In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…

An introductory course in algebra may cover various types of polynomial manipulation, here we cover the background of these topics and a relatively unknown property of polynomials, namely Viete's relations. We define relevant operations and properties of polynomials over the real numbers as well as their algebraic forms, divisibility properties,…

In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

Influenced by COVID-19, online learning has become one of the most important forms of education in the world. In the era of intelligent education, knowledge tracing (KT) can provide excellent technical support for individualized teaching. For online learning, we come up with a new knowledge tracing method that integrates mathematical exercise…

Within the "Australian Curriculum: Mathematics" the Understanding proficiency strand states, "Students build understanding when they connect related ideas, when they represent concepts in different ways, when they identify commonalities and differences between aspects of content, when they describe their thinking mathematically and…

PEMDAS is a mnemonic device to memorize the order in which to calculate an expression that contains more than one operation. However, students frequently make calculation errors with expressions, which have either multiplication and division or addition and subtraction next to each other. This article explores the mathematical reasoning of the…

One of the most important applications of the definite integral in a modern calculus course is the mean value of a function. Thus, if a function "f" is defined on an interval ["a", "b"], then the mean, or average value, of "f" is given by [image omitted]. In this note, we will investigate the meaning of other statistics associated with a function…

The online deployment of Technology Engineered online Student Ratings of Instruction (SRIs) by colleges and universities in the United States has dynamically changed the deployment of course evaluation. This research investigation is the fourth part of a post hoc study that analytically and psychometrically examines the design, reliability, and…

Many students have difficulty seeing the conceptual link between bivariate data displayed in a scatterplot and the statistical summary of the relationship, "r." This article shows how to teach (and compute) "r" such that each datum's direct and indirect influences are made apparent and used in a new formula for calculating Pearson's "r."