The authors discuss the use of "real life" activities that are interesting to children in the teaching of measurement and number concepts. In this article, they present a series of lessons targeting volume and capacity that seamlessly incorporate genuine "real-life" experiences with practical mathematical applications. In…

In this paper, we explore the following research questions: How do first-grade students define even and odd numbers? What types of justifications do they use to support their generalizations using these definitions? We report the ways in which first-grade students define even and odd numbers and how they justify generalizations that use their…

On the lookout for and with a vested interest in Canadian mathematics education matters, this article is dedicated to hockey cards. More specifically, the statistics found on the back of hockey cards. The combination of taking a trip down memory lane, thrifting in British Columbia, traipsing around Toronto, and having coffee (one cream) at Tim…

Learning the concept of fractions is among the most challenging topics in school mathematics. One of the main sources of difficulties in learning fractions is related to "natural number bias" (Van Hoof, Verschaffel & Van Dooren, 2015). Applying properties of the natural numbers incorrectly in situations involving rational numbers can…

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…

The issue of mathematical knowledge in teaching has been widely discussed over the years. In this study, we carried out a systematic review of the literature with the aim of understanding, quantitatively and qualitatively, the studies developed related to the mathematical knowledge necessary for the teaching of Mathematics, with a focus on Numbers…

Assessing and monitoring the mathematics progress of students is a key role for teachers. It is important for assessment tools to identify students who are not yet thriving and provide guidance for teachers about how to support these students. In our study, teachers assessed 396 Grade 1 students midway through the school year using the Mathematics…

The decomposition of numbers when solving subtraction tasks is regarded as more powerful than counting-based strategies. Still, many students fail to solve subtraction tasks despite using decomposition. To shed light upon this issue, we take a variation theoretical perspective (Marton, 2015) seeing learning as a function of discerning critical…

Metacognitive monitoring, recognizing when one is accurate or not, is important because judgments of one's performance or knowledge often relate to control decisions, such as help seeking. Unfortunately, children and adults struggle to accurately monitor their performance during number-magnitude estimation. People's accuracy in estimating number…

Number books are an effective tool to increase math talk and promote children's mathematical thinking, but little is known about book genre effects. How do different types of number books impact mathematical input? This study examined whether book genre affects the amount and types of teachers' math talk. Using a within-subjects design, we asked…

Number line estimation has been found to be strongly related to mathematical reasoning concurrently and longitudinally. However, the relationship between number line estimation and mathematical reasoning might differ according to children's level of performance. This study investigates whether findings from previous studies that show number line…

Number sense is fundamental to the development of numerical problem-solving skills. In early childhood, children establish associations between non-symbolic (e.g., a set of dots) and symbolic (e.g., Arabic numerals) representations of quantity. The developmental estrangement theory proposes that the relationship between non-symbolic and symbolic…

This study evaluates the efficacy of a physically-active number learning game for young preschoolers. The intervention adapts Ramani and Siegler's (Child Develop 79(2):375-394, 2008) successful The Great Race by modifying the mode of play from seated at a table to jumping with two feet on a large game mat. 75 children (mean age: 46 months) in the…

How do children construct a concept of natural numbers? Past research addressing this question has mainly focused on understanding how children come to acquire the cardinality principle. However, at that point children already understand the first number words and have a rudimentary natural number concept in place. The question therefore remains;…

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…