On the surface, the number line may seem like a basic tool with obvious applications. However, using a number line is not always intuitive for students. Students may not recognize significant features such as the size of the unit, how units are represented by iterated equal lengths, or that the accumulation of iterated units is a magnitude 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…

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"…

Get a deeper understanding of teaching functions, 9-12 with our concise and comprehensive Go-To Guide. Based on "Developing Essential Understanding of Functions 9-12" and "Putting Essential Understanding of Functions into Practice 9-12," this summary distills the key concepts and ideas into a quick-reference guide that's…

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…

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…

The fact that the mathematics course is abstract, that it is not possible to associate it with daily life, and that it is impossible to concretize abstract expressions causes a prejudice against the this course and leads to a decrease in the academic achievements of students. It is seen that throughout history, various studies have been carried…

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…

Many education researchers have advocated grounding abstract mathematical and scientific concepts in students' lived experiences, environmental interactions, and perceptions. This dissertation explores the causal effects of various grounding strategies in instructional settings, specifically on the topic of statistical sampling. The first chapter…

The present review intends to show the current state of teaching quantum-related content, to analyze and compare its learning efficiency, and to give a systemized overview of quantum-educational activities in the last years. We focus on teaching and learning elements, their innovative tools, and process-oriented studies that are empirically…

To improve understanding of identities and inverses, and to provide a stronger foundation for future mathematics, Sandra Miles designed a two-part lesson that makes the relationship between identities and inverses explicit. This article illustrates Miles' teaching of the first part of the lesson, focused on addition and subtraction, and then gives…

This study investigated the impact of integrating design-technological activities on developing mathematical competencies among construction engineering students. A mixed methods approach compared curriculum delivery with and without digital tools across universities in Kazakhstan and Turkey. First, semi-structured interviews of faculty provided…

This article describes an inquiry-oriented real analysis classroom in which students were guided to discover mathematics for themselves. To support student inquiry, the framework of "five practices" from K-12 education was used. To illustrate this framework, two case examples are given from actual discussions that took place in this…

This paper reports on a teaching experiment on mathematical modelling in an upper secondary school class that investigates how the constructs of "model eliciting" and "emergent modelling" may be brought together to inform teaching and learning. A prominent role is covered by the process of task design, seen as a complex process…