Folk wisdom of the state of Montana asserts that Flathead Lake, located in the state's northwest corner, is the largest natural freshwater lake west of the Mississippi. But what does it mean to be the "largest?" And, how does one respond to Californians' claims that Lake Tahoe, located on the California-Nevada border, is the rightful…

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…

In this paper, the application of fuzzy logic in mathematical education is viewed from the perspective of pre- school education. The aim of the paper is to give a brief overview of examples from the literature related to fuzzy logic and to point out the presence of fuzzy linguistic variables in the everyday life of a preschool child, as well as…

People use models every day without even realizing it. Models create a structure for predictions (inferences) that can be used or adapted as situations change. A model is a relational system that highlights aspects of a phenomenon that the modeler deems important and diminishes the rest. Statistical models capture variability of data, enabling…

This mixed-methods study focused on advanced student engagement, mathematics competence, and the influence of teachers in classrooms that used 3D printing to teach mathematics. Quantitative methods were used to understand changes in student perceptions of competence, engagement, and feelings regarding group work. Qualitative methods were used to…

We explored the mediating role of prior knowledge on the relation between intelligence and learning proportional reasoning. What students gain from formal instruction may depend on their intelligence, as well as on prior encounters with proportional concepts. We investigated whether a basic curriculum unit on the concept of density promoted…

The National Council of Teachers of Mathematics (NCTM, 2014) highlights that effective teaching practices promote students' reasoning and sense making through various problem-solving strategies. Rather than telling students what to do and how to solve problems, teachers are expected to engage learners in accessible real-life problem situations…

In order to promote the design of innovative instructional activities at the Linear Algebra, we perform a design-based research project to explore how to teach Linear Algebra at the university level. In this article, we present the results of three cycles of a teaching experiment that we carried out to design, try out, and improve a local…

I argue that emotion research needs formal (mathematical) theory to address two central questions. How does evolution shape mechanisms of emotion development across generations, depending on environmental conditions? How do these mechanisms generate emotions, based on lifetime experience and current context? Formal modeling enables researchers to…

Frequently, the shadow of financial insolvency is present in economies, whether between countries, companies or the general population (people) who contract the obligation of a loan, credit or other debt. Debt restructuring is one of the most effective financial tools to face this. Through mathematical modeling with algorithms designed for the…

In science education, building models of dynamical systems is a promising method for understanding various natural phenomena and artifacts with scientific concepts. It is, however, difficult to learn skills and concepts necessary for modeling. Though several model-building learning environments (MBEs) have been developed with potentially useful…

By modeling learning students enjoy learning and doing mathematics in new ways. This study aimed firstly to produce senior high school mathematics modeling tasks, lesson plan, and student worksheet for valid mathematical learning; secondly, to produce senior high school mathematics modeling, lesson plan, and student worksheet for practical…

Friction is one of the common forces that affect our everyday life and one of the oldest problems studied in physics. An interpretation of its nature is included in all general physics courses, in both high school and college. The desire and need to better understand it guided a long list of scientists who devoted themselves to the study of…

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

In this paper the muscular activity will be treated from a physical point of view, considering the main physical parameters that can be quantified. A brief and simple theoretical treatment will be followed by some homeworks for students. The problems have a difficulty degree typical of an undergraduate class, and the arguments have been chosen…