In this article, I argue that the common practice across many school mathematics curricula of using a variety of different representations of number may diminish the coherence of mathematics for students. Instead, I advocate prioritising a single representation of number (the number line) and applying this repeatedly across diverse content areas.…

This review covers the core concepts and design decisions of TensorFlow. TensorFlow, originally created by researchers at Google, is the most popular one among the plethora of deep learning libraries. In the field of deep learning, neural networks have achieved tremendous success and gained wide popularity in various areas. This family of models…

Representation is an important element for teaching and learning mathematics since utilization of multiple modes of representation would enhance teaching and learning mathematics. Representation is a sign or combination of signs, characters, diagram, objects, pictures, or graphs, which can be utilized in teaching and learning mathematics.…

Data rules schools and ignorance is far from bliss. From assessment results to questioning educational claims, there is a growing need to understand the numbers used in education. Education data blogger and teacher Richard Selfridge (aka Jack Marwood) unravels the complexities of dealing with educational data and explains statistics in an…

Adults with learning disabilities (LD) face educational and employment challenges and may also have other disabilities and health conditions. Little is known about these adults' numeracy skills and how they use numeracy at work or home. The article's objective was to investigate numeracy skills and skill use for U.S. adults with LD. The author…

The authors encourage consideration of the where mathematics learning takes place. They found that taking students outside engaged them with learning how to add and subtract integers and translate linear graphs.

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

Many existing methods of statistical inference and analysis rely heavily on the assumption that the data are normally distributed. However, the normality assumption is not fulfilled when dealing with data which does not contain negative values or are otherwise skewed--a common occurrence in diverse disciplines such as finance, economics, political…

The sample mean is sometimes depicted as a fulcrum placed under the Dot plot. We provide an alternative geometric visualization of the sample mean using the empirical cumulative distribution function or the cumulative histogram data.

This article reports on students' problem-solving approaches across three representations--number lines, coordinate planes, and function graphs--the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a "hierarchical representational…

To become scientifically literate, students need to interpret science concepts using numbers, text, and visuals (Lemke 2004). Scientists use multiple modes to communicate their ideas to each other and the public, including images, text, mathematical notations, symbols, diagrams, charts, and graphs. Several of the science and engineering practices…

This article aims to illustrate a process of making connections, not between mathematics and other activities, but within mathematics itself--between diverse parts of the subject. Novel connections are still possible in previously explored mathematics when the material happens to be unfamiliar, as may be the case for a learner at any career stage.…

Mrs. Fisher's class was learning about arithmetic functions by pretending to operate real-world "function machines" (Reeves 2006). Functions are a unifying mathematics topic, and a great deal of emphasis is placed on understanding them in prekindergarten through grade 12 (Kilpatrick and Izsák 2008). In its Algebra Content Standard, the…

WYTHOFF is played on a pair of nonnegative integers, (M, N). A move either subtracts a positive integer from precisely one of M or N such that the result remains nonnegative, or subtracts the same positive integer from both M and N such that the results remain nonnegative. The first player unable to move loses. RATWYT uses rational numbers…

The aim of this paper is to explore if English as a Foreign Language (EFL) learners' usage of an online workbook follows Benford's law, which predicts the frequency of leading digits in numbers describing natural phenomena. According to Benford (1938), one can predict the frequency distribution of leading digits in numbers describing natural…