An important use of statistical models and modeling in education stems from the potential to involve students more deeply with conceptions of distribution, variation and center. As models are key to statistical thinking, introducing students to modeling early in their schooling will likely support the statistical thinking that underpins later,…

Children have limited exposure to statistical concepts and processes, yet researchers have highlighted multiple benefits of experiences in which they design and/or engage informally with statistical modelling. A study was conducted with a classroom in which students developed and utilised data-based models to respond to the inquiry question,…

The present study aimed to investigate the effects of geometry instruction activities conducted in nature based on modeling, game-based, and cooperative learning methods on achievement, mathematical motivation, and visual mathematical literacy perceptions of third-grade elementary school students. The present study is a quantitative study…

The aim of this paper is to show how engaging students in real-life mathematical situations can stimulate their mathematical creative thinking. We analyzed the mathematical modeling of two girls, aged 10 and 13 years, as they worked on an authentic task involving the selection of a track team. The girls displayed several modeling cycles that…

When speaking to young children, adults adapt their language to that of the child. In this article, we suggest that this child-directed speech (CDS) is the result of a transactional process of dynamic adaptation between the child and the adult. The study compares developmental trajectories of three children to those of the CDS of their caregivers.…

From Piaget to the present, traditional and dual-process theories have predicted improvement in reasoning from childhood to adulthood, and improvement has been observed. However, developmental reversals--that reasoning biases emerge with development--have also been observed in a growing list of paradigms. We explain how fuzzy-trace theory predicts…

Children (N = 157) 4 to 8 years old participated 1 time (single) or 4 times (repeated) in an interactive event. Across each condition, half were questioned a week later about the only or a specific occurrence of the event ("depth first") and then about what usually happens. Half were prompted in the reverse order ("breadth first"). Children with…

Although learning mathematics certainly depends upon accurate understanding of the facts of multiplication, it requires much more. This study examines the relationship between a meaningful understanding of arithmetic operations and the mastery of basic facts. The study began with a joke about a mistaken mathematical fact. The children appreciated…

This study focuses on assessing the contribution of ELL services to Spanish-speaking students' mathematics learning in elementary schools. ELL students tend to have lower average math achievement at school entry and throughout elementary school. The term "ELL services" encompasses English-as-a-second-language (ESL) programs, bilingual…

Teaching experiments with pairs of children have generated several hypotheses about students' construction of fractions. For example, Steffe (2004) hypothesized that robust conceptions of improper fractions depends on the development of a splitting operation. Results from teaching experiments that rely on scheme theory and Steffe's hierarchy of…

Mature representations of space and number are connected to one another in ways suggestive of a "mental number line", but this mapping could either be a cultural construction or a reflection of a more fundamental link between the domains of number and geometry. Using a manual bisection paradigm, we tested for number line representations in adults,…

Affect Control Theory (ACT; Heise 1979, 2007) states that people control social interactions by striving to maintain culturally shared feelings about the situation. The theory is based on mathematical models of language-based impression formation. In a laboratory experiment, we tested the predictive power of a new German-language ACT model with…

Aim: The purpose of this study was to determine if our previously developed muscle model could be used to predict forces of the quadriceps femoris and triceps surae muscles of children with spastic diplegic cerebral palsy (CP). Method: Twenty-two children with CP (12 males, 10 females; mean age 10y, SD 2y, range 7-13y; Gross Motor Function…

This experiment aimed to expand previous findings on the development of mental number representation. We tested the hypothesis that children's familiarity with numbers is directly reflected by the shape of their mental number line. This mental number line was expected to be linear as long as numbers lay within the range of numbers children were…

This study aimed to evaluate the impact of individual differences in working memory capacity on number transcoding. A recently proposed model, ADAPT (a developmental asemantic procedural transcoding model), accounts for the development of number transcoding from verbal form to Arabic form by two mechanisms: the learning of new production rules…