Representing addition and subtraction : learning the formal conventions

The study was designed to test the effects of a structured intervention in teaching children to represent addition and subtraction. In a post-test only control group design, 90 five-year-olds experienced the intervention entitled Bi-directional Translation whilst 90 control subjects experienced typical teaching. Post-intervention testing showed some significant differences between the two groups both in terms of being able to effect the addition and subtraction operations and in being able to determine which operation was appropriate. The results suggest that, contrary to historical practices, children's exploration of real world situations should precede practice in arithmetical symbol manipulation

Galaxy Properties at the Faint End of the H I Mass Function

The Survey of H I in Extremely Low-mass Dwarfs (SHIELD) includes a volumetrically complete sample of 82 gas-rich dwarfs with ${M}_{{\rm{H}}\,{\rm\small{I}}}\lesssim {10}^{7.2}$ ${M}_{\odot }$ selected from the ALFALFA survey. We are obtaining extensive follow-up observations of the SHIELD galaxies to study their gas, stellar, and chemical content, and to better understand galaxy evolution at the faint end of the H I mass function. Here, we investigate the properties of 30 SHIELD galaxies using Hubble Space Telescope imaging of their resolved stars and Westerbork Synthesis Radio Telescope observations of their neutral hydrogen. We measure tip of the red giant branch (TRGB) distances, star formation activity, and gas properties. The TRGB distances are up to 4× greater than estimates from flow models, highlighting the importance of velocity-independent distance indicators in the nearby universe. The SHIELD galaxies are in underdense regions, with 23% located in voids; one galaxy appears paired with a more massive dwarf. We quantify galaxy properties at low masses including stellar and H I masses, star formation rate (SFRs), specific SFRs, star formation efficiencies, birth-rate parameters, and gas fractions. The lowest-mass systems lie below the mass thresholds where stellar mass assembly is predicted to be impacted by reionization. Even so, we find the star formation properties follow the same trends as higher-mass gas-rich systems, albeit with a different normalization. The H I disks are small ( $\langle r \rangle 0.7\,{\rm{kpc}}$ ), making it difficult to measure the H I rotation using standard techniques; we develop a new methodology and report the velocity extent, and its associated spatial extent, with robust uncertainties

Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study.

The extent that phonological, visual-spatial STM and non-symbolic quantitative skills support the development of counting and calculation skills was examined in this 14-month longitudinal study of 125 children. Initial assessments were made when the children were 4:8. Phonological awareness, visual-spatial STM and non-symbolic approximate discrimination predicted growth in early calculation skills. These results suggest that both the approximate number system and domain-general phonological and visual-spatial skills support early calculation. In contrast, only performance on a small non-symbolic quantity discrimination task (where the presented quantities were always within the subitising range) predicted growth in cardinal counting skills. These results suggest that the development of counting and calculation are supported by different cognitive abilities

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

Impact of High Mathematics Education on the Number Sense

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS

Environmental and Genetic Preconditioning for Long-Term Anoxia Responses Requires AMPK in Caenorhabditis elegans

Article on environmental and genetic preconditioning for long-term anoxia responses requires AMPK in Caenorhabditis elegans

Applying psychological learning theory to helping students overcome learned difficulties in mathematics: An alternative approach to intervention

The appearance of systematic errors in computation suggests relatively unlinked computational knowledge to conceptual knowledge, and hence difficulties with forward learning of mathematics. The provision of programs of good teaching, where concrete materials are used to exemplify and thus legitimize algorithmic processes, frequently are not effective for use with upper primary students: systematic errors often resurface. A novel and quite alternate approach to intervention is the Old Way/New Way (O/N) strategy (Lyndon, 1989) based on psychological principles of memory, forgetting and interference. In this article, issues associated with intervention, systematic errors and upper primary students are addressed through a discussion of results of previous research into seventh graders' subtraction knowledge development by overcoming error patterns in subtraction computation. By comparing re-teaching strategies and O/N, it is proposed that both good teaching and effective intervention strategies should be integral to the craft of teaching, particularly in the middle school