Mathematics is abstract for young children. One way to help children develop better understanding of core early mathematical concepts is by providing concrete learning experiences, thereby making mathematics more accessible to them. Additionally, children will choose to spend more time on subjects or activities they enjoy, which in turn leads to…

The practice assignments in a mathematics textbook or course can be arranged so that most of the problems relating to any particular concept are massed together in a single assignment, or these related problems can be distributed across many assignments--a format known as spaced practice. Here we report the results of two classroom experiments…

This paper presents the findings of an empirical research project, designed with a combination of qualitative and quantitative methodology. Our goal was to apply Wiener attribution theory with a mathematics-specific pedagogical focus as a lens for analysing reflections. Our database consists of the prospective teachers' reflections on…

Information and the information revolution have brought many changes to our lives. The most revolutionary is the unlimited access of most people to an incredible amount of information. Today we no longer must "keep important information and facts in our heads". With the right technology, we are always within reach. The new age also…

Within a single internet search, thousands of results occur when looking for a lesson or mathematics activity. However, the results are not all of good quality. In this article, the authors present a mathematics lesson planning protocol (MLP[superscript 2]) to help process the search results and offer experiences of teachers using the protocol.…

We use Taylor's formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subdivisions which are equally spaced. As a means for generating interesting examples of exact arc length calculations in calculus courses, we recall two large classes of…

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…

In this paper, we investigate leadership related to the instruction of lower division undergraduate courses at five university mathematics departments with strong calculus programs. We use social network analysis to identify patterns of influence on instruction, using the relations: advice seeking, instructional material sharing, discussion of…

This study investigated how teachers in China perceived the effects of online instruction on mathematics learning and examined the challenges they encountered when the country shifted to online instruction during the COVID-19 pandemic. We interviewed 152 mathematics teachers from 20 cities (municipalities) or provinces in China and adopted the…

In this study, we propose an integrated hierarchical model of computational estimation strategies (IHMCES), which can be used to organize a set of computational estimation strategies, used by a group of individuals, in strategy ranges. IHMCES can be used for the description of the repertoire, profile and flexibility of individuals regarding the…

Learning mathematics is a challenge in the current educational context. This is demonstrated by a high percentage of students who both fail to develop these numerical-type skills and have a low academic performance. This research performs a quasi-experiment to develop mathematical skills and knowledge. The sample consisted of 54 students (20…

This paper explores the potential of participatory action research to bring about significant changes in practice in a context in which more conventional approaches to research have had limited impact. It focuses on secondary mathematics classrooms where teaching approaches characterised by memorising and practising mathematical procedures, with…

"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 paper presents a study based on didactic engineering and the theory of didactical situations on the complexification of the Leonardo sequence, addressing its numbers in a two-dimensional way, with the insertion of the imaginary unit "i". This study is an excerpt from a masters' thesis research done in the postgraduate programme in…