This study shows how, in the initial training of mathematics teachers, it is possible to promote processes of abstraction and mathematisation through modelling a real situation with the support of auxiliary material to mediate understanding. By adapting elements of the theoretical and methodological framework called Abstraction in Context (AiC),…

Most children, when presented with the option between two drink items, will choose the one with "more." But what exactly do children consider when they recognize one object as having more than another? Is it the perceived surface area or volume of an object? Depending on children's cognitive development, the aspect of measurement on…

This research examined articles about models and modelling in the context of science education in Turkey by using content analysis method. Two specific academic databases; one of which was Dergipark, a platform including the academic journals published in Turkey, and Scholar Google were examined in detail so that totally 71 articles on models and…

We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however,…

Have you ever noticed trash collecting in streams or waterways? How does trash influence our environment, and what can be done to enact change? These are questions middle school students explored as the authors launched the Great Pacific Garbage Patch (GPGP) task. The Great Pacific Garbage Patch activity involves an urgent environmental issue that…

One promising approach for connecting undergraduate content coursework to secondary teaching is using teacher-created representations of practice. Using these representations effectively requires seeing teachers' use of mathematical knowledge in and for teaching (MKT). We argue that Rowland's (2013) Knowledge Quartet for MKT, in particular, the…

In this dissertation study, I report on six middle school students' construction and interpretation of graphs and associated dynamic situations. Constructing and interpreting graphs represents a critical moment in middle school mathematics due to its opportunity to provide a powerful foundation for learning. Nevertheless, researchers have…

To be literate in a society where the information shared online is often exploited, learners should be exposed to multiple aspects of contemporary predictive modeling. This article explores an activity in which grade 10 students learned how a famous AI algorithm (the Apriori algorithm) uses conditional probability to automate the process of…

The teaching of mathematical modeling is limited in P-12 classrooms. Little is known in regards to how to support teachers to successfully enact modeling activities. Teachers do not always appreciate the value of modeling activities in mathematics learning and often feel unprepared to implement modeling in their classrooms. Teachers often struggle…

This article presents a proposal to analyze student perceptions, through a mathematical model, using a previously designed and validated questionnaire. This approach attempts to describe and explain the different positions and interpretations which inhabit students regarding the notion of professorial quality. For this, a question that sums up the…

We present our experience with an open-ended lab activity that we designed for students with a Calculus 1 background. With the goal of learning how scientists study transport in streams, the students collected data on how a pulse of leaves travels down a nearby stream. Students who had little to no experience with data with two independent…

This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design theory of Realistic Mathematics Education. The sequence of modeling tasks and examples of student…

Understanding the nature and purpose of models, including mathematical models, is critical to enabling undergraduate chemistry students to use models to predict and explain phenomena. However, students often do not have systematic conceptions about different kinds of models. To gain a sense of how students understand different models in the…

Mathematical modeling has been recognized and highlighted in most standards and reports as an important concept to the teaching and learning of mathematics. The study investigated 208 PK-8 preservice teachers' (PSTs') familiarity and experiences with mathematical modeling. The study adopted a survey-design perspective to collect data from 10…

We present a simple activity based on the liquid-drop model which allows secondary school students to explore the uses of mathematical models and gain an intuitive understanding of the concept of binding energy, and in particular the significance of positive binding energy. Using spreadsheets provided as supplementary material, students can…