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…

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…

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…

Existing studies have defined and assessed disciplinary literacy, mathematical literacy, and general academic language. However, there is a need to define and assess mathematics discipline-specific language (MDL), particularly for elementary school teachers. Therefore, the purpose of this study was to develop a research instrument to assess the…

This theoretical paper describes how Community-based Mathematical Modeling can advance equity and cultivate civic empathy in elementary school settings. We provide a framework for community-based mathematical modeling instruction consisting of five goals: facilitating connections, fostering engagement, promoting rigor, cultivating civic empathy,…

This paper brings together studies on the future and design methodologies to develop a novel proposal for prospective analysis in the field of education. We apply mixed research methods in combination with design methodologies to open up new routes for studying the evolution, impact and behaviour of trends in future scenarios. Our research is…

There has been much research and discussion on the principles of standards-based grading, and there is a growing consensus of best practice. Even so, the actual process of implementing standards-based grading at a school or district level can be a significant challenge. There are very practical questions that remain unclear, such as how the grades…

Another year of COVID-19 meant another virtual meeting but the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM) made the best of the situation and found ways to learn together and share connections. Having learned a lot from the 2021 virtual meeting, the executive was able to once…

To address the upcoming reform curriculum initiative following competency-based learning in Vietnam, this study examines how variations of a contextualized task allow students to experience the mathematical modelling process. We explore how Grade 10 students respond to tasks with different levels of authenticity when they first attempt such tasks.…

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,…