Students in introductory physics struggle with vector algebra and these challenges are often associated with contextual and representational features of the problems. Performance on problems about cross product direction is particularly poor and some research suggests that this may be primarily due to misapplied right-hand rules. However, few…

Formative assessments have been deemed the key to effectively measuring if students have mastered the understanding of curriculum standards. Thus, allowing teachers to use the results to tailor remediation and use other efforts to support mastery of student learning before the end of the school year has positive effects on student achievement.…

Proportional thinking, which requires understanding fractions, ratios, and proportions, is an area of mathematics that is cognitively challenging for many children and adolescents (Fujimura, 2001; Lamon, 2007; Lobato, Ellis, Charles, & Zbiek, 2010; National Mathematics Advisory Panel [NMAP], 2008) and "transcends topical barriers in adult…

We describe methods for assessing all possible criteria (i.e., dependent variables) and subsets of criteria for regression models with a fixed set of predictors, x (where x is an n x 1 vector of independent variables). Our methods build upon the geometry of regression coefficients (hereafter called regression weights) in n-dimensional space. For a…

Beginning algebra is a gatekeeper course into the pipeline to higher mathematics courses required for respected professions in engineering, science, statistics, mathematics, education, and technology. Beginning algebra can also be a perfect storm if the necessary foundational skills are not within a student's grasp. What skills ensure beginning…

The purpose of this study was to: (a) investigate the effects of email to enhance learners' use of self-regulation strategies; (b) examine different effects between email list and individually addressed notes on the enhancement of self-regulation; (c) observe and record changes in self-regulation and self-efficacy; and (d) explore the…

The study of a real function of two real variables can be supported by visualisation using a Computer Algebra System (CAS). One type of constraint of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the given function and can provide very…