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…

Our mental representation of the infinite has received little research attention in cognitive psychology. In countably infinite sets, the infinity symbol (8) is presumed to be perceived as larger than any finite natural number. The present study sought to explore if the infinity symbol is processed as "larger than" natural numbers, and,…

This paper reports on an experiment involving 108 sixth-grade French students in which the history of Chinese numeration was used in mathematics education. The aim of this study is to evaluate the relevance of using ancient number systems in mathematics education, which is common in French textbooks. In the experiment a pre-test with usual…

Mastery of the cardinality principle (CP) is foundational for children's mathematical development. Children's age and subitizing and counting skills contribute to their CP acquisition. This study aimed to investigate the effectiveness of different types of instruction for supporting 3-4-year-olds' CP development and its interplay with child…

This paper makes a proposal, from the perspective of a research mathematician interested in mathematics education, for broadening and deepening whole number arithmetic instruction, to make it more relevant for the twenty-first century, in particular, to enable students to deal with large numbers, arguably an essential skill for modern citizenship.…

Understanding negative numbers can be challenging for many students, as these concepts may seem less tangible than counting objects, which are commonly represented by positive numbers. In addition, the multiplication of two negative numbers resulting in a positive might appear inconsistent and puzzling to young learners who are used to seeing the…

The Numeracy Kit for Kindergarten 5-Year-Olds (NyKK-5) is a tool to support kindergarten teachers' numeracy practices. Based on a pedagogy of enactment, the NyKK-5 was designed to simulate the types of in-class supports that have been identified as critical elements of effective mathematics professional development (PD). Two groups of teachers…

In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes,…

Mathematics education researchers have long pursued--and many still pursue--an ideal instructional model for operations on integers. In this chapter, I argue that such a pursuit may be futile. Additionally, I highlight that ideas of relativity have been overlooked; and, I contend that current uses of translation within current integer…

In this work, recurrent and linear sequences are studied, exploring the teaching of these numbers with the aid of a computational resource, known as Google Colab. Initially, a brief historical exploration inherent to these sequences is carried out, as well as the construction of the characteristic equation of each one. Thus, their respective roots…

Developing a positive relationship with mathematics in early elementary is vital for success in future mathematics education. Students who do not develop an understanding of mathematical number sense in early grade levels struggle to make connections in later courses. Mathematical discourse sessions, specifically Number Talks, encourage students…

In this paper, dialogue among a group of adult women with basic adult education is examined. Women read books of mathematics in the context of a "dialogic mathematics gathering" (DMG). There is limited evidence in research on how adults develop their 'numerical understanding'. The objective of this study is to analyze how adults engage…

Many students face difficulties with fractions. Research in mathematics education and cognitive psychology aims at understanding where and why students struggle with fractions and how to make teaching of fractions more effective. Additionally, neuroscience research is beginning to explore how the human brain processes fractions. Yet, attempts to…

Number Talks, created in the early 1990s by Ruth Parker and Kathy Richardson, have gained popularity in the mathematics education community over the past decade with the publication of the book series "Number Talks" (Parrish, 2010, 2014), and especially since the publication of "Making Number Talks Matter" (Humphreys &…

Many studies have shown the difficulties of learning and teaching the decimal number system for whole numbers. In the case of numbers bigger than one hundred, complexity is partly due to the multitude of possible relationships between units. This study was aimed to develop conditions of a resource which can help teachers to enhance their teaching…