Mathematical modeling plays an important role in improving students' interests and attitudes in reasoning, communicating and solving problems. In order to understand modeling in the popular mathematics textbooks for primary schools in China, this study developed a modeling framework for K-12 mathematics textbooks, and used content analysis method…

The Cell Phone modeling task centers on a Fermi real-world estimation question. The task and rubric can be used at different grade levels to focus on the modeling process and classroom community. Finding time and space to engage students, especially novice modelers, in mathematical modeling can be a challenge, yet the benefits of modeling are…

This theoretical article explores the affordances and challenges of Euler diagrams as tools for supporting undergraduate introduction-to-proof students to make sense of, and reason about, logical implications. To theoretically frame students' meaning making with Euler diagrams, we introduce the notion of logico-spatial linked structuring (or…

Educational reform priorities such as emphasis on quantitative modelling (QM) have positioned undergraduate biology instructors as designers of QM experiences to engage students in authentic science practices that support the development of data-driven and evidence-based reasoning. Yet, little is known about how biology instructors adapt to the…

The importance of mathematical problem posing has been acknowledged by many researchers. In this theoretical paper, we want to capture different meanings and aspects of problem posing by approaching it from three different levels: (1) by comparing definitions, (2) by relating it to other constructs, and (3) by referring to research and teaching…

This article presents an analysis of contradictions expressed by pre-service mathematics teachers when performing two modeling tasks using their own technological devices. The study is based on theoretical aspects of contradictions in the fields of expansive learning and modeling with digital technologies. Technology and modeling tasks were…

We discuss classroom activity comprised of small groups of students collaboratively tinkering with programs of dynamically manipulable figural models, posing problems regarding their mathematical properties and behaviors. We analyzed data from students' discourse taken from two classroom interventions employing a framework of creative mathematical…

Modelling competencies are currently included in numerous curricula worldwide and are generally accepted as a complex, process-oriented construct. Therefore, effective measurement should include multiple dimensions, like the sub-competencies required throughout the modelling process. Departing from the characteristics of modelling problems as open…

In this article, we describe the generation of a Design and Implementation Framework for Mathematical Modelling Tasks (DIFMT) through a researcher-teacher collaboration. The purpose of the framework is to support holistic approaches to instructional modelling competency. This framework is underpinned by principles drawn from theory and praxis…

In the paper, the authors propose a variant of the mathematical model for justifying the optimal ratio of researchers of different categories to conduct scientific research of the highest possible quality in conditions of limited resources. The discrepancy is formulated between the quality of scientific research and the restriction on financial…

A chemical engineering analysis course was modified to include analytics with advanced numerical methods. The course uses the MATLAB computational environment to develop student programming, modeling, analytics, and optimization skills. Case studies reinforce MATLAB, numerical methods, and advanced optimization skills. Students reported confidence…

The teaching quality evaluation of college teachers is an important indicator of school evaluation, performance assessment and teacher promotion. However, the existing evaluation methods are only limited to the formal evaluation of teaching behavior, and have not achieved objective, reasonable and scientific evaluation results. The purpose of this…

Simple mathematical models can serve to reveal the essence of experimental phenomena and scientific concepts. The particle in a box (PIB), for example, is widely used in undergraduate programs to teach the quantum mechanical principles behind the UV--vis spectra of conjugated polyenes and polyynes. In this work, the particle on a ring (POR) and…

This paper explores use of a set of diagrammatic tools for representation and analysis of the moves a teacher makes implementing a mathematical modelling task. The focus here is on identifying what the teacher did so we can subsequently interrogate this, as to the why. Data include pre and post lesson teacher interviews and transcripts of a video…

According to expectancy-value models, two important motivational constructs are task value and self-efficacy expectations. As students work intensively on mathematical problems in the classroom, teachers need the competence to judge whether students value solving the problem and how confident they are that they will succeed. However, not much is…