On the Nature of Numerosity and the Role of Language in Developing Number Concepts: A Reply to Everett

We respond to Caleb Everett’s (2013) critique of our 2012 Current Anthropology article “Numerosity, Abstraction, and the Emergence of Symbolic Thinking.” We refute Everett’s criticisms, including his claim that we overemphasized paleoanthropological evidence in our argument, noting that recent experimental research in numerical cognition comprised 60% of our references. We also identify two key misunderstandings by Everett, first, the idea that numerosity is not uniform in extant Homo sapiens (we believe that experimental findings, including those of Everett himself, demonstrate that quantity perception is cross-culturally uniform) and second, the idea that language necessarily shapes human numerosity (in fact, the two are largely independent cognitive processes, and the evidence shows that numerosity, as a perceptual primitive, precedes language, not the other way around as argued by Everett). We note our focus on the fundamental question of how discrete quantities emerge out of the undifferentiated ‘many’, given numerosity, and reiterate our 2012 suggestion that the answer lies in the interaction of quantity appreciation with material scaffolds.

Numerosity, Abstraction, and the Emergence of Symbolic Thinking

In this paper we tentatively propose that one of the feral cognitive bases for modern symbolic thinking may be numerosity, that is, the ability to appreciate and understand numbers. We proffer that numerosity appears to be an inherently abstractive process, which is supported by numerous human infant and monkey studies. We also review studies that demonstrate that the neurological substrate for numerosity is primarily the intraparietal sulcus of the parietal lobes, the angular and supramarginal gyri in the inferior parietal lobes, and areas of the prefrontal cortex. We also speculate that the lower level of abstraction involved in numerosity may serve as a basis for higher-level symbolic thinking, such as number and letter symbolism and sequencing. We further speculate that these two levels of abstraction may give rise to highly sophisticated characteristics of modern human language, such as analogizing and metaphorizing.

Cognitive Development (Symbolic Thinking) of Early Childhood Through the Innovation of Bowling Media

The use of bowling media in RA Muslimat NU 1 Tulus Rejo Kec. Pekalongan has not been used. Researchers are interested in developing bowling media with the aim of developing cognitive, because early childhood in RA Muslimat NU 1 Tulus Rejo Kec. Pekalongan in terms of cognitive ability is still undeveloped. The purpose of this study is to find out the development of Media Bowling Against Cognitive Development (Symbolic Thinking) Early Childhood. This research methodology uses (research and development). The development procedure according to Borg and Gall's theory consists of seven stages. Based on the results of the study it can be concluded that, the use of bowling media in children aged 5-6 years in RA Muslimat NU 1 Tulus Rejo Kec. Pekalongan can improve children's cognitive abilities.

Smart Toys in Early Childhood and Primary Education: A Systematic Review of Technological and Educational Affordances

The present paper presents a systematic review of the last 30 years that concerns records on Smart Toys and focuses on toys regarding early childhood and primary education children (3–12 years old). This paper aims to analyse and categorise smart toys (50 articles) in terms of their technological and educational affordances. The results show that the toys are designed based on four main technological affordances and their combinations. The educational affordances of smart toys are studied in terms of different use modes and their learning objectives aimed to identify specific objectives in different subjects and objectives based on transversal competencies such as problem solving, spatial thinking, computational thinking, collaboration and symbolic thinking. Finally, with the multiple correspondence analysis, the correlations between smart toys’ individual technological and educational affordances are grouped with the evolution of affordances related to their development date. In conclusion, in recent years, smart toys concern special sciences (programming) and some 21st-century skills (STEM and computational thinking). In contrast, in the first 20 years, the interest focused more on transverse skills, such as collaboration, emotional thinking, symbolic thinking, story-telling and problem solving.

The Effectiveness of the Android-Based Calistung Digital Game Application to Improve Early Childhood Cognitive Skills

This article aims to determine Android-based digital calistung game application's effectiveness to improve early childhood cognitive skills. The experimental method was carried out on 26 kindergarten students aged 5-6 years. The research design used was pre-experimental. The sampling technique used in this study was purposive sampling. Cognitive skill data collection used observation guidelines consisting of cognitive dimensions (1) symbolic thinking recognizing concepts, (2) learning problem solving and cause and effect, (3) association and classification. The assessment of cognitive skills used a scale of 1 - 4. The study results concluded an increase in the average value of cognitive skills of kindergarten students aged 5-6 years through the Calistung game. This research implies that teachers' competence in using digital calistung media needs to be improved through in-service training kindergarten students' cognitive skills.

Mathematical Knowledge and the Origin of Phenomenology

The paper is divided into two parts. In the first one, I set forth a hypothesis to explain the failure of Husserl’s project presented in the Philosophie der Arithmetik based on the principle that the entire mathematical science is grounded in the concept of cardinal number. It is argued that Husserl’s analysis of the nature of the symbols used in the decadal system forces the rejection of this principle. In the second part, I take into account Husserl’s explanation of why, albeit independent of natural numbers, the system is nonetheless correct. It is shown that its justification involves, on the one hand, a new conception of symbols and symbolic thinking, and on the other, the recognition of the question of “the formal” and formalization as pivotal to understand “the mathematical” overall.

Potential Influence of Bilingualism on the Development of Abstract Thinking

When studying the effect of individual bilingualism on the academic achievements of bilingual students in mathematics, many researchers emphasize the potential difficulties they are experiencing. Currently, a large number of various researches are devoted to studying the possible cognitive advantages of students associated with bilingualism. This paper uses an alternative approach based on the hypothesis that bilingualism gives students an advantage when solving complex abstract mathematical problems. The results of a pedagogical experiment conducted among first-year students of the Institute of Philology and Intercultural Communication at Kazan (Volga) Federal University give grounds to consider this hypothesis to be correct. They prove the assumption that bilinguals can better understand the meaning of symbols than monolinguals. There is a clear advantage of bilingual students in performing complex symbolic mathematical tasks. This advantage may be due to the fact that bilingual participants have more developed abstract-symbolic thinking. The results of the pedagogical experiment can also be explained by group differences in operating control or in the socio-economic status of the participants. Consideration of alternative explanations for the results of the pedagogical experiment will be the subject of further research.

MENGEMBANGKAN KEMAMPUAN BERPIKIR SIMBOLIK PADA ANAK USIA DINI MELALUI MEDIA PEMBELAJARAN STIK BERGAMBAR

The ability to think symbolically is the ability to formulate consepts learned by children for the provision of life in the future. The pictorial ice cream sticks media in learning activities can be used in developing childrens symbolic thinking skills. This research aims to find out the simbolic thinking ability of children. This study aims to determine the development of symbolic thinking abilities through pictorial stick media. The media of ice cream stick was chosen to be the solution of the problems that exist in, because these ice cream sticks have not been widely used as a mediun for the development of symbolic thinking skills, besides ice cream sticks are also easily available and familiar to chldren, so it expected through stick media illustrated ice cream will fasilitate researchers in developing symbolic thinking skills in children. This study uses an experimental method where the sampel in this study amounted to 26 children. Data processing using SPSS 22.0. The average gain test results between the experimental group and the control group were 7,07 for the experimental group and 6,38 for the control group. Thus it shows that pictorial ice cream sticks are able to develop symbolic numeracy skills at SPS Permata Bunda. With the application of pictorial ice cream stick learning media can increase childrens learning interest, students can be directly involved in learning can be more meaningful and meaningful for children.Kemampuan berpikir simbolik merupakan kemampuan dalam merumuskan konsep-konsep yang dipelajari anak guna bekal dikehidupan yang akan datang. Media stik eskrim bergambar dalam kegiatan pembelajaran dapat digunakan dalam mengembangkan kemampuan berfikir simbolik anak. Penelitian ini bertujuan untuk mengetahui kemampuan berpikir simbolik anak. Penelitian ini bertujuan untuk mengetahui pengembangan kemampuan berpikir simbolik melalui media stik bergambar. Media stik es krim bergambar dipilih untuk menjadi solusi dari permasalahan yang ada di SPS Permata Bunda, karena stik eskrim ini belum banyak digunakan sebagai media pengembangan kemampuan berpikir simbolik, selain itu stik eskrim juga mudah didapatkan dan tidak asing lagi bagi anak-anak, sehingga diharapkan melalui media stik es krim bergambar akan memudahkan peneliti dalam mengembangkan kemampuan berpikir simbolik pada anak. Penelitian ini meggunakan metode eksperimen dimana sampel terbagi menjadi kelompok eksperimen dan kontrol, sampel dalam penelitian ini berjumlah 26 orang anak. Pengolahan data menggunakan SPSS Versi 22.0. Hasil dari penelitian ini hasil uji postest dengan menggunakan SPSS 22.0. Hasil uji gain rata-rata antara kelompok eksperimen dan kelompok kontrol yaitu 7.07 untuk kelompok eksperimen dan 6.38 untuk kelompok kontrol. Dengan demikian menunjukkan bahwa stik es krim bergambar mampu mengembangkan kemampuan berpikir simbolik di SPS Permata Bunda. Dengan penerapan media pembelajaran stik bergambar ini dapat meningkatkan minat belajar anak, peserta didikpun dapat terlibat langsung dalam kegiatan pembelajaran, sehingga pembelajaran dapat lebih berarti dan bermakna bagi anak.

MENINGKATKAN KEMAMPUAN BERPIKIR SIMBOLIK ANAK USIA DINI KELOMPOK A (USIA 4-5 TAHUN) DENGAN MEDIA PEMBELAJARAN LESUNG ANGKA

Cognitive development is an important aspect. One of them is the ability to think symbolically. To improve the ability of symbolic thinking of early childhood certainly cannot be separated from the role of educators. Indicators of cognitive development that must be achieved by children aged 4-5 years are: numbers 1-10, recognizing the concept of numbers, recognizing the symbol of numbers, and recognizing the symbol of letters. For this reason, it is appropriate for educators to work hard to improve the ability to think symbolically in early childhood by providing stimulation through appropriate learning media like children, one of which is the media learning of dimples. This research was conducted with a class action research method. From the two cycles that have been done show the results that there is an increase in the ability of symbolic thinking in early childhood group A using the media learning dimples.Perkembangan kognitif merupakan aspek yang tidak kalah penting. Salah satunya adalah kemampuan berpikir simbolik. Untuk meningkatkan kemampuan berpikir simbolik anak usia dini tentu tak lepas dari peranan pendidik. Indikator perkembangan kognitif yang harus dicapai anak usi 4-5 tahun adalah: membilang benda 1-10, mengenal konsep bilangan, mengenal lambang bilangan, dan mengenal lambang huruf. Untuk itu sudah selayaknya pendidik berusaha dengan keras untuk meningkatkan kemampuan berpikir simbolik anak usia dini dengan cara memberikan stimulasi melalui media pembelajaran yang tepat bagai anak, salah satunya adalah media pembelajaran lesung angka. Penelitian ini dilakukan dengan metode peneletian tindakan kelas. Dari dua siklus yang telah dilakukan menunjukkan hasil bahwa terdapat peningkatan kemmapuan berpikir simbolik pada anak usia dini kelompok A dengan menggunakan media pembelajaran lesung angka.