In this article, we investigated how a class engaged in whole-class discussions of modeling solutions, across two different types of modeling tasks: a Model Eliciting Activity (MEA) and a Three-Act Task. We analyzed whole-class discourse as small groups presented and responded to each other's solutions to a MEA and a Three-Act Task. We have also…

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…

There exist many studies on modeling competencies and their promotion; however, there is a need to investigate what modeling competencies are and how they vary in lower and higher-achieving groups of students in mathematics within the current modeling literature domain. This study examined how mathematical modeling competencies were displayed in…

This study explored how students develop meaning of functions by building on their understanding of expressions and equations. A teaching experiment using design research was conducted in a sixth-grade classroom. The data was analyzed using a grounded theory approach to provide explanations about why events occurred within this teaching episode…

This study aimed to reveal mathematical modeling processes and difficulties encountered in model-eliciting activities (MEAs) of 8thgrade students in a STEM education setting. This qualitative research is a case study conducted at a public school located in the central districts of a large province in the Mediterranean Region. The participants of…

We explored the mediating role of prior knowledge on the relation between intelligence and learning proportional reasoning. What students gain from formal instruction may depend on their intelligence, as well as on prior encounters with proportional concepts. We investigated whether a basic curriculum unit on the concept of density promoted…

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 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…

The aim of this study is to investigate how an augmented reality mobile math trails program can provide opportunities for students to engage in meaningful mathematical modelling activities. An explorative research design was conducted involving two mathematics teachers and 30 eight grades in Semarang, Indonesia. An Augmented Reality Mobile Math…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

The purpose of this study was to introduce a rubric named "Rubric for the Assessment of Modeling Skills" for assessing cognitive modeling skills and explaining the rubric's development process. The dimensions of the rubric are understanding the problem, simplifying, mathematizing, working mathematically, interpreting and validating.…

This study aims to produce a learning trajectory using the mathematical modeling in helping students to understand the concept of algebraic operations. Therefore, the design research was chosen to meet the research aims and to give in formulating and developing local instructional theory in learning algebraic operations. Learning trajectory…

In this study, we investigated how elementary pre-service teachers (PSTs) perceive using representations in teaching mathematics and what fractional representations (e.g., manipulatives or models) they suggest to guide students' incorrect use of representations in learning fractions. A written questionnaire was administrated to 151 PSTs at a large…

Forming part of a wider research study, the current study investigated prospective middle school mathematics teachers' ways of covariational reasoning on tasks involving simultaneously changing quantities. As the introductory theme of a larger unit on derivative, a model development sequence on covariational reasoning was designed and experimented…