Mathematical concepts have been a consensus goal for decades, yet there is little consensus on what is meant by the terms "mathematical concept" and "mathematical understanding." This article attempts to discuss these terms in a way that can be of practical use to teachers. Greater clarity on "mathematical concept"…

We discuss student conceptions of improper integrals and infinity in the context of a second-semester calculus course (in a three-course sequence). Our observations stem from a sequence of activities used in an online course over a three-day period. Throughout the enactment of these activities, students are challenged to develop conceptions of…

Beginning a mathematics lesson involving a challenging task with a carefully chosen preliminary experience is an effective means of activating student cognition. In this article, the authors highlight a variety of preliminary experiences, each with a different structure and form, all designed to support students to more successfully engage with…

Early understanding of base-10 concept has been shown to be associated with superior mathematical achievement among East Asian children. In addition to their base-10 structured number system, teacher support in kindergarten is also crucial to children's development of this complex mathematical concept. Therefore, this study examined how Japanese…

Math educators must engage students in deep learning and talk spanning shorter, medium, and longer time frames to offer both the structures and language so that secondary English learners can participate fully alongside their classmates. In this article, the authors present: (1) "structure and language" to facilitate full participation…

The purpose of this study is to implement an a-didactical activity relating to the acquisition of the triangle inequality, prepared within the framework of the "Didactic Situations Theory" (TDS), and to report the experiences of the students during the implementation process. The study employs a case study method based on a qualitative…

Cyclic voltammetry (CV) is the most popular electrochemical technique for the study of electrode processes. One of the reasons for its popularity is its adjustable timescale which can vary several orders of magnitude simply by varying the rate at which the potential is scanned. Changing the scan rate affects CV features including the current,…

This article aims to show some activities based on non-routine problems with different levels of difficulty and from different classes that are integrated into the curriculum, additionally two spaces were opened for students to interact with recreational mathematics activities with the purpose of providing opportunities to all students access the…

Traditional methods of teaching differentiation calculus usually involve lectures. Nevertheless, this process impedes students' thorough comprehension of concepts and their practical application by promoting dependence on memorisation and procedural learning. Numerous studies have also denoted that teaching experiments and technology can enhance…

English Learners benefit from small group sorting activities with clear structures to participate. Early in a lesson, students can sort to surface prior knowledge and develop categories. Later, sorting helps English Learners coordinate and connect multiple representations. As they extend understanding, English Learners can make new connections and…

Children often learn abstract mathematics concepts with concrete manipulatives. The current study compared different ways of using specific manipulatives -- base-ten blocks -- to support children's place value knowledge. Children (N = 112, M age = 6.88 years) engaged in place value learning activities in one of four randomly assigned conditions in…

This research explores two methods through which ten preservice math teachers develop an understanding of trigonometric values. Using the unit circle, preservice math teachers engage in knowledge-building activities such as paper folding and GeoGebra application. Grounded in Altman and Kidron's 2016 didactical design research, this study examines…

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K--8. Readers are provided with a strong mathematical background, downloadable copies…

Several studies have pointed out difficulties of various types encountered by students in both secondary and high schools to acquire the exact meaning of the integral and to master the ability to invest it correctly in different domains. This contribution attempts to explore the effectiveness of some cognitive activities engaged in teaching…

This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…