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…

Units coordination, defined by Steffe (1992) as the mental distribution of one composite unit (i.e., a unit of units) "over the elements of another composite unit" (p. 264) is a powerful tool for modeling students' mathematical thinking in the context of whole number and fractional reasoning. This paper proposes extending the idea of a…

In order to teach Computational Thinking (CT) skills to young students, Block-Based Programming Environments (BBPEs) are integrated into secondary school computer science (CS) education curricula. As a CT skill, abstraction is one of the prominent skills, which is difficult to enhance and measure. Researchers developed some scales for measuring…

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…

Sampling distributions are fundamental for statistical inference, yet their abstract nature poses challenges for students. This research investigates the development of high school students' conceptions of sampling distribution through informal significance tests with the aid of digital technology. The study focuses on how technological tools…

Mathematics education often grapples with the challenge of teaching abstract mathematical concepts, particularly those existing in 3D space. Visualizing, manipulating, and comprehending these abstract objects can be a formidable task for learners. While 3D printing technology has found applications in various fields, its utilization in mathematics…

This paper focuses on the analysis of Bebras Challenge tasks to find Informatics tasks that develop abstract thinking. Our study seeks to find which Bebras tasks develop abstraction and in what way. We analysed hundreds of tasks from the Czech contest to identify those tasks requiring participants to abstract directly or use abstract structures.…

This study explores learner engagement with Advanced Computational Thinking (ACT) in the New Zealand digital curriculum. "Advanced" in ACT refers to an expansive, transdisciplinary, and future-looking understanding of computational thinking (CT). ACT promotes CT beyond narrow modes of problem-solving (abstraction, algorithmic thinking,…

The aim of this study is to develop a self-efficacy measuring tool that can predict the computational thinking skill that is seen as one of the 21st century's skills. According to literature review, an item pool was established and expert opinion was consulted for the created item pool. The study group of this study consists of 319 students…

Simulation and modeling activities, a key point of computational thinking, are currently not being integrated into the science classroom. This paper describes a new visual programming tool entitled the Simulation Creation Toolkit. The Simulation Creation Toolkit is a high level pattern-based phenomenological approach to bringing rapid simulation…

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

In classrooms today, teachers continue to strive to enhance student knowledge and application by designing learning environments which create experiences for students to interact collaboratively, solve problems, think critically, and learn by doing. Research has indicated that teacher knowledge of the experiential learning cycle has become…

Based on insights into the nature of vocational mathematical knowledge, we designed a computer tool with which students in laboratory schools at senior secondary vocational school level could develop a better proficiency in the proportional reasoning involved in dilution. We did so because we had identified computations of concentrations of…

This paper addresses how secondary students might reason about amounts of change in covarying quantities. Two empirically based forms of covariational reasoning are distinguished. The first form-- reasoning about quantities as varying simultaneously and independently--supports tandem comparison of amounts of change. The second form--coordination…

Computational thinking aims to outline fundamental skills from computer science that everyone should learn. As currently defined, with help from the National Science Foundation (NSF), these skills include problem formulation, logically organizing data, automating solutions through algorithmic thinking, and representing data through abstraction.…