This research investigates the question of what growth, if any, is shown by teachers in identifying the components of children's reasoning using an upper and lower bounds argument for a fraction task. Specifically, it reports on assessment outcomes from design-based research in teacher education that measures teachers' identification of children's…

Upper primary school students' difficulties with decimal place value are widely recognised due largely to the availability of assessment tools that accurately identify students' misconceptions in this domain. Yet, many students' decimal difficulties seem to stem from a lack of understanding of whole number place value for which there are few, if…

Whether human infants spontaneously represent number remains contentious. Clearfield & Mix (1999) and Feigenson, Carey & Spelke (2002) put forth evidence that when presented with small sets of 1-3 items infants may preferentially attend to continuous properties of stimuli rather than to number, and these results have been interpreted as evidence…

Two types of calculation processes have been distinguished in the literature: approximate processes are supposed to rely heavily on the non-verbal quantity system, whereas exact processes are assumed to crucially involve the verbal system. These two calculation processes were commonly distinguished by manipulation of two factors in addition…

Eight six-year old German children with development disabilities regarding such number competencies as have been demonstrated to be among the most relevant precursor skills for the acquisition of elementary mathematics received intensive training with the program "Mengen, zählen, Zahlen" ["quantities, counting, numbers"] (MZZ,…

The purpose of this study was to investigate the effect of using computer games in teaching mathematics on developing the number sense of fourth grade students. To achieve this purpose a study sample of (81) students was selected from the fourth grade. This sample was divided into two groups. One group was randomly chosen to be the experimental…

We examined the role of executive attention, which encompasses the common aspects of executive function and executive working memory, in children's acquisition of two aspects of mathematical skill: (a) knowledge of the number system (e.g., place value) and of arithmetic procedures (e.g., multi-digit addition) and (b) arithmetic fluency (i.e.,…

The purpose of this study was to determine whether multiple-choice and constructed-response items assessed prospective secondary mathematics teachers' understanding of the concept of function. The conceptual framework for the study was the Dreyfus and Eisenberg (1982) Function Block. The theoretical framework was Sierpinska's (1992, 1994)…

The purpose of this study was to examine the effects on four-year-olds' knowledge of mathematics by introducing professional development and center-based mathematics activities around four mathematical domains to early educators' teaching in Head Start programs. Because of the need to provide necessary mathematical experiences to young children to…

School gardening has become increasingly popular as a context for learning in which children construct new knowledge, learn cultural and societal values related to ecological awareness, and develop and practice authentic or real-world skills (Blair, 2009; Bowker & Tearle, 2007). The present research was a longitudinal case study of children's…

This classroom note is presented as a suggested exercise--not to have the class prove or disprove Goldbach's Conjecture, but to stimulate student discussions in the classroom regarding proof, as well as necessary, sufficient, satisfied, and unsatisfied conditions. Goldbach's Conjecture is one of the oldest unsolved problems in the field of number…

Lee and Sarnecka (2010) developed a Bayesian model of young children's behavior on the Give-N test of number knowledge. This paper presents two new extensions of the model, and applies the model to new data. In the first extension, the model is used to evaluate competing theories about the conceptual knowledge underlying children's behavior. One,…

Recreational Programming (RecPro) is the discipline that encourages the study of computer programming through ludic problems. Problems that are typically studied within this discipline are similar to those of Recreational Mathematics (RecMat), which sometimes leads to the confusion of these two disciplines. The objective for RecPro is to write…

Specific Language Impairment (SLI) is understood to be a disorder that predominantly affects phonology, morphosyntax and/or lexical semantics. There is little conclusive evidence on whether children with SLI are challenged with regard to Gricean pragmatic maxims and on whether children with SLI are competent with the logical meaning of quantifying…

The main purpose of this research is to determine whether the attainment of the number concept by children aged between 4-7 differs depending on age variant as well as receiving preschool education or not. Attainment of the number concept has been examined by means of One-to-One Matching Test consisting of Piaget's experiments. The test was…