This paper details an integrated inquiry-based mathematics and science method course for preservice teachers designed around STEM problem-based learning. It documents how problem-based learning (PBL) activities supported PSTs' envisioning of equitable approaches for diverse children. The overarching research question was: "How did preservice…

The present study aimed to describe teachers' instructional flows when implementing a mathematical problem-posing task using scriptwriting technique. With matchsticks, a growing pattern that increases by a constant unit was created and presented to the teachers as a problem-posing situation. We analyzed the instructional flows in 50 scripts,…

This report details a set of three tasks used in an exploratory study of pre-service teachers' (PSTs) experiences of task design for the mathematics classroom. The three tasks, which I call the "Orange Dot Tasks," were constructed in Desmos, a dynamic geometry environment (DGE), and participants engaged each task through manipulating…

The aim of this article is to buid a Guide to the Analysis of Probability Textbook Lessons for secondary education (students aged 12-14), using the framework of Didactic Suitability. The facets, components and indicators of the didactic suitability construct are applied to categorize and organize didactic-mathematical knowledge on teaching and…

This study aims (1) to develop an instructional model to enhance mathematical literacy for secondary students and (2) to examine the effects of using this instructional model. The sample group consisted of students from Lampabpla Wittayakarn School, under the jurisdiction of the Surin Secondary Educational Service Area Office in Thailand by using…

This article reports on the design and implementation of a didactic sequence in the frame of a design-based research study. The research aim is to test the hypothesis that affordances of dynamic geometry may support students' awareness of logical relationships between geometrical properties of constructed figures. We elaborate on the task design…

Mathematical concepts have been a consensus goal for decades, yet there is little consensus on what is meant by the terms "mathematical concept" and "mathematical understanding." This article attempts to discuss these terms in a way that can be of practical use to teachers. Greater clarity on "mathematical concept"…

Mathematical writing in school is difficult to teach. Reasons include that it is a domain in which there are rules for some parts of the writing like for example mathematical notation while others must be negotiated locally in the classroom. Writing is also seldom separated from the process of solving mathematical problems, creating a situation…

In this theoretical paper, I use an empirically based example to illustrate particular design features of the Learning Through Activity (LTA) design framework and examine the impact of particular design principles. The LTA design framework is based on our elaboration of Piaget's construct of reflective abstraction. The example discussed here,…

Multiple representations can enhance students' understanding of mathematical concepts and complex information but can also pose well-documented challenges for students. Whereas instructional designs have been optimized to support students' "learning" with multiple representations, little is known about supportive "teaching"…

This study aims to identify teachers' selection/adoption of valuing pedagogy (VP) to implement an affect-focused mathematics teaching design with technological support. Valuing pedagogy is defined as teaching methods to address educational values and operationally defined as perceived, implemented, and received curricula, manifested by teacher…

This paper reports on a key representation, a triple number line, designed as part of the first author's doctoral study. The study sought ways to represent multiple constructs of fractions in the context of merging music and mathematics to support learners' understanding of fractions. A problem scenario was designed guided by Realistic Mathematics…

Designing and implementing purposefully developed tasks have been linked to students' understanding of mathematical topics. We report on design principles and intentions that guided the development of "inquiry-oriented tasks." Through a qualitative analysis of the tasks, we identified seven themes that encapsulated these design…

Mathematical abstraction constitutes the foundational cornerstone for the establishment and evolution of mathematical disciplines, serving as the pathway through which mathematical concepts emerge. As one of the information technologies widely applied in mathematics education, the Dynamic Mathematics Systems (DMS) have been found to have a…

Climate change is a complex issue that requires collective actions from various disciplines, including educating future generations about sustainability. Some countries such as Indonesia and Australia have included sustainability into their school curricula, which require teachers to design and implement tasks related to a sustainability issue.…