Early mathematical learning: Number processing skills and executive function at 5 and 8 years of age

This research investigated differences and associations in performance in number processing and executive function for children attending primary school in a large Australian metropolitan city. In a cross-sectional study, performance of 25 children in the first full-time year of school, (Prep; mean age = 5.5 years) and 21 children in Year 3 (mean age = 8.5 years) completed three number processing tasks and three executive function tasks. Year 3 children consistently outperformed the Prep year children on measures of accuracy and reaction time, on the tasks of number comparison, calculation, shifting, and inhibition but not on number line estimation. The components of executive function (shifting, inhibition, and working memory) showed different patterns of correlation to performance on number processing tasks across the early years of school. Findings could be used to enhance teachers’ understanding about the role of the cognitive processes employed by children in numeracy learning, and so inform teachers’ classroom practices.

Forms of generalization in students experiencing mathematical learning difficulties

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The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed and oral language) and numerical factors that include single-digit processing efficiency and multi-digit skills such as number system knowledge and estimation. This study of third graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in three significant arithmetic skills: basic calculation fluency, written multi-digit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill and their contributions are both independent of each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multi-digit skills. These findings indicate that many factors matter but multi-digit skills matter most in third grade mathematical achievement.

Effects of Number-Way Curriculum on Pre-Schoolers’ Mathematical Learning for Low Socioeconomic Status Children

The objective of this research is to test the effectiveness of a game-based mathematical curriculum Number-Way in preschools for low socioeconomic status (SES) children. This curriculum contains fifteen interesting number games representing four main principles. The result indicated that this curriculum promoted early mathematical competence for preschoolers significantly.

Early childhood teachers' mathematical content knowledge

The process of becoming numerate begins in the early years. According to Vygotskian theory (1978), teachers are More Knowledgeable Others who provide and support learning experiences that influence children’s mathematical learning. This paper reports on research that investigates three early childhood teachers mathematics content knowledge. An exploratory, single case study utilised data collected from interviews, and email correspondence to investigate the teachers’ mathematics content knowledge. The data was reviewed according to three analytical strategies: content analysis, pattern matching, and comparative analysis. Findings indicated there was variation in teachers’ content knowledge across the five mathematical strands and that teachers might not demonstrate the depth of content knowledge that is expected of four year specially trained early years’ teachers. A significant factor that appeared to influence these teachers’ content knowledge was their teaching experience. Therefore, an avenue for future research is the investigation of factors that influence teachers’ content numeracy knowledge.

Student identities in a mathematical community of practice : radical visible pedagogy and the teacher collective

This study investigated the practices of two teachers in a school that was successful in enabling the mathematical learning of students in Years 1 and 2, including those from backgrounds associated with low mathematical achievement. The study explained how the practices of the teachers constituted a radical visible pedagogy that enabled equitable outcomes. The study also showed that teachers’ practices have collective power to shape students’ mathematical identities. The role of the principal in the school was pivotal because she structured curriculum delivery so that students experienced the distinct practices of both teachers.

Perspectives on Reconceptualizing Early Mathematics Learning

This introductory section provides an overview of the different perspectives on reconceptualizing early mathematics learning. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualizing the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed. Although these themes are diffused throughout the chapters, we restrict our introduction to the core focus of each of the chapters.

Mathematics Learning Support in Ireland in 2015

The provision of mathematics learning support in higher-level institutions on the island of Ireland has developed rapidly in recent times with the number of institutions providing some form of support doubling in the past seven years. The Irish Mathematics Learning Support Network aims to inform all mathematics support practitioners in Ireland on relevant issues. Consequently it was decided that a detailed picture of current provision was necessary. A comprehensive online survey was conducted to amass the necessary data. The ultimate aim of the survey is to benefit all mathematics support practitioners in Ireland, in particular those in third-level institutions who require further support to enhance the mathematical learning experience of their students. The survey reveals that the majority of Irish higher-level institutions provide mathematics learning support to some extent, with 65% doing so through a support centre. Learners of service mathematics are the primary users: first-year science, engineering and business undergraduates, with non-traditional students being a sizeable element. Despite the growing recognition for the need to offer mathematics learning support almost half of the centres are subject to annual review. Further, less than half the support offerings have a dedicated full-time manager, while 60% operate with a staff of five or fewer. The elevation of mathematics support as a viable and worthwhile career in order to attract and retain high quality staff is seen by many respondents as the crucial next phase of development.

Cooperative Multi-robot Patrolling: A study of distributed approaches based on mathematical models of game theory to protect infrastructures

El principio de Teoría de Juegos permite desarrollar modelos estocásticos de patrullaje multi-robot para proteger infraestructuras criticas. La protección de infraestructuras criticas representa un gran reto para los países al rededor del mundo, principalmente después de los ataques terroristas llevados a cabo la década pasada. En este documento el termino infraestructura hace referencia a aeropuertos, plantas nucleares u otros instalaciones. El problema de patrullaje se define como la actividad de patrullar un entorno determinado para monitorear cualquier actividad o sensar algunas variables ambientales. En esta actividad, un grupo de robots debe visitar un conjunto de puntos de interés definidos en un entorno en intervalos de tiempo irregulares con propósitos de seguridad. Los modelos de partullaje multi-robot son utilizados para resolver este problema. Hasta el momento existen trabajos que resuelven este problema utilizando diversos principios matemáticos. Los modelos de patrullaje multi-robot desarrollados en esos trabajos representan un gran avance en este campo de investigación. Sin embargo, los modelos con los mejores resultados no son viables para aplicaciones de seguridad debido a su naturaleza centralizada y determinista. Esta tesis presenta cinco modelos de patrullaje multi-robot distribuidos e impredecibles basados en modelos matemáticos de aprendizaje de Teoría de Juegos. El objetivo del desarrollo de estos modelos está en resolver los inconvenientes presentes en trabajos preliminares. Con esta finalidad, el problema de patrullaje multi-robot se formuló utilizando conceptos de Teoría de Grafos, en la cual se definieron varios juegos en cada vértice de un grafo. Los modelos de patrullaje multi-robot desarrollados en este trabajo de investigación se han validado y comparado con los mejores modelos disponibles en la literatura. Para llevar a cabo tanto la validación como la comparación se ha utilizado un simulador de patrullaje y un grupo de robots reales. Los resultados experimentales muestran que los modelos de patrullaje desarrollados en este trabajo de investigación trabajan mejor que modelos de trabajos previos en el 80% de 150 casos de estudio. Además de esto, estos modelos cuentan con varias características importantes tales como distribución, robustez, escalabilidad y dinamismo. Los avances logrados con este trabajo de investigación dan evidencia del potencial de Teoría de Juegos para desarrollar modelos de patrullaje útiles para proteger infraestructuras. ABSTRACT Game theory principle allows to developing stochastic multi-robot patrolling models to protect critical infrastructures. Critical infrastructures protection is a great concern for countries around the world, mainly due to terrorist attacks in the last decade. In this document, the term infrastructures includes airports, nuclear power plants, and many other facilities. The patrolling problem is defined as the activity of traversing a given environment to monitoring any activity or sensing some environmental variables If this activity were performed by a fleet of robots, they would have to visit some places of interest of an environment at irregular intervals of time for security purposes. This problem is solved using multi-robot patrolling models. To date, literature works have been solved this problem applying various mathematical principles.The multi-robot patrolling models developed in those works represent great advances in this field. However, the models that obtain the best results are unfeasible for security applications due to their centralized and predictable nature. This thesis presents five distributed and unpredictable multi-robot patrolling models based on mathematical learning models derived from Game Theory. These multi-robot patrolling models aim at overcoming the disadvantages of previous work. To this end, the multi-robot patrolling problem was formulated using concepts of Graph Theory to represent the environment. Several normal-form games were defined at each vertex of a graph in this formulation. The multi-robot patrolling models developed in this research work have been validated and compared with best ranked multi-robot patrolling models in the literature. Both validation and comparison were preformed by using both a patrolling simulator and real robots. Experimental results show that the multirobot patrolling models developed in this research work improve previous ones in as many as 80% of 150 cases of study. Moreover, these multi-robot patrolling models rely on several features to highlight in security applications such as distribution, robustness, scalability, and dynamism. The achievements obtained in this research work validate the potential of Game Theory to develop patrolling models to protect infrastructures.

Brief report: preliminary proposal of a conceptual model of a digital environment for developing mathematical reasoning in students with Autism Spectrum Disorders

There is clear evidence that in typically developing children reasoning and sense-making are essential in all mathematical learning and understanding processes. In children with autism spectrum disorders (ASD), however, these become much more significant, considering their importance to successful independent living. This paper presents a preliminary proposal of a digital environment, specifically targeted to promote the development of mathematical reasoning in students with ASD. Given the diversity of ASD, the prototyping of this environment requires the study of dynamic adaptation processes and the development of activities adjusted to each user’s profile. We present the results obtained during the first phase of this ongoing research, describing a conceptual model of the proposed digital environment. Guidelines for future research are also discussed.

Young children's early modelling with data

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (i.e., identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Results are reported from the first year of a three-year longitudinal study in which three classes of first-grade children and their teachers engaged in activities that required the creation of data models. The theme of “Looking after our Environment,” a component of the children’s science curriculum at the time, provided the context for the activities. Findings focus on how the children dealt with given complex attributes and how they generated their own attributes in classifying broad data sets, and the nature of the models the children created in organising, structuring, and representing their data.

Trailblazers

A recent study in the United Kingdom (Ofsted Report 2008) provides strong evidence that well-organized activities outside the classroom contribute significantly to the quality and depth of children's learning, including their personal, social, and emotional development. Outdoor math trails supply further evidence of such enhanced learning: They are meaningful, stimulating, challenging, and exciting for children. Most important, these trails invite all students, irrespective of their classroom achievement level, to participate successfully in the problem activities and gain a sense of pride in the mathematics they create. Additionally, Math trails empower lifelong learning. Integrating "outside" mathematics with "inside" classroom mathematics can sow the seeds to develop flexible, creative, future-oriented mathematical thinkers and problem solvers. Here, English et al discuss how to design and implement math trails to promote active, meaningful, real-world mathematical learning beyond the classroom walls.

‘Wanna do more math’: engaging underachieving Indigenous learners the YuMi Deadly way.

The Accelerating Indigenous Mathematics (AIM) Program offered by the YuMi Deadly Centre from QUT accelerates the mathematics learning of underperforming students in Years 8 - 10 by a) apportioning Years 2-10 Australian Curriculum: Mathematics content into three years, and b) provides a teaching approach that accelerates the mathematical learning. The philosophy of the YuMi Deadly teaching approach for mathematics is one that requires a ‘body’, ‘hand’, ‘mind’ pedagogy. This presentation will provide examples of the “‘body’, ‘hand’, ‘mind’” mathematics pedagogy. In AIM classrooms, mathematics is presented this approach is having a positive impact. Students are willing ‘to have a go’ without shame; and they develop the desire to learn and improve their numeracy.

Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.