GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the "two square difference identity" expressed for the square, which is a flat polygon, made with different approaches.…

The present study aims to examine 8th grade students' proof writing and justification skills. The research was conducted using the document analysis method. The participants of the study consisted of 16 voluntary 8th grade students. The participants were determined according to the convenience sampling method. Data were collected with the…

This study lies within the field of early-age algebraic thinking and focuses on describing the functional thinking exhibited by six sixth-graders (11- to 12-year-olds) enrolled in a curricular enhancement program. To accomplish the goals of this research, the structures the students established and the representations they used to express the…

Generalization is considered to be an essential part of mathematical reasoning and proving, and it has many definitions in mathematics education research. Despite its centrality, teachers often have difficulty identifying and responding to generalization in students' work. In this study, we focus on preservice teacher's (PTs) ability to describe…

Tangent lines are often first introduced to students in geometry during the study of circles. The topic may be repeatedly reintroduced to students in different contexts throughout their schooling, and often each reintroduction is accompanied by a new, nonequivalent definition of tangent lines. In calculus, tangent lines are again reintroduced to…

Understanding fraction as a quantity has been identified as a key developmental understanding. In this study, students in Grades 5, 8, and 11 were asked to compare the areas of two halves of the same square--a rectangle and a right triangle. Findings from this study suggest that students who understand fraction as a quantity use reasoning related…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

Researchers point at the need to study the creative processes of students in problem solving, as these may indicate how to encourage creative problem solving. The present research attempts to study, based on the heuristic framework of Polya, pre-service teachers' flexibility processes when they solve a mathematical problem with technology. The…

The purpose of this study was to analyze the prompts that preservice secondary mathematics teachers used for the acquisition of mathematics knowledge in dynamic geometry environment tasks. The participants, four preservice secondary mathematics teachers who were enrolled in a computer-supported mathematics education course, designed a dynamic…

This study explores the progression from student justification to generalization in the course of example-based reasoning. Data was collected through group interviews with high school students who were working collaboratively on a task of determining connections between perimeter and area of tile shaped patterns. The task called for making and…

We developed generalizable affect detectors using 133,966 instances of 18 affective states collected from 69,174 students who interacted with an online math learning platform called Algebra Nation over the entire school year. To enable scalability and generalizability, we used generic interaction features (e.g., viewing a video, taking a quiz),…

This study aims to analyze how the Mathematics Teacher Candidates (MTCs) define the "prism" and "pyramid" concepts in geometry. The research was carried out in 2017-2018 academic year with 92 MTCs. This test consists of 3 open-ended questions that MTCs can answer conceptually. The first openended question was as "Define a…

The study reported in this article addresses the question of how professional development can increase teacher noticing of student thinking over time. The data come from five teachers' participation in a two-year professional development intervention that combined lesson study, video clubs, and animation discussions. The analysis focuses on…

Previous research has verified the benefits obtained when learners trace out worked examples with the index finger. Our study conducted two experiments to explore the reasons for this phenomenon and its generalizability. Experiment 1 compared the learning effects among tracing, non-tracing, and cueing methods. The cueing method was included to…

This article examines the development of professional knowledge in pre-service mathematics teachers. From the discussion of a task associated with the multiplication of consecutive integer numbers, generalization is recognized as a process that allows to explore, to explain, and to validate mathematical results, and as an essential ability to…