by those cues. We used the think-aloud protocol in interviews with sixteen graduate students as they worked on two types of tasks: one, in which…

Analogies are important tools in human reasoning and learning, for resolving problems and providing arguments, and are extensively used in medicine. Analogy and similarity involve a structural alignment or mapping between domains. This cognitive mechanism can be used to make inferences and learn new abstractions. Through analogies, we try to…

Being able to dive and breathe underwater has been a challenge for thousands of years. In 1980, Fuji Systems of Tokyo developed a series of prototype gills for divers as a way of demonstrating just how good its membranes are. Even though gill technology has not yet reached the point where recipients can efficiently use implants to dive underwater,…