The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

Researchers have proposed a variety of methods to make a connection between real life and mathematics so that it can be learned in a practical way and enable people to utilise mathematics in their daily lives. Model-eliciting activities (MEAs) were developed to fulfil this need and are very capable of serving this purpose. The reason MEAs are so…

This study analyzes the development of percentages knowledge by seventh graders given a sequence of activities starting with a realistic modeling task, in which students were expected to create a model that would facilitate the reinvention of percentages. In the first two activities, students constructed their own pricing model using fractions and…

The solving of structured multi-step word problems has been a dominant practice in schools and is seen as a way to develop students' mathematical reasoning abilities. Unfortunately, it is limited in scope and does not provide opportunities for eliciting deeper reasoning as they are neither rich enough nor anchored in authentic data that resemble…

Multiple representations, multiple modalities, and technology can be helpful in the understanding of mathematical concepts when used in an appropriate manner (Shah & Freedman, 2003; Goldman, 2003), but this alone does not account for the student benefits of creating and using dynamic models over teacher generated graphs to construct…

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…

Sometimes the best mathematics problems come from the most unexpected situations. Last summer, a Corvette raced down a local quarter-mile drag strip. The driver, a family member, provided the spectators with time and distance-traveled data from his time slip and asked "Can you calculate how many seconds it took me to go from 0 to 60…

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Randomized experiments are commonly used to evaluate the effectiveness of educational interventions. The goal of the present investigation is to develop small-sample corrections for multiple contrast hypothesis tests (i.e., F-tests) such as the omnibus test of meta-regression fit or a test for equality of three or more levels of a categorical…

Vince Wright makes a convincing argument for presenting children with a different "prototype" of a fraction to the typical one-half. Consider how the prototype that Wright mentions may be applied to a variety of fraction concepts. We are sure that you will never look at a doughnut in quite the same way.

We describe a collaboration between mathematicians and ecologists studying the cyanobacterium "Gloeotrichia echinulata" and its possible role in eutrophication of New England lakes. The mathematics includes compartmental modeling, differential equations, difference equations, and testing models against high-frequency data. The ecology…

The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…

The lithium ion battery will be a reliable electrical resource for many years to come. A simple model of the lithium ions motion due to changes in concentration and voltage is presented. The battery chosen has LiCoO[subscript 2] as the cathode, LiPF[subscript 6] as the electrolyte, and LiC[subscript 6] as the anode. The concentration gradient and…

Information changes as it is passed from person to person, with this process of cultural transmission allowing the minds of individuals to shape the information that they transmit. We present mathematical models of cultural transmission which predict that the amount of information passed from person to person should affect the rate at which that…

Interdisciplinary research in computer science requires the development of computational techniques for practical application in different domains. This usually requires careful integration of different areas of technical expertise. This dissertation presents image and time series analysis algorithms, with practical interdisciplinary applications…