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 unsatisfactory academic performance of students in Nigerian secondary schools has been blamed on the quality of teachers, and professional development has been identified as a remedy. Hence, this study examined the effects of teacher collaboration as a form of professional development on students' academic achievement in mathematics. The…

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…

Drawing on a larger, cross-institutional study that examines equitable elementary mathematics education, this article reports initial findings related to tensions that emerged for preservice teachers (PSTs) related to trusting students with open-ended, challenging mathematics tasks. Data composed of 194 PSTs' written responses to a survey…

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…

The National Association for Gifted Children and The National Council of Teachers of Mathematics both call for problem posing. This article illustrates the strategies used during a series of three Three-Act Tasks to foster second grade students' abilities to problem pose. The students' problem posing improved across the three Three-Act Tasks and…

This study investigates the mediating roles of mathematics interest and perseverance on the effects of cognitive activation on mathematics achievement. We analysed data from a large-scale survey involving 25,969 eighth grade students from 86 schools in central China. The results show that (1) cognitive activation had a direct and positive effect…

There are many people whose actions and behaviours can influence the mindset and beliefs that students have toward learning math. In addition to other factors such as social media, which are beyond the scope of this article, parents, teachers, and peers all have different influences on children's mindsets, and often those people do not recognize…

Teacher training is a key element of any quality education system. In the field of mathematics education, identifying the factors that determine positive attitudes towards the teaching of this discipline in the context of initial teacher training is an inherent challenge. This work approaches the issue from a multivariate point of view through a…

The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even the way we interpret mathematical equations. Learning to think about physics with math instead of just calculating involves a number of general…