Sixty (35 girls and 25 boys) 9th-grade students' conceptual understanding of the number line was qualitatively assessed through verbal explanations and visual representations. The assessment included an open-ended question focused on students' number line descriptions and the explanations coalesced around six features: sequential ordering (i.e.,…

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…

Integer operations are typically introduced in sixth grade, but they are a consistent area of struggle among these students. This struggle also inhibits their understanding of algebraic computations involving positive and negative terms. In this article, the author provides introductory tasks and models for adding and subtracting integers that can…

Students' understanding of negative integers is an important aspect of learning mathematics as it is a requirement for learning broader mathematical concepts. The purpose of this research is to explore students' initial perceptions in understanding negative integers on a number line. This descriptive exploratory qualitative research was conducted…

Teachers can make number talks more ambitious and increase learning opportunities for students by debugging errors, promoting multi-student thinking, and orienting to make connections. This article describes the basic number talks routine and examines some common tendencies, such as "Serial Sharing." It concludes with a vignette to…

Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milestone in developing a concept of number. Researchers in early number development have endeavored to theorize its development. Here we critique two widely…

This paper focuses on the definitions and the mis-out and mis-in examples of rational numbers that four prospective elementary teachers presented while working on rational number assignments. The participants were first asked to respond, individually, to an Individual Rational Number Assignment, consisting of items aiming at detecting their…

Mastery of mathematics depends on the people's ability to manipulate and abstract values such as negative numbers. Knowledge of arithmetic principles does not necessarily generalize from positive number arithmetic to arithmetic involving negative numbers (Prather & Alibali, 2008, https://doi.org/10.1080/03640210701864147). In this study, we…

Leading on from a paper published in the previous edition of the "AMEJ" (Kissane, 2023), which looked at scientific calculators and irrational numbers, Barry Kissane now turns his attention to the attributes of modern calculators as environments for learning about rational numbers.

Email filters classify new messages as either spam or not spam based on word frequency, syntax, and metadata. A "classifier" is an algorithm that maps input data into categories based on distinguishing characteristics, or "features." Features can be raw data or attributes derived from that data. "Feature engineering"…

In this article, we direct attention to what becomes critical in teaching activities for toddlers (1-3-year-olds) to learn the meaning of numbers. One activity we thoroughly explore is interactive book reading, based on previous research indicating positive learning outcomes from this type of mathematical activity, as it has shown to…

This paper is part of a broader study which explores South African pre-service teachers' use of the jump strategy on the empty number line for enhancing their confidence to do and teach mental mathematics computation strategies. The focus of this paper is the use of micro-teaching in the form of video recordings by pre-service teachers. Forty…

As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…

This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…

Learning the meaning of number words is a lengthy and error-prone process. In this review, we highlight outstanding issues related to current accounts of children's acquisition of symbolic number knowledge. We maintain that, despite the ability to identify and label small numerical quantities, children do not understand initially that number words…