This article analyses students' thinking as they interacted with a dynamic geometric sketch designed to explore eigenvectors and eigenvalues. We draw on the theory of instrumental genesis and, in particular, attend to the different dragging modalities used by the students throughout their explorations. Given the kinaesthetic and dynamic…

Given a parabola in the standard form y[superscript 2] = 4ax, corresponding to three points on the parabola, such that the normals at these three points P, Q, R concur at a point M = (h, k), the equation of the circumscribing circle through the three points P, Q, and R provides a tremendous opportunity to illustrate "The Art of Algebraic…

We produce a continuum of curves all of the same length, beginning with an ellipse and ending with a cosine graph. The curves in the continuum are made by cutting and unrolling circular cones whose section is the ellipse; the initial cone is degenerate (it is the plane of the ellipse); the final cone is a circular cylinder. The curves of the…

We show that inside every triangle the locus of points satisfying a natural proportionality relationship is a parabola and go on to describe how this triangle-parabola relationship was used by Archimedes to find the area between a line and a parabola.

Given a family of "p" greater than or equal to 3 points in the plane, some three of them have the property that the smallest circle encompassing them encompasses all "p" points. Similarly, we show that for "p" greater than or equal to 3 circles, there are three of them such that the smallest circle encompassing them…

Studies of the impact of various types of computer use on the results of learning and student motivation have indicated that the use of computers can increase learning motivation, and that computers can have a positive effect, a negative effect, or no effect at all on learning outcomes. Some results indicate that it is not computer use itself that…

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a…

In this study, the representations preferred by prospective teachers in the teaching of note values were determined and the accuracy of these representations was analyzed in the context of mathematics and music. The case study, one of the qualitative research designs, was used in the study. Study group of the research consisted of 113 pre-school…

Numeracy needs of nursing students are often underestimated by students when they enter university. Even when students are aware of the mathematics required, students underestimate or overestimate the skills they have. Research has highlighted the mathematics and numeracy skills required of nurses and nursing students and numerous studies have…

The purpose of this qualitative study was to understand the perceptions of high school mathematics teachers regarding the support provided through professional development (PD) as they engage in the implementation of the Common Core State Standards (CCSS). By means of a qualitative instrumental case study, eight high school mathematics teachers…

The results of educational research studies are only as accurate as the data used to produce them. Drawing on experiences conducting large-scale efficacy studies of classroom-based algebra interventions for community college and middle school students, I am developing practice-based data cleaning procedures to support scholars in conducting…

On the Partnership for Assessment of Readiness for College and Careers (PARCC) assessments, the attainment of performance level 4 is intended to indicate college readiness or being "on track" to college and career readiness. Students who achieve Level 4 should have a 0.75 probability of attaining at least a C in entry-level,…

Mathematics curricula are frequently rich with visuals, but these visuals are often not designed for optimal use of students' limited cognitive resources. The authors of this study revised the visuals in a mathematics lesson based on instructional design principles. The purpose of this study is to examine the effects of these revised visuals on…

With the introduction of "Next Generation Science Standards" ("NGSS"), teachers have been called to find meaningful and engaging ways to teach science content while incorporating engineering practices and, to a lesser extent, computing and computational thinking. The task becomes even more complex when they also have to…

Dual credit courses are legislated course enrollment options available to ninth- to twelfth-grade students in the State of Texas. The dual credit program provides the opportunity for all high school students, regardless of grade level, to earn college credits while working toward a high school diploma (Houston ISD, 2018). There is no limit to the…