Whole number thinking, learning and development: neuro-cognitive, cognitive and developmental approaches

The participants of working group 2 presented a broad range of studies, 11 papers in total, related to whole number learning representing research groups from 11 countries as follows. Two large cross-sectional studies focused on developmental aspects of young children’s number learning provide a lens for re-examining ‘traditional’ features of number acquisition. van den Heuvel-Panhuizen (the Netherlands) presented a co-authored paper with Elia (Cyprus; Elia and van den Heuvel-Panhuizen 2015) on a cross-cultural study of kindergartners’ number competence focused on counting, additive and multiplicative thinking. Second, Milinković (2015) examined the development of young Serbian children’s initial understanding of representations of whole numbers and counting strategies in a large study of 3- to 7-year-olds. Children’s invented (formal) representations such as set representation and the number line were found to be limited in their recordings. In a South African study focused on early counting and addition, Roberts (2015) directs attention to the role of teachers by providing a framework to support teachers’ interpretation of young disadvantaged learners’ representations of number when engaging with whole number additive tasks. Some papers reflected the increasing role of neuroscientific concepts and methodologies utilised in research on WNA learning and development. Sinclair and Coles (2015) drew upon neuroscientific research to highlight the significant role of symbol-to-symbol connections and the use of fingers and touch counting exempli- fied by the TouchCounts iPad app. Gould (2015) reported aspects of a large Australian large study of children in the first years of schooling aimed at improving numeracy and literacy in disadvantaged communities. A case study exemplified how numerals were identified by relying on a mental number line by using location to retrieve number names. This raised the question addressed in the neuroscientific work of Dehaene and other papers focused on individual differences in how the brain processes numbers. The Italian PerContare1 project (Baccaglini-Frank 2015) built upon the collaboration between cognitive psychologists and mathematics educators, aimed at developing teaching strategies for preventing and addressing early low achievement in arithmetic. It takes an innovative approach to the development of number sense that is grounded upon a kinaesthetic and visual-spatial approach to part-whole relationships. Mulligan and Woolcott (2015) provided a discussion paper on the underlying nature of number. They presented a broader view of mathematics learning (including WNA) as linked to spatial interaction with the environment; the concept of connectivity across concepts and the development of underlying pattern and structural relationships are central to their approach

Evidence for modulation of pericryptal sheath myofibroblasts in rat descending colon by Transforming Growth Factor β and Angiotensin II.

BACKGROUND: Absorption of water and Na(+) in descending colonic crypts is dependent on the barrier function of the surrounding myofibroblastic pericryptal sheath. Here the effects of high and low Na(+) diets and exposure to whole body ionising radiation on the growth and activation of the descending colonic pericryptal myofibroblasts are evaluated. In addition the effect of a post-irradiation treatment with the angiotensin converting enzyme inhibitor Captopril was investigated. METHODS: The levels of Angiotensin II type 1 receptor (AT1), ACE, collagen type IV, transforming growth factor-β type 1 receptor (TGF-βR1), OB cadherin and α-smooth muscle actin in both descending colon and caecum were evaluated, using immunocytochemistry and confocal microscopy, in rats fed on high and low Na(+) diets (LS). These parameters were also determined during 3 months post-irradiation with 8Gy from a (60)Co source in the presence and absence of the angiotensin converting enzyme inhibitor, Captopril. RESULTS: Increases in AT1 receptor (135.6% ± 18.3, P < 0.001); ACE (70.1% ± 13.1, P < 0.001); collagen type IV (49.6% ± 15.3, P < 0.001); TGF-β1 receptors (291.0% ± 26.5, P < 0.001); OB-cadherin (26.3% ± 13.8, P < 0.05) and α-smooth muscle actin (82.5% ± 12.4, P < 0.001) were observed in the pericryptal myofibroblasts of the descending colon after LS diet. There are also increases in AT1 receptor and TGF-β1 receptor, smooth muscle actin and collagen type IV after irradiation. Captopril reduced all these effects of irradiation on the pericryptal sheath and also decreased the amount of collagen and smooth muscle actin in control rats (P < 0.001). CONCLUSIONS: These results demonstrate an activation of descending colonic myofibroblasts to trophic stimuli, or irradiation, which can be attenuated by Captopril, indicative of local trophic control by angiotensin II and TGF-β release

Formal and informal home learning activities in relation to children's early numeracy and literacy skills: The development of a home numeracy model

The purpose of this study was to propose and test a model of children's home numeracy experience based on Sénéchal and LeFevre's home literacy model (Child Development, 73 (2002) 445-460). Parents of 183 children starting kindergarten in the fall (median child age = 58. months) completed an early home learning experiences questionnaire. Most of the children whose parents completed the questionnaire were recruited for numeracy and literacy testing 1. year later (along with 32 children from the inner city). Confirmatory factor analyses were used to reduce survey items, and hierarchical regression analyses were used to predict the relation among parents' attitudes, academic expectations for their children, reports of formal and informal numeracy, and literacy home practices on children's test scores. Parental reports of formal home numeracy practices (e.g., practicing simple sums) predicted children's symbolic number system knowledge, whereas reports of informal exposure to games with numerical content (measured indirectly through parents' knowledge of children's games) predicted children's non-symbolic arithmetic, as did numeracy attitudes (e.g., parents' enjoyment of numeracy). The home literacy results replicated past findings; parental reports of formal literacy practices (e.g., helping their children to read words) predicted children's word reading, whereas reports of informal experiences (i.e., frequency of shared reading measured indirectly through parents' storybook knowledge) predicted children's vocabulary. These findings support a multifaceted model of children's early numeracy environment, with different types of early home experiences (formal and informal) predicting different numeracy outcomes

Optimizing the home numeracy environments of 3- to 6-year-old children in the USA and Canada

Many children in the USA and Canada have access to a wide range of experiences that can support their early numeracy development. Nevertheless, children’s early numeracy knowledge varies considerably in these countries as a function of parents’ education, socioeconomic conditions, parents’ attitudes, beliefs, knowledge about mathematics, and preschool and school educators’ knowledge and experience. In this chapter we provide a selective overview of some of the factors that are related to children’s early numeracy experiences and suggest contexts and circumstances that may facilitate or hinder children’s learning. Parents’ provision of formal and informal opportunities that allow their children to experience number, space, and related concepts and their willingness to engage in meaningful activities may all influence the quality of children’s early experiences. We conclude with suggestions for further research to explore ways in which adults can enhance the home numeracy environments of preschool children

The Role of Child Interests and Collaborative Parent-Child Interactions in Fostering Numeracy and Literacy Development in Canadian Homes

Children's involvement in home literacy and numeracy activities has been linked to school achievement, but the subtleties in the home environment responsible for these gains have yet to be thoroughly investigated. The purpose of this study was to determine how children's interests and collaborative parent-child interactions affect exposure to home literacy and numeracy activities. Parents of 170 four-to-five year old children completed a survey about their child's home learning environment. They rated their children's interests in 14 activities, and the extent of parent-child collaboration on a cooking and card-making task. Follow up interviews were also initiated with four mothers to provide validation of the survey data in numeracy. Factor analyses reduced the number of survey items. Parents whose children preferred exploratory, active or crafts activities reported frequent engagement in literacy and numeracy activities. Parents seeking a collaborative approach during activities reported increased exposure to home literacy and numeracy activities than families with less collaborative involvement. Interview data confirmed that parents of children with high numeracy scores were exposing their children to rich numeracy activities during play. The findings suggest that children's interests and collaborative parent-child involvement impact literacy and numeracy exposure in the home

Do home numeracy and literacy practices of Greek and Canadian parents predict the numeracy skills of kindergarten children?

Children's experiences with early numeracy and literacy activities are a likely source of individual differences in their preparation for academic learning in school. What factors predict differences in children's experiences? We hypothesised that relations between parents' practices and children's numeracy skills would mediate the relations between numeracy skills and parents' education, attitudes and expectations. Parents of Greek (N = 100) and Canadian (N = 104) five-year-old children completed a survey about parents' home practices, academic expectations and attitudes; their children were tested on two numeracy measures (i.e., KeyMath-Revised Numeration and next number generation). Greek parents reported numeracy and literacy activities less frequently than Canadian parents; however, the frequency of home numeracy activities that involved direct experiences with numbers or mathematical content (e.g., learning simple sums, mental math) was related to children's numeracy skills in both countries. For Greek children, home literacy experiences (i.e., storybook exposure) also predicted numeracy outcomes. The mediation model was supported for Greek children, but for Canadian children, the parent factors had both direct and mediated relations with home practices

Refining the quantitative pathway of the Pathways to Mathematics model

In the current study, we adopted the Pathways to Mathematics model of LeFevre et al. (2010). In this model, there are three cognitive domains-labeled as the quantitative, linguistic, and working memory pathways-that make unique contributions to children's mathematical development. We attempted to refine the quantitative pathway by combining children's (N=. 141 in Grades 2 and 3) subitizing, counting, and symbolic magnitude comparison skills using principal components analysis. The quantitative pathway was examined in relation to dependent numerical measures (backward counting, arithmetic fluency, calculation, and number system knowledge) and a dependent reading measure, while simultaneously accountin