This study explores how bodily actions of iterating, sharing and grouping can contribute to the understanding of multiplication and division, going beyond their conventional framing as intuitive arithmetic models. Drawing on objectification theory, we reconceptualize these operations as historically and culturally situated relationships between…

Project-based learning (PBL) empowers students to become active learners. In this work computational reverse osmosis (RO) projects developed from industrial case studies and research were implemented in several chemical engineering courses to enhance student learning experience. Students not only gained knowledge in water treatment, but also…

Advances in graphing technologies and learning sciences pedagogy have the potential to equitably support students when exploring complex systems depicting dynamic relationships across multiple disciplinary topics in Science, Technology, Engineering, and Mathematics (STEM). We report on the cumulative impact of science units designed in a Research…

A test battery with two different levels of adaptation is presented: a within-subtest level for the selection of the items in the subtests and a between-subtest level to move from one subtest to the next. The battery runs on a two-level model consisting of a regular response model for each of the subtests extended with a second level for the joint…

This study aims to reveal how model eliciting principles are used in the process of designing, applying, and evaluating teacher candidates' model-eliciting activities. This study was conducted in three stages in a multi-tiered teaching experiment. Firstly, 15 teacher candidates designed activities for Grade 7 students after they were trained on…

The purpose of this publication is to bring attention to some physics problems whose answers seem to be paradoxical and, at first glance, do not agree with a limiting case check. Solving a problem on the motion of a system consisting of two masses and a spring, it is natural to examine the answer by considering a case when a spring constant is…

In recent years, mathematical models of decision making, such as the diffusion model, have been endorsed in individual differences research. These models can disentangle different components of the decision process, like processing speed, speed-accuracy trade-offs, and duration of non-decisional processes. The diffusion model estimates individual…

The aim of this study is to investigate pre-service mathematics teachers' beliefs towards mathematics and modelling in mathematical modelling processes. To achieve this aim, a phenomenology design was utilized. The study was conducted with 30 elementary level pre-service mathematics teachers receiving mathematical modelling courses. A…

Student modeling is one of the most important processes in adaptive systems. Although learning is individual, a model can be created based on patterns in student behavior. Since a student model can be created for more than one student, the use of machine learning techniques in student modeling is increasing. Artificial neural networks (ANNs),…

This paper addresses two aspects of integrating mathematics education with engineering education that may address persistence of engineering majors (and STEM majors more broadly): an emphasis on modeling as a vehicle for more authentic learning activity (Niss et al. 2007), and the need for measures that can support academic units' efforts to…

Synthesis and diffusion of a pigment molecule can be simulated using deterministic equations in computer software. These lesson materials describe how tiger stripes emerge from manipulations in this code, and how students can engage in mathematical inquiry by exploring these reaction-diffusion equations.

The SIMIODE Challenge for Undergraduates in Differential Equation Modelling (SCUDEM) offers students the opportunity to improve their mathematical capacity, ability to think critically, and communication skills through researching, developing, and presenting on a differential equations model for a natural phenomenon. During the fall 2019 SCUDEM,…

Mathematical modeling is a critical component of the current K-12 mathematics, science, and technology and engineering (T&E) educational standards in the United States. However, mathematical modeling is often overlooked or underemphasized in integrative STEM lessons. This could be attributed to teachers' limited content and pedagogical…

A concern in Mathematics Education is the professional development of the teacher and to promote effective training programs. The literature provides principles guiding the design of such programs, which were considered for an instruction intended to strengthen the teacher's practice in relation to the development of mathematical skills. The…

The effective teaching and learning of mathematics through mathematical modeling and connecting mathematics to the real world has gained rapid growth at various educational levels all over the world. The growth in modeling practices in the United States of America (US) and the international community is the result of the development and…