In this report, we present cases where students constructed new quantities through operating on quantities that does not fit the definitions of existing theories on quantitative operations. As a result, we identified five quantitative operators--operators that can be used on single qualities in order to transform the quantity to a new…

The purpose of this study is to gain understanding of how secondary teachers conceptualize the relationships between mathematical modeling and problem solving. Eight secondary teachers participated in semi-structured, think-aloud individual interviews. Some conceptualizations include (a) modeling and problem solving are two distinct processes; (b)…

This study elaborates on the pivotal roles of mathematical and statistical models in data-driven predictions in an integrated STEM context using the case of Year 4 students: (?) "a descriptive means" to describe the features of trends and variability of data and (?) "an explanatory means" to explain causal relationships behind…

The revised Australian curriculum presents a new emphasis in primary schools on the process of Mathematical Modelling. A modelling focus brings close attention to confidence and capability with a potentially new problem-solving process, associated language, and pedagogical processes. This paper presents a Year 4 classroom modelling experience that…

This research contributes to the need to identify and expand learning environments that encourage undergraduate students to develop collaborative work skills and apply their classroom knowledge to solve real-world problems. Using qualitative methods, we examine the effects of the interaction between two teams of students when solving a…

This article describes the results of an investigation based on a Models and Modeling Perspective [MMP]. We present the evolution of the models built by university students when solving a model development sequence designed to promote their learning of the exponential function. As a result, we observed that students' thinking was modified,…

Recently, abstracted quantitative structures (AQS), a construct from quantitative reasoning, has been offered as a means to conceptualize and study mathematization during mathematical modeling. Extending this theoretical work, we provide empirical evidence that an intervention targeting participants' AQS can assist in aligning modelers' models…

In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…

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…

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…

The context for this paper is the "Synthetic Training Environment Experiential Learning -- Readiness" (STEEL-R) project [1], which aims to estimate individual and team competence using data collected from synthetic, semi-synthetic, and live scenario-based training exercises. In STEEL-R, the "Generalized Intelligent Framework for…

In this theoretical paper we compare the Piagetian perspective on knowledge construction to mathematical model construction, with the aim to understand how mathematical modeling enables learning of mathematics and learning of science, as is often claimed. We do this by examining data through two lenses: (1) examining the role of cognitive conflict…

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…

Using data from teaching experiments and theories from quantitative reasoning, we built second-order accounts of students' mathematics with regards to how they conceived rate of change through operating on existing quantities. In this report, we explain three different ways STEM undergraduates structurally conceive rate of change as they…

There is growing recognition that mathematical modeling can be a lever for equity in elementary mathematics classrooms. This study focuses on the impact of a professional development program focused on culturally responsive mathematical modeling on 8 kindergarten through 2nd grade teachers' practices in modeling lessons. We use a project developed…