Number line models provide a visual aid for students to examine the relationship of integers with each other and facilitate learning of integers and integer operations. Such models are typically used when students are asked real-life problems. This study employs a qualitative case study design to perform an in-depth analysis of how middle grade…

Perceptual judgments result from a dynamic process, but little is known about the dynamics of number-line estimation. A recent study proposed a computational model that combined a model of trial-to-trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model--a situation in which…

Perceptual judgments result from a dynamic process, but little is known about the dynamics of number-line estimation. A recent study proposed a computational model that combined a model of trial-to-trial changes with a model for the internal scaling of discrete numbers. Here, we tested a surprising prediction of the model--a situation in which…

This qualitative case study of emergent practices in a multi-paradigmatic field at one department in Norway explores how performance metrics in science intra-act with staff composition and resource allocation, potentially affecting paradigm trends. Inspired by agential realism, we discuss four key metrics as the material core of an assemblage…

This review covers the core concepts and design decisions of TensorFlow. TensorFlow, originally created by researchers at Google, is the most popular one among the plethora of deep learning libraries. In the field of deep learning, neural networks have achieved tremendous success and gained wide popularity in various areas. This family of models…

Numerical comparison is a primary measure of the acuity of children's approximate number system. Approximate number system acuity is associated with key developmental outcomes such as symbolic number skill, standardized test scores, and even employment outcomes (Halberda, Mazzocco, & Feigenson, 2008; Parsons & Bynner, 1997). We examined…

Two experiments examined whether concrete models support place value learning. In Experiment 1 (N = 149), 7-year-olds were trained with either a) symbols alone or b) symbols and base-10 blocks. Children in both groups showed significant growth overall, but there were specific effects favoring one training type over another. Symbols-only training…

Representations of numerical value have been assessed by using bounded (e.g., 0-1,000) and unbounded (e.g., 0-?) number-line tasks, with considerable debate regarding whether 1 or both tasks elicit unique cognitive strategies (e.g., addition or subtraction) and require unique cognitive models. To test this, we examined how well a mixed log-linear…

Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions…

This article reports a study of educators differentiating aspects of mathematical knowledge for teaching in preschool as part of a further-education programme. Eight Swedish preschool educators participated in focus group discussions about documentations from their own practice during a school year, to enhance their awareness of their mathematics…

Barth and Paladino (2011) argue that changes in numerical representations are better modeled by a power function whose exponent gradually rises to 1 than as a shift from a logarithmic to a linear representation of numerical magnitude. However, the fit of the power function to number line estimation data may simply stem from fitting noise generated…

In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful…

The intention of the present study is to know how the pupils can learn to make a group of ten to understand the idea of unitizing. The pupils were given a contextual problem "Counting the Beads" in order to promote their understanding about the idea of unitizing. The process of designing the problem was based on the 5 tenets of…

How do our mental representations of number change over development? The dominant view holds that children (and adults) possess multiple representations of number, and that age and experience lead to a shift from greater reliance upon logarithmically organized number representations to greater reliance upon more accurate, linear representations.…

This article reviews a particular computational modeling approach to the study of psychological development--that of constructive neural networks. This approach is applied to a variety of developmental domains and issues, including Piagetian tasks, shift learning, language acquisition, number comparison, habituation of visual attention, concept…