In this paper, we discuss mathematical modeling opportunities that can be included in an introductory Differential Equations course. In particular, we focus on the development of and extensions to the single salty tank model. Typically, salty tank models are included in course materials with matter-of-fact explanations. These explanations miss the…

This article is about utilizing the process of building and exploiting models as a framework for inquiry in mathematics education research. We introduce and discuss a model of such a process and compare this model with key methodological features of design research in mathematics education. We argue that despite several communalities, educational…

How might fourth graders address the problem of measuring the size of a leaf? And why might their classroom teachers choose such a shape to measure? One group of fourth-grade students in an urban Australian school were interested in knowing the sizes of leaves on a passionfruit vine growing at their school. The children were excited after a visit…

Connections among the mathematics, science, and engineering disciplines have been recognized and affirmed in national standards. For example, the application of mathematical ideas and skills within science has been highlighted in national science standards for over 20 years. More recently, the Next Generation Science Standards (NGSS; NGSS Lead…

How to pedagogically integrate the four STEM (science, technology, engineering, and mathematics) disciplines is a main discussion issue in STEM education. Inquiry-based learning, mathematical modeling, and tool-based pedagogy could go hand in hand to provide a possible integrated STEM pedagogical framework for mathematics and science. This…

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,…

We present our experience with an open-ended lab activity that we designed for students with a Calculus 1 background. With the goal of learning how scientists study transport in streams, the students collected data on how a pulse of leaves travels down a nearby stream. Students who had little to no experience with data with two independent…

The Models and Modeling Working Group at PME-NA has provided a forum for discussing and collaborating on projects fundamental to research on mathematical modeling since the first PME-NA conference in 1978. We propose to convene this Working Group at PME-NA 41 with a dual purpose: (1) to build on a theme begun in Greenville, holding a focused…

Integrating the disciplines of mathematics and science is one way to place the calculations of volume and surface area into a real life context. The authors present an activity for middle-school students that aims to promote their learning of these key concepts in a personally meaningful way, whilst also developing inquiry and problem solving…

Students tend to see mathematical functions as static, mysterious objects that must be approached according to a set of rules and procedures laid out in mathematics textbooks (Clement 2001). Because learners so rarely experience functions as a meaning-making tool that matters to their understanding of the world, they miss critical opportunities to…

The use of method of imitational modeling to study forming the empirical knowledge in pupil's consciousness is discussed. The offered model is based on division of the physical facts into three categories: 1) the facts established in everyday life; 2) the facts, which the pupil can experimentally establish at a physics lesson; 3) the facts which…

The purpose of this paper is to explain how to use the scientific method as the framework to introduce mathematical model. Two interdisciplinary activities, targeted for students in grade 6 or grade 7, are explained to show the application of the scientific method while building a mathematical model to investigate the relationship between the…

The purpose of this paper is to explain how to use the scientific method as the framework to introduce mathematical model. Two interdisciplinary activities, targeted for students in grade 6 or grade 7, are explained to show the application of the scientific method while building a mathematical model to investigate the relationship between the…

The purpose of this paper is to describe the processes utilised to develop an online learning module within the Opening Real Science (ORS) project--"Modelling the present: Predicting the future." The module was realised through an interdisciplinary collaboration, among mathematicians, scientists and mathematics and science educators that…

This article presents four inquiry-based learning activities developed for a liberal arts math course. The activities cover four topics: the Pythagorean theorem, interest theory, optimization, and the Monty Hall problem. Each activity consists of a dialogue, with a theme and characters related to the topic, and a manipulative, that allow students…