Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a…

Discrete time models, one linear and one non-linear, are investigated, both with a herbivore species that consumes a basal food source species. Results are presented for coexistence of the species and to illustrate chaotic behaviour as parameters are varied in the non-linear model. The results indicate the benefit of fertilization in terms of the…

Integer operations are typically introduced in sixth grade, but they are a consistent area of struggle among these students. This struggle also inhibits their understanding of algebraic computations involving positive and negative terms. In this article, the author provides introductory tasks and models for adding and subtracting integers that can…

The reality is that textbooks and state standards have more content than can reasonably be covered for proficiency in most classrooms. In years past, this typically meant cutting the last unit or two or moving along regardless of who was keeping up, in many cases resulting in cutting statistics from the curriculum. This article provides five…

We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…

Two examples of mathematical modelling are explored. Firstly, optimising the distance travelled when jumping from a swing is discussed. The second concerns optimising the distance travelled by monkeys when swinging from branch to branch.

An university in Chile developed a Digital Learning Routes (DLR) for three elective courses in the area of mathematics: (1) limits, derivatives, and integrals; (2) probabilities and descriptive and inferential statistics; and (3) three-dimensional geometry. A DLR is a sequence of e-learning activities that seeks to enable learners to build…

How would students feel when learning through the use of mathematical modeling? On investigation, this article reveals that students felt better prepared for assessments, learned valuable life skills, and saw the relevance of mathematics to their lives outside of the classroom.

The Modelling Dance task is a mathematical modelling task that explores the relationship between mathematics and dance. The authors share the task sequence, adaptations made to support virtual implementation, and evidence of student learning related to learning goals.

We describe an activity that introduces students to population modelling, enables them to use estimates obtained from a sample to infer back to the population, and understands how the findings are translatable via penguins and their poo!

These notes discuss several related problems in geometry that can be explored in a dynamic geometry environment. The problems involve an interesting property of hexagons.

We present noncompetitive adsorption as "particles in a box with one sticky wall." We start with a general model that can be modeled as a simple ordinary differential equation (ODE). To verify the ODE students run a computer simulation. The ODE's solution imperfectly fits the simulation's data. This leads to the diffusion partial…

Three mathematics education researchers discuss their findings on the use of diagrams in math instruction for English language learners. The authors show how diagrams can help students who are English learners better develop mathematical thinking and communicate their mathematical understanding.

This article provides information to educational leaders about how to address the challenge of supporting students who are emergent multilingual--i.e., those identified as English Learners (ELs) by their schools--in middle grades mathematics classes. The ideas in this article draw on research and collaborations with hundreds of teachers across the…

Mathematical modelling is acknowledged to be one of the major dimensions of mathematical competence, and well-designed modelling activities can provide students with the opportunity to use mathematical concepts and procedures in a meaningful way. Additionally, modelling activities are regarded as suitable contexts for enabling students to use…