Engaging in the construction and interpretation of graphs is a complex process involving concerted activation of context-specific cognitive resources. As students engage in this process, they apply fine-grained, intuitive ideas to graphical patterns: graphical forms. Using data involving pairs of students constructing and interpreting graphs, we…

The Van Hiele model of geometric reasoning establishes five levels of development, from level 1 (visual) to level 5 (rigor). Despite the fact that this model has been deeply studied, there are few research works concerning the fifth level. However, there are some works that point out the interest of working with activities at this level to promote…

This study contributes to the growing body of research that highlights the usefulness of professional noticing of children's mathematical thinking for understanding the complexity and variability in teaching expertise. We explored the noticing expertise of 72 upper elementary school teachers engaged in multi-year professional development focused…

Despite the prominence of analogies in mathematics, little attention has been given to exploring students' processes of analogical reasoning, and even less research exists on revealing how students might be empowered to independently and productively reason by analogy to establish new (to them) mathematics. I argue that the lack of a cohesive…

Although augmented reality has become one of the most commonly used materials that support learning, especially in learning geometric concepts, it is avoided to be used in the lessons due to its complex structure. At that point, artificial intelligence working as a personal assistant in many fields can help us learn to produce our own model with…

Number line estimation has been found to be strongly related to mathematical reasoning concurrently and longitudinally. However, the relationship between number line estimation and mathematical reasoning might differ according to children's level of performance. This study investigates whether findings from previous studies that show number line…

This paper reports on a two-part investigation into how students think about and use summation (sigma) notation. During an instructional design experiment, two participating students struggled with this notation, but also reasoned about it in creative ways. This motivated a follow-up study in which we administered a free-response three-item survey…

Computational thinking is an essential ability for students in the 21st century. Therefore, this study described students' mathematical computational thinking process in terms of self-efficacy of eighth graders, consisting of 32 students. The applied instruments were self-efficacy questionnaires, computational thinking ability tests, and interview…

The aim of this study is to examine the effects of high school students' perceptions of computational thinking skills and perceptions of logical and mathematical intelligence on their programming self-efficacy. Descriptive survey model as a quantitative research design was used in the research. The data were collected face to face on a voluntary…

Learning standards such as the "Common Core State Standards for Mathematics" [CCSSM] (NGA Center & CCSSO, 2010) advocate that we develop students' algebraic thinking "beginning in kindergarten." Such a tall order requires innovative approaches that re-imagine what teaching and learning mathematics means for the elementary…

This paper presents the results of a study aimed at diagnosing how newly enrolled mathematics majors reason from a mathematical standpoint when they are required to perform inductive and deductive processes and validate or refute claims of a general nature. The theoretical framework underpinning this research comprises studies and investigations…

Determining preservice teachers' competence in proportional reasoning is a very complex task, and existing research methods do not provide effective tools in doing that. This study describes an interview structure and application of it in determining preservice teachers' competence in proportional reasoning. The interview structure consists of…

Mathematical modelling is endorsed as both a means and an end to learning mathematics. Despite its utility and inclusion as a curricular objective, one of many questions remaining about learners' modelling regards how modelers choose relevant situational attributes and express mathematical relationships in terms of them. Research on quantitative…

The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical…

Social interactions, including collaborative problem-solving situations, can trigger critical thinking skills. Giving questions that are not routine can trigger students' critical thinking skills in solving problems collaboratively. This research aims to develop non-routine mathematics problems that can be used to explore students' critical…