Symbolic Number Skills Predict Growth in Nonsymbolic Number Skills in Kindergarteners

There is currently considerable discussion about the relative influences of evolutionary and cultural factors in the development of early numerical skills. In particular, there has been substantial debate and study of the relationship between approximate, nonverbal (approximate magnitude system, AMS) and exact, symbolic (symbolic number system, SNS) representations of number. Here we examined several hypotheses concerning whether, in the earliest stages of formal education, AMS abilities predict growth in SNS abilities, or the other way around. In addition to tasks involving symbolic (Arabic numerals) and non-symbolic (dot arrays) number comparisons, we also tested children’s ability to translate between the two systems (i.e., mixed-format comparison). Our data included a sample of 539 Kindergarten children (mean=5.17yrs, SD=0.29yrs), with AMS, SNS and mixed comparison skills assessed at the beginning and end of the academic year. In this way, we provide, to the best of our knowledge, the most comprehensive test to date of the direction of influence between the AMS and SNS in early formal schooling. Results were more consistent with the view that SNS abilities at the beginning of Kindergarten lay the foundation for improvement in both AMS abilities and the ability to translate between the two systems. Importantly, we found no evidence to support the reverse. We conclude that, once one acquires a very basic grasp of exact number symbols, it is this understanding of exact number (and perhaps repeated practice therewith) that facilitates growth in the AMS. Though the precise mechanism remains to be understood, these data challenge the widely held view that the AMS scaffolds the acquisition of the SNS.

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Kindergarteners’ Symbolic Number Abilities Predict Non-Symbolic Number Abilities and Math Achievement in Grade 1

10.31234/osf.io/xpe9c ◽

2019 ◽

Author(s):

Nathan TT Lau ◽

Rebecca Merkley ◽

Paul F. Tremblay ◽

Samuel Zheng ◽

Stefanie De Jesus ◽

...

Keyword(s):

Math Achievement ◽

Number System ◽

Kindergarten Children ◽

Model Fit ◽

Future Research ◽

Time Points ◽

Parallel Development ◽

Theoretical Predictions ◽

Path Models ◽

Symbolic Number

Research has shown that two different, though related ways of representing magnitude play foundational roles in the learning of classroom math abilities: a non-verbal, approximate number system (ANS) and an exact, symbolic number system (SNS). While there have been a multitude of studies suggesting that the ANS and SNS are important predictors of math achievement (MA), there has recently been substantial debate regarding whether and how these basic numerical competencies may be developmentally interrelated. Specifically, there has been discussion on whether children’s ANS abilities predict later SNS abilities (the mapping account) or children’s SNS abilities predict later ANS abilities (the parallel development account). We modelled and contrasted multiple theoretical predictions posited by these two developmental accounts using multiple longitudinal path models. Our sample included 622 kindergarten children (M = 62 months, SD = 3.5), whose ANS, SNS and mixed-comparison skills were assessed over three time points and MA assessed over four time points. Results were most consistent with the parallel development account, suggesting that earlier SNS abilities are consistently the strongest predictor of ANS abilities, mixed-comparison abilities, and MA. Notably, our results demonstrated that, when individual models are examined in isolation, model fit either reached or approached adequate fit for all models tested. This highlights the need for future research to contrast competing accounts, as our results suggest that the examination of any one account in isolation may lead to misleading theoretical conclusions. In sum, our results are consistent with the view that children’s SNS abilities predicts later ANS abilities.

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Young children's non-numerical ordering ability at the start of formal education longitudinally predicts their symbolic number skills and academic achievement in maths

Developmental Science ◽

10.1111/desc.12645 ◽

2018 ◽

Vol 21 (5) ◽

pp. e12645 ◽

Cited By ~ 7

Author(s):

Patrick A. O'Connor ◽

Kinga Morsanyi ◽

Teresa McCormack

Keyword(s):

Academic Achievement ◽

Formal Education ◽

Symbolic Number ◽

Number Skills

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Genetics and Formal Education

Innumeracy in the Wild ◽

10.1093/oso/9780190861094.003.0012 ◽

2020 ◽

pp. 140-150

Author(s):

Ellen Peters

Keyword(s):

Formal Education ◽

Math Anxiety ◽

Number System ◽

Early Learning ◽

Genetic Influence ◽

Formal Schooling ◽

Approximate Number System ◽

Barriers To Learning ◽

Mathematical Concepts

This chapter, “Genetics and Formal Education,” reviews evidence for the genetic underpinnings of numeric competencies, the role of formal education in developing better numeric skills, and barriers to learning in school. Studies indicate some genetic influence on approximate number system (ANS) acuity (also called intuitive number sense), objective numeracy, and math anxiety. The lowest heritability exists for ANS acuity, presumably because it is an evolutionarily preserved core trait. Evidence also exists for the importance of formal schooling to development of ANS acuity, and, of course, objective numeracy. Educators generally design mathematical curricula to build understanding smoothly from one topic to the next. However, children (and adults) have more difficulty learning some mathematical concepts than others (e.g., arithmetic with fractions, decimals, probabilities, and proportions). Finally, other barriers to learning math can disrupt learning, including missed chances to maximize early learning and math anxiety.

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Longitudinal relations between the approximate number system and symbolic number skills in preschool children

Journal of Experimental Child Psychology ◽

10.1016/j.jecp.2021.105254 ◽

2021 ◽

Vol 212 ◽

pp. 105254

Author(s):

Xiangzi Ouyang ◽

Yawei Yang ◽

Xiao Zhang ◽

Qiusi Zhang

Keyword(s):

Preschool Children ◽

Number System ◽

Approximate Number System ◽

Symbolic Number ◽

Number Skills

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COGNITIVE DECLINE AMONG OLDER ADULTS IN RURAL CHINA: THE PROTECTIVE ROLE OF FORMAL SCHOOLING

Innovation in Aging ◽

10.1093/geroni/igz038.745 ◽

2019 ◽

Vol 3 (Supplement_1) ◽

pp. S205-S206

Author(s):

Yaolin Pei ◽

Bei Wu ◽

Zhen Cong ◽

Mengyao Hu

Keyword(s):

Older Adults ◽

Cognitive Decline ◽

Cognitive Functioning ◽

Formal Education ◽

Multilevel Models ◽

Life Experience ◽

Sampling Strategy ◽

Later Life ◽

Formal Schooling

Abstract Evidence shows that education is strongly associated with cognitive functioning; however, few studies have examined the effect of education on cognitive decline among older adults with very limited education. Our study analyzed six waves of panel data (2001, 2003 2006, 2009, 2012 and 2015) from the Longitudinal Study of Older Adults in Anhui Province, China. We estimated two-level multilevel models of cognitive functioning for older adults age 60+, sampled using probability sampling strategy. We found that having formal schooling was positively associated with better cognitive functioning. Older adults with formal schooling had slower decline in cognition and the gap in cognition between the literate and illiterate widened with age. These findings highlight the role of early life experience in affecting cognitive function in later life and suggest that disadvantages in cognitive functioning accumulate throughout the life course for persons with no formal education.

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Is Shadow Education Becoming the ‘New’ Formal? Effects of Pedagogical Approaches of IIT-JEE Coaching on School Education in the City of Delhi

Contemporary Education Dialogue ◽

10.1177/0973184919885485 ◽

2019 ◽

Vol 17 (1) ◽

pp. 14-44 ◽

Cited By ~ 3

Author(s):

Shalini Punjabi

Keyword(s):

Formal Education ◽

Indian Institute ◽

School Education ◽

Policy Implications ◽

Pedagogical Practices ◽

Shadow Education ◽

Formal Schooling ◽

Entrance Exam ◽

Institute Of Technology ◽

The City

Formal education has always been the principal model through which societies educate their young. Today, however, schools are seen as non-analytical and are being replaced by logic-based approach of competitive examinations. In India, the growth of shadow education, which is preponderant at the level of secondary education, is providing informal avenues through which the youth garner knowledge and skills. One such avenue is the private coaching for the Joint Entrance Exam to enter into the premier Indian Institute of Technology(s). The article draws on an exploratory study carried out in the city of Delhi and examines the credentialing strategies of IIT aspirants through Joint Entrance Exam coaching and how the pedagogical practices of coaching institutes influence the perceptions and proclivities of aspirants and their families towards school education. I also discuss the policy implications of such practices for formal schooling.

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‘British Values Are Also Values All Around the World’: Teaching Fundamental British Values through a Human Rights Lens

Journal of Human Rights Practice ◽

10.1093/jhuman/huaa042 ◽

2020 ◽

Author(s):

Alison E C Struthers ◽

Julie Mansuy

Keyword(s):

Human Rights ◽

Primary Schools ◽

Formal Education ◽

National Level ◽

Formal Schooling ◽

Desire For Children ◽

Global Citizens ◽

Global Context ◽

National Values ◽

The Uk

Abstract Since 2014, the promotion of Fundamental British Values (FBV) has been a requirement across formal schooling in England. The agenda has, however, faced criticism from various stakeholders. Much of this denunciation has been directed at the opaque nature of FBV, but the agenda is problematic for more concerning reasons. It is arguable that, in light of the current threat from ethno-nationalism, frameworks such as FBV that focus on a particular definition and formulation of national values run the risk of being interpreted in a manner that is exclusionary and liable to ‘other’ different ethnic groups in the classroom. The FBV framework furthermore overlooks the fact that the UK isalready subject to numerous international human rights obligations, including many that mandate the provision of holistic and effective human rights education at all levels of formal education. This article therefore draws upon the findings of a pilot study conducted with Year 5 learners in four primary schools in the West Midlands showing that teaching about human rights through the FBV agenda is possible, by linking discussion of values at the national level to broader human rights principles. Such an approach satisfies the government’s desire for children to learn about FBV, whilst highlighting that these values also exist in a global context. This, in turn, is likely to be a more effective way of encouraging learners to be global citizens who will contribute to the building of a broader culture that is respectful of human rights.

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Street-connectedness and education in Kenya: Experiences of formal schooling as rationale for inclusive pedagogies of practice

Prospects ◽

10.1007/s11125-020-09495-w ◽

2020 ◽

Vol 49 (3-4) ◽

pp. 265-280

Author(s):

Su Lyn Corcoran ◽

Lillian Aoko Awimbo ◽

Kelvin Mugwanga ◽

Irene Atieno Aluoch

Keyword(s):

Young People ◽

Empirical Evidence ◽

Inclusive Education ◽

Formal Education ◽

Original Research ◽

Data Generation ◽

Formal Schooling ◽

Research Findings ◽

Insight Into

AbstractThis article contributes to the literature on street-connectedness and inclusive education, presenting original research findings from two Kenyan studies. Both studies aim to understand street-connected young people’s experiences of education. The first focused on transitioning from the street into education or training, to explore the challenges of making that transition. The second focused on young people who had lived on the street for extended periods of time and were still there at the time of data generation. Both studies generated significant insight into (a) education as motivating initial migrations to the street, (b) the role of fear, embarrassment, and shame in preventing young people from going (back) into formal education, and (c) how acceptance and support are key to overcoming feelings of not belonging and other challenges when transitioning from the street into school. The article provides empirical evidence that should be considered when planning inclusive education provision for street-connected young people globally.

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Bala ga lili: Meeting Indigenous Learners Halfway

Australian Journal of Environmental Education ◽

10.1017/aee.2013.2 ◽

2012 ◽

Vol 28 (2) ◽

pp. 78-91 ◽

Cited By ~ 4

Author(s):

Susan Zela Bissett

Keyword(s):

Critical Pedagogy ◽

Formal Education ◽

Local Community ◽

Community Support ◽

Education For Sustainability ◽

Formal Schooling ◽

Culturally Appropriate ◽

Cultural Accommodation ◽

Pedagogy Of Place ◽

Indigenous Learners

AbstractThe author's experience of the day-to-day issues faced as an educator in an Aboriginal school are recounted, along with perspectives gained as part of a research project. The proposition is argued that an Education for Sustainability approach, where learning is structured around a negotiated environmental issue within local community, represents a cultural accommodation or halfway point between mainstream formal schooling and the needs of Indigenous learners. This article contends that such an educative approach meets Indigenous learners ‘halfway’, through compatibility with Indigenous values frameworks and employing culturally appropriate pedagogical methods. The argument is made that by demonstrating a willingness to negotiate worthwhile environmentally based projects that address community ecological concerns, EfS may be able to improve community support and mitigate impediments to the engagement of Indigenous learners with formal education. A critical pedagogy of place (Grunewald, 2003) is discussed as a theoretical framework that combines place-based pedagogy with empowering educational theory. Indigenous learners’ connection with place is recognised in this approach and ascribed a positive rather than negative value.

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