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 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 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,…

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"…

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 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…

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…

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.…

Instructional routines, like "Number Talks" and "Notice and Wonder," engage students in doing and then talking about their mathematical thinking. Number Talk routines are short mathematical discussions where students mentally solve and share the strategies they used to make sense of the problem. In comparison, the Notice and…

Pupils' ability to represent mathematical concepts in multiple ways is a central aspect of mathematical competence and communication. Thus, classroom instructions should be able to support learners in using multiple representations (MRs) to increase the quality and quantity of connections to a network of ideas. Given the importance of bansho…

This article describes an instructional sequence used with inservice secondary mathematics teachers as part of a graduate course. The instructional sequence focused on designing tasks using Interactive Geometry Software (IGS). This study answers a call for replication studies to investigate the use of an established instructional sequence. Results…

For students to develop adequate conceptual understanding about fractions, they require experiences that afford them opportunities to think flexibly about multiple interpretations of fractions. This article presents a sequence of lessons designed to offer such experiences for students in Years 3 and Year 4. The lessons adopt a challenging tasks…