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1
Rasmusson, Malin. "Teaching Number Sense to Kindergarteners." Thesis, Malmö högskola, Lärarutbildningen (LUT), 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-34824.
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Då jag tidigare besökt förskoleklasser i USA har jag förvånats över hur mycket tid som ägnats åt laborativ matematik. När nationella läroplanen i matematik i USA, Principles and Standards for School Mathematics, omarbetades blev fokus inom matematik att arbeta för att stärka elevers taluppfattning. Lockad av tidigare erfarenheter från det amerikanska skolsystemet beslutade jag mig därför för göra en deltagande observation med löpande protokoll för att se hur man arbetar med taluppfattning i en förskoleklass i Texas. Under observationen fokuserade jag på att se samband mellan undervisningen, läroplaner och teorier inom matematikundervisning. Resultatet av min undersökning visar att nittio minuter varje dag ägnades åt laborativa matematikaktiviteter anpassade för att hjälpa eleverna att uppnå läroplanens mål. Därtill fanns en tydlig anknytning till teorier inom matematikundervisning.Arbetet är skrivet på engelska. Detta för att termer, dialoger etc. inte ska översättas inkorrekt och för att skolan som observationen skedde på ska kunna ta del av resultatet.As I earlier visited Kindergarten classes in the United States, I was surprised to see how much time that was set aside for mathematical activities in a hands-on fashion. In the reform of the United States Principle and Standards for School Mathematics, number sense was an essential outcome. Hence, the purpose of my study was to investigate, using participant observation with running records as a method, how number sense is taught in a Kindergarten class in Texas. During my observation, I especially looked at the educations connection to the guidelines and mathematics education theories. The result of my investigation shows that ninety minutes every day was set aside for mathematical activities in hands-on fashion, adapted to meet the guideline requirements and goals. In addition, the teaching observed in the class was closely associated with the mathematics educational theories.
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Moomaw, Sally Coup. "Measuring Number Sense in Young Children." University of Cincinnati / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1204156224.
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Forslund, Lena. "Taluppfattningens betydelse i matematiken : Undervisning och bedömning av taluppfattning och skriftliga räknemetoder ur ett lärarperspektiv." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-25621.
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Syftet med studien är att bidra till ökad förståelse av och fördjupad kunskap om taluppfattningens och skriftliga räknemetoders betydelse för hinder i elevers matematikutveckling, särskilt avseende addition och subtraktion, samt undersöka hur lärare arbetar med dessa områden för att förebygga och möta hinder för matematikutveckling. Elevers matematikkunskaper sjunker och på senare år har brister i taluppfattning uppmärksammats som en möjlig orsak. Denna studie med kvalitativ ansats har intervjuer och skriftliga dokument som datainsamlingsmetod. Hur uppfattar nio lärare som undervisar i år 1-6 nödvändiga kunskaper i taluppfattning för att hantera skriftliga räknemetoder i addition och subtraktion och vilka förklaringar till brister lyfter de. Vilka verktyg används för att få kännedom om elevers kunskaper i matematik vad gäller taluppfattning och skriftliga räknemetoder? Av resultatet av studien framkommer att det finns variationer i uppfattningar om nödvändiga kunskaper och undervisning om taluppfattning och skriftliga räknemetoder. Resultaten på Nationella prov vad gäller de båda studerade områdena visar på ett bättre resultat då det gäller taluppfattning jämfört med skriftliga räknemetoder. Detta kan bero på den komplexitet som det sociala samspelet mellan olika strukturer i samhället innebär.
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Mellott, Mallory. "The Effects of 'Number Talks' on Number Sense in a Second Grade Math Class." Otterbein University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=otbn1594306261084857.
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Hanrahan, Frances M., and res cand@acu edu au. "Number Sense or No Sense: Pre-service teachers learning the mathematics they are required to teach." Australian Catholic University. School of Education, 2002. http://dlibrary.acu.edu.au/digitaltheses/public/adt-acuvp19.16082005.
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As a result of two years working with the pre-service primary teachers in a College in Fiji I became aware of the difficulty many of the students were having understanding the primary school mathematics they would be required to teach. During that time I had attempted to help them overcome the difficulties by using different teaching approaches and activities but was far from satisfied with my efforts. Hence I decided to make a concerted effort to help the students by planning, implementing and partially evaluating a mathematics education unit, known as the Teaching Program for the first semester of their course. This work formed the basis of my study. For the Teaching Program I chose a constructivist teaching approach with number sense as the underlying theme. To examine the aspects of the Program I used my observations and those of the students especially ones reported in their mathematics journals. To evaluate the effectiveness of the Teaching Program I collected and analysed quantitative data from traditional testing of the class of forty students as well as data from case studies of six of the pre-service teachers in the class. To determine what features of the Teaching Program were linked to positive changes my main source of data was the case studies, especially entries from their journal writings. The findings suggested that a significant development of the cognitive aspects of the students’ number sense did occur during the time of the Teaching Program but not as much as was hoped for. As a result of the analysis of the data I came to a greater realisation of the importance of the non-cognitive aspects of number sense and the necessity for a greater consideration of them in the development of a Program. I also realise now that a major development that did occur was in my understanding of the knowledge and learning of mathematics. My ideas of a teaching paradigm of social constructivism had not guided me sufficiently to incorporate activities and procedures to develop the non-cognitive aspects. I suggest that a paradigm which extends the theory of social constructivism to give greater consideration of these aspects of learning in general, and hence numeracy and number sense in particular, was needed. As a result of this study, my introduction to the theory of enactivism appears to be giving me some direction in this search at this stage.
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Hanrahan, Frances M. "Number sense or no sense : pre-service teachers learning the mathematics they are required to teach /." Fitzroy, Vic. : Australian Catholic University, 2002. http://dlibrary.acu.edu.au/digitaltheses/public/adt%2Dacuvp19.16082005.
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Thesis (Ed.D.) -- Australian Catholic University, (2002)."A thesis submitted in partial fulfilment of the requirements for the Degree of Doctor of Education. Bibliography: p. 279-293. Also available in an electronic format via the internet.
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Chow, Valeen Marie. "Elementary teachers' thinking (beliefs) about number sense and its pedagogy." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/MQ65095.pdf.
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Mathews, Elizabeth Leigh. "Improving a Second Grade Student's Number Sense: An Instructional Intervention." MSSTATE, 2007. http://sun.library.msstate.edu/ETD-db/theses/available/etd-04082007-162641/.
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The purpose of this qualitative case study was to help a second grade student, who struggled with mathematics but excelled in reading, to develop a conceptual understanding of number sense, using a teacher researcher-created intervention. The five-step, one-on-one intervention included the following: (1) use trade books to build mathematical knowledge and vocabulary (2) teacher modeling of concepts, (3) guided practice with manipulatives, (4) review using games and a ?Fact Pack?, and (5) journal writing to explain concepts. The Early Mathematics Assessment-3 (TEMA-3) was used as a pre- and post-test assessment the student?s mathematical knowledge. Other data included transcriptions of audio taped intervention sessions, notes from video-taped intervention sessions, fieldnotes, and artifacts from the classroom and intervention sessions. Data sources were triangulated. On the TEMA-3 Pretest, the student scored at the first grade, fourth month (1.4) level. After 13 Lessons covered in 22 sessions (approximately 11 hours of one-on-one instruction), the student scored at the second grade, second month (2.2) level. She also scored Proficient on the state curriculum test in mathematics. Four aspects of the intervention seem to help the student most in her development of number sense. They included the use of (1) a number line; (2) a number structure, which visually depicted the value of numbers; (3) trade books to provide an anchor for each skill and a memorable context; and (4) journaling. In addition, the data revealed that once the student understood the concept of ten?s and one?s, her ability to count and add extended to include numbers 1 to 100. Recommendations for students who excel in reading and writing, but struggle with mathematics, include the following: the use of trade books and writing may help them better understand mathematics concepts; review of mathematical concepts through enjoyable, meaningful games and the use of a Fact Pack are useful; the use a horizontal number line and number structure, which is consistent with left-to-right directionality of reading and writing, may help students better understand the concepts of more, less, before, and after; and consistent use of vocabulary during instruction may help students better understand number concepts.
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Harris, Callie. "The impact on computational fluency through instruction in number sense." Thesis, A link to full text of this thesis in SOAR, 2008. http://hdl.handle.net/10057/2047.
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O'Reilly, Declan. "Visualising number : a study of children's developing sense of number in the computational medium of Boxer." Thesis, University College London (University of London), 1995. http://discovery.ucl.ac.uk/10021586/.
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The aim of this study is to investigate children's developing sense of number in the computational medium of Boxer. Boxer's combination of graphical and symbolic elements afforded the opportunity for children to visualise numbers in an operational way while simultaneously offering insights into how this operational approach mediated their thinking. There were three inter-related aspects to the study, with visualisation being the common feature of all three. • (i) How does the visual structure of Boxer influence students' (aged 9 - 11) ability to program? • (ii) What interpretations do students place on a number system extended beyond the natural numbers and how did they choose to represent these? • (iii) How can the learning environment of Boxer be exploited as a context for developing students' sense of number? Following an exploratory study, pedagogical models for investigating issues (i) and (iii) were developed. For issue (i), Boxer was exploited as a means of introducing itself. This, in turn, meant documenting the issues involved in a process of iterative design. For issue (iii), a model of learning was developed which proposed that the children should construct their own microworlds. Following an off-computer investigation of issue (ii), the model was refined to that of children constructing operational computational objects, and the research aim broadened to include an investigation of how these objects mediated their expression of number. This part of the research consisted of a longitudinal study lasting two years. It entailed case studies with four pairs of children, while the rest of the class learned Boxer independently. None of the children had previous Boxer or Logo experience. The research setting was a normal classroom in an inner-London primary school. Data for issues (i) and (iii) was obtained by means of video recordings and annotated print-outs, while data for issue (ii) was obtained by written records and audio recordings. Evidence from the research suggests that students' programming is significantly more structured in Boxer relative to Logo, and this structure is directly related to the visual nature of Boxer. Moreover, data from the number studies suggests that this visual structure was also instrumental in providing students with the means to connect number processes with number concepts, thus enabling them to engage with number ideas which might otherwise have been beyond their reach.
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Cheung, Siu-pun, and 張兆斌. "The effective use of number sense for assisting students with learningdifficulties." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B40039924.
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Courtney-Clarke, Magret Anna Eugenie. "Exploring the number sense of final year primary pre-service teachers." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/19943.
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Thesis (MEd)--Stellenbosch University, 2012.ENGLISH ABSTRACT: This study explored the number sense of 47 final year primary school pre-service teachers in Namibia and was motivated by the poor performance of Namibian primary school learners in both national and international standardised assessment tests. The literature review revealed that learner performance is linked to teacher subject knowledge (Ball, 1990, Ma, 1999) and that teachers’ confidence in doing and teaching mathematics influences the way they teach and their willingness to learn mathematics (Ball, 1990; Graven 2004). Number sense studies of pre-service teachers (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) have indicated that the development of number sense should be a focus of primary pre-service teacher education. The data in this mixed method research design were obtained from a Number Sense Questionnaire, a Written Computations Questionnaire and a Mental Calculations Questionnaire. These questionnaires were adapted from instruments developed by Professor Der-Ching Yang for 6th and 8th grade learners in Taiwan. Teacher confidence was measured by the McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Six randomly selected pre-service teachers were interviewed to determine their use of number-sensible strategies. The correlation analysis shows a strong relationship between number sense and mental calculations; between number sense and confidence in both the ability to do and the ability to teach mathematics and between mental and written calculations. The overall results of this study reveal that the final year primary pre-service teachers demonstrate limited number sense and possess very few of the indicators of number sense that were described by Kalchman, Moss and Case (2001). The findings expose a lack of conceptual understanding of the domain numbers and operations, particularly in the domain of rational numbers and the operations of multiplication and division. The pre-service teachers have little or no access to a variety of flexible number-sensible strategies to solve problems and calculate mentally. They lack the fluency in basic facts and procedures to perform written calculations efficiently and correctly. Unexpectedly, the analysis of the confidence survey shows that they are confident in both their ability to do mathematics and their ability to teach mathematics. It is recommended that mental calculations and computational estimation should become a focus of primary school mathematics education. Institutions responsible for teacher training should develop the number sense of pre-service teachers and research effective and long-term professional development programmes. The confidence and willingness of the teachers to learn can be used as an important resource.
AFRIKAANSE OPSOMMING: Hierdie studie ondersoek die getalbegrip van 47 finale jaar primêre skool voordiens-onderwysers in Namibië en is gemotiveer deur die swak prestasie van die Namibiese primêre skool leerlinge in beide nasionale en internasionale gestandaardiseerde assesseringstoetse. Die literatuurstudie het aan die lig gebring dat leerlinge se prestasie gekoppel is aan onderwyservakkennis (Ball, 1990, Ma, 1999) en dat onderwysers se vertroue in hulle vermoë om wiskunde te doen en te onderrig, die manier waarop hulle onderrig en hul bereidwilligheid om wiskunde te leer beïnvloed (Ball, 1990, Graven 2004 ). Studies van voordiens primêre onderwysers se getalbegrip (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) toon dat die ontwikkeling van getalbegrip 'n fokus van primêre voordiensonderwyseropleiding behoort te wees. Die data in hierdie gemengde metode navorsing is verkry uit 'n Getalbegrip, 'n Skriftelike Berekeninge en 'n Hoofrekene Vraelys. Hierdie vraelyste is gebaseer op die instrumente wat ontwikkel is deur Professor Der-Ching Yang vir graad 6 en 8 leerlinge in Taiwan. Onderwyservertroue is gemeet deur die McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Ses ewekansig geselekteerde voordiens-onderwysers is ondervra om te bepaal watter sinvolle strategieë hulle gebruik om vrae oor getalbegrip te beantwoord. Die korrelasie-analise toon 'n sterk verband tussen getalbegrip en hoofrekene; tussen getalbegrip en vertroue in die vermoë om wiskunde te doen en te leer, en tussen vermoë om hoofrekene en skriftelike bewerkinge te doen. Die algehele resultate van hierdie studie dui daarop dat die finale jaar primêre voordiens-onderwysers oor beperkte getalbegrip en baie min van die aanwysers van getalbegrip wat deur Kalchman, Moss en Case (2001) beskryf is, beskik. Die bevindinge toon ‘n gebrek aan begrip van die domein van getalle en bewerkings, veral in die domein van rasionale getalle en die bewerkings vermenigvuldiging en deling. Die voordiens-onderwysers beskik oor min of geen soepel strategieë om probleme op te los en hoofrekene te doen nie. Hulle beskik nie oor die vlotheit in basiese feite en bewerkings om skriftelike berekeninge doeltreffend en korrek uit te voer nie. Die vertroue wat voordiens-onderwysers uitgespreek het in hulle vermoë om wiskunde te doen en onderrig staan in sterk teenstelling met hierdie bevindige. Dit word aanbeveel dat hoofrekene en skatting 'n fokus van primêre skool wiskunde-onderwys behoort te wees. Instansies gemoeid met onderwyseropleiding behoort die getalbegrip van voordiensonderwysers te onwikkel en navorsing te doen oor effektiewe en lang-termyn programme vir professionele ontwikkeling. Onderwysers se vertroue en bereidwilligheid om te leer kan as 'n belangrike hulpbron gebruik word.
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Turvill, Rebecca Anne. "How are young children developing number sense, post national numeracy strategy." Thesis, Brunel University, 2016. http://bura.brunel.ac.uk/handle/2438/13798.
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This thesis examines number sense in primary mathematics. I begin by presenting literature to demonstrate how a cognitive definition of number sense, dominates understandings of mathematical development. I argue that this has influenced fixed-ability practices in mathematics (e.g. Boaler, 1997; Marks, 2014) presenting number-sense as a natural ability. I outline the political landscape and explore data which demonstrates that mathematics education systematically disadvantages some people (Zevenbergen, 2001). After reviewing mathematics learning from a range of theoretical perspectives, I demonstrate a gap in the literature: a sociological exploration of number sense in primary school and illustrate the need to examine school structures and their implications for equitable outcomes for all children. To address this gap I have employed Bourdieusian tools of habitus, field and capital, to explore number sense development. Through ethnographic methods in Year 4 classrooms, I examine how number sense positions children in the field of primary mathematics. This research was undertaken during the first year of statutory implementation of the National Curriculum (DfE, 2013) allowing insight into the lived experiences of children at this time. My findings show that facts, fluency and flexibility are key ways children demonstrate their number sense. Through rapid recall of facts children are seen by their teachers, peers and themselves as ‘able’ at mathematics, leading to explicit reproduction of social class, as these facts are usually learned at home. Similarly, a demand for fluency has led to a focus on procedural accuracy with calculation. Based on this, children are sorted into ability groups magnifying infinitesimally small differences between them (Bourdieu, 1986). Finally, children demonstrate flexibility through different calculation strategies; however, lessons usually rehearse single methods, hiding this key mathematical practice. Each aspect of number sense differentiates children, advantaging those with middle-class habitus and therefore reproducing educational inequalities.
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Andersson, Carina. "Taluppfattning : En undersökning av elevers förståelse av decimaltal." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5820.
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I detta examensarbete har jag studerat hur elever i år 6 tänker vid decimalform inom taluppfattningens område. Begreppet taluppfattning är ett mycket brett område där det dessutom finns många olika uppfattningar om vad som ingår i begreppet. Därför har jag fokuserat mitt arbete på övergången från heltal till decimaltal. Syftet med undersökningen är att belysa vikten av att lärare har goda matematiska och metodiska kunskaper, hur elever utvecklar sin taluppfattning och förhoppningsvis ge lite tips och idéer som kan användas i undervisningen med elever. Studien omfattar en litteraturgenomgång som behandlar begreppet taluppfattning där jag delat upp kapitlet i tre underrubriker: Vad innebär det att elever har en grundläggande taluppfattning? Hur utvecklar elever en god taluppfattning? Vilka speciella svårigheter finns vid övergången från heltal till decimaltal? Under metoddelen skriver jag om hur pilot- och huvudundersökningen gjordes innan läsaren får ta del av undersökningarnas resultat. Resultatet av undersökningen är att många elever har svårt för övergången från heltal till decimaltal. Det finns tre moment i förståelsen av positionssystemet som tycks orsaka större svårigheter och det är platssiffrans värde, multiplikation med tal mindre än ett och uppskattning av rimligheten av svaret i en beräkning. Uppsatsen innehåller också ett avsnitt om vad vi lärare kan göra för att underlätta elevers förståelse för övergången från heltal till decimaltal.
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Hanrahan, Frances May. "Number sense or no sense: Pre-service teachers learning and understanding the mathematics they are required to teach." Thesis, Australian Catholic University, 2002. https://acuresearchbank.acu.edu.au/download/a6472bad472e43ca5e5c199bffda69e711e1e6d893055c402bd7f3ea8730fd1b/2215394/64903_downloaded_stream_128.pdf.
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As a result of two years working with the pre-service primary teachers in a College in Fiji I became aware of the difficulty many of the students were having understanding the primary school mathematics they would be required to teach. During that time I had attempted to help them overcome the difficulties by using different teaching approaches and activities but was far from satisfied with my efforts. Hence I decided to make a concerted effort to help the students by planning, implementing and partially evaluating a mathematics education unit, known as the Teaching Program for the first semester of their course. This work formed the basis of my study. For the Teaching Program I chose a constructivist teaching approach with number sense as the underlying theme. To examine the aspects of the Program I used my observations and those of the students especially ones reported in their mathematics journals. To evaluate the effectiveness of the Teaching Program I collected and analysed quantitative data from traditional testing of the class of forty students as well as data from case studies of six of the pre-service teachers in the class. To determine what features of the Teaching Program were linked to positive changes my main source of data was the case studies, especially entries from their journal writings. The findings suggested that a significant development of the cognitive aspects of the students' number sense did occur during the time of the Teaching Program but not as much as was hoped for. As a result of the analysis of the data I came to a greater realisation of the importance of the non-cognitive aspects of number sense and the necessity for a greater consideration of them in the development of a Program. I also realise now that a major development that did occur was in my understanding of the knowledge and learning of mathematics.;My ideas of a teaching paradigm of social constructivism had not guided me sufficiently to incorporate activities and procedures to develop the non-cognitive aspects. I suggest that a paradigm which extends the theory of social constructivism to give greater consideration of these aspects of learning in general, and hence numeracy and number sense in particular, was needed. As a result of this study, my introduction to the theory of enactivism appears to be giving me some direction in this search at this stage.
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Cheung, Siu-pun. "The effective use of number sense for assisting students with learning difficulties." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/hkuto/record/B40039924.
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Moss, Joan. "Developing children's rational number sense, a new approach and an experimental program." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0026/MQ51566.pdf.
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Johansson, Karin. "Med perspektiv på taluppfattning : Studie om lärares arbete med elever i svårigheter med grundläggande taluppfattning." Thesis, Umeå University, Department of Science and Mathematics Education, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-32141.
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En god taluppfattning är grunden till matematisk förståelse som eleven skall bygga sina kunskaper på. Utan en god grund i taluppfattning uppstår svårigheter för den undervisning som lärare vill åstadkomma i skolan. Ett vidare begrepp av taluppfattning är number sense som är en känsla för talens storlek och rimligheten i matematikuppgifter. Syftet är att undersöka hur lärare arbetar med matematiksvårigheter inom området taluppfattning för att utveckla elevens lärande. Undersökningen beskriver hur lärare identifierar elever i matematiksvårigheter med tanke på grundläggande taluppfattning. Detta gjordes genom kvalitativa undersökningar i form av intervjuer samt studier av åtgärdsprogram gällande hur lärare identifierar problemen. Informanterna är sex yrkesverksamma lärare med olika matematiska utbildningar inom grundskolans årskurser. Det framkom att den vanligaste åtgärden enligt åtgärdsprogram var arbete i liten grupp, vilket enligt forskning är en handling som inte gynnar eleven, om undervisningen är oförändrad. Däremot ansåg flesta lärare att den bästa metoden för att både upptäcka och avhjälpa svårigheter med taluppfattning var resonemang i matematik med eleven. Brist på resurser gjorde att detta var svårt att organisera. Lärare angav tidbrist som orsak till att kartläggningar av elevers behov saknades i de flesta underlag till åtgärdsprogram.
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Kunert, Rachel. "Number Sense Intervention: A Comparison of a Packaged Program and a Research-Based Strategy." University of Dayton / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1405513267.
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Leung, Yun-hing. "The relationship between numerical estimation and number sense in students' learning of mathematics." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/hkuto/record/B40040173.
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Leung, Yun-hing, and 梁潤興. "The relationship between numerical estimation and number sense in students' learning of mathematics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B40040173.
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Perkins, Allison L. "EXAMINING THE EFFECTS OF A FRACTION INTERVENTION ON SIXTH GRADESTUDENTS RATIONAL NUMBER SENSE." Miami University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=miami1495632664241827.
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McIntosh, Brinley Rachel. "Using computer assisted instruction to build fluency in multiplication : implications for the relationship between different core competencies in mathematics." Thesis, University of Canterbury. School of Educational Studies and Human Development, 2014. http://hdl.handle.net/10092/10477.
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Dyscalculia is a specific learning disability that affects an individual’s core skills in mathematics, including calculation, recall of number facts, and approximating/comparing number. Research into the origins and aetiology of dyscalculia have suggested the presence of two different networks in the brain used for mathematics; one for verbal (symbolic) tasks such as recalling number facts, and one for non-verbal (non-symbolic) tasks such as approximation and number comparison. While these networks are located in different brain areas, they are often used together on calculation tasks, they are known to impact each other over the course of development, and they both appear to be impacted in dyscalculia. The current study used entertaining computer assisted instruction software, “Timez Attack”, to target the symbolic network, i.e. to improve the fluency of multiplication fact recall in three 9 and 10 year old children who were performing below the expected level on multiplication. An ABA (applied behaviour analysis) multiple-baseline across subject design was used to track participants’ performance on multiplication, addition, and number comparison over the course of the intervention. Results showed improved fluency of multiplication fact recall in all three participants; however this improvement did not generalise to addition or number comparison. This finding suggests that the symbolic and non-symbolic brain networks involved in mathematics are largely independent from each other by middle childhood, and that training targeting one network does not affect the other.
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Grönlund, Elin, and Hanna Nordström. "Den viktiga taluppfattningen - En studie om lärares undervisning för att stärka elevers taluppfattning." Thesis, Umeå universitet, Institutionen för naturvetenskapernas och matematikens didaktik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-172901.
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Studiens syfte är att öka kunskapen om hur ett antal lärare i årskurs 1 planerar, undervisar och reflekterar över sin undervisning i matematik för att stärka elevers taluppfattning. Taluppfattningen är grundläggande för förståelsen för tals sammanhang och strukturer och är således avgörande för elevernas fortsatta utveckling inom matematik. Studien presenterar fem kategorier av undervisningsprinciper som enligt forskningen är viktiga gällande hur lärare kan bedriva sin undervisning för att stärka elevernas taluppfattning. Studien undersöker de deltagande lärarnas undervisning i relation till dessa principer genom klassrumsobservationer och intervjuer. På så sätt studeras både hur lärarnas verksamhet i klassrummen kan se ut samt hur lärarna uppger att de undervisar i syfte att stärka elevers taluppfattning. Resultatet pekar mot att lärarna har kunskap om samt bedriver en undervisning som verkar stärkande för taluppfattningen men i varierande omfattning. Detta leder även till att eleverna får varierande möjligheter till att utveckla sin taluppfattning.
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Briand-Newman, Hannah. "Teacher perceptions of their professional knowledge, learning and practice: Insights into early number sense pedagogy." Thesis, The University of Sydney, 2019. https://hdl.handle.net/2123/21614.
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Student mathematics underperformance across grade levels within Australian schools remains a growing concern. Current concerns regarding the quality of student learning and levels of achievement, position a strong focus on the quality of teacher preparation and practice. The development of sound number sense in the early years of school has been shown to be critical for ongoing learning and success in mathematics. Therefore, teachers of early mathematics play a vital role in building the foundational number knowledge on which children can build further understanding and competence. Previous research has established that young children who have under-developed number sense are at risk of continued underachievement, highlighting the importance of their teachers being equipped with deep knowledge of early number development and effective practices for early intervention. This study aimed to interpret how teachers acquire their knowledge and translate it into their core instructional practices for early mathematics teaching. The research was guided by a conceptual framework that links the key components of teacher knowledge, professional learningand teacher practicethrough the mediating process of teacher perception. The study focused on investigating the following questions: What knowledge for the teaching of number sense do teachers bring with them to their early learning classroom? How do teachers’ classroom practices address the learning needs of their students? How does teacher perception interrelate with teacher knowledge and their classroom practice? Underpinning the research design for this study were the characteristics of a naturalistic, inquiry research paradigm, where meaning arises out of real-life settings, (that is, classrooms), through an interpretative, sequential process. The participants in the collective case-studyapproach were three Kindergarten (first year of school in NSW) teachers from the same school. As a stimulus for the collection of rich qualitative data, the teachers engaged in a practice-based interconnected professional learningmodel (IPLM). Each of the four domains in the IPLM (design, enactment, analysis, reflection), became the structure for individual cycles of teaching. A series of recorded teacher interviews (including video-stimulated teacher reflection) and classroom observations over an intensive period of three weeks, was supplemented by student assessment data and field notes. Data collection began with an assessment to identify children in each class who were ‘at risk’ in number learning, to become the focus of later classroom observations. Transcripts of teacher interviews were analysed through a process of coding, ‘memo writing’, and supported by manual in-vivo coding. Classroom observational data were analysed using initial/open coding, axial coding and memo writing. Cross-case themes and a data reduction matrix were subsequently used to build a multiple case report, with an embedded single-case study for deeper analysis. While this study found that each of the three teacher participants presented reasonable pedagogical content knowledge within their teaching of early mathematics learning, their understanding of the need for a more specialised content knowledge or deeper subject matter knowledge was not always evident. All three teachers were driven by the curriculum content leaving a noticeable gap between the translation of formal knowledge into their own instructional practice. Professional knowledge was mostly acquired through their own teaching experiences. Each teacher’s own perception of their preparedness to teach early mathematics was found to drive their beliefs about the knowledge needed to teach mathematics. Teacher perception was also a key element in how the learning needs of their students were identified and approached. Instructional core practices were often generalised across whole class learning, being collective and repetitive rather than targeted. While there is much yet to learn about the complexities of how teachers translate their professional knowledge into instructional practice, this study has revealed the important role that teacher perception plays in the approaches that teachers use to translate their present knowledge into what they teach and how they teach it. A teacher’s perception of their own thinking, learning and practice was pivotal to the adoption of particular practices, how they viewed teaching outcomes, and their view of the role of teaching itself. These findings highlighted the importance of ongoing support for teachers in developing the specialised knowledge and the pedagogy needed to provide quality access to early learning experiences that are vital to their student’s foundational number skills, achievement and ongoing mathematics success.
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Shumway, Jessica F. "A Counting-Focused Instructional Treatment for Developing Number System Knowledge in Second-Grade: A Mixed Methods Study on Children's Number Sense." DigitalCommons@USU, 2016. https://digitalcommons.usu.edu/etd/4954.
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Instruction for developing students' number sense is a critical area of research in mathematics education because of the role number sense plays in early mathematics learning. Specifically, number system knowledge has been identified as a key cognitive mechanism in number sense development. The purpose of this mixed methods study was to explore variations in second-grade students' number sense development as they engaged in a counting-focused instructional treatment, geared towards developing number system knowledge, for differing amounts of time. Sixty second-grade students participated in number sense assessments and two students participated in in-depth, task-based interviews to provide quantitative and qualitative data to investigate the change and development of students' number sense during the instructional treatment.
A generalized estimating equations (GEE) analysis showed an associated average increase in test scores for students participating int 9 weeks of the instructional treatment as compared to students participating in 3 weeks of the instructional treatment. This indicated that the counting-focused instructional treatment influenced and changed students' number sense. An important implication of this result is that it highlights the importance of number sense developing over time with multiple, connected experiences.
The in-depth analyses of two cases showed learning growth from pretest to posttest for a low-achieving and high-achieving student. However, the two students' number sense developed in different ways and their access of number system knowledge varied. Shifts in learning mainly occurred after 6 weeks of the instructional treatment and depended on the student's existing use of number sense. The implication of this result is that the multiple access points and the high-ceiling of the instructional treatment benefited low- and high-achieving students in this study.
Findings from the study showed that the counting-focused instructional treatment provided number sense learning opportunities for students from a wide range of abilities and backgrounds within the classroom setting. For many teachers, it is difficult to orchestrate differentiated, whole-class mathematics instructional activities due to their students' wide ranging mathematics abilities. This study identifies a promising instructional practice for elementary mathematics teachers that can facilitate opportunities for students to develop their number sense during whole-class mathematics instruction.
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Azizifarsani, Sahar, and Evelina Söderberg. "Grundläggande taluppfattning : Metoder som gynnar lågpresterande elevers grundläggande taluppfattning." Thesis, Linköpings universitet, Institutionen för beteendevetenskap och lärande, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-144355.
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Vårt syfte med denna litteraturstudie var att undersöka vilka undervisningsmetoder som var gynnande för lågpresterande elevers grundläggande taluppfattning i årskurs F-3. Den grundläggande taluppfattningen är viktig för eleven för att kunna utvecklas vidare i sitt matematiska kunnande. Det är ingenting eleven kan utveckla själva utan det krävs tydlig vägledning av läraren och många möjligheter för eleven att praktisera kunskapen. I och med det ville vi se vilka metoder som var gynnande. Vi sökte artiklar på databaserna Eric och Unisearch och fick i resultatet fram fyra metoder som var gynnande. De metoderna var att jobba med konkret – abstrakt, laborativt material, lekfulla aktiviteter och ”tänka högt”. Tillsamman med metoderna framförs även betydelsen av att jobba i olika konstellationer.
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Macken, Wendy. "Utilizing the empty number line to facilitate sense making in the mental math classroom." Thesis, University of British Columbia, 2014. http://hdl.handle.net/2429/46456.
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The purpose of this study was to explore the possibilities of the Empty Number Line to further develop and strengthen students’ numeracy skills, specific to addition and subtraction. The Empty Number Line (ENL) is a Dutch approach to developing numeracy and mental math skills in the elementary classroom. Internationally acknowledged, the Empty Number Line (ENL) boasts to solving computational tasks in a manner that builds on users intuitive understanding of number. Typically, this model is introduced in the primary years to support early numeracy development. However, this study set out to determine if the tool could be utilized to strengthen the computational skills and fundamental numerical understanding of a sample of 28 Grade 4 students, having no prior exposure to this model. Specifically, the researcher sought to determine what the ENL could reveal about students' sense of number, while utilizing the tool in a manner that supported sense making and self generated strategies. Central to this study was to establish student opinion of this tool, in regards to its effectiveness and ease of use. Over a four week period, students were asked to commit to eight one hour blocks focusing on the exploration of this tool. Three strategies, stringing, bridging and splitting were presented. Via whole class lessons, independent tasks and group activities, students completed a variety of tasks by applying a presented strategy. Student samples and journals were analyzed to determine students performance and opinions over the four week period. Overall students responded very favourably to this tool, and the majority of students developed a good understanding of how to utilize the ENL. However, data unveiled much about students’ numerical capabilities, and in many cases highlighted gaps in children’s number sense. In addition, data analysis highlighted some important future considerations for those considering using this tool, including the delivery of solutions as well as the challenge of applying splitting to subtraction tasks. To conclude, this study highlights advantages and disadvantages when using the ENL to solve 2 and 3 digit computation tasks, as well as considerations to educators intending to present this approach in future teaching endeavours.
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Dunphy, Elizabeth. "An exploration of young children's number sense on entry to primary school in Ireland." Thesis, Open University, 2006. http://oro.open.ac.uk/49167/.
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Betenson, Julie. "Mathematics at your fingertips : an intervention study using fingers and games to improve number sense." Thesis, University of Bristol, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.688347.
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In recent times a positive relationship between mathematical achievement and the ability to distinguish between fingers has been observed and training to develop finger acuity has been shown to lead to gains in mathematical skills. An association between mathematical achievement and non-symbolic number magnitude comparison has also been established. This mixed methods two phase study therefore addressed whether an intervention programme designed to increase connections between the symbolic and non-symbolic representations of number using fingers as a tool could help students construct a deeper understanding of number and thereby increase their scores on mathematical tests. The phase one studies trialled the intervention programme with classes, groups and one individual who were experiencing difficulties in learning mathematics for a variety of different reasons in order to see if improvements in their mathematical skills could be observed irrespective of these reasons. Phase two was designed to evaluate the effectiveness of using the combination of fingers and games in the intervention activities in comparison to using either part separately or no intervention at all. Results demonstrated that the pupils involved in the intervention demonstrated gains in mathematical achievement greater than those who did not take prut regardless of the reasons for their initial difficulties with mathematics. Results also confirmed that the full intervention groups made significantly more increases in mathematics achievement tests than those who experienced part or no intervention. This suggests that the combined intervention of finger gnosis training and mathematical games with the visual representation of fingers and dot patterns acting as mediators could help children to make connections between symbolic and non-symbolic representations of number and thereby raise their mathematical achievements.
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Tosto, Maria. "The aetiology of the number sense and its relationship with mathematics : a genetically sensitive investigation." Thesis, Goldsmiths College (University of London), 2012. http://research.gold.ac.uk/9150/.
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Number sense is defined as the process of extracting numerical information by estimating numerosity and magnitudes of numerical symbols. Humans show great variability in estimation skills from an early age. Although little is known about the origin of individual differences in number sense, these individual variations positively correlate with mathematics. This thesis presents the first large-scale genetically sensitive investigation into the origins of number sense and into the nature of its relationship with mathematics. The research plan can be devised in two parts. In the first phase, a battery of web-tests age appropriate for 16-year olds, designed to assess number sense (as measured by numerosity and magnitude estimation), mathematics and cognitive abilities was created and validated. The battery was then administered to the large UK representative of twins of the Twins Early Development Study (TEDS). In the second phase, using data from 7,598 sixteen year-old twins from the TEDS sample, this thesis used univariate and multivariate genetic analyses to investigate the contribution of genes and environment to individual differences in number sense and to its association with mathematics. The results suggested that individual differences in number sense abilities were mostly driven by non-shared environmental factors, with modest contribution of genetic factors. No average or aetiological sex differences were found in number sense. The relationship between mathematics and number sense was largely genetically mediated. However, contrary to the predictions, the genetic relationship between number sense and mathematics was found to be mediated by g. The existing longitudinal data in the TEDS sample was used to investigate the retrospective relationship between number sense, measured at 16, and mathematics and a range of cognitive abilities, measured at 16 and at previous ages as far back as age 7. The results suggest that the relationship between mathematics and number sense may be uneven across development. In particular, numerosity estimation may be important only at the very early stages of mathematical learning. Overall, this investigation did not find evidence that number sense is what is "special" about mathematics. The results support the Generalist Genes Hypothesis that same genes contribute to individual differences in various aspects of cognition and learning.
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Björkström, Angela. "Is it all in their heads? : A study of the strategies used in mental arithmetic by Swedish pupils in their last years of the obligatory school and in the upper secondary school." Thesis, Mälardalen University, School of Education, Culture and Communication, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-4615.
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Competence in mental arithmetic is recognised by many as essential to be active participants in the fast flowing, high technological society we live in today. Many have noticed pupils’ unwillingness to set their calculators aside and practice this aspect of mathematics when possible. Furthermore, some studies show that pupils’ ability to compute mentally deteriorates as they pass through the school system. Through testing classes in a Swedish obligatory school and an upper secondary school, the aim of this thesis is to see if the goals set by The National [Swedish] Agency for Education regarding mental arithmetic, are being fulfilled. Through using questionnaires to collect the strategies and ideas of the pupils, a wide range of problematic mathematical misconceptions became evident. These are highlighted since they are important aspects teachers should be aware of. The results of this study show that the obligatory school classes are far from reaching the goals set for them whereas the upper secondary classes show good results. Furthermore, there is an apparent improvement in their progression, resulting in a fulfilment the official goals. Many pupils however, seem reluctant to rely on their mental arithmetic capabilities and resort to algorithmic strategies. Other problems to emerge are in carrying out table calculations and in a lack of number sense when deeming if the answers are reasonable.
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Lopes, Ana Paula. "Desenvolvimento do sentido de número no ensino básico: um estudo no sétimo ano de escolaridade." Master's thesis, Universidade de Évora, 2010. http://hdl.handle.net/10174/20773.
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A sociedade contemporânea exige do cidadão raciocínio quantitativo e os novos paradigmas económico-sociais colocam a Matemática escolar perante um novo desafio: desenvolver a literacia matemática dos alunos. A literacia matemática contempla um vasto conjunto de conhecimentos e capacidades entre eles o sentido de número. O desenvolvimento do sentido de número dos alunos tem suscitado alguns trabalhos de pesquisa, em particular ao nível do primeiro e segundo ciclos do Ensino Básico. O objectivo desde estudo é recolher evidências sobre o sentido de número de alunos do terceiro ciclo, mais concretamente sobre o sentido de número racional dos alunos do sétimo ano de escolaridade. Para tal foi necessário considerar uma vasta e complexa rede de competências que caracterizam o sentido de número, entre elas o sentido de operação, mas também os subconstructos que definem os números racionais. Desta forma emergem deste objectivo duas questões: (i) que compreensão têm os alunos das formas equivalentes (inteiros, fracções, decimais, percentagens) dos números? (ii) como entendem os alunos o efeito das operações nos números, as propriedades e as relações entre as operações? Este estudo é uma investigação de natureza qualitativa com recurso ao design de caso. A recolha de dados empíricos foi realizada ao longo do ano lectivo 2007/2008 numa turma de sétimo ano de escolaridade onde a investigadora era a docente da disciplina de Matemática. A investigadora assumiu um papel de observadora participante e foram considerados três estudos de caso: dois alunos e a turma. A informação analisada resultou de vários métodos de recolha: a) inquéritos por questionário e entrevista com tarefas; b) observação da resolução das tarefas em ambiente de sala de aula; c) análise documental. A análise deste conjunto de contributos foi feita tendo em conta as questões de investigação e de forma individual para cada um dos casos. O estudo mostrou que os alunos atribuem pouco significado aos números, às operações e aos contextos. Revelam alguma compreensão dos números racionais escritos na forma de fracção e na forma decimal, mas têm dificuldade em compreender e manipular racionais escritos com recurso a outras formas de representação e a maioria dos alunos revela poucas competências de comparação e ordenação de números racionais. Nesta investigação ressalta também o fraco sentido de operação dos alunos. Mostram pouca compreensão do efeito das operações nos números e têm dificuldade em reconhecer, no contexto do problema, a operação que mais se adequa à situação, manifestando dificuldade quer na interpretação das situações quer na definição de estratégias apropriadas. ABSTRACT: Nowadays society requires of the citizen quantitative reasoning and the new economic-social paradigms place the school Mathematics before a new challenge: to develop the mathematical literacy of the pupils. The mathematical literacy contemplates a vast set of knowledge and capacities such as number sense. The number sense development has excited some works of research, in particular referring to grades 1-6. The aim of this study is to collect evidences about the number sense of pupils of grades 7-9, more concretely on the 7th grade pupils' sense of rational numbers. For such it was necessary to consider vast and complex net of abilities that characterize number sense, including operation sense, but also the rational numbers' sub constructs. Therefore, of this aim two questions emerge: (i) which understanding pupils have of the equivalents forms (entire, fractions, decimals, percentages) of numbers? (ii) how pupils understand the effect that operations have on numbers, the properties and relations between the operations? This study is a qualitative nature investigation that resorts to case studies. Empirical data collection was carried along the school year of 2007/2008 in a 7th grade class where the investigator was the Mathematics teacher. The investigator assumed the role of participant observer and had been considered three studies of case: two pupils and the class. The analyzed data was collected by means of: a) survey - questionnaire and interview with tasks; b) observation of the resolution of the tasks in classroom environment; c) documentary analysis. The data analysis was made according to the questions of the study and individually for each one of the cases. The study showed that pupils attribute slight meant to the numbers, to the operations and the contexts. They reveal some understanding of rational numbers represented as fractions or decimal numbers but disclose difficulty in understanding and manipulating rational numbers' other forms of representation. The majority of the pupils shows few abilities of comparison and ordinance of rational numbers. This investigation also revealed the weak sense of operation of the pupils. They show little understanding of the effect that operations have on numbers as well as difficulty in recognizing, according to the problem's context, the operation that more suits the situation. Pupils disclose difficulty in the interpretation of the situations and in the definition of appropriate strategies.
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Merkley, Rebecca. "Beyond number sense : contributions of domain-general processes to the development of numeracy in early childhood." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:fec8b13e-0693-4c5b-ac0b-759dd6595db8.
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A large proportion of recent research on the development of numerical cognition has focused on the foundational role of approximate number sense, yet number sense alone cannot fully explain how young children acquire numeracy skills. This thesis aims to investigate how other domain-specific processes and domain-general cognitive processes relate to numeracy in early childhood and whether they play a role in learning about mathematics. The experiments presented in Chapter 2 explored how domain-general processes relate to young children's attention to discrete number in non-symbolic representations through a correlational approach. Results supported the role for inhibitory control in selecting numerosity as the relevant stimulus dimension. In order to investigate causal relationships in emerging maths performance, Chapter 3 reports a cognitive training study aimed at contrasting transfer effects of domain-general and domain-specific training in pre- schoolers. Findings suggested caution in interpreting published transfer effects without the highest level of control. The latter chapters targeted learning mechanisms by tackling a specific process in mathematical cognition: acquiring the meaning of numerical symbols. Specifically, the experiments presented in Chapter 4 employed an artificial learning paradigm to test factors influencing adults' and children's formation of novel symbolic numerical representations. Congruency between discrete and continuous non-symbolic quantity influenced novel representations and numerical order information facilitated learning, especially in children. In order to explore symbolic representations of real numbers, Chapter 5 focuses on associations between different representational formats of real numbers in young children and how this relates to both domain-specific and domain-general factors. Children had stronger mappings between symbols and precise non-symbolic representations for numbers smaller than four, than between larger numbers and approximate non-symbolic representations. Taken together, results from the experiments presented in this thesis highlight the need to incorporate factors beyond number sense in theories of numeracy development.
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Owens, Rick. "A number sense approach to written calculation: Exploring the effects in the middle years of schooling." Thesis, Australian Catholic University, 2012. https://acuresearchbank.acu.edu.au/download/5f6d90fdac781dc0b71033c0ed6b5e47aef60d621db25305f8c4323c324bee07/1610774/Owens_2012_A_number_sense_approach_to_written.pdf.
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The purpose of this research was to investigate some of the effects on teachers and students of positioning written calculation within a commitment to building students’ number sense. The focus on number sense took shape initially through explicit teaching of a strategies approach to mental computation, followed by an exploration of approaches to written calculation which made use of effective mental computation strategies. The impetus for this research came from the following observations of many classrooms and a review of the available literature: the dominant aspect of calculation in many schools in the primary and middle years of schooling (here deemed as up to Year 8 in schools in the Australian Capital Territory) is the teaching and using of formal written algorithms for many students this emphasis works against overall facility with calculation and the development of number sense. This study investigated the following research question: What are some of the effects on teachers and students within a junior high school setting, of aligning written calculation with a strategies approach to teaching and using mental computation?
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Enoma, Agbon Osa Stephen. "Understanding the Number Sense Competence of High School Students with Borderline, Mild and Moderate Intellectual Disabilities." Thesis, Curtin University, 2017. http://hdl.handle.net/20.500.11937/57126.
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The study investigated selected teacher- and student-related factors aimed at understanding their influence on the mathematics achievements of students with intellectual disabilities (ID). The relationship between students’ achievements and instructional approaches as well as the suitability of assessment tools were also evaluated. Findings have demonstrated that no singular factor accounted for the mathematics achievements of the students but the interplay of several factors. IMPELS, an assessment tool was also developed as part of this study.
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ADRIANO, ANDREA. "Visual Illusions and Fourier analysis as psychophysical tools to support the existence of the Number Sense." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/379213.
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L'ambiente naturale in cui gli animali sono costretti a sopravvivere modella il loro cervello e il modo in cui si comportano per adattarsi e superare le pressioni naturali. Queste pressioni selettive potrebbero aver determinato l'emergere di un antico sistema neurale adatto a estrarre rapidamente informazioni astratte da set di oggetti, come la loro numerosità, per prendere decisioni informate fondamentali per la sopravvivenza e l'adattamento. La teoria del "Senso numerico" rappresenta il modello neurale più influente che tiene conto delle prove neuropsicologiche e psicofisiche negli esseri umani e negli animali.
Tuttavia, questo modello è ancora ampiamente dibattuto a causa delle difficoltà metodologiche nell'isolare i segnali neurali relativi all'elaborazione della numerosità astratta "discreta" (cioè il numero reale di oggetti in un set) da quelli relativi ad altre caratteristiche correlate o confuse con la numerosità nell’input sensoriale grezzo (p. es., area, densità, frequenza spaziale, ecc.). La presente tesi si proponeva di indagare quali meccanismi potrebbero essere alla base delle rappresentazioni della numerosità visiva, superando le difficoltà nell'isolare le caratteristiche discrete da quelle continue. Dopo aver esaminato i principali modelli teorici e i risultati della letteratura (Capitolo 1 e 2), nel Capitolo 3 abbiamo presentato un paradigma psicofisico in cui le linee dei contorni illusori (IC) simili alla famosa illusione di Kanizsa, sono state utilizzate per manipolare la connessione (ad es., grouping) degli elementi nel set, controllando tutte le caratteristiche continue attraverso i livelli di connessione. Abbiamo mostrato che la numerosità era sottostimata quando le connessioni aumentavano, suggerendo che la numerosità si basa su oggetti percettivi segmentati piuttosto che su caratteristiche grezze di basso livello. Nel Capitolo 4, abbiamo controllato la luminosità illusoria che accompagna gli ICs.
Sfruttando le proprietà percettive dell'illusione di Kanizsa generata con induttori con contrasto inverso, abbiamo scoperto che la sottostima era insensibile alla direzione del contrasto dell'induttore, suggerendo che l'effetto era specificamente indotto da un raggruppamento di bordi indipendente dalla polarità del contrasto e non dovuto alla luminosità percepita. Nel Capitolo 5, abbiamo manipolato contemporaneamente il raggruppamento con le linee IC e la dimensione percepita dei set numerici usando illusioni di dimensioni classiche (Ponzo Illusion). Utilizzando una combinazione di illusioni visive, abbiamo dimostrato che la percezione della numerosità non si basa su segnali continui percepiti, nonostante il segnale continuo possa influenzare la percezione numerica. Nel capitolo 6 abbiamo affrontato la questione con un approccio fisico diretto: utilizzando l'analisi di Fourier per equalizzare la frequenza spaziale (SF) negli stimoli, abbiamo mostrato che l'energia dello stimolo non è coinvolta nella rappresentazione della numerosità. Piuttosto la segmentazione degli elementi e l'organizzazione percettiva hanno spiegato i nostri risultati principali. Nel capitolo 7 abbiamo anche mostrato che l'effetto del rapporto, un importante segno distintivo della codifica Weber-like della percezione numerica, non è principalmente spiegato dall'energia dello stimolo o SF. Infine, nel Capitolo 8, abbiamo anche fornito la prima evidenza empirica che la numerosità non simbolica è rappresentata spazialmente indipendentemente dal contenuto fisico (SF) degli stimoli. Nel complesso, questa tesi supporta l'idea che l'elaborazione della numerosità non si basa semplicemente su caratteristiche di basso livello, ma suggerisce piuttosto direttamente che le informazioni discrete sono al centro del senso del numero.The natural environment in which animals are forced to survive shapes their brain and the way in which they behave to adapt and overcome natural pressures. These selective pressures may have determined the emergence of an evolutionary ancient neural system suited to rapidly extract abstract information from collections, such as their numerosity, to take informed decisions pivotal for survivance and adaptation. The “Number Sense” theory represents the most influential neural model accounting for neuropsychological and psychophysical evidence in humans and animals. However, this model is still largely debated because of the methodological difficulties in isolating neural signals related to “discrete” (i.e., the real number of objects in a collection) abstract numerosity processing from those related to other features correlated or confounded with numerosity in the raw sensory input (e.g., visual area, density, spatial frequency, etc). The present thesis aimed to investigate which mechanisms might be at the basis of visual numerosity representations, overcoming the difficulties in isolating discrete from continuous features. After reviewing the main theoretical models and findings from the literature (Chapter 1 and 2), in the Chapter 3 we presented a psychophysical paradigm in which Kanizsa-like illusory contours (ICs) lines were used to manipulate the connectedness (e.g., grouping strength) of the items in the set, controlling all the continuous features across connectedness levels. We showed that numerosity was underestimated when connections increased, suggesting that numerosity relies on segmented perceptual objects rather than on raw low-level features. In Chapter 4, we controlled for illusory brightness confounds accompanying ICs. Exploiting perceptual properties of the reverse-contrast Kanizsa illusion, we found that underestimation was insensitive to inducer contrast direction, suggesting that the effect was specifically induced by a sign invariant boundary grouping and not due to perceived brightness confounds. In Chapter 5, we concurrently manipulated grouping with ICs lines and the perceived size of the collections using classic size illusions (Ponzo Illusion). By using a combination of visual illusions, we showed that numerosity perception is not based on perceived continuous cues, despite continuous cue might affect numerical perception. In Chapter 6 we tackled the issue with a direct physical approach: using Fourier analysis to equalize spatial frequency (SF) in the stimuli, we showed that stimulus energy is not involved in numerosity representation. Rather segmentation of the items and perceptual organization explained our main findings. In Chapter 7 we also showed that the ratio effect, an important hallmark of Weber-like encoding of numerical perception, is not primarily explained by stimulus energy or SF. Finally, in Chapter 8, we also provided the first empirical evidence that non-symbolic numerosity are represented spatially regardless of the physical SF content of the stimuli. Overall, this thesis strongly supports the view that numerosity processing is not merely based on low-level features, and rather strongly suggests that discrete information is at the core of the Number Sense.
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Dervisevic, Edina, and Nadia Tamar. "Taluppfattningens och tallinjens betydelse i matematiken för årskurserna 1-6. : En kvalitativ studie om lärares uppfattningar om taluppfattningen och tallinjen i matematikundervisningen." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-48910.
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Syftet med denna studie är att ta reda på hur lärare i årskurserna 1–6 beskriver begreppen tallinje och taluppfattning, samt hur de använder tallinjen i matematikundervisning för att utveckla elevers taluppfattning. Studien är en kvalitativ studie som baseras på semistrukturerade intervjuer. Vi valde att intervjua sju informanter med samma yrke. Studiens resultat visar att samtliga lärare beskriver att taluppfattning handlar om att förstå talraden, värdet av talet, vad som är större och mindre, förståelse för storleken med mera. Vidare i resultat visas det att tallinjen ses som ett bra verktyg i undervisningen som kopplas bland annat till linjalen. Tallinjen medför att eleverna utvecklar en god taluppfattning, de får upptäcka mer av det konkreta till exempel genom aktiviteter i klassrummet. Studiens resultat visar att samtliga lärare beskriver att elever utan de grundläggande kunskaperna kommer möta på svårigheter i ämnet matematik. Studiens slutsats blir därmed att elever måste ha en god taluppfattning utifrån de olika grunderna för att sedan kunna operera med de fyra räknesätten tillsammans med verktyget tallinjen. Det innebär att tallinjen bidrar till att eleverna får en större talförståelse.The purpose of this study is to find out how teachers in grades 1–6 describe the concepts number line and speech perception, and how they use the number line in mathematics teaching to develop student speech perception. The study is based on a qualitative study with semi structured interviews. We chose to interview seven informants with the same professions. The study's results show that all teachers describe that speech perception is about understanding the number line, the value of the speech, what is bigger and smaller, understanding the size and so on. Further in the results, it is shown that the number line is shown as a good tool in teaching which is linked among other things such as the ruler. The number line means that the students develop a good speech perception, they can discover more of the concrete for example through activities in the classroom. The results also show that all teachers mention that students without the basic knowledge for a good speech perception will encounter difficulties in the subject of mathematics. The study's conclusion becomes that students must have a good speech perception on the basis of the different bases in order to then be able to operate with the four methods of calculation together with the tool number line. This means that the number line helps students gain a greater understanding of speech.
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Hebe, Gasenakeletso Ennie. "Investigating Grade 3 learners’ changing mathematical proficiency in a maths club programme focused on number sense progression." Thesis, Rhodes University, 2018. http://hdl.handle.net/10962/62200.
Full textAbstract:
Recent international reports, for example TIMSS (2011 & 2015), point to serious challenges in South African learner performance in Mathematics and Science. Of greatest concern is that research findings (e.g. Graven, Venkat, Westaway and Tshesane 2013) suggest that many South African learners show signs of mathematical knowledge gaps in the lower grades. Hence, there is a need to address challenges of this nature very early in Foundation Phase. This study was undertaken with a view to contribute towards addressing mathematical challenges encountered by learners in Foundation Phase This empirical enquiry was undertaken under the auspices of the South African Numeracy Chair Project (SANCP) at Rhodes University whose mission is to develop sustainable ways of improving quality teaching and learning of Mathematics in South Africa. A relatively new SANCP programme called Pushing for Progression (PfP) run as part of the after-school Maths Clubs to develop the number sense and four Operations in learners was used to achieve the research aims of this study. Research participants were drawn from the Maths Clubs established by the researcher in a small rural town of Ottosdal in the North West Province of South Africa. This Study is grounded on the Vygotskian perspective and uses the interpretivist qualitative research method for data collection and analysis. Sampling was done opportunistically by enlisting participants (12 teachers and 117 learners) on the basis of their availability and willingness to participate. Pre- and post-assessment of learners’ proficiency on the four Basic Operations was conducted at the beginning and at the end of the research project, respectively. This was done to determine the impact of the project on learner performance. Data analysis was done thematically and through the comparison of learner results of the pre- and post-assessment. The findings point to the effectiveness of the PfP Programme in learner performance. This can be deduced from improved scores between pre- and post-assessment and the observations made by participant-teachers on their respective club learners’ mathematical proficiencies. Accordingly, based on the findings, this study recommends, inter alia, that since the PfP programme is still in its early stages, similar research be conducted elsewhere. Additionally, the Department of Basic Education could consider exploring the PfP programme as one of several other strategies to help improve learner proficiency in Mathematics.
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Chien, Hung-Chin, and 簡宏晉. "The Study of Six Elementary School Teachers’ Number Sense Performance and Perception about Number Sense." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/02132123560185703350.
Full textAbstract:
碩士國立嘉義大學
數學教育研究所(Graduate Institute of Mathematic Educa
98
The purposes of this study were to examine six elementary school teachers’ number sense performance when solving number sense related problems and their perceptions about number sense. The researcher designed the number sense tasks and related perception questions as the instruments via the semi-structured interview to collect data. The interview results indicated that: The results of teachers’ number sense performance showed that the participants have poor insight on numerical relations and do not perform well on the use of number sense methods. Moreover, the proportion on the use of rule-based methods was lower than the number sense methods. This demonstrated that participants were not limited by the rule-based methods comparatively. In addition, the number sense performance showed that participants who are not majored in mathematics have higher frequency on using number sense methods than participants majored in mathematics. However, the participants majored in mathematics showed that they have higher efficiency on using number sense methods to solve problems. The results of teachers’ perceptions about number sense showed that all the participants showed the positive influence on number sense to the mathematics learning. Furthermore, based on the understanding of the positive effects on number sense, five out of six of the participants expressed willingness to teach number sense in mathematics classes. However, referring to the number sense teaching, the participants concerned about the content of teaching materials and time limits of teaching hours. In addition, the results of interviews also indicated that there is a concern that the number sense was lacking publicity and therefore it is not emphasized by the educators in here.
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Sood, Sheetal Kern Lee Jitendra Asha K. Hojnoski Robin Manz Patricia. "Teaching number sense: Examining the effects of number sense instruction on mathematics competence of kindergarten students." 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3373089.
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Hshu, Ching-Yang, and 許清陽. "The Study of Elementary Students’ Number Sense Theoretical Model Construction and Computerized Number Sense Diagnostic Test System." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/27135988546651727957.
Full textAbstract:
博士國立高雄師範大學
教育學系
94
The main purpose of this study is to construct the theoretical model of number sense and to develop “Computerized Number Sense Diagnostic Test System” in order to understand the general situation of sixth graders in number sense performance as well as to further analyze the error types and misconception of the subjects. This study firstly selected 539 sixth graders from southern counties and cities for computerized online test to construct the reliability and the validity of number sense diagnostic test. Then, 3,462 sixth graders from 22 counties and cities from Taiwan island were selected for computerized online test to construct number sense theoretical model and to understand the general conditions of sixth graders in number sense performance. The data was then used to further analyze the frequent error type and misconception of the students in number sense diagnostic test. Data collection and statistical analyses of this study are concluded as the following: 1.The test of goodness of fit for “Elementary Students Number Sense Theoretical Model” adopts the three standards suggested by Bagozzi and Yi (1988): preliminary fit criteria, overall model fit, and fit of internal structure of model. The three models were used in assessment and results revealed that besides those indexes which are easily affected by samples, all other indexes conformed to the assessment standards. This shows that “Elementary Students Number Sense Theoretical Model” is perfectly appropriate. 2.In the analysis of number sense differences among the students from various backgrounds, school scales and father’s education level show significant differences while gender shows no significant difference. In the correlation test between number sense and mathematics achievement, there were only 6 out of 64 schools failed to reach 0.05 significance level. Most of the students show significant relation between number sense and mathematics achievement. 3.Computerized number sense diagnostic test system can provide PR value for the test and it also possesses the function in diagnosing error type and misconception. The subjects get to know their own PR value immediately after the online computer test. With this, the students learn about their relative position in the group and aware of their own strengths and weaknesses of number sense. Besides, computerized number sense diagnostic test system also provides the subjects with their error types and misconception so that the subjects can do self-review for improvement. Moreover, teachers can carry out remedial teaching base on the diagnostic results. Base on the findings, this study proposes suggestions to school teachers and further studies respectively.
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Chih-I-Lin and 林姿飴. "Development of a Computerized Number Sense Scale for the 5th Graders and their Performance on Number Sense." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/06141069439855392052.
Full textAbstract:
碩士國立嘉義大學
數學教育研究所
93
To examine the the 5th grade students’ performance on number sense, a cmputerized number sense scale was developed. On-line field test data from public elementary school kids ( N=1212) were analyzed using SPSS and AMOS. Based on the data analysis, the major findings of the study are summarized as follows: 1. The computerized number sense test, developed for students just completing the 5th grade’s math, is empirically reliable and substantially valid. Cronbach’s α coefficient of the scale was .8696 and its construct reliability was .916 and the reliability of test and re-test was.832. 2. The CFA results show that the four-factor number sense model fits better then the proposed 5-factor model. 3. The newly-established 4-factor model includes a new component named as “the relationship of number and operation” and excludes one of the proposed factors called “the relative effect of operation on numbers”. Also, the fifth factor named “understanding the basic number meanings” is highly correlated with the other four factors and thus eliminated from the model. This demonstrates both a qualitative and quantitative change in students’ number sense development. 4. There is a statistically significant difference between the number sense components. The students perform best on “recognizing the number size” and perform worst on “judging the rationality of computational results”. This finding is consistent with previous studies of Hsu (2001) and Li (2004). It shows that students in Taiwan seem quite weak on judging the rationality of computational results.0 5. In spite of merely a small effect size found, the female students, on average, have higher scores on recognizing the number size than the male students. 6. Students’ mathematics achievements were significantly correlated with number sense.
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Li, Wei-Jin, and 李威進. "A Study of Computerized Number Sense Test for the 1-3 Graders and their Number Sense Development." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/64136705480170913265.
Full textAbstract:
碩士國立嘉義大學
數學教育研究所
92
The major purposes of this study were to design a computerized number sense test for the 1-3 graders and to investigate their number sense development. In order to investigate the reliability and validity of the newly-developed number sense test, 808 fourth graders from public primary school in Taiwan were selected and participated this on-line number sense test. Based on the statistical analysis, the results of this study indicated: 1. Construct reliability and validity for the first-stage computerized number sense test is very good. 2. There are five major components in the number sense test. 3. There is a significant difference among the number sense components for the fourth graders. This result also indicates the practical value for application due to its medium effect size. 4. There is a significant statistical difference between male and female, yet the practical value of this difference in the real world is not useful due to the small effect size. Finally, this study proposed several suggestions to teachers and researchers based on the research conclusions.
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DeWind, Nicholas Kurshan. "The Neural Basis of the Number Sense." Diss., 2014. http://hdl.handle.net/10161/9417.
Full textAbstract:
The ability to enumerate approximately without counting is an evolutionarily ancient and developmentally early core cognitive ability known as the "number sense". We use the number sense when we estimate a number without counting individual items, as when we guess the number of people in a crowded room. The number sense is theorized to form an instinctual building block upon which we create the conceptual structures of mathematics. This dissertation addresses three research questions regarding the number sense.
The first is the question of whether the number sense is malleable, and if so, what are the neural correlates of malleability. In Chapter 2 we gave adults number sense training, which we found improved the accuracy of numerical estimation. In Chapter 4 we recorded from single neurons in monkeys while they viewed arrays of items on a computer screen. Similar recordings have been made previously, but usually using monkeys that were trained to discriminate sets based on number. Recordings in trained animals demonstrated that individual neurons in the monkey's brain track the number of items in a set. We reasoned that if the neural correlates of the number sense were altered by the training experience, then we would get different results in untrained monkeys. We did find neurons encoding numerical information in untrained monkeys, but at lower rates than described previously. Thus, we demonstrated that the number sense can improve with experience, and our data suggest that changes in the proportion of neurons encoding number may subserve this improvement.
The second question is how to resolve the problem of stimulus control in laboratory tests of the number sense. Typically, number sense function is assessed by presenting arrays of dots on a computer screen. In such stimuli, however, non-numerical features necessarily covary with numerical features. By counter-balancing different stimulus conditions, it is possible to determine if number and not some other feature is influencing a dependent measure. In Chapter 3, we develop a technique to go further and determine which of eleven stimulus features is influencing a dependent measure.
The third question is whether the intraparietal sulcus (IPS), a brain area known to be engaged during numerical cognition, is specialized for it. To address this question, we apply the technique developed in Chapter 3 to the neural data recorded from monkeys in Chapter 4. We show that the IPS does contain number neurons; however, it also contains neurons that encode many other features in equal proportion, indicating that it is not specialized for number. In Chapter 5, we use drugs injected into the IPS to reversibly inactivate it. We found that after IPS inactivation, performance on a numerical discrimination task was impaired but no more so than a color discrimination control task. Again, our data do not support the theory that the IPS is specialized for numerical processing.
Dissertation
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Yang, Tsang-I., and 楊璨伊. "Number sense and foraging decision in cuttlefish." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/18707779236385878105.
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碩士國立清華大學
系統神經科學研究所
104
Identifying the amount of prey available is an important part of an animal’s foraging behavior. The risk-sensitive foraging theory predicts that an organism’s foraging decisions with regard to food rewards depend upon its satiation level. However, the precise interaction between optimal risk-tolerance and satiation level remains unclear. In the present study, we examined, firstly, whether cuttlefish, with one of the most highly evolved nervous system among the invertebrates, have number sense, and secondly, whether their valuation of food reward is satiation state-dependent. When food such as live shrimps is present, without training, cuttlefish turn toward the prey and initiate seizure behavior. Using this visual attack behavior as a measure, cuttlefish showed a preference for a larger quantity when faced with two-alternative forced choice tasks (1 vs. 2, 2 vs. 3, 3 vs. 4, and 4 vs. 5). However, cuttlefish preferred the small quantity when the choice was between one live and two dead shrimps. More importantly, when the choice was between one large live shrimp and two small live shrimps (a prey size and quantity trade-off), the cuttlefish chose the large single shrimp when they felt hunger, but chose the two smaller prey when they were satiated. These results demonstrate that cuttlefish are capable of number discrimination and that their choice of prey number depends on the quality of the prey and on their appetite state. The findings also suggest that cuttlefish integrate both internal and external information when making a foraging decision and that the cost of obtaining food is inversely correlated with their satiation level, a phenomenon similar to the observation that metabolic state alters economic decision-making under risk among humans.
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irene, togoli. "The number sense in the human brain." Doctoral thesis, 2018. http://hdl.handle.net/2158/1119013.
Full textAbstract:
Humans and other species are endowed with perceptual mechanisms dedicated to estimating approximate quantity, an ability that has been defined as a sense of number. Converging evidence gathered from neurophysiological, behavioural and imaging studies, support the idea that this number sense has a truly abstract nature, being capable of encoding the numerosity of any set of discrete elements, displayed simultaneously or sequentially, and across different sensory modalities (Nieder et al., 2006; Piazza et al., 2006; Burr & Ross, 2008). It has been shown that numerosity, like most other primary visual attributes, is highly susceptible to adaptation: visually inspecting for a few seconds a large number of items, simultaneously presented, results in the perceived numerosity of a subsequent ensemble to be strongly underestimated, and vice-versa after adaptation to low numbers (Burr & Ross, 2008). Given that processing numerical information is also fundamental for the motor system to program sequences of self- movement, a further level of generalization of the number sense would be the possibility that a shared numerical representation exists between action and perception – that is, according to this view, the number sense would be generalized across presentation formats, sensory modalities, and perceptual and motor domains. In this work, we investigate numerosity perception within this theoretical framework. The first study was designed to investigate the perception of numerosity for stimuli presented sequentially by using an adaptation paradigm. This study tested whether, and to what extent, adaptation to a high or low number of events distorts the perceived numerosity of a subsequent sequence of visual events presented in the adapted location. In line with the typical dynamics of adaptation aftereffects, adapting to few events caused an overestimation of the perceived numerosity of the test stimuli, whilst adaptation to high-numerosity yielded a robustly underestimation.
We further showed that adaptation effects transcend the sensory modality and presentation format: adapting to sequences of tones affected the perceived numerosity of a subsequently presented series of flashes (and vice versa), and adapting to sequences of flashes affected the perceived numerosity of spatial arrays of items. Similar results were obtained with tactile stimuli. Moreover, adaptation occurred only when test and adaptor positions were presented at the same location in spatiotopic (external world) coordinates, as demonstrated by introducing a saccadic eye movement between the offset of the adapting stimuli and the onset of the test stimuli (Arrighi et al., 2014). In the second part of this work, we present a subsequent work examining the possibility that the perceptual and the motor system might share a common numerical representation by using again the psychophysical technique of adaptation. In different sessions, we asked the subjects to produce either a fast (high number) or slow (low number) tapping routine. At the end of this adaptation phase subjects had to estimate the number of pulses presented sequentially, or of a cloud of dots simultaneously presented either on the same side where the motor actions were performed or on the opposite side. We found that motor adaptation strongly affected numerosity estimation of the test stimuli only when they were presented on the congruent side, with no effect when the visual stimuli were displayed on the neutral, not adapted, location. Moreover, to verify the robustness of the spatial selectivity, we repeated the experiment with a new subject pool, changing the tapping hand and location. Again, the spatial selectivity of the adaptation resulted to be in external – not hand-based – coordinates (Anobile, Arrighi et al., 2016).
In the third part of this work we present another work where we evaluated the possibility that vision could drive the development of an external coordinate
system for perceived numbers. In this study, congenitally blind (CB) and sighted controls (SC) were asked to evaluate the numerosity of sounds after performing either slow or fast motor adaptation (tapping), with the dominant hand, either in an uncrossed or in a crossed posture. Robust adaptation effects were observed in both groups of participants: an underestimation of the numerosity presented was observed after the execution of fast movements and an overestimation of the numerosity was observed after the execution of slow movements, in the crossed as well as in the uncrossed posture. Taken together, these results expand previous findings showing that adaptation to self-produced actions distorts perceived numerosity of sounds. Moreover, we demonstrate that visual experience is not necessary for the development of an external coordinate system for the shared numerical representation across action and perception. Finally, in the last part of this work, we examine the possibility of a common neural mechanism for different magnitude dimensions. Indeed, it has been recently proposed that space, time, and number might share a common representation in the human brain. For example, adaptation to visual motion affects both perceived position and duration of subsequent stimuli presented in the adapted location, suggesting that adaptation to visual motion distorts spatial maps as well as time processing (Johston et al. 2006, Burr et al., 2007; Fornaciai et al., 2016).
In this study, we tested whether motion adaptation also affects perceived numerosity. Adaptation to fast translational motion yielded a significant reduction in the apparent numerosity of the adapted stimulus (of about 25%), while adaptation to slow translational or circular motion (both 20Hz and 5Hz) yielded a weaker but still significant compression of perceived numerosity. Our results generally support the idea of a common system for processing of space, time and number.
However, as changes in perceived numerosity co-varied with both adapting motion profiles and speed, our evidence suggest a complex and asymmetric interactions between the representations of space, time and number in the brain.
Taken together, the results obtained across these studies point to the existence of a generalized mechanism for numerical representation in the brain that is amodal, independent of the presentation format, shared between the perceptual and the motor systems, and based on external coordinate system.
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Hsu, Chun-Jen, and 徐俊仁. "A study of developing sixth-graders'' number sense." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/01511238753043224033.
Full textAbstract:
碩士國立嘉義大學
國民教育研究所
89
The teaching for developing number sense has been emphasized by many advanced countries. Central to the design of mathematics curricula is the development of number sense. But, the study of number sense is limited in Taiwan. Due to these reasons, the main goal of this study was to investigate sixth-graders’ number sense and explore the effectiveness of an instructional intervention program designed to develop their number sense. The instrument of this study included number sense paper-and-pencil tests: pre- and post- instruction. In the meanwhile, number sense questions were designed to interview six students individually. Students were asked to provide explanations for their answers and were assessed about their changes. The results showed that thirty students increased their development of number sense at paper-and-pencil tests after instruction. Especially in number sense magnitude and computational estimation. Before instruction, most students gave rule-based explanations during interviews for all three levels, few number sense strategies were used (such as benchmarks, estimation and number magnitude) Students in middle and low levels misused the rules and formulas seriously. After instruction, students used number sense to provide explanations for their answers. Besides, this study describes realistic problems of teaching activities and brings up the programs in solving problems. We also analyze teaching activities on each teaching stage to probe into how teacher make use of teaching activities in the classroom to help students to develop number sense. We knew the sequence of ideas of students’ number sense by way of the process of discussion. From the teaching activities of this study, we discovered that students could emerge the higher-order reasoning and thinking mathematically on the problem-solving process by cooperative learning and interactive encouragement. According to the process of teaching activities, the lower-level student can use their own symbols to discuss and bring up the positive and valued ideas if we set up reasonable classroom rules, fair chance of issues and form the culture of classroom discussion gradually. We also realized that students don’t know how to discuss at first, and now they can question the problem-solving methods in the light of problems. We saw the use of mathematics languages of students refined more and more, and the types of number to symbolize are having a variety. We can realize that students can develop more rich number sense in a learning environment where encourages exploring, discussions, communication, and questions. It is perceived that, standards involved in agitating of thinking on a process of discussion and questioning. When teacher guided them at the right moment, students could issue many creative problem-solving strategies and develop their number sense.
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Creighan, Samantha. "Investigating the Effects of the MathemAntics Number Line Activity on Children's Number Sense." Thesis, 2014. https://doi.org/10.7916/D8ZG6QDW.
Full textAbstract:
Number sense, which can broadly thought of as the ability to quickly understand, approximate, and manipulate numerical quantities, can be a difficult construct for researchers to operationally define for empirical study. Regardless, many researchers agree it plays an important role in the development of the symbolic number system, which requires children to master many tasks such as counting, indentifying numerals, comparing magnitudes, transforming numbers and performing operations, estimating, and detecting number patterns, skills which are predictive of later math achievement. The number line is a powerful model of symbolic number consistent with researchers' hypotheses concerning the mental representation of number. The MathemAntics Number Line Activity (MANL) transforms the number line into a virtual manipulative, encourages estimation, provides multiple attempts, feedback, and scaffolding, and introduces a novel features where the user can define his own level of risk on the number line. The aim of the present study was to examine how these key features of MANL are best implemented to promote number sense in low-income second-graders. Sixty-six students from three schools were randomly assigned to one of three conditions; MANL User-Defined Range (UDR), and MANL Fixed Range (FR), and a Reading comparison condition and underwent a pretest session, four computer sessions, and a posttest session. During the computer sessions, researchers coded a child's observed strategy in placing targets on the number line. The results showed that children with higher number sense ability at pretest performed better on a posttest number line estimation measure when they were in the UDR condition than in the FR condition. Conversely, children with low number sense ability at pretest performed better on the number line estimation posttest measure when they were in the FR condition than UDR. Although in general, all children improved over time, children with low number sense ability at pretest were more likely to use the UDR tool ineffectively, thus negatively impacting performance. When children were not coded as responding quickly, target number significantly impacted performance in the computer sessions. Finally, children in the UDR condition utilized better expressed strategies on the number line estimation posttest than children in the Reading comparison group. These findings indicate that prior number sense ability plays a role in how children engage with MANL, which in turn affects the learning benefits the child receives. Implications for researchers, software designers, and math educators, as well as limitations are discussed.
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Hsiao-Ting, Chen, and 陳筱婷. "Using Fraction Number Sense Digital Game-based Teaching Materials to Improve Fractional Number Sense Ability and Learning Motivation of Sixth Graders." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/81431063757884173132.
Full textAbstract:
碩士國立臺中教育大學
教育測驗統計研究所
101
The purpose of study was to assess the effects on fraction number sense ability and learning motivation of sixth graders by two different teaching models: “fractional number sense digital game-based teaching materials” and “traditional fraction number sense working sheets.” Hence, the researcher designed fractional number sense digital teaching materials based on five dimensions of number sense to assist teachers teaching in experiment group. The working sheets, based on same material content, were used in control group. The assessment was based on an quasi-experimental design. Subjects were selected from two public elementary schools in Taichung city. The experiment group was two classes of sixth graders (n = 47), and control group was consisted of the other two different classes (n = 49). The control and experiment groups were carried out fractional number sense test and mathematical learning motivation scale test before teaching. After three classes of teaching, the parallel tests were conducted again. The data were analyzed by description statistics, one way ANCOVA, and Johnson – Neyman method. By comparing the performance from the experiment group and the control group, the conclusions were obtained as follows: 1. Based on performances of the experimental group in exercises of each game, the students in the "domino challenge game" and "sparklers game" got better scores, and two games were designed to assess three dimensions of number sense: "understanding the relative effect of operations on fraction", "recognizing the magnitude of fraction." and " ability to represent fraction in multiple ways." 2. After teaching with fractional number sense digital teaching materials, the average score(17.597) of the experiment group in fractional number sense test was significantly better than that of the control group(16.244). 3. Instruction with fractional number sense digital game-based teaching materials were more effective than instruction with traditional fraction number sense working sheets on “understanding the relative effect of operations on fraction” and “ability to represent fraction in multiple ways.” 4. After teaching with fractional number sense digital teaching materials, the average score (82.439) of the experiment group in mathematical learning motivation scale is better than that of the control group(79.130), although the difference is not significant. 5. In the experimental group, no matter fractional number sense or mathematical learning motivation, students with different genders are all progressive significant, but there were no significant.