Mathematisation of realistic situations is an on-going focus of research. Classroom data from a Year 9 class participating in a program of structured modelling of real situations was analysed for evidence of Niss's theoretical construct, implemented anticipation, during mathematisation. Evidence was found for two of three proposed aspects. In…

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

This article offers modelling opportunities in which the phenomena of the spread of disease, perception of changing mass, growth of technology, and dissemination of information can be described by one differential equation--the logistic differential equation. It presents two simulation activities for students to generate real data, as well as…

We introduce a dc/dc boost power converter as a didactic prototype intended to support courses on electric circuit analysis experimentally. The corresponding mathematical model is obtained, the converter is designed and an experimental setup is described, constructed and tested. Simplicity of construction as well as low cost of components renders…

Many science problems require students to convert units. While this skill may not get the attention that more central science concepts do, teachers in the middle school and early high school grades will be doing their students a great service by leaving them with a strong understanding of both the skill itself and the reasons behind it. When the…

Linear programming (LP) is taught in different departments across college campuses with engineering and management curricula. Modeling an LP problem is taught in every linear programming class. As faculty teaching in Engineering and Management departments, the depth to which teachers should expect students to master this particular type of…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

Given the Common Core's dual emphases on mathematical modeling, there is a need to understand modeling as a practice and content standard to develop students' mathematical modeling skills. This study of 12 students from differing levels of mathematics instruction and English Language proficiency includes analysis of their modeling with mathematics…

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

This study explores the impact that co-designing a virtual manipulative, Fractions Lab, had on teachers' professional development. Tapping into an existing community of practice of mathematics specialist teachers, the study identifies how a cooperative enquiry approach utilising workshops and school-based visits challenged 23 competent primary…

We discuss a quantum-mechanical model of two particles that interact by means of a harmonic potential and are confined to a one-dimensional box with impenetrable walls. We apply perturbation theory to the cases of different and equal masses and analyse the symmetry of the states in the latter case. We compare the approximate perturbation results…

In the frame of a laboratory training course for medicine students, a new approach for laboratory exercises has been applied to teach the phenomena of circulation. The exercise program included measurements of radial artery blood flow waveform for different age groups using a noninvasive optical sensor. Arterial wave reflection was identified by…

Math in the City is an interdisciplinary mathematics course offered at University of Nebraska-Lincoln in which students engage in a real-world experience to understand current major societal issues of local and national interest. The course is run in collaboration with local businesses, research centers, and government organizations, that provide…

A common theme of models of conceptual growth is to establish the hierarchical structures of abilities that can be interpreted along developmental lines. Integrating the literature on the development of mathematical concepts and skills in children, a comprehensive 6 level model for describing, explaining and predicting the development of key…

The goal of this work is to provide instructors with detailed information about their classes at each assignment during the term. The information is both on an individual level and at the aggregate level. We used the large number of grades, which are available online these days, along with data-mining techniques to build our models. This enabled…