Previous research has highlighted the importance of social relationships in mathematical group work while working on modelling activities. This study analyses the interaction of sixth-grade students in Primary Education (11 to 12 years old) carrying out a modelling task in groups with a Fermi problem used as the modelling activity. The focus of…

A growing consensus holds that preservice K-8 teachers (PSTs) need to experience the modeling process as learners to understand it and envision teaching modeling in their future classrooms. We examine this recommendation by exploring how PSTs construct models and how collaborative learning practices influence them in revising and refining their…

The variational thinking of high school students based on mathematical connections was analyzed through a laboratory on linear functions. This qualitative research based on design was developed in three phases: diagnostic test, implementation of the mathematics laboratory and final test, with students from a public institution in Barranquilla,…

Although culturally responsive mathematics teaching is important, post-secondary education for preservice teachers (PTs) does not typically lead to learning opportunities for them to use mathematics to recognize the roles of social agents. To address this issue, we created a culturally responsive mathematical modeling task in which we invited PTs…

Mathematization is a critical competency in the modelling process. This study aims to elicit prospective mathematics teachers' mathematizing through the analysis of their solution approaches to a modelling problem related to the bales of straw. This study was conducted with 75 fourth-year prospective mathematics teachers (PMTs) enrolled in a…

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 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…

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…

In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the…

As a first step toward automatic feedback based on students' strategies for solving histogram tasks we investigated how strategy recognition can be automated based on students' gazes. A previous study showed how students' task-specific strategies can be inferred from their gazes. The research question addressed in the present article is how data…

We present here the lessons learned by iteratively designing a tutorial for first-year university students using computer programming to work with mathematical models. Alternating between design and implementation, we used video-taped task interviews and classroom observations to ensure that the design promoted student understanding. The final…

Literature typically describes mathematization, the process of transforming a real-world situation into a mathematical model, in terms of desirable actions and behaviors students exhibit. We attended to STEM undergraduate students' quantitative reasoning as they derived equations. Analysis of the meanings they held for arithmetic operations (+, -,…

This study adopts a holistic single-case design to explain the task design processes of mathematics student teachers (MSTs) regarding History, Theory, Technology, and Modeling (HTTM). A criterion sampling method was used to select nine MSTs who had successfully completed "algorithms and programming" course. Video analyses, written answer…

The term speed-accuracy tradeoff is used when an increase in response speed comes at the expense of response accuracy. Although originally a concept from experimental psychology, the speed-accuracy tradeoff has been a topic in psychological assessment, too. In the first part of the manuscript, we discuss motivational factors that may be…

In linear programming, many students find it difficult to translate a verbal description of a problem into a valid mathematical model. To better understand this, we examine the existing characteristics of college engineering students' errors across linear programming (LP) problems. We examined textbooks to identify the types of problems typically…