This study was conducted to examine the effectiveness of proof tasks in the transition from conjecture to proof in Euclidean geometry on freshmen's proof schemes. In line with this aim, the proof schemes of the freshmen who performed conjecture-proof and theorem-proof tasks were compared. The freshmen were composed of 109 pre-service middle school…

Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after…

Background/purpose. Geometric reasoning is essential for students' cognitive development, yet middle school learners in Morocco face major difficulties in this area. This study investigates the challenges perceived by teachers and aims to identify effective pedagogical strategies to enhance students' geometric reasoning skills. Materials/methods.…

In this work, we show the results of a research with pre-service mathematics secondary teachers about their Van Hiele level regarding the proof in Geometry. We observe three different profiles whose characteristics are described. These descriptions allow us to foresee certain differences when carrying out proof teaching in secondary school. The…

This study aims to address the teaching of integrals in multivariable calculus concerning the role taken by geometry, specifically, geometrical content dealing with boundaries in integrals that appear as curves and surfaces in R[superscript 2] and R[superscript 3]. Adopting the framework of the Anthropological Theory of the Didactic, we approached…

In this article special sequences involving the Butterfly theorem are defined. The Butterfly theorem states that if M is the midpoint of a chord PQ of a circle, then following some definite instructions, it is possible to get two other points X and Y on PQ, such that M is also the midpoint of the segment XY. The convergence investigation of those…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

Understanding the concept of area requires an understanding of the relationship between geometry and multiplication. The multiplicative reasoning required to find the areas of regular figures is used in many courses in elementary mathematical education. This paper explores various methods in which multiplicative reasoning is incorporated into the…

This study investigates the use of GeoGebra, a Dynamic Geometry Software (DGS) for math learning in Virtual Reality (VR) using head-mounted displays. We conducted a study with n = 20 middle school students receiving a mathematics tutoring intervention over time in a VR environment. Using theories of embodied cognition and playful mathematics, this…

The purpose of this resource is to help math teachers unpack, understand, and implement the current math content and practice standards. This resource describes the progressions of learning within each course and provides content support, which includes broad ideas about effective instruction as well as practical instructional strategies. Math…

We conducted a multimedia survey experiment with a nationally representative sample (n = 405) of secondary geometry teachers. Participants were shown storyboard depictions of instructional episodes and asked to rate the appropriateness of the (hypothetical) teacher's actions using a Likert-like response format. We analyzed participants responses…

Fermat's principle states that a light ray refracted across different media will traverse the fastest path as the physics for Snell's law. A geometric proof of Fermat's principle will be demonstrated as an intuitive approach to learn high school geometry and physical optics. It will be proved explicitly by showing that all alternative paths need…

The investigation at scale of the tensions that teachers need to manage when deciding to follow recommendations for practice has been hampered by the problem of occurrence: The conditions in which those decisions could be made need to occur during an observation in order for observers to document how teachers handle them. Simulations have been…

Not-knowing is an underexplored concept defined as an individual's ability to be aware of what they do not know to plan and effectively face complex situations. This paper focuses on analyzing students' articulation of not-knowing while completing geometric reasoning tasks. Results of this study revealed that not-knowing is a more cognitively…

Eye-tracking (ET) method provides a promising channel for educational researchers to connect learning outcomes to cognitive processes. The main principle of ET is that our gaze and our focus of attention are connected. Due to the advent of digital technologies, eye tracking studies are increasingly growing in different fields and in mathematics…