The research this report belongs to aims at exploring the functional reasoning of high-school students from a covariation approach and proposing a framework to describe and predict the student's responses to modeling tasks in Dynamic Geometrical Situations. Items were designed for the students to build/construct the corresponding function guided…

We investigated whether early algebra lessons that explicitly aimed to elicit mathematical discussions (shift-problem lessons) invoke more and qualitatively better mathematical discussions and raise students' mathematical levels more than conventional lessons in a small group setting. A quasi-experimental study (pre- and post-test, control group)…

This study questions the dominant approach in the presentation of the concept of slope in undergraduate education through mathematics textbooks. For this purpose, five mathematics textbooks, were analyzed for problems related to slope, and similarities and differences were revealed. First, the subjects related to the slope in the textbooks were…

As educators, it is important for us to recognize that our assessment methods affect student attitudes. If we want students to learn from their mistakes and counteract a fixed-mindset of learning, perhaps we should look at what we incentivize in the classroom. Some professors are attempting to counteract math and test anxiety, poor STEM retention,…

In this article, we use a simple lattice model to illustrate the concepts of entropy, free energy, and thermodynamic equilibrium from a microscopic perspective. These physical concepts are based on elementary knowledge of discrete probability distribution and weighted average. Calculations about this model involve basic algebra and counting, which…

We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The…

Newton's law of cooling describes an object whose temperature decreases exponentially with time. Because of its many applications, it is a frequent topic of introductory physics labs. In this article, I describe an experiment designed for the freshman year algebra-based physics course that applies this law to answering the question, "Why…

Grade inflation is pervasive in American high schools. Is rampant grade inflation cause for concern? How teachers' grading standards affect student success is an empirical question--one that the author addresses in this article in a new study of roughly 350,000 North Carolina students taking Algebra I between 2006 and 2016. The author first…

Due to low success of traditional, postsecondary remediation mathematics, The Maryland Mathematics Reform Initiative First in the World Grant (MMRI-FITW) sought to develop and implement a statistics pathway as an alternative to traditional algebra-based math, to accelerate developmental mathematics students' progress into credit-bearing…

The study tested the hypothesis that there are sex differences in the pathways to mathematical development. Three-hundred and 42 adolescents (169 boys) were assessed in various mathematics areas from arithmetic fluency to algebra across 6th to 9th grade, inclusive, and completed a battery of working memory, spatial, and intelligence measures in…

Adults with learning disabilities (LD) face educational and employment challenges and may also have other disabilities and health conditions. Little is known about these adults' numeracy skills and how they use numeracy at work or home. The article's objective was to investigate numeracy skills and skill use for U.S. adults with LD. The author…

The ways teachers converse about their work in relation to information and communications technologies (ICTs) are worth studying. We analyse how a teacher converses about her local practices in relation to two spreadsheet algebra programs (SAPs) on variables. During the conversations we noticed that the teacher keeps different policy documents --…

The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

The gap between skilled workers needed and skilled workers available increased since the start of the fourth industrial revolution. Employees now need different knowledge, skills, and abilities to enter the workforce and stay current with new technologies than they did in the past. One way this knowledge gap and skilled worker shortage could be…

Nearly two thirds of students are not ready for college level work in mathematics as evidenced by the inability to succeed on standardized math placement tests. Unfortunately, this necessitates developmental coursework, which is not credit bearing, and ultimately makes these students significantly less likely to earn a college degree. This study…