It is known that active exploration of a new environment leads to better spatial learning than does passive visual exposure. We ask whether specific components of active learning differentially contribute to particular forms of spatial knowledge--the "exploration-specific learning hypothesis". Previously, we found that idiothetic…

Flavio Azevedo, Peggy Martalock and Tugba Keser have initiated an important conversation in science education as they use sociocultural theory to introduce design based scenarios into the science classroom. This response seeks to expand Azevedo, Martalock and Keser's article "The discourse of design-based science classroom activities" by…

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.

A vehicle starts from rest at constant acceleration, then cruises at constant speed for a time. Next, it decelerates at a constant rate.… This and similar statements are common in elementary physics courses. Students are asked to graph the motion of the vehicle or find the velocity, acceleration, and distance traveled by the vehicle from a given…

Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…

Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM…

The purpose of this qualitative practitioner research study was to describe middle school algebra students' experiences of learning linear functions through kinesthetic movement. Participants were comprised of 8th grade algebra students. Practitioner research was used because I wanted to improve my teaching so students will have more success in…

Reactions of neural, psychological, and social systems are rarely, if ever, independent of previous inputs and states. The potential for serial order carryover effects from one condition to the next in a sequence of experimental trials makes counterbalancing of condition order an essential part of experimental design. Here, a method is proposed…

We review the history of snarks and give a selected survey of recent research. The article and snarks themselves are much more interesting than this summary makes them sound.

The ability to use numerical information in different contexts is a major goal of mathematics education. In health risk communication, outcomes of a medical condition are frequently expressed in probabilities. Difficulties to accurately represent probability information can result in unfavourable medical decisions. To support individuals with…

This article comments on mathematics textbooks for lower secondary schools. Authors do not focus on texts in the books but on the nonverbal elements instead. A possible system of categories which enables mapping and classifying of such elements is suggested in this article. As a result of that, it is possible to evaluate and compare the textbooks…

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…

The aim of this paper is to explore if English as a Foreign Language (EFL) learners' usage of an online workbook follows Benford's law, which predicts the frequency of leading digits in numbers describing natural phenomena. According to Benford (1938), one can predict the frequency distribution of leading digits in numbers describing natural…