This article aims to problematize the role of programming in mathematics education. Problematizing involves acknowledging a deeper complexity in the understanding of programming than originally perceived and questioning its assumed value in mathematics education. This approach entails identifying its underlying paradigmatic assumptions in relation…

Despite substantial research exploring multiplicative thinking and students' difficulty in the domain, the topic of multi-digit multiplication is under-researched. In this paper, I share a learning trajectory for multi-digit multiplication that combined social and cognitive perspectives of learning. Using Design Research methods and involving 45…

The development of the mathematical concept of the infinite, through the reflections that arise from personal notions and perceptions and the analysis of some ideas of Galileo and Cantor, invites us to investigate the relationship between intuition and formalization for the understanding of the said concept. This paper aims to observe and describe…

This paper aims at using a Use-Modify-Create approach to explore students' mathematical problem solving by means of computational thinking (CT) and programming activities. The data collection method is participant observation, in which the researcher also has the role as teacher, guiding the group activities. In our study, two groups of students…

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 construct of static and emergent shape thinking (Moore & Thompson, 2015) characterizes differences in students' reasoning about graphs. In our previous work with middle school students, we found that this construct may also be useful in characterizing students' reasoning about other representations such as simulations and tables. In this…

Mechanical reasoning is crucial for many engineering fields, yet undergraduate engineering students struggle to understand discipline-specific formalisms from their courses that model mechanical concepts. The current investigation observed undergraduate engineering students' speech during mechanical reasoning and the benefits of attending to…

One of the most significant objectives of the learning and teaching processes is to achieve meaningful learning for the individual; in line with this objective, educators are searching for various methods to accomplish meaningful learning and make it enduring. Following the present age, the sought-after and essential qualified human profile should…

This paper is a part of a larger research study that we are conducting to develop a framework consisting of the data-driven best practices around teaching and learning algebra in K-12 classrooms. The purpose of this paper is to develop a usable definition for algebra interventions for the second stage of screening within the larger study, which…

Angularity is a persistent quantity throughout K-12+ school mathematics, and many studies have shown that individuals often conflate angularity with linear attributes (e.g., the length of an angle model's sides). However, few studies have examined the productive ways in which students might reason about angularity while attending to linear…

This full paper concerns an exploratory study that investigates students' reasoning about torsion. Mechanical reasoning is critical to engineering applications and yet students still struggle to accurately predict, analyze, and model mechanical systems using formal symbolic notations (i.e., formalizations). To understand the nature of students'…

This short paper describes an early look at a project aimed at aiding students to understand various viewpoints through the advocacy of a museum visit. It aims to both improve historical reasoning and allow for more open-mindedness. This is done by combining a process of citizen curation with the use of de-polarization techniques. [For the…

Minimum Competency Assessment (MCA) is the latest assessment conducted nationally in Indonesia. MCA measures students' cognitive in literacy and numeracy. This study illustrates the difficulty of students in solving numeracy questions in the minimum competency assessment. This research is included in case study research with a qualitative…

There is emerging evidence that professional noticing is embodied. Yet, there is still a need to better under embodied noticing at a fundamental level, especially from the preservice teachers. This study used traditional and holographic video, along with eye-tracking technology, to examine how preservice teachers' physical act of looking interacts…

Thinking skills are instruments for meaningful learning and academic achievement and in relation, they are indispensable components of 21st century competencies. However, current Turkish policies do not define what thinking is and some inconsistencies regarding forms of thinking exist in different documents. Also, while teachers might not feel…