We automate and randomize the building of linear systems with a parameter, appropriate for assigning to students. When the parameter takes on a specific value, the system has no solutions. When the parameter takes on a different value, the system has an infinite number of solutions.

Introductory courses in biology often lack sufficient emphasis on quantitative skills and interdisciplinary problem solving, leaving many students unprepared for more advanced biology coursework and hampering their ability to pursue biology research careers. MathBench Biology Modules were created to enhance the quantitative skills of biology…

Students need a robust understanding of the derivative for upper-division mathematics and science courses, including thinking about derivatives as ratios of small changes in multivariable and vector contexts. In "Raising Calculus to the Surface" activities, multivariable calculus students collaboratively discover properties of…

The Energy and Momentum Conceptual Survey (EMCS) is a multiple-choice survey that contains conceptual problems involving a variety of energy and momentum concepts covered in a typical introductory physics course for science and engineering majors. Prior studies suggest that many concepts on the survey are challenging for introductory physics…

Adjusting the Calculus I curriculum by putting modelling and differential equations literally at its centre leads to a better-organised and better-motivated course. The biggest change is including a section on "qualitative" and "numerical" solutions to ordinary differential equations between the customary sections on…

This article explores secondary teachers' opportunities to learn from an innovative real analysis course, as reflected in their actual classroom teaching. The course used cases of teaching as a site for applying mathematics and developing pedagogical mathematical practices. This article explores particular teaching moments in (N = 6) secondary…

School algebra serves as the language of mathematics and a foundational subject for learning advanced mathematics courses. This makes developing learners' proficiency in algebra the most desirable instructional goal of school mathematics. Despite having such importance emphasis, however, studies indicate that the vast majority of learners are…

It has become increasingly important for future business professionals to understand statistical computing methods as data science has gained widespread use in contemporary organizational decision processes in recent years. Used by scores of academics and practitioners in a variety of fields, Monte Carlo simulation is one of the most broadly…

Understanding the rate at which STEM faculty move from traditional, lecture-intensive teaching practices to more effective, student-centered practices and the institutional conditions that favor this shift are crucial for supporting faculty change. This study investigated the instructional practices of biology, chemistry, and physics faculty at…

This study aims to evaluate the effectiveness of the online learning platform Brilliant.org in improving the academic performance of 60 tenth-grade students from four public schools in the city of Barranquilla, Colombia. A quasi-experimental design with two groups will be used: an experimental group that will use Brilliant.org platform to learn…

In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

After the COVID-19 pandemic was over, the teaching and learning process in the world of education underwent several changes. The COVID-19 pandemic forced the global learning community to transition within a very short period of time from the traditional in-class method of learning to a mode of online learning. After the pandemic started to…

This paper aims to show how through plausible reasoning financial mathematics can be taught at the university level, the work is based on a model designed by García (2019), who created it to teach linear algebra in engineering careers, using technology, of all this model, only the design with methodological procedure is adapted. In this grade The…

This study examined the receptive vocabulary knowledge and lexical developmental patterns of the 3000 most frequent words among 953 university L2 learners of Spanish at different stages in their language studies, taking into consideration the effect of high school instruction on high-frequency vocabulary knowledge. Results confirm that even…

This paper is written to provide ideas and guide faculty who want to design a mathematical modeling course for undergraduate mathematics majors and minors. We discuss course goals, assignments, and projects that can be used to help students gain experience relevant for careers and mathematical modeling opportunities. The authors designed this…