In this article, the authors describe how a theoretical framework--the modeling cycle of Bliss, Fowler, and Galluzzo (2014)--came to life in their classroom as students struggled with an open-ended modeling task. The authors share their high school students' work--warts and all. They explain how they used their students' ideas and errors to help…

Students' mathematics achievements in secondary school have an influential effect on their performance in university and their future careers. There are numerous innovative teaching strategies which are promising and have shown to improve students' achievement in mathematics; one will wonder if there will be corresponding achievement growth in…

Mathematics can be viewed as complex structures comprising intricate and profoundly useful webs of relationships. Students can experience mathematics in this way when working on mathematical tasks such as problem-solving, modelling, investigations or problem posing. Yet these kinds of tasks are seldom implemented in many upper-secondary and…

In this study, we investigated how elementary pre-service teachers (PSTs) perceive using representations in teaching mathematics and what fractional representations (e.g., manipulatives or models) they suggest to guide students' incorrect use of representations in learning fractions. A written questionnaire was administrated to 151 PSTs at a large…

Incorporating modeling activities into classroom instruction requires flexibility with pedagogical content knowledge and the ability to understand and interpret students' thinking, skills that teachers often develop through experience. One way to support preservice mathematics teachers' (PSMTs) proficiency with mathematical modeling is by…

Forming part of a wider research study, the current study investigated prospective middle school mathematics teachers' ways of covariational reasoning on tasks involving simultaneously changing quantities. As the introductory theme of a larger unit on derivative, a model development sequence on covariational reasoning was designed and experimented…

We present a new learning activity that enables students to apply eigenvalue theory to investigate a practical modeling problem. We demonstrate how to build a spring-coupled pair of pendula and describe how students can measure the movements of these pendula using open-source image processing software. We then illustrate how to analyze this…

This article describes the development, initial validation, and psychometric evaluation of the mathematical modeling attitude scale (MMAS). Specifically, both qualitative and quantitative techniques were used to generate relevant items. The MMAS assesses K-12 teachers' attitude toward mathematical modeling and examines their experiences with…

Understanding large-scale patterns in student course enrollment is a problem of great interest to university administrators and educational researchers. Yet important decisions are often made without a good quantitative framework of the process underlying student choices. We propose a probabilistic approach to modelling course enrollment…

The relevance of this problem is primarily determined by a necessity of improving production efficiency in conditions of innovative development of the economy and implementation of Import Substitution Program. The purpose of the article is development of set of criteria and procedures for the comparative assessment of alternative volume production…

Students are well aware of the effect of the deflection of sports balls when they have been given a spin. A volleyball, tennis, or table tennis ball served with topspin results in an additional downward force that makes the ball difficult to catch and return. In soccer, the effect of sidespin causes the ball to curve unexpectedly sideways,…

Sternberg (2017) summarizes the history of identification of giftedness in the 20th century and presents a case for the shortcomings of measures such as IQ for problem-solving skills required in the 21st century. The Active Concerned Citizenship and Ethical Leadership (ACCEL) model is proposed to replace the outdated construct of IQ, particularly…

The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). In their work with practicing secondary teachers, the authors found that teachers may make some tacit…

Two simple discrete-time models of mutation-induced cannibalism are introduced and investigated, one linear and one nonlinear. Both form the basis for possible classroom activities and independent investigative study. A range of classroom exercises are provided, along with suggestions for further investigations.

It is well known that mechanical engineering students often find mechanics a difficult area to grasp. This article describes a system of equations describing the motion of a balanced and an unbalanced roller constrained by a pivot arm. A wide range of dynamics can be simulated with the model. The equations of motion are embedded in a graphical…