We present adaptable activities for models of drug movement in the human body -- pharmacokinetics -- that motivate the learning of ordinary differential equations with an interdisciplinary topic. Specifically, we model aspirin, caffeine, and digoxin. We discuss the pedagogy of guiding students to understand, develop, and analyze models,…

Metamodeling ideas move beyond using a model to solve a problem to consider the nature and purpose of a model, such as reasoning about a model's empirical basis and understanding why and how a model might change or be replaced. Given that chemistry relies heavily on the use of models to describe particulate-level phenomena, developing…

Mathematical modeling, a key strand in mathematics, engages students in rich, authentic, exciting, and culturally relevant problems and connects abstract mathematics to the surrounding world. In this, article, the authors describe a modeling activity that can be used when teaching linear equations. Modeling problems, in general, are typically high…

Teaching about wave structure and function is a critical element of any physical science curriculum and supported by "Next Generation Science Standards (NGSS)" PS4: Waves and Their Applications in Technologies for Information Transfer. To support students' learning of these ideas, teachers often rely on developing graphic models of a…

Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…

Mathematical modeling is an important and accessible process for elementary school students because it allows them to use mathematics to engage with the world and consider if and when to use it to help them reason about a situation. It fosters productive struggle and twenty-first-century skills that will aid them throughout their lifetime.

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

Many fraction activities rely on the use of area models for developing partitioning skills. These models, however, are limited in their ability to assist students to visualise a fraction of an object when the whole changes. This article describes a fraction modelling activity that requires the transfer of water from one container to another. The…

This article proposes a framework for classroom teachers to use in making pedagogical decisions regarding which mathematical materials (concrete and digital) to use, when they might be most appropriately used, and why. Two iPad apps ("Area of Shapes (Parallelogram)" and "Area of Parallelogram") are also evaluated to demonstrate…

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

The phenomenon of outbreaks of dangerous diseases is both intriguing to students and of mathematical significance, which is exactly why the authors engaged eighth graders in an introductory activity on the growth that occurs as an epidemic spreads. Various contexts can set the stage for such an exploration. Reading adolescent literature like…

A model for division of fractions using money as manipulative material is presented. Eight levels are described, ranging from the development of language and concept introduction through types of problems to rule discovery and application. (MNS)

Reviews the history of the concept of function, looks at its relationship with other sciences, and discusses its use in the study of real world situations. Discusses the process of constructing mathematical models of function and emphasizes the importance of the roles of the numerical, graphical, and algebraic representational forms. (MDH)

Presents an approach to the concept of absolute value that alleviates students' problems with the traditional definition and the use of logical connectives in solving related problems. Uses a model that maps numbers from a horizontal number line to a vertical ray originating from the origin. Provides examples solving absolute value equations and…