Educational fun items can be readily found and used to increase student motivation and learning. We illustrate resources and strategies for a specific piece of content: Simpson's paradox.

Differing research worldviews have typically resulted in interpretations at odds with one another. Yet, leveraging distinct perspectives can lead to novel interpretations and theoretical construction. Via an empirically grounded research commentary, we describe the value of such activity through the lens of previously reported findings. This…

The aim of mathematics education research is to develop comprehensive understandings of the problems of mathematics teaching and learning, and the ambition is, at least in the long run, to support the development of institutionalised teaching-learning practices. Looking back at the attempts to structure syllabi and other curricular materials and…

In the late 1800s and early 1900s, increases in metallurgic technology and better manufacturing methods made naval artillery a more powerful force. Guns could fire more powerful shells that could travel farther and hit a target with much greater accuracy. Torpedoes represented a major threat to even the most powerful of warships, forcing captains…

Ritual teaching, which provides students with ritual opportunities to learn, is common worldwide, notwithstanding extensive research calls for more reform-oriented teaching. Such resilience to change suggests that there are gains for ritual teaching. Therefore, in this study, we search for possible goals of ritual teaching. For this purpose, we…

In this paper, learning is conceptualized as a process of routinization of learners' actions. We begin by operationalizing the keyword "routine." Two categorizations of routines are then offered. First, we distinguish between "practical" and "discursive" routines, discuss the process of their historical…

Mistakes are a window into students' mathematical understanding. Taking the time to analyze mistakes can inform you of where students are in their thinking. They can also guide you with respect to how to proceed with instruction. Introduced here are two categories of mistakes: meaty mistakes and minor mistakes. Meaty mistakes demonstrate gaps in…

A method based on oblique projection is presented for construction of sundials. The derived formulas are classical, but usage of vectors and projections renders a coherent presentation rather than a number of special cases. The presented work is aimed to be useful for those taking a beginning module on vector algebra.

Over the years, we have noticed our students constructing proofs that commutativity is preserved by isomorphism that do not explicitly use the fact that the isomorphism is surjective. These proofs are typically valid otherwise. However, such proofs are invalid because they would prove the false claim that commutativity is preserved by any…

The purpose of this article is to contribute to the discussion of mathematics teacher knowledge, and the question of what makes it specialized. In the first part of the article, central orientations in conceptualizing mathematics teacher knowledge are identified and the more serious limitations of the grounds on which they stand are explicated. In…

Problem solving lies at the core of engineering and remains central in school mathematics. Word problems are a traditional instructional mechanism for learning how to apply mathematics to solving problems. Word problems are formulated so that a student can identify data relevant to the question asked and choose a set of mathematical operations…

Rational number knowledge is critical for mathematical literacy and academic success. However, despite considerable research efforts, rational numbers present perennial difficulties for a large number of learners. These difficulties have led some to posit that rational numbers are not a natural fit for human cognition. In this chapter, we…

The integration of technology in entrepreneurship arithmetic that uses realistic mathematic education as the basis into learning processes is instrumental in creating understanding and problem-solving abilities among students. However, until recently only a few technology-based learning media have been developed to accommodate the aforementioned…

Artificial intelligence (AI) shows increasing potential to improve mathematics instruction, yet integrative quantitative evidence currently is lacking on its overall effectiveness and factors influencing success. This systematic review and meta-analysis investigate the effectiveness of AI on improving mathematics performance in K-12 classrooms…

Project-based learning (PBL) is increasingly recognised as a transformative alternative to traditional, instructor-centred education, fostering positive student attitudes towards learning. However, public schools in Pakistan largely adhere to conventional teaching methods, contributing to poor mathematics achievement and negative student…