This paper examines the conceptions of 'number sense' as promoted in pre-service primary mathematics education courses at 11 South African Higher Education Institutions through the texts used by ...academics or prescribed for students. While all the participating institutions agree that the development of primary school learners' 'number sense' is central to their mathematics methodology courses and that there is an overwhelming amount of research and literature on 'number sense' nationally and internationally, their conceptualisations of the nature of 'number sense' vary. Teacher educators, who develop pre-service teacher education courses, were asked to provide the texts, used to underpin the 11 universities' mathematics education modules in the Bachelor of Education (Foundation and Intermediate Phases) and Post Graduate Certificate in Education (Foundation and Intermediate Phases) programmes. These texts were analysed drawing on Whitacre et al.'s emphasis on three 'number sense constructs' identified as Innate Number Sense, Early Number Sense and Mature Number Sense. The results show that there is no common language of description for 'number sense' across the 11 universities. This research implies that there is a need to develop a consistent understanding of 'number sense' and how it is developed across institutions.
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BFBNIB, NUK, PILJ, SAZU, UL, UM, UPUK
Number Sense is a basic thing to learn mathematics, especially on numbers material. As a matter of fact, the preliminary research showed that students' number sense ability was so poor. Therefore, ...using students' worksheet as learning media on numbers material are expected to help students to understand the material. It implies, students' number sense ability can be better. The aim of this study is to figure out the effect of using worksheet on students' number sense ability. This study is using quantitative method with Wilcoxon Test. The number of 37 students were involved as a sample and chosen by random sampling technique. The result showed that the average score = 75.24 after students got the worksheet are higher than before they got the worksheet = 55.04. The result of hypothesis with Z score = -5.314 and p value = 0.000, so Ht was accepted. It means that there was different between before and after using the students' worksheet. This result also showed that there was the effect of using worksheet on students' number sense ability with an average increase of 19,00.
Both humans and non‐human animals exhibit sensitivity to the approximate number of items in a visual array, as indexed by their performance in numerosity discrimination tasks, and even neonates can ...detect changes in numerosity. These findings are often interpreted as evidence for an innate ‘number sense’. However, recent simulation work has challenged this view by showing that human‐like sensitivity to numerosity can emerge in deep neural networks that build an internal model of the sensory data. This emergentist perspective posits a central role for experience in shaping our number sense and might explain why numerical acuity progressively increases over the course of development. Here we substantiate this hypothesis by introducing a progressive unsupervised deep learning algorithm, which allows us to model the development of numerical acuity through experience. We also investigate how the statistical distribution of numerical and non‐numerical features in natural environments affects the emergence of numerosity representations in the computational model. Our simulations show that deep networks can exhibit numerosity sensitivity prior to any training, as well as a progressive developmental refinement that is modulated by the statistical structure of the learning environment. To validate our simulations, we offer a refinement to the quantitative characterization of the developmental patterns observed in human children. Overall, our findings suggest that it may not be necessary to assume that animals are endowed with a dedicated system for processing numerosity, since domain‐general learning mechanisms can capture key characteristics others have attributed to an evolutionarily specialized number system.
We present a computational model based on deep neural networks that simulates the developmental trajectory of numerosity perception in human children. Numerosity sensitivity in the model emerges both in controlled environments, and when the statistical structure of the training set mirrors that of natural environments.
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DOBA, FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UILJ, UKNU, UL, UM, UPUK
•A novel, descriptive, non-redundant specification of dot array stimuli is given.•A model of the ANS that accounts for non-numerical stimulus features is proposed.•The Weber fraction (w) from the ...model is shown to be more valid and reliable.•All participants are biased by non-numerical stimulus features.•Most participants primarily rely on number, as instructed.
The approximate number system (ANS) subserves estimation of the number of items in a set. Typically, ANS function is assessed by requiring participants to compare the number of dots in two arrays. Accuracy is determined by the numerical ratio of the sets being compared, and each participant’s Weber fraction (w) provides a quantitative index of ANS acuity. When making numerical comparisons, however, performance is also influenced by non-numerical features of the stimuli, such as the size and spacing of dots. Current models of numerosity comparison do not account for these effects and consequently lead to different estimates of w depending on the methods used to control for non-numerical features. Here we proffer a new model that teases apart the effects of ANS acuity from the effects of non-numerical stimulus features. The result is an estimate of w that is a more theoretically valid representation of numerical acuity and novel terms that denote the degree to which a participant’s perception of number is affected by non-numerical features. We tested this model in a sample of 20 adults and found that, by correctly attributing errors due to non-numerical stimulus features, the w obtained was more reliable across different stimulus conditions. We found that although non-numerical features biased numerosity discriminations in all participants, number was the primary feature driving discriminations in most of them. Our findings support the idea that, while numerosity is a distinct visual quantity, the internal representation of number is tightly bound to the representation of other magnitudes. This tool for identifying the different effects of the numerical and non-numerical features of a stimulus has important implications not only for the behavioral investigation of the ANS, but also for the collection and analyses of neural data sets associated with ANS function.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Anak TK mengalami kesulitan mengidentifikasi angka dan menghubungkan banyaknya benda dengan jumlah yang tepat. Hal ini berimplikasi pada number sense sebagai bagian penting dalam perkembangan ...kognitif anak usia TK. Empat orang ustadzah dan 32 siswa TK A Aisyiyah Bustanul Athfal 31 Surabaya terlibat dalam penelitian deskriptif eksploratif untuk mendeskripsikan proses membangun number sense. Penelitian ini bersifat fleksibel dan tidak kaku karena disesuaikan dengan tema setiap minggunya selama tiga bulan dimulai bulan Juni 2022 sampai dengan Agustus 2022. Proses pembelajaran direkam menggunakan handycam, diobservasi, dan dilakukan pencatatan lapangan selama penanaman number sense. Selama pengumpulan data, peneliti mengobservasi pembelajaran menggunakan lembar observasi dan dianalisis secara deskriptif berdasarkan kesejajaran dan konstruksi semantiknya melalui pemilihan data, pengelompokkan data, dan menyimpulkan. Hasil penelitian ini menunjukkan proses yang dilakukan ustadzah untuk membangun number sense pada anak TK A melalui proses (1) membilang tanpa makna, (2) mengenalkan korespondensi satu-satu antara bilangan dengan objek nyata, (3) mengurutkan bilangan, dan (4) mengenalkan konsep kardinalitas.
Global and country-specific mathematics performance constitutes a major challenge, both for educators and policymakers. Realisation of the African Union Agenda 2013 hinges significantly upon ...transformation of education. In this regard, mathematics and science education, specifically, are instruments for scientific and technological development to position Africa on the same level as the global league of continents in the future. It is, therefore, important to develop amongst learners a good understanding of a mathematical concept such as number sense from an early age, given that students who have a good sense of numbers can manipulate figures to simplify calculations and have the confidence to approach problems in a variety of ways. It is for this reason that the present study investigates the intervention strategies implemented by educators in enhancing learners’ understanding of number sense in the Ekurhuleni North District schools, Gauteng Province, South Africa. The study used a case study design and a qualitative research approach, both of which were supported by an interpretivist paradigm. The study made use of a semi-structured interview to gather data from mathematics teachers, learners, and a principal in the selected school. Research findings revealed that although mental computation, use of concrete props, use of the number line, and a counting strategy are some of the various strategies employed to enhance learners’ understanding of number sense, teachers need to develop a sound understanding of number sense and be flexible in their approaches in order to assist learners. Based on the findings, it was recommended that curriculum designers and teachers concentrate on teaching methods to help students develop learners’ number sense, as this can lead to potential mathematics success.
In the literature on numerical cognition, the presence of the capacity to distinguish between numerosities by attending to the number of items, rather than continuous properties of stimuli that ...correlate with it, is commonly taken as sufficient indication of numerical abilities in cognitive agents. However, this literature does not take into account that there are non-numerical methods of assessing numerosity, which opens up the possibility that cognitive agents lacking numerical abilities may still be able to represent numerosity. In this paper, I distinguish between numerical and non-numerical methods of assessing numerosity and show that the most common models of the internal mechanisms of the so-called number sense rely on non-numerical methods, despite the claims of their proponents to the contrary. I conclude that, even if it is established that agents attend to numerosity, rather than continuous properties of stimuli correlated with it, an answer to the question of the existence of the number sense is still pending the investigation of a further issue, namely, whether the mechanisms the brain uses to assess numerosity qualify as numerical or non-numerical.
Penggunaan media pembelajaran matematika di Sekolah Dasar (SD) dimaksudkan agar siswa dapat mempelajari matematika yang obyeknya abstrak dengan menggunakan pendekatan atau benda yang konkrit. Di sisi ...lain, kemampuan pemahaman bilangan dan penggunannya atau biasa dikenal sebagai number sense bagi siswa SD merupakan landasan penting bagi kesuksesannya belajar dimasa depan. Tulisan ini menyajikan hasil penelitian tentang pengembangan media pembelajaran “Saku Operasi Bilangan Bulat (KUPERAN)” dan “Batang Operasi Bilangan Bulat (BAPERAN)” untuk pembelajaran number sense. Tujuan yang hendak dicapai adalah terbangunnya media pembelajaran yang dapat digunakan dalam pembelajaran number sense yang memenuhi kriteria media berkualitas yakni valid, praktis, dan efektif. Metode pengembangan yang digunakan adalah model pengembangan ADDIE. Hasil yang diperoleh yakni dapat dibangun media pembelajaran KUPERAN dan BAPERAN yang valid (berdasarkan hasil validasi), praktis (berdasarkan hasil penerapan pada tahap ujicoba), dan efektif (berdasarkan capaian pada proses dan hasil pembelajaran) dalam pembelajaran number sense pada materi operasi hitung bilangan bulat.
In this review, we are pitting two theories against each other: the more accepted theory, the number sense theory, suggesting that a sense of number is innate and non-symbolic numerosity is being ...processed independently of continuous magnitudes (e.g., size, area, and density); and the newly emerging theory suggesting that (1) both numerosities and continuous magnitudes are processed holistically when comparing numerosities and (2) a sense of number might not be innate. In the first part of this review, we discuss the number sense theory. Against this background, we demonstrate how the natural correlation between numerosities and continuous magnitudes makes it nearly impossible to study non-symbolic numerosity processing in isolation from continuous magnitudes, and therefore, the results of behavioral and imaging studies with infants, adults, and animals can be explained, at least in part, by relying on continuous magnitudes. In the second part, we explain the sense of magnitude theory and review studies that directly demonstrate that continuous magnitudes are more automatic and basic than numerosities. Finally, we present outstanding questions. Our conclusion is that there is not enough convincing evidence to support the number sense theory anymore. Therefore, we encourage researchers not to assume that number sense is simply innate, but to put this hypothesis to the test and consider whether such an assumption is even testable in the light of the correlation of numerosity and continuous magnitudes.
A Sensorimotor Numerosity System Anobile, Giovanni; Arrighi, Roberto; Castaldi, Elisa ...
Trends in cognitive sciences,
January 2021, 2021-01-00, 20210101, Volume:
25, Issue:
1
Journal Article
Peer reviewed
Open access
Incoming sensory input provides information for the planning and execution of actions, which yield motor outcomes that are themselves sensory inputs. One dimension where action and perception ...strongly interact is numerosity perception. Many non-human animals can estimate approximately the number of external elements as well as their own actions, and neurons have been identified that respond to both. Recent psychophysical adaptation studies on humans also provide evidence for neural mechanisms responding to both the number of externally generated events and self-produced actions. Here we advance the idea that these strong connections may arise from dedicated sensorimotor mechanisms in the brain, part of a more generalized system interfacing action with the processing of other quantitative magnitudes such as space and time.
Behavioral studies show that humans and other animals can estimate the numerosity of both external stimuli and self-produced actions.Recent psychophysical studies using motor-adaptation techniques have characterized the link between action and magnitude perception, advancing the concept of a sensorimotor system encoding both external stimuli and internally generated actions.The sensorimotor numerosity system might reside in the parietal cortex.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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