Numeracy

The results from a small pilot study (n=60) that probes the validity of a semi-automated tool, the Quantity / Magnitude Comparison (QMC) scale, used for assessing the K-3 student’s growth in number sense, are shared. The study revealed that scores on the QMC do fluctuate with grade level and these scores also correlate strongly (r = .69) with chronological age. These results reveal preliminary validity for using the QMC as a progress monitoring tool for evaluating on-going growth toward competence with number sense.

Rechnen mit Prozentangaben spielt in vielen Berufen eine Rolle. Prozentangaben werden dabei ganz unterschiedlich eingesetzt. Das gängige Bild – 100% steht für das ‚Ganze’, Angaben wie ‚70%’ spezifizieren einen Teil daraus – ist dabei oft nicht anwendbar.

Ausführlicher: Kaiser, H. (2011). Vorbereiten auf das Prozentrechnen im Beruf. Praxis der Mathematik in der Schule, 53(41), 37-44.

The numerical knowledge of children from low-income backgrounds trails behind that of peers from middle-income backgrounds even before the children enter school. This gap may reflect differing prior experience with informal numerical activities, such as numerical board games. Experiment 1 indicated that the numerical magnitude knowledge of preschoolers from low-income families lagged behind that of peers from more affluent backgrounds. Experiment 2 indicated that playing a simple numerical board game for four 15-minute sessions eliminated the differences in numerical estimation proficiency. Playing games that substituted colors for numbers did not have this effect. Thus, playing numerical board games offers an inexpensive means for reducing the gap in numerical knowledge that separates less and more affluent children when they begin school.

Founded in 1908, the National Governors Association (NGA) is the collective voice of the nation's governors and one of Washington, D.C.'s most respected public policy organizations. Its members are the governors of the 50 states, three territories and two commonwealths. NGA provides governors and their senior staff members with services that range from representing states on Capitol Hill and before the Administration on key federal issues to developing and implementing innovative solutions to public policy challenges through the NGA Center for Best Practices. For more information, visit www.nga.org.

While maths can be viewed as enabling learning in science and medicine, in reality we see students are bringing their maths anxiety with them to their studies. Our work focuses on dissecting the maths problem as it relates to teaching and learning in these so-called hard disciplines. We have been challenging the inertia of what we see as a stand off with students taking the view that they are unable to do maths and educators frustrated at their disengagement. We have found that the maths problem resonates with several pedagogical frameworks (e.g. Meyer and Land’s Threshold Concepts Framework, Perkins and Simmons’ four frames of understanding) and we have found these useful for unpicking where our students become disengaged. We have applied a number of interventions to assist student learning and are now using our findings to inform the design of an online diagnostic to more explicitly address dysfunctional stances that students adopt when asked to manipulate their quantitative data....

We present results of a computer-assisted intervention (CAI) study on number skills in kindergarten children. Children with low numeracy skill (n = 30) were randomly allocated to two treatment groups. The first group played a computer game (The Number Race) which emphasized numerical comparison and was designed to train number sense, while the other group played a game (Graphogame-Math) which emphasized small sets of exact numerosities by training matching of verbal labels to visual patterns and number symbols. Both groups participated in a daily intervention session for three weeks. Children's performance in verbal counting, number comparison, object counting, arithmetic, and a control task (rapid serial naming) were measured before and after the intervention. Both interventions improved children's skills in number comparison, compared to a group of typically performing children (n = 30), but not in other areas of number skills. These findings, together with a review of earlier computer-assisted intervention studies, provide guidance for future work on CAI aiming to boost numeracy development of low performing children.

Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing collections (i.e., non-symbolic number magnitude). Moreover, they automatically processed number magnitude when comparing the physical size of Arabic digits in an Stroop paradigm adapted for processing speed differences. Finally, no evidence was found for differential patterns of performance between MD and MD/RD children in these tasks. These findings suggest that children with mathematics learning disabilities have difficulty in accessing number magnitude from symbols rather than in processing numerosity per se.

As recent research efforts have focused on preventing reading difficulties and enhancing the effectiveness of special education services for students with reading problems, similar efforts in mathematics have not been realized. This article describes the development and preliminary field testing of a set of measures designed to screen students in kindergarten and first grade to identify those at risk for potential mathematics difficulties. Evidence-based steps to streamline the screening process are described, and plans for testing the predictive validity of the measures are outlined.

This paper discusses the use of Numicon number teaching materials with children with Down syndrome. The theory underlying the design of the materials is discussed, the teaching approach and methodology are described and evidence supporting effectiveness is outlined.

This report forms part of the research program Longitudinal surveys of Australian youth (LSAY), conducted by the Australian Council for Educational Research (ACER) and financially supported by the Department of Employment, Education, Training and Youth Affairs (DEETYA).

How do our mental representations of number change over development? The dominant view holds that children (and adults) possess multiple representations of number, and that age and experience lead to a shift from greater reliance upon logarithmically organized number representations to greater reliance upon more accurate, linear representations. Here we present a new theoretically motivated and empirically supported account of the development of numerical estimation, based on the idea that number-line estimation tasks entail judgments of proportion. We extend existing models of perceptual proportion judgment to the case of abstract numerical magnitude. Two experiments provide support for these models; three likely sources of developmental change in children's estimation performance are identified and discussed. This work demonstrates that proportion-judgment models provide a unified account of estimation patterns that have previously been explained in terms of a developmental shift from logarithmic to linear representations of number.

Quantitative and scientific reasoning is a critical student learning outcome in higher education. Data are presented for large samples of undergraduate students who were assessed as entering freshmen and then again after completing 45-70 credit hours. Results are presented around four key issues that are central to educational assessment. First, entering freshmen with transfer credits for quantitative and scientific reasoning courses that fulfill general education requirements, on average, score similar to entering freshmen without such credit. About 97% of entering freshmen who had transfer credits received their credits through dual enrollment programs. As a sophomore-junior, students who had completed their general education requirements performed similar to students who had started, but not yet finished these requirements. Second, small to moderate correlations were observed between grade-point averages in relevant general education coursework and quantitative and scientific reasoning. Third, students' quantitative and scientific reasoning, on average, increases from freshmen to sophomore/junior years. Finally, the proportion of students who meet faculty-set standards substantially increases from pre-test to post-test. Taken together, results suggest that changes in quantitative and scientific reasoning are a function of relevant courses. Additional research is needed to examine the role of lower-level versus higher-level courses in student performance. Results also indicate a need to investigate how differences in the quality of dual enrollment courses facilitate quantitative and scientific reasoning.

The residue number system (RNS) has been an important research field in computer arithmetic for many decades, mainly because of its carry-free nature, which can provide high-performance computing architectures with superior delay specifications. Recently, research on RNS has found new directions that have resulted in the introduction of efficient algorithms and hardware implementations for RNS with much better performance than previous ones. Furthermore, the applicability of RNS in many computer and digital signal processing (DSP) applications has simultaneously greatly increased. Hence, the need is evident for the development of a new and well-organized RNS teaching method with emphasis on recent achievements. In this paper, a step-by-step teaching process for RNS that describes RNS design in separate parts is presented. Each part is investigated in detail, taking into account the recent research performed on RNS. The compatibility of the proposed method with the new RNS research trends makes this method suitable for researchers as well as students.

Notre environnement est saturé de nombres et de données chiffrées. De fait, comment ne pas avoir confiance dans ces instruments jugés spontanément efficaces pour appréhender le monde ? Or, c’est occulter un peu vite les usages dont ils dépendent et le sens qu’on leur donne… Toute leur histoire le prouve.
Si les nombres sont de nos jours des outils au service de la rhétorique médiatique, politique ou scientifique, dans plusieurs sociétés du passé ils appartenaient surtout au monde des marchands et des administrateurs, voire à la sphère sacrée. Penser, utiliser et écrire un nombre, tout cela ne va pas de soi !
D’où vient le zéro ? Qui a inventé notre système de numération ? En posant ces questions et en s’appuyant sur de nombreux exemples, Grégory Chambon vous invite à partir à la découverte de la fabuleuse histoire des chiffres et des êtres…

The findings, interpretations, and conclusions expressed in this document are entirely those of the authors and should not be attributed in any manner to the World Bank, to its affiliated organizations, or to members of its Board of Executive Directors or the countries they represent. 1. Starting at grade 7, female enrollments drop from more than 35 percent of the total to less than 28 percent, and continue to decline thereafter; in higher education, only about 20 percent of university entrants are female (MoE 2007). Afghan women become computer literate (left); a woman is trained in tailoring as part of the National Skills Development Program (right).

In this paper we present new evidence on the impact of school characteristics on secondary student achievement using a rich data set from rural Bangladesh. We deal with a potentially important selectivity issue in the South Asian context: the non-random sorting of children into religious schools. We do so by employing a combination of fixed effects and instrumental variable estimation techniques. Additionally, we use the variation between two classrooms of the same grade within individual schools to identify causal class-size effects. Our empirical results do not reveal any difference in test scores between religious and secular schools when selection into religious school is taken into account. Net of school fixed-effects, we do not find evidence in support of smaller class size. However, we document significant learning deficit by gender and primary school type: girls and graduates of primary madrasas have a lower test score even after controlling for school and classroom-specific unobservable correlates of learning.

Number sense development was tracked from the beginning of kindergarten through the middle of first grade, over six time points. Children (n = 277) were then assessed on general math achievement at the end of first grade. Number sense performance in kindergarten, as well as number sense growth, accounted for 66 percent of the variance in first-grade math achievement. Background characteristics of income status, gender, age, and reading ability did not add explanatory variance over and above growth in number sense. Even at the beginning of kindergarten, number sense was highly correlated with end of first-grade math achievement (r = 0.70). Clarifying the observed slope effect, general growth mixture modeling showed that children who started kindergarten with low number sense but made moderate gains by the middle of kindergarten had higher first-grade math achievement than children who started out with similarly low number sense with flat growth. The majority of children in the low/flat growth class were from low-income families. The findings indicate that screening early number sense development is useful for identifying children who will face later math difficulties or disabilities.

This paper discusses changes in young children’s learning performance and efficiency during clinical interviews in which each child interacted with a variety of virtual manipulative mathematics apps on iPads. Researchers interviewed 100 children ages 3 to 8 using a protocol format with two pre-assessment apps, four learning apps, and two post-assessment apps. Data were gathered quantitatively and qualitatively, using wall and screen-capture videos, pre and post assessments of performance, and time-stamping to record efficiency. Following 30-40 minute interviews where children interacted individually with the mathematics apps, results showed that children in the Preschool group increased efficiency while maintaining performance, children in the Kindergarten group increased performance while maintaining efficiency, and children in the Grade 2 group increased their performance and efficiency in skip counting, but not in place value. Overall, children in different age groups responded i...

Learners in South African schools have been found to perform poorly in mathematics because they do not understand the language used in solving mathematical problems. In order to improve academic performance teachers need to be made aware of the importance of language in the development of numeracy. A continued professional development (CPD) programme addressed this need. The purpose of the research was to understand how the participants implemented the strategies developed during the programme and how they perceived the support provided by the programme. The research was conducted over 2 years in semi-rural and urban contexts. As part of a more comprehensive mixed method study, the qualitative data referred to in this article were obtained through open-ended questions in questionnaires, focus groups, reflections in portfolios, and a research diary. Results showed that numeracy terminology was often used by learners that differed from standard terminology prescribed by the curriculum. The participants themselves did not necessarily understand the numeracy terminology and thus found it a challenge to implement curriculum outcomes. Issues related to language use of the participants in teaching numeracy were associated with the lack of resources available in the language of learning and teaching (LoLT). Some of the participants taught numeracy in English, rather than LoLT. The results indicated low teacher expectations of the learners. The CPD programme was considered valuable and effective. SLPs in schools need to be expand their role to provide CPD opportunities for teachers.

Some rights reserved This work is a product of the staff of The World Bank with external contributions. The findings, interpretations, and conclusions expressed in this work do not necessarily reflect the views of The World Bank, its Board of Executive Directors, or the governments they represent. The World Bank does not guarantee the accuracy of the data included in this work. The boundaries, colors, denominations, and other information shown on any map in this work do not imply any judgment on the part of The World Bank concerning the legal status of any territory or the endorsement or acceptance of such boundaries. Nothing herein shall constitute or be considered to be a limitation upon or waiver of the privileges and immunities of The World Bank, all of which are specifically reserved.

nouns Refer to general concepts, qualities, feelings and ideas, e.g. freedom or honesty Algebra The part of maths that uses symbols or letters (called pro numerals) to stand for numbers, values or quantities, e.g. A = L x W Algebraic representation The conventions, symbols and letters used in writing algebraic sentences and formulae Analogy A similarity between like features of two things, on which a comparison may be based, e.g. the analogy between the heart and a pump Autonomous learner Independent learner with the willingness and capacity to take charge of own learning AQF Australian Qualifications Framework which is a single, 10 level coherent framework for the school, VET and higher education sectors in Australia Chance events An event or happening of which the outcome is uncertain, e.g. rolling a six with a die Complex sentence A sentence that contains one independent clause and one or more dependent clauses which are joined by words (subordinators) such as because, since, alt...

In recent years, there has been an increasing focus on the role played by basic numerical magnitude processing in the typical and atypical development of mathematical skills. In this context, tasks measuring both the intentional and automatic processing of numerical magnitude have been employed to characterize how children's representation and processing of numerical magnitude changes over developmental time. To date, however, there has been little effort to differentiate between different measures of 'number sense'. The aim of the present study was to examine the relationship between automatic and intentional measures of magnitude processing as well as their relationships to individual differences in children's mathematical achievement. A group of 119 children in 1st and 2nd grade were tested on the physical size congruity paradigm (automatic processing) as well as the number comparison paradigm to measure the ratio effect (intentional processing). The results reveal that measures of intentional and automatic processing are uncorrelated with one another, suggesting that these tasks tap into different levels of numerical magnitude processing in children. Furthermore, while children's performance on the number comparison paradigm was found to correlate with their mathematical achievement scores, no such correlations could be obtained for any of the measures typically derived from the physical size congruity task. These findings therefore suggest that different tasks measuring 'number sense' tap into different levels of numerical magnitude representation that may be unrelated to one another and have differential predictive power for individual differences in mathematical achievement.

Literacy educators have been actively theorising the demands of literacy in New Times yet mathematics educators have taken little of this debate up. If, as literacy educators suggest, literacy demands are different in these New Times, what are the implications for numeracy or mathematics educators? This paper explores perceptions of young and older people who are engaged in work practices. It was found that there were statistically significant differences in a number of areas. Numeracy was found to be an important variable in discerning differences between older and younger people, and that technology was also seen to differentiate the two cohorts. Within numeracy, older people were more like to see number as important, whereas younger people were more likely to identify statistics, applied areas of mathematics and the use of technology to support numeracy as being important. These finding shave implications for theorising and practice in mathematics education.

"Es gibt so gut wie keine berufliche Tätigkeit, bei welcher der Umgang mit Größen, Zahlen, Plänen, Graphiken etc. keine Rolle spielt. Berufsbezogene Mathematik im weitesten Sinn oder „Fachrechnen“ ist daher aus der Berufsbildung nicht wegzudenken.

Auf der anderen Seite generiert das Fachrechnen – zumindest in der Schweiz – einen grossen Bedarf an Stütz- und Fördermassnahmen. Viele Lernende werden von ihren Lehrkräften in Zusatzkurse geschickt. Das ist unbefriedigend und wirft die Frage auf, wie man Fachrechnen in der Be-rufsbildung sinnvoll und wirksam gestalten kann."

Over the last 15 years, numeracy has become more and more prominent in curriculum initiatives around the world. Yet, the notion of numeracy is still not well defined, and as such, often not well understood by the teachers who are charged with the responsibility of helping our students to develop their numeracy skills. In this article I explore the work of a team of mathematics teachers brought together for the purpose of developing a set of numeracy tasks for use within district wide numeracy assessments. Results indicate that these teachers’ experience designing these tasks, and pilot testing them in their own classrooms, propelled them to make massive changes in their own mathematics teaching practice. Through a lens of Rapid and Profound Change (Journal of Mathematics Teacher Education 13:411–423, 2010) the mechanism and catalyst behind these changes are revealed.

This research study investigates how selected Grade R teachers implement numeracy in their classrooms, based on their experiences, personal beliefs and perceptions. This study adopts the view that a teacher's practice is not only informed on what she believes about her learners, but also on how she organises her classroom environment and her own teaching practice. However, the teacher cannot be divorced from the political and historical background of Early Childhood Development (ECD), as these factors have an impact on her numeracy implementation. Integrated in this research study is thus not only a comprehensive historical analysis of the historical and political background of ECD, but also an in-depth look at the complex curriculum road the Grade R teacher had to travel over the past twelve years. The aim of this case study is to understand and describe what is happening in Grade R classrooms when numeracy is implemented, as well as identifying possible barriers which Grade R ...

Children's symbolic number sense was examined at the beginning of first grade with a short screen of competencies related to counting, number knowledge, and arithmetic operations. Conventional mathematics achievement was then assessed at the end of both first and third grades. Controlling for age and cognitive abilities (i.e., language, spatial, and memory), number sense made a unique and meaningful contribution to the variance in mathematics achievement at both first and third grades. Furthermore, the strength of the predictions did not weaken over time. Number sense was most strongly related to the ability to solve applied mathematics problems presented in various contexts. The number sense screen taps important intermediate skills that should be considered in the development of early mathematics assessments and interventions.

This paper describes a limited longitudinal study of young children's early numeracy development within three testing cycles, at the mid-point and towards the end of their reception year (at five years-of-age) and again at the mid-point of Year 1 (at six years-of-age), located within the broader context of progress through to Key Stage 1 SAT results (at seven years). Assessment was carried out using the Utrecht Early Mathematical Competence Test (Van Luit et al., 1994). This comprised eight sub-topics, five items in each, including comparison, classification, correspondence, seriation, counting, calculation and real-life number problem solving. Broadly, one set of sub-tests related to understanding of relations in shape, size, quantity and order, whilst a second set of sub-tests related to basic arithmetic. Three hundred pupils were selected from twenty-one schools, large and small, from rural and urban areas, with high and low concentrations of children eligible for free school meals and/or with special educational needs, as well as representing a broad range of achievements levels based on standards assessment tasks. Whilst this paper focuses upon the performance of English pupils, reference is also made to the larger European sample which involved children from Flemish-speaking Belgium, Germany, Greece, Slovenia and the Netherlands. Results showed that children's total scores at around the mid-point of reception year were indeed predictive of later achievement at the end of KS1 though the combined scores over three testing cycles which extended to the mid-point of Year 1, were more so. Discriminant analysis confirmed that a combination of a counting sub-test (one seemed sufficient) and a sub-test focusing on understanding of relations in shape, size, order or quantity (a different one at each testing cycle), together with the general number knowledge sub-test was best predictive of final SAT levels. Comparison with the international data set suggested a different trajectory for English pupils, with more of a bias towards arithmetic sub-tests than their European counterparts who start school later. Moreover, the pattern of dependence of scores on age in

Any Internet search will reveal a myriad of articles and blogs on this topic. The variety of comment is not surprising since formal education of some kind affects every family and every individual in almost every country. Informal education has probably effected just about everyone since humans evolved. What the online material does show is that while the process is universal, the objectives are diverse and often in conflict. Indeed much of the discussion seems to be at cross purposes. I have been a teacher, mostly to young adults, for 35 years in seven countries with quite different cultures, so I am deeply familiar with the currents of intention and counter-intention which touch everyone in the enterprise of education. My own doctoral dissertation was an analysis of 20 case studies in institutions where the publicly expressed purposes of education were often sabotaged. Although I have seen some of the failures, the institutional reasons for such failures are so embedded and so internationally widespread that I can see little direct hope for major changes. What I do see is that for technological and cultural reasons, the relationships between public mass education and personal self-education are changing drastically. The outcomes of that melding are still unclear, but the process offers hope.

Sting, el famoso bajista de rock y jazz, participó en el programa The Musical Mind transmitido por National Geographic en el cual el Dr. Daniel Levitin analizó la actividad cerebral del artista mientras escuchaba diferentes estilos de música. Imagen tomada de

This paper focuses on the increasing prevalence of devices for self-evaluation in the context of social media. It suggests that self-measurement - i.e. aggregates of user activities, received likes, comments, retweets and other algorithmic indicators of reputation and influence - patterns and presents user data in new ways to act upon and modify the self. Furthermore, the technologies involved in self-evaluation are not designed to merely capture user engagement with social media, but act as framing devices, making certain types of insight and action possible while ruling out others. In this sense, self-evaluation can be understood as part of recommendation and premediation culture online and as devices to curate and organise streams of real-time web content.

Social media platforms like Twitter and Facebook are based on the continuous engagement of users in activities made possible through their software design and so far these platforms have only offered limited possibilities for users to access and make sense of data they generate in interaction with their contacts. But with the proliferation of user actions, especially Facebook has started to introduce devices that increasingly aggregate and cluster user activities into stories, ranks or numbers. Focusing on Facebook and Twitter, the paper will trace modes of self-evaluation both emerging within social media and from third-party plug-ins, apps and services build on top of platforms.

Special attention will be paid to so-called influence measurement devices, most particularly the Klout rank, that attempt to evaluate users’ engagement with and impact on their network. The analysis will explore how the Klout rank encourages users to act on their data and will reflect on the role of numbers, more specifically counts and rankings, seeking to describe them as media of self-evaluation. It will unfold the affective states involved in rankings and will draw on mathematical concepts of ordinality to reflect on their performative capacities. Finally, the paper will position the emergence of self-evaluative media in the context of recommendation cultures, indicating that it not only enables users to transform the self based on data, but is embedded in corporate attempts to channel user engagement into particular directions. In this sense, the investigation of self-evaluative media will draw attention to issues of temporality, numbering and measurement in social media platforms while singling out new modes of pre-structuring user activities through devices.

This paper was written by Analice C. Schwartz for the Global Partnership for Education (GPE), formerly known as The Fast Track Initiative, under the guidance of Helen Abadzi (Senior Education Specialist at the Global Partnership for Education). Special thanks to Collette Chabbott (The George Washington University) who provided valuable insights and comments of earlier drafts. The paper also benefited from feedback from World Bank's country officers, education specialists, and selected program developers. The findings, interpretations, and conclusions expressed in this work are of the author's only and do not necessarily reflect the views of the GPE, the World Bank, its Board of Executive Directors, or the governments they represent.

Research in clinical samples suggests that the relationship between intelligence and academic achievement might be moderated by sustained attention. The present study aimed to explore whether this interaction could be observed in a non-clinical sample. We investigated a sample of 11th and 12th grade students (N =231). An overall performance score and a quality of performance score in sustained attention as well as verbal, numerical, and general intelligence scores served as predictors. Achievement criteria were grades in math and German as well as Grade Point Average (GPA) obtained after testing. Both types of sustained attention scores were significantly related to school performance, but only the quality of performance score incrementally contributed to the prediction of school performance above and beyond intelligence. Overall differences in the sustained attention test significantly moderated the relationship between verbal intelligence and German grades. Quality of performance moderated the relationship between general intelligence and GPA as well as the one between numerical intelligence and math grades. The study elucidates the interplay between sustained attention, intelligence, and school performance in a non-clinical sample.

Recent studies have documented positive effects for early intervention in improving the mathematics performance of low-achieving children. Consequently, educators need technically sound mathematics screening measures to identify children at risk and then intervene to improve achievement. In this article, we describe preliminary technical adequacy evidence for four early numeracy measures (number identification, quantity discrimination, quantity array, and missing number). We assessed over 300 kindergarten and first-grade students in two states to evaluate the reliability and criterion validity of the four measures. Fall and spring administrations of the measures for one subgroup provided preliminary evidence of students' growth on the measures over time. The results supported three of the four measures as potential tools for screening in the early grades.

This longitudinal study examined how children's early numeracy assessed in kindergarten predicts their mathematical performance in the first grade, after controlling for the effects of age, gender, and parents' education. The participants were 212 Finnish children (107 girls and 105 boys). At the time of the first assessment (kindergarten), the mean age was six years, and the second assessment was conducted one year later. The results demonstrate that the acquisition of counting and relational skills before formal schooling are predictive of the acquisition of basic arithmetical skills and overall mathematical performance in grade one, above and beyond the effects of demographic factors.

The famous dedication by Xenokrateia to the river god Kephisos and other divinities not far from the city of Athens in c. 400 BC (NM 2756; IG I3 987; IG II2 4547) is a rare example of a sizeable, public ego-document by a citizen woman. Close reading of the iconography of the votive relief, of the dedicatory epigram and the inscribed offering list, and comparison with other private foundations allow reconstructing Xenokrateia’s sense of her identity and the religious, intellectual and economic competences she must have had to bring this dedication about. As a literate, self-confident and pious Athenian citizen, mother, widow and heiress, she spent on estimation several hundred drachmas on her dedication, pace the law quoted at Is. 10.10. The plot of land involved was either her own property or a place already sacred to Kephisos and the Nymphs, to which she added her own dedication. For the latter possibility, a double relief dedicated by Kephisodotos to the hero Echelos and other deities (NM 1783) provides additional evidence. Xenokrateia’s dedication is exceptional for the detailed, qualitative analysis it allows, but it is not exceptional in quantitative terms: numerous dedications by women show them using similar competences. This approach to the evidence, initiated in recent scholarship, may open new windows on women’s agency in classical Athens.
Mots-clés : Xenokrateia – private foundation – citizenship – identity – competence – literacy – numeracy – votive relief – dedication – women’s agency – Is. 10.10 – classical Athens

This review contains current information on research, policy, and practice in adult literacy and learning for individuals and organizations focused on adult basic education (ABE), adult English for speakers of other languages (ESOL), and adult secondary education (ASE) programs.

In this study, we investigated how early numeracy skills develop in kindergarten-age children. The participants were 235 Finnish children (111 girls and 124 boys). At the time of the first measurement, the average age of the children was 6 years. The measurements were conducted three times during 1 year of kindergarten. We used a between-group repeated-measures analysis of variance and post hoc group comparisons for three measurement times on two related mathematical scales. The results showed that differences in mathematics skills among children are already visible in kindergarten before formal primary education in mathematics starts. The early numeracy skills measured, namely, relational skills in a numerical context and counting skills, were weaker over the kindergarten year in low-performing children, and, although their skills improved, they did not catch up to their average peers.

„Agrarpraktiker/Agrarpraktikerin“ ist ein Ausbildungsberuf in der Schweiz. Die schulischen Anforderungen in dieser Ausbildung sind nicht besonders hoch. Interessanterweise spielt aber auch in diesem Beruf gerade das mathematische Modellieren eine nicht zu unterschätzende Rolle. Und dabei werden gewisse Abstraktionsleistungen gefordert, wie beispielsweise bei der Frage des Düngerverbrauchs pro Hektare.