This paper describes a project assigned in a multivariable calculus course. The project showcases many fundamental concepts studied in a typical course, including the distance formula, equations of lines and planes, intersection of planes, Lagrange multipliers, integrals in both Cartesian and polar coordinates, parametric equations, and arc length.

Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to…

Research has shown the importance of helping students, especially those with mild-to-moderate learning disabilities, to offload information during problem-solving. When students can get their thoughts onto paper, number line strategies can help them develop a firm foundation in mathematical problem-solving while understanding the relationships…

Many gifted students fail to be diagnosed, preventing them from receiving an education that is adapted to their characteristics, with activities that challenge their minds. Mathematics is one of the subjects in which they can demonstrate talent, where they often exhibit high skills in solving problems, handling numbers and performing spatial…

Problem solving and proofs have always played a major role in mathematics. They are, in fact, the heart and soul of the discipline. The using of a number of different proof techniques for one specific problem can display the beauty, and elegance of mathematics. In this paper, we present one specific, interesting geometry problem, and present four…

The multiplication principle (MP) is foundational for combinatorial problem-solving. From a units-coordination perspective, applying the MP with justification entails establishing unit relationships between the number of options at each independent stage of a counting process and the total number of combinatorial outcomes. Existing research…

This work is devoted to exploring proof abilities in Graph Theory of undergraduate students of the Degree in Computer Engineering and Technology of the University of Seville. To do this, we have designed a questionnaire consisting of five open-ended items that serve as instrument to collect data concerning their proof skills when dealing with…

An important element to doing mathematics and developing conceptual understanding in mathematics is creating and making sense of visual representations. Developing mathematical understanding happens when students invent (or reinvent) strategies and think deeply about why a strategy works. Although societal and political pressures may say otherwise…

This article analyzes Malaysian and Japanese educators' reactions to a mathematics lesson observed by a subset of researchers. The main aims are to reveal the cultural scripts about mathematical learning that are held by, but often invisible to, members of a culture; and to address educators' conceptions of teaching mathematics across cultures.…

Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…

This contribution focuses on reasoning about quadrilaterals provided by lower secondary school students when working with pre-prepared dynamic constructions. On this topic, we present an exploratory empirical qualitative study carried out within a GeoGebra Classroom environment, and our diagnostic instrument consists of a set of dynamic…

The problem solving performed by students in solving mathematical literacy problems shows that at the developmental stage of proportional reasoning students have different strategies, especially at the developmental stage of functional and scalar relationships. The purpose of this study is to identify and explore the developmental stages of…

Studies in online STEM education have shown that instructional platforms enhance communication and students' engagement. Despite the relevance of these platforms as communicative tools to support online learning, we cannot neglect the impact of the human connection if we want to ensure an equitable learning environment for online asynchronous…

Retention is crucial to the mission of an institution, and University leaders must strategize to increase student persistence. Introductory math can be a gatekeeper or a gateway. Supplemental instruction (SI) can help students' chances of success in math. This study reports on the three-term pilot of an SI program at a private mid-size…

Developing both conceptual and procedural knowledge is important for students' mathematics competence. This study examined whether U.S. Grade 9 general education mathematics teachers' self-reported use of concept-focused instruction (CFI) and procedure-focused instruction (PFI) were associated differently with ninth graders' algebra achievement…