Recent educational studies in mathematics seek to justify a thesis that there is a conflict between students' intuitions regarding infinity and the standard theory of infinite numbers. On the contrary, we argue that students' intuitions do not match but to Cantor's theory, not to any theory of infinity. To this end, we sketch ways of measuring…

Geometry, calculus and in particular integrals, are too often seen by young students as technical tools with no link to the reality. This fact generates a loss of interest in students with a consequent removal of motivation in the study of such topics and more widely in pursuing scientific curricula. With this note we put to the fore a simple…

This article presents ways to explore mathematical concepts using Catan, a popular board game. After a brief overview of game play, we explore considerations with many potential entry points for mathematical modeling, such as which resource is the best, which resources will be rare or plentiful, where to build, and risk assessment.

This paper outlines the development and implementation of a ten-week micro-curriculum, "Booked on Math," designed to introduce preschool children to foundational mathematics concepts through interactive read-alouds. The "Booked on Math" curricula includes ten book readings and associated inquiry-based lesson plans. "Booked…

This study aims to investigate and compare mathematics teachers' knowledge of pedagogical content, knowledge of students' understanding and knowledge of instructional strategies, subcomponents of pedagogical content knowledge, student errors in the relationship between perimeter and areas in rectangles, squares, and parallelograms. 10…

The aim of this paper is to narrate a significant part of the experience of a professor over several semesters teaching fundamental ideas of the "Theory of Calculus." The narrative explains how his didactic and mathematical mentality evolved as he witnessed students' conceptual difficulties, as they were confronted with situations that…

"Productive Struggle" refers to a strategy that gives students an opportunity to increase their background mathematical knowledge. Productive Struggle helps students connect key concepts, determine how and where an error occurs, and supports students in figuring out how to use their own thinking and reasoning skills to correct an error.…

The aim of this study is to identify the basic components of the mathematical proof process in abstract algebra and to organize the proof process into phases with the help of these basic components. A basic component form was prepared by arranging a draft basic component form, which was created as a result of a document analysis in accordance with…

This study examined the learning of Pi (p) numbers in elementary school mathematics. This research was conducted by employing case study method containing a single case concerning the Pi (p) numbers. A total of 432 preservice teachers participated in the study from the academic year of 2019-2020. This research employed observation, interview, and…

We analyzed the written answers and explanations by 26 Brazilian high-school students who attempted to solve double and multiple proportionality problems using the cross-product algorithm. We focused on students' awareness of the scalar and functional relations among the quantities described in verbal problems, an aspect that has been part of…

This article discusses algebraic thinking regarding positive integers and rational numbers when students, 6 to 9 years old in multilingual classrooms, are engaged in an algebraic learning activity proposed by the El'konin and Davydov curriculum. The main results of this study indicate that young, newly arrived students, through tool-mediated joint…

The ability to understand mathematics is a faculty crucial to be possessed by pre-service teachers who will enter into the education sphere. It is one of the professional competencies essential for teachers since satisfactory lessons' delivery engenders more comprehensible instruction in teachers' students. Qualitative research employs a…

Current recommendations for school mathematics include teaching algebra as a K-12 content stranding beginning in the elementary-school grades. The focus of this study was on preservice elementary mathematics teachers' knowledge of algebra content in the intended curriculum for K-8 mathematics. In the Common Core State Standards for Mathematics…

This study is situated at the confluence of three calls for research within mathematics education: 1) work using novel approaches for studying students' understanding of nonlinear meanings of multiplication; 2) work using discrete mathematics to explore social issues related to equity; and 3) work at the intersection of mathematical learning and…

Introductory group theory provides the foundational course on algebraic structures. Yet, we know little about students' underlying conceptual understandings. In this paper, I introduce the Group Theory Concept Assessment (GTCA), a measure created for the purpose of conducting large-scale studies of student conceptual understanding in group theory.…