Taking into consideration that young children engage with mathematics outside of the preschool classroom, this study focuses on adults' awareness of numerical ideas raised by young children without and with adult involvement. Ninety adults in Israel, the majority of whom were parents or grandparents of children aged 3-6 years, participated in this…

This chapter focuses on the development of concepts that children draw on as they work toward understanding negative numbers. Framed from a conceptual change lens, I discuss different interpretations children have of minus signs, numerical order, numerical values, and addition and subtraction operations and how children draw on these varied…

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…

A growing body of evidence reveals the need for research on, and consideration for, children's and students' own--self-guided--spontaneous use of mathematical reasoning and knowledge in action. Spontaneous focusing on numerosity (SFON) and quantitative relations (SFOR) have been implicated as key components of mathematical development. In this…

Mathematics educators advocate for the use of models as an instructional practice that can potentially aid in building students' understanding of difficult topics. Integers and integer operations are historically problematic for students and are critically important in both arithmetic and the future study of algebra. In this chapter, I explore one…

This chapter identifies the ways in which 15 prospective teachers engage the strands of mathematical proficiency as they solve word problems involving integer addition and subtraction. The prospective teachers, through think-aloud interviews, demonstrated a strong focus on solving problems using procedures, which some did not explain and others…

This article sets out to evaluate the English Early Years Foundation Stage Goal for Numbers, in relation to research evidence. The Goal, which sets out to provide "a good foundation in mathematics", has greater breadth of content and higher levels of difficulty than previous versions. Research suggests that the additional expectations…

We report a randomised controlled trial evaluation of an intensive one-to-one numeracy programme--"Numbers Count"--which formed part of the previous government's numeracy policy intervention--"Every Child Counts." We rigorously designed and conducted the trial to CONSORT guidelines. We used a pragmatic waiting list design to…