Number sense Research Papers - Academia.edu (original) (raw)

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- Psychology, Cognitive Science, Eye tracking, Cognitive development
- by Chaitanya Ramineni
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- Psychology, Mathematics, Learning Difficulties, Numeracy

In this research, it is aimed to examine the using conditions of the
number sense of the primary school 4th grade students, the relationship
between number sense and mathematics academic achievement of students. The workgroup has consisted of 115 4th grade students who were studying in a primary school in the Kadıkoy district of Istanbul. As a measuring tool the number sense test which was developed by the researchers were used. Also, in order to determine the relationship between the number sense success of the students and their mathematics success, the fall semester of 2014-2015 mathematics lesson school report card grades have been utilized. In consequence of the research, number sense performances of the primary school 4th grade students have been concluded as very low ( X =13.27, %30.16). When the students' solutions and explanations investigate, it has been seen that the students apply rule-operation based strategy rather than number sense in every components of the number sense. Also positive, significant and a medium-level correlation has been found between the number sense success of the students and their mathematics success [rho= .569, p<.05].
Keywords: Number Sense, Standard Calculation, Number Sense Components, 4th Grade Students, Student

- by sıtkı çekirdekci
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- Number sense, Number sense-Elementary-aged children

In this paper I argue against both neuropsychological and cognitive accounts of our grasp of numbers. I show that despite the points of divergence between these two accounts, they face analogous problems. Both presuppose too much about what they purport to explain to be informative, and also characterize our grasp of numbers in a way that is absurd in the light of what we already know from the point of view of mathematical practice. Then I offer a positive methodological proposal about the role that cognitive science should play in the philosophy of mathematics.

- by oliver marshall
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- Bertrand Russell, Number Sense (Education), Saul Kripke, Tyler Burge

Copyright: © 2014. The Authors. Licensee: AOSIS OpenJournals. This work is licensed under the Creative Commons Attribution License. Number sense studies have indicated that the development of number sense should be the focus of primary school mathematics education. The literature review revealed that learner performance is linked to teacher subject knowledge and that teachers' confidence in doing and teaching mathematics influences the way they teach and their willingness to learn mathematics. This study was motivated by the poor performance of Namibian primary school learners in both national and international standardised assessment tests and explored the number sense of 47 final-year primary school pre-service teachers (PSTs) in Namibia. The data in this mixed method research design were obtained from a number sense questionnaire, a written computations questionnaire, a mental calculations questionnaire and the McAnallen confidence in mathematics and mathematics teaching surv...

- by Magret Courtney-Clarke
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- Mathematics Education, Pythagoras, Number sense
- by Denes Szucs
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- Numerical Cognition, Number sense, Calculation

How are concepts from mathematics necessary for a realist
ontology? How does philosophy of mathematics account for an
ontological perspective that seeks to ground a non-essentialist
theory of subject and subjectivation, in which mathematics
produces formal parameters that are extra-linguistic and show
partial independence from logic? Is philosophy of mathematics
necessarily reducible to analytic philosophical principles and
theorems, or does a variation in philosophical traditions also
imply a variation in the reading of at least certain aspects of
mathematics? What are the consequences mathematical ontology holds for research led by Stanislas Dehaene on the
neuropsychology of the “number sense”?

El Test de Evaluación Matemática Temprana está orientado a medir el nivel de competencia matemática temprana. Se ha desarrollado para de educación infantil y 1º y 2º de primaria. Dispone de tres versiones paralelas, de 40 ítems cada una. Consta de 8 tareas, divididas en grupos de 5: Comparación, clasificación, correspondencia, seriación, conteo verbal, conteo estructurado, conteo resultante y conocimiento general de los números. Tiene una puntuación máxima de 40 puntos (uno por cada ítem correcto). El objetivo fundamental de este estudio consistió en adaptar el test a la población española con todas las garantías de validez y fiabilidad, que permita tener un instrumento para detectar posibles problemas en el aprendizaje de las matemáticas en los inicios de la escolaridad. El TEMT se ha baremado con una muestra de 1.053 niños/as pertenecientes a 14 colegios. 539 eran varones y 514 mujeres. Nos da un índice cuantitativo del nivel de competencia matemática temprana, posee un buen valor...

- by Esperanza Consejero and +1
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- Assessment, Cognition, Number sense

Malgré l’imposant corpus soutenant l’existence du “Approximate Number System” (ANS), certains proposent d’expliquer notre comportement dans des études sur la cognition numérique en se fiant à un système dédié au traitement de grandeurs continues comme la durée, la taille, la luminosité, etc. Selon ces sceptiques de l’ANS, les méthodes expérimentales utilisées pour étudier l’ANS ne nous permettent pas d’identifier ce système comme étant responsable de notre comportement dans de telles études, puisque la quantité d’objets discrets varie toujours avec une autre grandeur continue. Dans cet article, je soutiens qu’un tel scepticisme n’est pas tenable pour des raisons conceptuelles, étant donné l’opposition fondamentale entre le contenu mental associé au discret et celui associé au continu. Pour soutenir ma thèse, je propose un bref résumé de la conception de la relation entre le continu et le discret dans l’histoire de la philosophie, en particulier telle que conçue par le mathématicien intutionniste L.E.J Brouwer, selon qui il est impossible de construire un continu à partir d’éléments discrets, et vice versa.

- by Sulistiawati Sulistiawati
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- Number sense, Mathematical Games

The aim of this study is to examine the number sense skills of preservice elementary school mathematics teachers. This study was conducted by using the survey model among descriptive research methods. A total of 111 preservice teachers studying at second and third grades in the elementary school mathematics teaching program at a state university participated in the study. The data of the study were collected by using the number sense test consisting of 17 questions and developed by Kayhan-Altay (2010). The findings of the study indicated that the number sense performances of preservice elementary mathematics teachers were lower than expected and there was a significant difference in favour of third-grade students. It is considered that the “Special Training Methods I and II” courses and the “Mathematics Curriculum” course, which are taught in third grades and in which subjects such as estimation and making mental calculations, etc. superficially related to number sense are mentioned, may cause this difference. Thus, it was suggested that it was necessary to include courses consisting of number sense and how it can be developed in the curriculum.

- by Open Access Publishing Group
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- Teaching and Learning, Education, Mathematics Education, Didactics
- by Elizabeth Toomarian and +1
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- Cognitive Psychology, Mathematics, Education, Cognition
- by Klaus Willmes
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- Psychology, Number sense, FRONTIERS

Humans and other animals are able to make rough estimations of quantities using what has been termed the approximate number system (ANS). Much evidence suggests that sensitivity to numerosity correlates with symbolic math capacity, leading to the suggestion that the ANS may serve as a start-up tool to develop symbolic math. Many experiments have demonstrated that numerosity perception transcends the sensory modality of stimuli and their presentation format (sequential or simultaneous), but it remains an open question whether the relationship between numerosity and math generalizes over stimulus format and modality. Here we measured precision for estimating the numerosity of clouds of dots and sequences of flashes or clicks, as well as for paired comparisons of the numerosity of clouds of dots. Our results show that in children, formal math abilities correlate positively with sensitivity for estimation and paired-comparisons of the numerosity of visual arrays of dots. However, precision of numerosity estimation for sequences of flashes or sounds did not correlate with math, although sensitivities in all estimations tasks (for sequential or simultaneous stimuli) were strongly correlated with each other. In adults, we found no significant correlations between math scores and sensitivity to any of the psycho-physical tasks. Taken together these results support the existence of a generalized number sense, and go on to demonstrate an intrinsic link between mathematics and perception of spatial, but not temporal numerosity.

Introduction: Congenital amusia is a developmental disorder associated with deficits in pitch height discrimination or in integrating pitch sequences into melodies. This quasiexperimental pilot study investigated whether there is an association between pitch and numerical processing deficits in congenital amusia. Since pitch height discrimination is considered a form of magnitude processing, we investigated whether individuals with amusia present an impairment in numerical magnitude processing, which would reflect damage to a generalized magnitude system. Alternatively, we investigated whether the numerical processing deficit would reflect a disconnection between nonsymbolic and symbolic number representations. Method: This study was conducted with 11 adult individuals with congenital amusia and a control comparison group of 6 typically developing individuals. Participants performed nonsymbolic and symbolic magnitude comparisons and number line tasks. Results were available from previous testing using the Montreal Battery of Evaluation of Amusia (MBEA) and a pitch change detection task (PCD). Results: Compared to the controls, individuals with amusia exhibited no significant differences in their performance on both the number line and the nonsymbolic magnitude tasks. Nevertheless, they showed significantly worse performance on the symbolic magnitude task. Moreover, individuals with congenital amusia, who presented worse performance in the Meter subtest, also presented less precise nonsymbolic numerical representation. Conclusions: The relationship between meter and nonsymbolic numerical discrimination could indicate a general ratio processing deficit. The finding of preserved nonsymbolic numerical magnitude discrimination and mental number line representations, with impaired symbolic number processing, in individuals with congenital amusia indicates that (a) pitch height and numerical magnitude processing may not share common neural representations, and (b) in addition to pitch processing, individuals with amusia may present a deficit in accessing nonsymbolic numerical representations from symbolic representations. The symbolic access deficit could reflect a widespread impairment in the establishment of cortico-cortical connections between association areas.

- by Marília Nunes
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- Music Cognition, Congenital Amusia, Number sense

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic.

- by Pierre Pica
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- Approximation Theory, Languages and Linguistics, Arithmetic, Number sense
- by Annelise Júlio-costa
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- Psychology, Number sense

There is a misperception th represents the ability to rap ing a problem [1]. For exam efficient to picture pies tha pends on developing these k Some students possess matical problems but are r inefficient (but correct) stra dents to consider alternative ... Fig. 1. Race. Students position the car relative to the lane dividers. ... 1Carnegie Learning r, tnixon}@carnegielearning.com 2Carnegie Mellon University mas@gmail.com, john@stamper.org 3New York University dixie@nyu.edu ... Fig. 2. Numberline. Students identify the ship&amp;amp;#x27;s position on a numberline.

- by Derek Lomas
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- Mathematics, Evaluation, Intelligent Tutoring Systems, Number sense
- by noraini noordin
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- Estimation, Number sense, Logit
- by Véronique Izard
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- Mathematics, Approximation Theory, Languages and Linguistics, Cognition
- by Robert Reys
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- Mathematics, Mathematics Education, Science, Numbers
- by Giannis N Karagiannakis
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- Number sense

Marcus Giaquinto claims that finite cardinal numbers are sensible properties, and that the smallest ones are known by acquaintance. In this paper I compare Giaquinto’s epistemology to the Russellian one with which it invites comparison, before showing how it is subject to a version of Jody Azzouni’s “epistemic role” objection. Then I argue that the source of this problem is Giaquinto’s misconception that numbers, like quantities, are sensible properties. Finally, I offer a sketch of a theory of how we grasp finite cardinals on the assumption that they are not sensible, and show why this is not subject to the epistemic role objection.

This paper reports on a longitudinal study of teaching and learning in the subject of fractions in two matched groups of ten 9-10-year-old-students. In the experimental group fractions are introduced using the bar and the number line as (mental) models, in the control group the subject is introduced by fair sharing and the circle model. In the experimental group students are invited to discuss, in the control group students work individually.. The groups are compared on several occasions during one year. After one year, the experimental students show more proficiency in fractions than those in the control group.

- by Jan Terwel and +1
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- Psychology, Mathematics, Teaching and Learning, Comparative Study

Dados oriundos de investigações recentes em psicologia cognitiva, neuropsicologia e neurociência cognitiva tem permitido um crescente consenso de que as representações numéricas nos adultos e o pensamento matemático culturalmente construído dependem da interação entre o chamado “senso numérico”, observado em bebês humanos e em outras espécies animais, e a linguagem. Na pesquisa com bebês, a técnica do “olhar preferencial” tem permitido a descoberta de habilidades sofisticadas em idades precoces,
entre elas as de soma e subtração. A neuropsicologia apresenta casos de lesões em áreas do cérebro que causam prejuízos a habilidades específicas, com preservação de outras. E a neurociência cognitiva, por meio de modernos recursos de neuroimagem, tem permitido a localização precisa de áreas cerebrais responsáveis pelo processamento numérico. Todas essas contribuições lançam luzes sobre a natureza da cognição numérica subjacente à matemática. São apresentados e discutidos dados produzidos por pesquisas nas referidas áreas, bem como suas implicações para as teorias clássicas do desenvolvimento cognitivo e do conceito de número, em particular. Discute-se também a visão decorrente sobre a relação entre biologia e cultura, que passam a ser vistas não mais de maneira dicotômica e sim como continuidade
uma da outra, bem como implicações pedagógicas e sobre a formação de educadores.

- by melissa jenkins
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- Psychology, Special Education, Mathematics Education, Early Childhood Education

The goal of this study was to investigate understanding of inservice elementary school teachers in Taiwan about number sense, teaching strategies of number sense and the development of number sense of students; and the profile of integrating number sense into mathematical instruction , and teaching practice. Data wase gathered through interviews of two elementary mathematics teachers regarding their understanding about number sense followed by observations of the teachers instructing in their mathematics classes. The data included the categorization and comparison of these teachers’ understanding and teaching practices. The conclusions are as follows: The common point shared by two teachers was that in the teaching of four fundamental operations of fraction, they tended to ask the students to repeat and memorize the four fundamental operations of arithmetic or the arithmetic rules of addition, subtraction, multiplication and division of fraction. It was only the instruction valuing ...

- by yea-ling tsao
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- Teacher Education, Qualitative Research, Numbers, Numeracy
- by Brent Davis
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- Psychology, Mathematics Education, Numbers, Teaching Methods
- by Lucia Regolin and +2
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- Cognitive Science, Numerical Cognition, Number sense
- by Derek Lomas
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- Intelligent Tutoring Systems, Engagement, Games, Number sense

This paper addresses the relationship between basic numerical processes and higher level numerical abilities in normal achieving adults. In the first experiment we inferred the elementary numerical abilities of university students from the time they needed to encode numerical information involved in complex additions and subtractions. We interpreted the shorter encoding times in good arithmetic problem solvers as revealing clearer or more accessible representations of numbers. The second experiment shows that these results cannot be due to the fact that lower skilled individuals experience more maths anxiety or put more cognitive efforts into calculations than do higher skilled individuals. Moreover, the third experiment involving non-numerical information supports the hypothesis that these interindividual differences are specific to number processing. The possible causal relationships between basic and higher level numerical abilities are discussed.

- by Catherine Thevenot
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- Psychology, Cognitive Science, Mathematics, Cognition
- by Maria Tosto
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- Mathematics, Number Line, Number sense
- by munirah razak
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- Data Analysis, United Kingdom, Resource use, Pedagogical Content Knowledge
- by Rohana Alias and +1
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- Data Analysis, United Kingdom, Resource use, Pedagogical Content Knowledge
- by Rosa Rugani
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- Numerical Cognition, Number sense

ABSTRACT This paper presents the progress of an ongoing research aimed at developing the number sense in third graders. Based on assessment results of a sample of elementary schools in the Municipality of Zapopan, Jalisco, Mexico, we investigate the problem of mathematics learning with a cognitive approach. The study identifies the student's weakness related to their abilities to conceptualize the meaning of the numbers and its relationships. We present the main ideas of pedagogical design of a serious game developed in Scratch 2.0 that enhances the ability to identify and build sequences. Preliminary results suggest the use of a webcam to increase student's interaction and improve their numerical abilities.

- by Miguel Garcia
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- Design, Interaction, Number sense

accompanied by the development of efficient strategies for mental maths, in the foundation and intermediate phase. We do this through documentary analysis of the Curriculum and Assessment Policy Statements (CAPS) for these phases and the Annual National Assessments (ANAs). We argue that number sense and mental agility are critical for the development and understanding of algorithms and algebraic thinking introduced in the intermediate phase. However, we note from our work with learners, and broader evidence in the South African landscape, that counting-based strategies in the foundation phase are replaced in the intermediate phase with traditional algorithms. We share experiences in the form of vignettes to illuminate this problem. Whilst literature and the CAPS curriculum emphasise the important role of mental computation within number sense, we note that the ANAs do not include a “mental mathematics” component. This absence in assessment, where assessment often drives teaching, is...

- by Herman Tshesane
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- Psychology, Assessment, Number sense, Caps

Development of number sense in students at an early age has been the concern of most educators worldwide including Malaysia. The school system produced students who performed on examinations, but are lost when given a problem that is not from a textbook. There is cause to worry because students may not understand enough of numbers to proceed to higher mathematics. This has already been proven by research works in this area. Development of number sense among students can help to identify the proficient learners. Students who have developed number sense display some defined characteristics, such as a) able to focus more on strategies than a right answer, b) able to think instead of operating with mathematical rules, and c) able to work at finding his own solution than waiting to be provided with one by the teacher. Studies on number sense carried out from time to time help teachers and educators understand the minute details of problems students go through coping with numbers. This pa...

- by noraini noordin
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- Psychology, Estimation, Number sense, Logit

Using the online educational game Battleship Numberline, we have collected over 8 million number line estimates from hundreds of thousands of players. Using random assignment, we evaluate the effects of various adaptive sequencing... more

- by Kishan Patel
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- Intelligent Tutoring Systems, Number sense, Intelligent Tutoring
- by Nobuo Masataka
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- Mathematics, Education, Cognitive Load Theory, Creative Education
- by Koleen McCrink
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- Psychology, Cognitive Science, Cognition, Culture
- by Amy Devine and +1
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- Psychology, Numerical Cognition, Number sense
- by Vitor Cruz
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- Cognitive development, Number sense, Math
- by Annelise Júlio-Costa
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- Psychology, Computer Science, Medicine, Number sense
- by Johannes van Luit
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- Education, Numeracy, Language Teaching, Computation
- by Ronald Keijzer
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- Psychology, Mathematics, Teaching and Learning, Comparative Study
- by Beverly Woolf
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- Textiles, Ubiquitous Computing, Cognition, Game Based Learning