Incorporating open-ended real-world tasks enhances students' access to mathematical and real-life knowledge and maximizes learning experiences. This article examines how a secondary mathematics teacher used an open-ended problem on distributing pay raises to teach mathematical concepts and fairness to students. The teacher's actions exemplify…

This study investigates the interplay between student reasoning and instructional strategies in trigonometry education. A qualitative case study was conducted to examine how Grade 10 students employ various reasoning approaches -- deductive, inductive, abductive, analogical, and algorithmic -- when solving trigonometry problems. Each approach…

Multiple representations are widely recognized for their significant role in concept learning. This study aimed to investigate the multiple representation translation skills of high school students at different grade levels about the concept of one-dimensional motion. 239 9th, 10th, and 11th-grade students participated in the study using a…

In statistical inference, importance of sampling is recognized as one of its key concepts, which has allowed its incorporation internationally in different curricular guidelines and specifically in the Chilean curriculum, since the first notions of sampling are introduced in 7th Grade. This paper presents an analysis of the responses to an…

This study examines how joint exploration is established and maintained among students and the teacher in secondary mathematics classrooms. We use the theoretical perspective of positioning to conceptualize joint exploration as involving the negotiation and coordination among participants to position students with epistemic agency and authority.…

One popular advanced technology nowadays is smartphone. Smartphones allow various functions beyond the traditional function of mobile phones as communication devices. The technology in smartphones has potential applications in many areas including education. In this study, we report our research which aims to: (1) produce a smartphone app as media…

In this research report, the question of the role of the teacher in problem-solving contexts is addressed, particularly in relation to the development of mathematical concepts. Data extracts from a problem-solving session are used to draw out three sorts of teaching actions that aim to push forward the mathematics in the classroom. These teaching…

The main aim of this research was to measure 10th and 12th grade students' biological conceptual understanding and competences through their upper secondary school studies. Data collection started at the beginning of the upper secondary school biology studies in the 10th grade. The same students participated in this research when they were in the…

Identifying and expressing relations between quantities is a key aspect of understanding and using functions. We are aiming to understand the development of functions understanding throughout school years in Israel. A survey instrument was developed with teachers and given to 20 high and average achieving students from each of years 7-11 and to 10…

Senior secondary mathematics students who develop conceptual understanding that moves them beyond "rules without reasons" to connections between related concepts are in a strong place to tackle the more difficult mathematics application problems. Current research is examining how the use of challenging tasks at different levels of…

As part of curriculum changes in South Africa, an introductory programming language, Scratch, must first be taught before switching to the well-established teaching of Delphi. The nature of programming in Scratch is considerably different from that in Delphi. It was assumed that the teaching of Scratch as introductory programming language could…

The difficulty in observing, recording, and examining internal representations has been well documented (Goldin & Shteingold, 2001). However, the important role that these internal representations play in the learning and understanding of mathematical concepts has been noted (Yackel, 2000). This study sought to develop a framework for…

The present study investigated the underlying reasons for difficulties faced by students when they applied the concept of inertia across varying contexts. The participants of the study included five high school students. Data obtained from interviews were interpreted from the perspectives of the coordination class and epistemological framing…

The purpose of this study was to assess student knowledge of numeric, visual and algebraic representations. A definite gap between arithmetic and algebra has been documented in the research. The researchers' goal was to identify a link between the two. Using four "Guess My Number" problems, seventh and tenth grade students were asked to write…

This paper reports a cross-grade comparative study of Chinese precollege students' epistemological beliefs about physics by using the Colorado Learning Attitudes Survey about Sciences (CLASS). Our students of interest are middle and high schoolers taking traditional lecture-based physics as a mandatory science course each year from the 8th grade…