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…

We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

Our planet is facing a biodiversity crisis and mathematics is involved. In this article, I focus on reports of a wolf hunt to examine different ways in which mathematics contributes to this crisis, shapes our understanding of the ecosystem and guides future actions. My examination contributes to understanding the ethical dimension of mathematics…

In the article 'How Long Is My Toilet Roll--A Simple Exercise in Mathematical Modelling' several models of increasing complexity are introduced and solved to calculate indirectly the length of paper on a toilet-roll. All these results are presented without errors. The authors of this comment believe the error analysis of measurements made in a…

The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels of…

How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring-mass system. We provide a sequence of discovery-based exercises that foster physical and…

In this article, we question the prevalent assumption that teaching and learning mathematics should always entail movement from the concrete to the abstract. Such a view leads to reported difficulties in students moving from manipulatives and models to more symbolic work, moves that many students never make, with all the implications this has for…

In this paper, six mathematics curriculum changes in Iran are reviewed, spanning from 1900 to 2021. Change of forces, barriers, and the main features of each reform are represented. Specifically, the first five curriculum changes are described briefly and the sixth and most recent one is elaborated upon, with more detail as contemporary school…

The Compulsory Education Course Standards for Mathematics 2022 have highlighted the educational objectives of junior secondary mathematics by emphasizing the development of mathematical competence and practical learning. Model consciousness, as one of the fundamental mathematical competencies to be developed at the junior secondary level, can…

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and…

We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however,…

Mathematics educators advocate for the use of models as an instructional practice that can potentially aid in building students' understanding of difficult topics. Integers and integer operations are historically problematic for students and are critically important in both arithmetic and the future study of algebra. In this chapter, I explore one…

The proposed revisions to the "Australian Curriculum: Mathematics" highlight the importance of learning to mathematise, problem-solve and reason in real world contexts, including financial contexts. Through the Economics + Maths = Financial Capability research project, the authors have been imagining fresh ideas for connecting the…

Research identifies two domains by which mathematics allows learning physics concepts: a technical domain that includes algorithmic operations that lead to solving formulas for an unknown quantity and a structural domain that allows for applying mathematical knowledge for structuring physical phenomena. While the technical domain requires…

Problems are part of our lives. It causes stress, tension, emotional instability, and physical strain to us. It is very essential to deal with our problems before they deal with our happiness. Problem solving skill is an irreplaceable life skill and it is cognitive or thinking activity essential to our day-to-day lives. In order to lead a…