Rational numbers are represented by multiple notations: fractions, decimals, and percentages. Whereas previous studies have investigated affordances of these notations for representing different types of information (DeWolf et al., 2015; Tian et al., 2020), the present study investigated their affordances for solving different types of arithmetic…

Number-recognition tasks, such as the how-many task, involve set-to-word mapping, and number-creation tasks, such as the give-n task, entail word-to-set mapping. The present study involved comparing sixty 3-year-olds' performance on the two tasks with collections of one to three items over three time points about 3 weeks apart. Inconsistent with…

Informal Australian discussion suggests that calculators are still widely regarded as devices for calculation, consistent with their naming, and are rarely recognised as potentially helpful to support students learning mathematics. In this paper, Barry Kissane explores some of the ways in which modern calculators might support students learning…

This study reports the results of 4 experiments that addressed whether the domains of deictic time and number exert a cross-domain link. Such a link would be consistent with A Theory of Magnitude (i.e., ATOM). In contrast, no link between the two domains would support the conceptual metaphor theory (CMT), which assumes that each domain is only…

Cover, Copy, Compare (CCC) has been shown to be an effective intervention at improving single-digit multiplication fluency within the academic intervention literature. The application of the three-term contingency trial embedded within CCC provides the intervention with several key components of evidence-based interventions. Given that teachers…

Estimation supports the development of higher level mathematical thinking and reasoning; however, has received relatively little research attention. We examined whether making predictions influences the accuracy of numerosity estimates in elementary-aged children, and whether the amount of information available to the estimator determines the…

Background: People report negative attitudes towards fractions and percentages relative to whole numbers (WNs, Sidney, Thompson, Fitzsimmons, & Taber, 2021), and these attitudes may relate to an individual's interpretation of what experiences with these number types signify. Because fractions are challenging, individual differences related to…

There is growing interest in mathematics learning progressions in early childhood education. Counting is a skill usually developed early in life. The application of the counting principles in early childhood typically entails counting objects. This poses challenges for learning about zero. Indeed, the word "zero" is seldom used in the…

Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students' numerical magnitude understanding: number type…

Mathematical understanding in early childhood lays the foundation for children's later academic achievement, yet little is known about individual differences in U.S. early childhood educators' mathematics instruction in preschool classrooms. The present study explored the range of intentional mathematics instruction occurring in early childhood…

Integer arithmetic is difficult for students worldwide. Although students' integer thinking has frequently been studied, little is known about typical instructional practice for this difficult topic. Thus, to investigate what resources teachers use, we surveyed U.S. middle-grade teachers who teach negative numbers. About half the teachers said…

In this paper, we first focus on the sum of powers of the first n positive odd integers, T[subscript k](n)=1[superscript k]+3[superscript k]+5[superscript k]+...+(2n-1)[superscript k], and derive in an elementary way a polynomial formula for T[subscript k](n) in terms of a specific type of generalized Stirling numbers. Then we consider the sum of…

After making a lineup identification, eyewitnesses remember being more confident in their identification and having a better view of the initial crime if they are told they correctly identified the suspect compared to witnesses not given this feedback. The present studies investigated whether this effect of feedback occurs similarly when witnesses…

Is the natural number 7 rational? Is it complex? We argue that the answers to these questions relate to the ways numbers are taught. Commonly, a new kind of numbers is presented as an expansion of a previously familiar kind of numbers, which results in a nested image of the relations between number sets. In this article, we introduce an…

Numerosity perception has been studied for at least 150 years and its psychophysics have been well characterized by experimental work. However, the origins of many of its key properties remain obscure. For instance, people estimate the numerosity of small sets (up to four) much more rapidly and accurately than larger sets; people tend to…