Many bandpass signals can be sampled at rates lower than the Nyquist rate, allowing significant practical advantages. Illustrating this phenomenon after discussing (and proving) Shannon's sampling theorem provides a valuable opportunity for an instructor to reinforce the principle that innovation is possible when students strive to have a complete…

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

Limited Singapore research indicated a lack of exposure of modelling tasks at primary levels. Teacher reflection is used as a tool in design research cycles exploring the potentials of modelling tasks in a Singapore primary five classroom. Findings reveal that the teacher identified three potentials of a modelling task on children's…

This publication presents estimates of apprentice and trainee activity in Australia for the June quarter 2012. The figures in this publication are derived from the National Apprentice and Trainee Collection no.73 (September 2012 estimates). The most recent figures in this publication are estimated (those for training activity from the December…

The quantitative results of Sources of Self-Efficacy in Science Courses-Physics (SOSESC-P) are presented as a logistic regression predicting the passing of students in introductory Physics with Calculus I, overall as well as disaggregated by gender. Self-efficacy as a theory to explain human behavior change [Bandura [1977] "Psychological…

It is common for both algebra and calculus instructors to use power functions of various degrees as well as exponential functions to examine and compare rates of growth. This can be done on a chalkboard, with a graphing calculator, or with a spreadsheet. Instructors often are careful to connect the symbolic and graphical (and occasionally the…

"When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data," notes the Common Core State Standards Initiative (2010, p. 72). This exploration of the recursive process in the Devil and Daniel Webster problem reveals that the symbolic spreadsheet fits this bill.…

The article presents the consideration of grading scales used for education outcomes in different countries, describes likeness and differences of applied grading scales. Application of the European Credit Transfer and Accumulation System (ECTS) grading scale is investigated according of the analysis of scientific literature as well as cases of…

A mathematical model of HIV/sexually transmitted infections (STI) transmission was used to examine how linearity or nonlinearity in the relationship between the number of unprotected sex acts (or the number of sex partners) and the risk of acquiring HIV or a highly infectious STI (such as gonorrhea or chlamydia) affects the utility of sexual…

Sensitivity analysis is the study of how the different input variations of a mathematical model influence the variability of its output. In this paper, we review the principle of global and local sensitivity analyses of a complex black-box system. A simulated case of application is given at the end of this paper to compare both approaches.…

From Piaget to the present, traditional and dual-process theories have predicted improvement in reasoning from childhood to adulthood, and improvement has been observed. However, developmental reversals--that reasoning biases emerge with development--have also been observed in a growing list of paradigms. We explain how fuzzy-trace theory predicts…

The Cartesian diver experiment certainly occupies a place of honour in old physics textbooks as a vivid demonstration of Archimedes' buoyancy. The original experiment, as described in old textbooks, shows Archimedes buoyancy qualitatively: when the increased weight of the diver is not counterbalanced by Archimedes' buoyancy, the diver sinks. When…

Freely rising air bubbles in water sometimes assume the shape of a spherical cap, a shape also known as the "big bubble". Is it possible to find some objective function involving a combination of a bubble's attributes for which the big bubble is the optimal shape? Following the basic idea of the definite integral, we define a bubble's surface as…

We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…