Since the content of the Theory of Interest course in an actuarial science program is tied to an external exam, instructors may be hesitant to attempt to use inquiry-based learning. In this paper, I outline how and why I did so, including descriptions of the materials that I wrote. I found that student performance on the final exam improved…

Background: The ability to translate concrete manipulatives into abstract mathematical formulas can aid in the solving of mathematical word problems among students, and metacognitive prompts play a significant role in enhancing this process. Aims: Based on the concept of semantic congruence, we explored the effects of metacognitive prompts and…

STACK is an online testing system that can automatically assess mathematical formulae. When working with STACK on a smartphone, inputting mathematical formulae is time-consuming; therefore, to solve this problem a mathematical formula input interface for smartphones has been developed based on the flick operation. However, since the time of…

Multiple representations are widely recognized for their significant role in concept learning. This study aimed to investigate the multiple representation translation skills of high school students at different grade levels about the concept of one-dimensional motion. 239 9th, 10th, and 11th-grade students participated in the study using a…

Studies that address preservice teachers' knowledge of area measurement emphasize their lack of knowledge and their tendency towards the use of formulas, without offering a body of knowledge that helps to address such difficulties. This study offers an approximation of the mathematical knowledge necessary for preservice teachers to solve area…

This article explains how explorations into the quadratic formula can offer students opportunities to learn about the structure of algebraic expressions. In this article, the author leverages the graphical interpretation of the quadratic formula and describes an activity in which students derive the quadratic formula by quantifying the symmetry of…

The calculation of the total surface area of prisms forms part of the Mathematics curriculum in South Africa. This paper explores Grade 8 students' errors when learning about the surface area of prisms. The study was guided by the interpretive paradigm and adopted a qualitative approach in a form of a case study design. Data from diagnostic test's…

In an online asynchronous vector calculus course, we observed exam answers solved with a formula from online homework instead of the formula from lecture. Our exploratory study investigated (1) why students learned from homework instead of lecture for this topic and (2) their epistemological frames (e-frames) for lecture and homework. Per (1),…

Recently a teacher friend enquired about the S-I-R equations for disease spread, and what follows was stimulated by that exchange. COVID-19 provides an opportunity to put mathematical flesh on verbal bones such as "self-isolation", "lockdown", "herd immunity", "flattening the curve", "closed…

Students are more likely to obtain correct solutions in solving derivative problems. Even though students can complete it correctly, they may not necessarily be able to explain the solution well. Cognition and communication by the students will greatly affect the subsequent learning process. The aim of this study is to describe students'…

Permutations and combinations are generally taught by requiring students to memorize formulas and solve problems using the appropriate formula. Students who learn these topics may succeed in gaining high scores on end-of-chapter exams in textbooks, while lacking the conceptual understanding required to deal with problems in the real world.…

In issue 31(2) of the "Australian Senior Mathematics Journal", Kok (2017) describes a useful four-step process for investigating number patterns and identifying the underlying function. The process is demonstrated for both linear and quadratic functions. With respect to the quadratic example, I provide an additional idea relevant to step…

Combination problems are a cornerstone of combinatorics courses, but little research has been done examining the ways that students perceive and differentiate among different combination problems. In this article, we investigate how mathematics education students (n = 18) in a discrete mathematics course view two categorically different…

The fundamental theorem of calculus (FTC) plays a crucial role in mathematics, showing that the seemingly unconnected topics of differentiation and integration are intimately related. Indeed, it is the fundamental theorem that enables definite integrals to be evaluated exactly in many cases that would otherwise be intractable. Students commonly…

Students in secondary school often struggle with symbol sense, that is, the general ability to deal with symbols and to recognize the structure of algebraic formulas. Fostering symbol sense is an educational challenge. In graphing formulas by hand, defined as graphing using recognition and reasoning without technology, many aspects of symbol sense…