This qualitative case study aims to address the ways that pre-service mathematics teachers (PSTs) used a rope in a daylong research meeting for cognitive development of children's understanding of counting numbers in Tanzanian elementary schools. Three university mathematics pre-service teachers volunteered participating in this study. Collective…

One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations.…

Being able to perform computational estimations efficiently is an important skill. Furthermore, computational estimation experiments are used to study general principles in strategy development. Rounding strategies are common in computational estimation. However, little is known about whether and when children use a mixed-rounding strategy (i.e.,…

Here, we assess whether quantity representations are influenced by the perceptual biases hypothesized to manifest in depressive individuals. In contrast to this clinical model, several prominent models of numerical cognition assume that quantity representations are abstract, and therefore are independent of the items that are being quantified. If…

Exact arithmetic abilities require symbolic numerals, which constitute a precise representation of quantities, such as the Arabic digits. Numerical thinking, however, also engages an intuitive non-linguistic number sense, the Approximate Number System (ANS). The ANS allows us to discriminate quantities, approximate arithmetic transformations, and…

This study was to determine how teacher candidates perceive zero. In this study, which used the case study method from qualitative research approaches, 264 teacher candidates constituted the participants. The participants consisted of 66 elementary mathematics, 58 special education, 82 primary school and 58 preschool teacher candidates. The…

In the target article, Xing and colleagues (2021) claimed that 6- to 8-year-olds who spontaneously referenced the midpoint of 0-100 number lines made more accurate magnitude estimates and scored higher on a standardized math achievement test than other children. Unlike previous studies, however, the authors found no relation between accuracy on…

While symbolic number processing is an important correlate for typical and low mathematics achievement, it remains to be determined whether children with high mathematics achievement also have excellent symbolic number processing abilities. We investigated this question in 64 children (aged 8 to 10), i.e., 32 children with persistent high…

Background: Children's numerical and arithmetic skills differ greatly already at an early age. Although research focusing on accounting for these large individual differences clearly demonstrates that mathematical performance draws upon several cognitive abilities, our knowledge concerning key abilities underlying mathematical skill development is…

Research on mathematical equivalence, and to some extent, on number structure in early grade mathematics, has shown that most students at primary and secondary levels understand these concepts instrumentally rather than relationally. The study reported in this paper uses a design research approach to explore both mathematical equivalence and…

The aim of this study is to investigate the effect of teaching integers by lesson study model on students' success and attitudes in mathematics. The research uses quantitative technique, "quasi-experimental design" with pre-test post-test control groups. The participants of the study are 62 sixth grade students and 4 teachers in three…

In this study, it was aimed to reveal the explanatory strategies that preservice teachers use in the process of explaining the concept of divisibility by zero. It was investigated how the concept of divisibility by zero, which can be used in expressing the case where the denominator is present in the definition of important concepts of the…

Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and…

The construction of the exponential function of a real exponent from the definition of the powers of a real number, and its properties, requires the notion of successions, a decimal approximation of a rational number, convergence, and limit of a function. In Argentina, this construction would exceed what could be taught at the secondary level, but…

Rational number knowledge is critical for mathematical literacy and academic success. However, despite considerable research efforts, rational numbers present perennial difficulties for a large number of learners. These difficulties have led some to posit that rational numbers are not a natural fit for human cognition. In this chapter, we…