In an interplay between the Fundamental Theorem of Arithmetic and topology, this paper presents material for a capstone seminar that expands on ideas from number theory, analysis, and linear algebra. It is designed to generate an immersive way of learning in which students discover new connections between familiar concepts, create definitions, and…

In this article, the authors focus on five instructional approaches with a strong evidence base for the teaching and learning of math: (a) plan, model, and practice: systematic and explicit instruction; (b) focus on the language of math; (c) use multiple representations, including number lines; (d) build fluency; and (e) provide word problem…

This activity provides students with opportunities to practice addition strategies and explore probability in this adaptation of the classic probability game Greedy Pig. To play, you will need a 6-sided dice, a number chart, and a brown counter to represent the mouse, and a yellow counter to represent the cheese. The game is suitable for two or…

Advancement of testing of mathematical problem-solving skills calls for open-ended, realistic tasks particularly susceptible to bias, compromising the score validity and fairness of tests. Informed by universal design principles, this study framed 360 prototype items developed for the "Problem-solving Measures Grades 6-8 Computer Adaptive…

In this short note I present an elementary proof of irrationality for the number "e," the base of the natural logarithm. It is simpler than other known proofs as it does not use comparisons with geometric series, nor Beukers' integrals, and it does not assume that "e" is a rational number from the beginning.

The small angle approximation sin[theta approximately theta] is central to all treatments of the simple pendulum as a harmonic oscillator and is typically asserted as a result that follows from calculus. Here, however, we show that the geometry of the pendulum "itself" offers a route to understanding the origin of the small angle…

Visual illusions provide a means of investigating the rules and principles through which approximate number representations are formed. Here, we investigated the developmental trajectory of an important numerical illusion--"the connectedness illusion," wherein connecting pairs of items with thin lines reduces perceived number without…

An important question is to know why the didactics of mathematics (DM) goes from being only teaching techniques to consolidate as a science and also to locate what kind of science it is. The objective of this article is, through a modern classification of sciences, such as the theory of categorial closure, to locate the DM. Likewise, a very brief…

This collection of artworks expresses the artist's profound passion for mathematics and life's complex balance. As a female mathematician, she uses artistic expression and intricate patterns to evoke mathematical beauty and feminine strength, celebrating the presence and resilience of women in mathematics.

Definitions are an integral aspect of mathematics. In particular, they form the backbone of deductive reasoning and facilitate precision in mathematical communication. However, when multiple non-equivalent definitions for the same term exist, their ability to serve these purposes can be called into question. While ambiguity can be productive, the…

This mathematics classroom based experimental study determined the relative effectiveness of formative assessment techniques on students' academic achievement in Mathematics. Factorial research design was adopted for the study involving 100 students from 2 co-educational secondary schools drawn through multistage sampling procedure. Mathematics…

This article provides teachers with a toolkit for assessing students in the context of data-based individualization (DBI) in mathematics. Assessing students is a critical component of DBI because it provides teachers with information about what they may need to modify in their instructional programs. In this article, we provide teachers with…

Mathematics coaches are often positioned as important mediators between district administrators and teachers regarding messages about ambitious and equitable instruction. Despite this, little research has sought to unpack the connection between what coaches learn at professional development and how they make their learning available to teachers.…

This study explored 54 preservice elementary teachers' identification and modification of mathematical tasks in raising cognitive demand and examined the features of their modified tasks. The study collected data using a three-phase activity: (a) identifying the level of cognitive demand of the given task, (b) modifying the low cognitive demand…

Identifying mathematically gifted students is an important objective in mathematics education. To describe skills typical of these students, researchers pose problems in several mathematical domains whose solutions require using different mathematical capacities, such as visualization, generalization, proof, creativity, etc. This paper presents an…