When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…

At the end of primary school all children more of less know what a percentage is, but yet they often struggle with percentage problems. This article describes a study in which students of 13 and 14 years old were given a written test with percentage problems and a week later were interviewed about the way they solved some of these problems. In a…

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…

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…

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…

Policymakers and education scholars recommend incorporating mathematical modeling into mathematics education. Limited implementation of modeling instruction in schools, however, has constrained research on how students learn to model, leaving unresolved debates about whether modeling should be reified and explicitly taught as a competence, whether…

The purpose of this study is implementation of a structured inquiry learning model in instruction of geometry. The model used is a model with a quasi-experimental study amounted to two classes of samples selected from the population of the ten classes with cluster random sampling technique. Data collection tool consists of a test item…

In an introductory chemical engineering course, the conceptual framework of a holistic problem-solving methodology in conjunction with a problem-based learning approach has been shown to create a learning environment that nurtures deep learning rather than surface learning. Based on exam scores, student grades are either the same or better than…

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.…

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…

As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…

This study evaluates the effects of an intervention aimed at improving representational flexibility in linear-function problems. Forty-nine students aged 13-16 participated in the study. A pretest-intervention-posttest design with an experimental and control group was used. At pretest, both groups solved a choice test, where they could freely…

This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…

One of the most important issues in the reorganisation of engineering education is to consider new pedagogical techniques to help students develop skills and an adaptive expertise. This expertise consists of being able to recognise the nature of a problem intuitively, and also recognising recurring patterns in different types of problems. In the…

To protect and conserve the Earth's biodiversity and ecosystem services, it is important not only to understand and conserve species and ecosystems, but also to instill an understanding and appreciation for biodiversity and ecosystem services in the next generations of both scientists and citizens. Thus, this dissertation combines research into…