Nowadays, mathematics teachers in K-12 strive to promote their students' mathematical knowledge and computational thinking (CT) skills. There is an increasing need for effective CT-embedded mathematics learning material and a better understanding of students' views toward them. In this work, we present the results of a research study, which…

College physics textbooks (algebra based) tend to shy away from topics that are usually thought to require calculus. I suspect that most students are just as happy to avoid these topics. Occasionally, I encounter students who are not so easily satisfied, and have found it useful to maintain a storehouse of non-calculus solutions for some common…

Recently, Wilmer III and Costa introduced a method into the mathematics education research literature which they employed to construct solutions to certain classes of ordinary differential equations. In this article, we build on their ideas in the following ways. We establish a link between their approach and the method of successive…

This study examines students' visual behaviors when they tackle two types of synthesis problems, sequential and simultaneous problems. Sequential synthesis tasks can be solved by applying pertinent concepts consecutively, whereas simultaneous synthesis tasks require concurrent application of multiple concepts. Twenty-two students from an…

Mathematical connections play an important role in achieving mathematical understanding. Therefore, in this article, we report research whose objective was to identify mathematical connections that pre-university students make when they solve problems that involve the derivative and the integral. In this research, we consider a mathematical…

The contents of calculus, known for their complexity, present significant challenges for students, particularly in mastering multiple integrals and effectively visualizing related concepts. The transition to distance learning prompted by the COVID-19 pandemic has further complicated the learning process in multiple integrals. In line with this and…

In Thai mathematics classrooms, there is a lack of attention to support students' mathematical problem-solving skills by working from real-world contexts that make sense to students. This study aimed to investigate how preservice mathematics teachers' problem-solving can be explored in their content course, intervening with technology and…

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),…

Storytelling has proved to be an effective way of passing on information from one generation to the next. Whether the information relates to history, culture, health, or morality, the story provides a framework so that complex ideas can be better understood and retained. In this article, we consider the role of narrative in the design and…

There is a growing interest in using comparative judgement as a peer assessment tool involving students choosing the 'better' of two pieces of work. However, it has not been shown whether peer assessment through comparative judgement is effective for students' learning. To gain a better understanding of the comparative judgement process, we…

In this paper the authors described the influence of the computer-based environment on students' learning achievement of the multidimensional calculus, in particular double integrals. The research was conducted with the second year students at the University of Kragujevac, Serbia, with two groups of students: the experimental and the control one.…

Background: Many engineering students fail to proceed through required prerequisite mathematics courses. Since these courses strongly influence engineering student attrition, we should examine to what degree these courses truly serve as prerequisites for following engineering coursework. Purpose/Hypothesis: We examined two research questions:…

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…

The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed.

Teaching and learning Calculus concepts and procedures, particularly the definite integral concept, is a challenge for teachers and students in their academic careers. In this research, we supplement the analysis made by different authors, applying the theoretical and methodological tools of the Onto-Semiotic Approach to mathematical knowledge and…