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Journal articles on the topic 'Number sense'

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Author: Grafiati

Published: 4 June 2021

Last updated: 10 March 2023

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1

Ronau, Robert N. "Number Sense." Mathematics Teacher 81, no. 6 (September 1988): 437–40. http://dx.doi.org/10.5951/mt.81.6.0437.

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Good number sense is fundamental for success in estimation, approximation, and problem solving. We need to develop a sense of large numbers because newspaper and television news reports contain many references to large quantities. The federal budget is expressed in billions and trillions of dollars, space distances in millions of light years or trillions of miles, computer speeds in nanoseconds (1 nanosecond = 1 billionth of a second), computer storage memory in gigabytes (1 gigabyte = 1 billion bytes), world populations in millions and billions of individuals, and nuclear weapons in millions of tons of TNT. Clearly, the average citizen needs a well-developed sense of large numbers to understand many of the news items that invade the home. Large-number concepts a re appropriate for development in upper elementary school, high school, and beyond. This article presents some examples to enhance a sense of large numbers in middle and high school students.

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2

Gersten, Russell, and David Chard. "Number Sense." Journal of Special Education 33, no. 1 (April 1999): 18–28. http://dx.doi.org/10.1177/002246699903300102.

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3

Hadi, Sutarto. "Number sense." Math Didactic: Jurnal Pendidikan Matematika 1, no. 1 (April 30, 2015): 1–7. http://dx.doi.org/10.33654/math.v1i1.89.

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Pemahaman anak mengenai bilangan bertujuan untuk menambah dan mengembangkan keterampilan berhitung dengan bilangan sebagai alat dalam kehidupan sehari-hari. Salah satu aspek utamanya adalah menekankan pengembangan kepekaan terhadap bilangan atau dikenal dengan number sense. Number sense dapat diartikan sebagai berpikir fleksibel dan intuisi tentang bilangan. Untuk menilai sifat number sense yang dimiliki seorang individu, kita harus memeriksa fleksibilitas terhadap bilangan yang ditunjukkan oleh individu tersebut. Fleksibilitas ini dapat diamati ketika seseorang melakukan empat komponen number sense, yaitu menilai besaran bilangan, komputasi mental, estimasi, dan menilai kerasionalitasan atau kewajaran hasil perhitungan yang diperoleh.

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4

Berch, Daniel B. "Making Sense of Number Sense." Journal of Learning Disabilities 38, no. 4 (July 2005): 333–39. http://dx.doi.org/10.1177/00222194050380040901.

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5

Moomaw, Sally, Victoria Carr, Mary Boat, and David Barnett. "Preschoolers' number sense." Teaching Children Mathematics 16, no. 6 (February 2010): 332–40. http://dx.doi.org/10.5951/tcm.16.6.0332.

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6

Howden, Hilde. "Teaching Number Sense." Arithmetic Teacher 36, no. 6 (February 1989): 6–11. http://dx.doi.org/10.5951/at.36.6.0006.

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Of all the Standards in the K–4 component of NCTM's working draft of Curriculum and Evaluation Standards for School Mathematics, the one concerning number en e raised the most questions from teachers, parents, and administrators in session held to acquaint our educational community with the Standards. These four questions were most frequently asked: What is number sense? Why is number sen e important? How is number cnse taught? How is number sense measured?

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7

Lock, Robin H., and Susan Gurganus. "Promote Number Sense." Intervention in School and Clinic 40, no. 1 (September 2004): 55–58. http://dx.doi.org/10.1177/10534512040400010501.

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8

Wagner, David, and Brent Davis. "Feeling number: grounding number sense in a sense of quantity." Educational Studies in Mathematics 74, no. 1 (January 19, 2010): 39–51. http://dx.doi.org/10.1007/s10649-009-9226-9.

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9

Er, Zübeyde, and Perihan Dinç Artut. "Gifted students' number sense skills in terms of number sense components." Journal of Education and Learning (EduLearn) 16, no. 1 (February 1, 2022): 92–102. http://dx.doi.org/10.11591/edulearn.v16i1.20424.

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As a descriptive survey research, this study aimed to investigate the number sense skills of gifted in terms of number sense components. Participant of this research consisted of 123 gifted secondary school students, who were selected according to the convenience sampling method in Turkey. The data of this research were collected in the 2021-2022 academic year. The number sense test was used as the data collection tool. This test is comprised of 20 items which were prepared in line with five basic number sense components. The data obtained from the data collection tool were analysed by quantitative analysis methods. As a result of the analysis, it was confirmed that the number senses of gifted secondary school students differed according to gender and this difference was in favour of the male students. The highest number sense performance according to grade levels belonged to eight grade level students. Furthermore, it was observed that the number sense performance increased in parallel with the grade levels of the students. In addition, when the mean of correct answers for the number sense components was considered, it was concluded that the highest mean was in the understanding of the effect of the operation and the lowest mean was in the understanding of the number concept, respectively.

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10

He, L., T. Zhou, J. Zhang, Y. Zhuo, and L. Chen. "The Number Sense Follows the Object Sense." Journal of Vision 11, no. 11 (September 23, 2011): 895. http://dx.doi.org/10.1167/11.11.895.

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11

Turkel, Susan, and Claire M. Newman. "What's Your Number? Developing Number Sense." Arithmetic Teacher 35, no. 6 (February 1988): 53–55. http://dx.doi.org/10.5951/at.35.6.0053.

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In a recent article in Newsweek, a mathematics professor bemoaned innumeracy, a widespread disability among otherwise sophisticated Americans. Such innumerate adults, he feels, have only a hazy understanding of numbers and the way they are used. These adults succumb easily to specious arguments that refer to numbers they do not understand. Many have no appreciation of number magnitudes—no grasp of very large numbers and little understanding of small ones (Paulos 1986).

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12

Woods, Dawn Marie, Leanne Ketterlin Geller, and Deni Basaraba. "Number Sense on the Number Line." Intervention in School and Clinic 53, no. 4 (June 14, 2017): 229–36. http://dx.doi.org/10.1177/1053451217712971.

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A strong foundation in early number concepts is critical for students’ future success in mathematics. Research suggests that visual representations, like a number line, support students’ development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction to transition from concrete to visual to abstract representations of mathematics concepts supports students’ conceptual understanding. This column describes and illustrates how teachers can use number lines and features of explicit and systematic instruction to support students’ early development of number sense.

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13

Lee, Joanne, Donna Kotsopoulos, Anupreet Tumber, and Samantha Makosz. "Gesturing about number sense." Journal of Early Childhood Research 13, no. 3 (March 25, 2014): 263–79. http://dx.doi.org/10.1177/1476718x13510914.

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14

Lipton, Jennifer S., and Elizabeth S. Spelke. "Origins of Number Sense." Psychological Science 14, no. 5 (September 2003): 396–401. http://dx.doi.org/10.1111/1467-9280.01453.

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15

Bay, Jennifer M. "Developing Number Sense on the Number Line." Mathematics Teaching in the Middle School 6, no. 8 (April 2001): 448–51. http://dx.doi.org/10.5951/mtms.6.8.0448.

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One of the most important lessons that I have learned as a teacher is that seemingly boring problems on paper can come alive if I can find a way to lift them off the page. This transformation took place when the number line in my classroom became a brightly colored rope that stretched the length of the room, held by a student at each end. I first saw this idea as an approach to help young children order numbers from 1 to 10, then adapted it for middle school students. The scope of the activity eventually expanded to include explorations of large numbers, rational numbers, and algebra. As I saw improvement in students' conceptual understanding and their enjoyment of the life-sized number line, I used it more often in my classroom. I also found that the activities with the number line involved communication, reasoning, and justification— important processes in learning mathematics (NCTM 1989, 2000).

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16

Booker, George. "Promoting number sense rather than number skills." Set: Research Information for Teachers, no. 2 (August 1, 1998): 1–4. http://dx.doi.org/10.18296/set.0851.

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17

Helmy, N. F., R. Johar, and Z. Abidin. "Student’s understanding of numbers through the number sense strategy." Journal of Physics: Conference Series 1088 (September 2018): 012098. http://dx.doi.org/10.1088/1742-6596/1088/1/012098.

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18

Kaminski, Eugene. "Number Sense: Developing Mathematical Understanding." Curriculum and Teaching 11, no. 1 (January 1, 1996): 79–86. http://dx.doi.org/10.7459/ct/11.1.08.

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19

Sztajn, Paola. "Celebrating 100 with Number Sense." Teaching Children Mathematics 9, no. 4 (December 2002): 212–17. http://dx.doi.org/10.5951/tcm.9.4.0212.

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Joe woke me up. “Mom,” he said, “it's today!” “Today, what?” I managed to mumble. “The hundredth day of school, Mom; it is so special. I want to dress up to go to school and be real nice for our party,” he added. And so he did.

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20

Hope, Jack. "Promoting Number Sense in School." Arithmetic Teacher 36, no. 6 (February 1989): 12–16. http://dx.doi.org/10.5951/at.36.6.0012.

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Number sense is considered a desirable trait to foster, although its meaning, as other notions of thinking, such as common sense, horse sense, and savoir faire, can be defined only broadly. It can refer to a feeling for number and their various use and interpretations, to an appreciation for various levels of accuracy when figuring, and to a common-sense approach to using figures to support an argument. It can refer to the ability to produce reasonable estimates, to detect arithmetical errors, to choose the most efficient calculating procedure, and to recognize number patterns.

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21

Sowder, Judith T. "Mental Computation and Number Sense." Arithmetic Teacher 37, no. 7 (March 1990): 18–20. http://dx.doi.org/10.5951/at.37.7.0018.

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22

Xu, Fei, Elizabeth S. Spelke, and Sydney Goddard. "Number sense in human infants." Developmental Science 8, no. 1 (January 2005): 88–101. http://dx.doi.org/10.1111/j.1467-7687.2005.00395.x.

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23

Arrighi, Roberto, Irene Togoli, and David C. Burr. "A generalized sense of number." Proceedings of the Royal Society B: Biological Sciences 281, no. 1797 (December 22, 2014): 20141791. http://dx.doi.org/10.1098/rspb.2014.1791.

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Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense . Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats : adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time.

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24

Clark, Robin. "Generalized Quantifiers and Number Sense." Philosophy Compass 6, no. 9 (September 2011): 611–21. http://dx.doi.org/10.1111/j.1747-9991.2011.00419.x.

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25

Brugger, P. "Chicks with a number sense." Science 347, no. 6221 (January 29, 2015): 477–78. http://dx.doi.org/10.1126/science.aaa4854.

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26

Burr, D., and J. Ross. "A visual sense of number." Journal of Vision 8, no. 6 (March 29, 2010): 691. http://dx.doi.org/10.1167/8.6.691.

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27

Burr, D. "A visual sense of number." Journal of Vision 9, no. 8 (March 21, 2010): 12. http://dx.doi.org/10.1167/9.8.12.

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28

Dehaene, Stanislas. "Precis of The Number Sense." Mind and Language 16, no. 1 (February 2001): 16–36. http://dx.doi.org/10.1111/1468-0017.00154.

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29

Mohamed, Mohini, and Jacinta Johnny. "Investigating Number Sense Among Students." Procedia - Social and Behavioral Sciences 8 (2010): 317–24. http://dx.doi.org/10.1016/j.sbspro.2010.12.044.

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30

Giurfa, Martin. "An Insect’s Sense of Number." Trends in Cognitive Sciences 23, no. 9 (September 2019): 720–22. http://dx.doi.org/10.1016/j.tics.2019.06.010.

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31

Clark, Robin, and Murray Grossman. "Number sense and quantifier interpretation." Topoi 26, no. 1 (April 6, 2007): 51–62. http://dx.doi.org/10.1007/s11245-006-9008-2.

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32

Faulkner, Valerie N., and Chris Cain. "The Components of Number Sense." TEACHING Exceptional Children 41, no. 5 (May 2009): 24–30. http://dx.doi.org/10.1177/004005990904100503.

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33

McGregor, William B. "Language and the number sense." Functions of Language 14, no. 2 (December 7, 2007): 231–49. http://dx.doi.org/10.1075/fol.14.2.07mcg.

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34

Burr, David, and John Ross. "A Visual Sense of Number." Current Biology 18, no. 6 (March 2008): 425–28. http://dx.doi.org/10.1016/j.cub.2008.02.052.

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35

Van Hoof, Jo, Lieven Verschaffel, and Wim Van Dooren. "Number sense in the transition from natural to rational numbers." British Journal of Educational Psychology 87, no. 1 (October 31, 2016): 43–56. http://dx.doi.org/10.1111/bjep.12134.

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36

Lafay, Anne, Marie-Catherine St-Pierre, and Joël Macoir. "The Mental Number Line in Dyscalculia: Impaired Number Sense or Access From Symbolic Numbers?" Journal of Learning Disabilities 50, no. 6 (March 25, 2016): 672–83. http://dx.doi.org/10.1177/0022219416640783.

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Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a physical number line. However, it remains unclear whether they have a deficit with the mental number line per se or a deficit with accessing it from nonsymbolic and/or symbolic numbers. Quebec French-speaking 8- to 9-year-old children with (24) and without (37) dyscalculia were assessed with transcoding tasks ( number-to-position and position-to-number) designed to assess the acuity of the mental number line with Arabic and spoken numbers as well as with analogic numerosities. Results showed that children with dyscalculia produced a larger percentage absolute error than children without mathematics difficulties in every task except the number-to-position transcoding task with analogic numerosities. Hence, these results suggested that children with dyscalculia do not have a general deficit of the mental number line but rather a deficit with accessing it from symbolic numbers.

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37

Reynvoet, Bert, Andrew D. Ribner, Leanne Elliott, Manon Van Steenkiste, Delphine Sasanguie, and Melissa E. Libertus. "Making sense of the relation between number sense and math." Journal of Numerical Cognition 7, no. 3 (November 30, 2021): 308–27. http://dx.doi.org/10.5964/jnc.6059.

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While several studies have shown that the performance on numerosity comparison tasks is related to individual differences in math abilities, others have failed to find such a link. These inconsistencies could be due to variations in which math was assessed, different stimulus generation protocols for the numerosity comparison task, or differences in inhibitory control. This within-subject study is a conceptual replication tapping into the relation between numerosity comparison, math, and inhibition in adults (N = 122). Three aspects of math ability were measured using standardized assessments: Arithmetic fluency, calculation, and applied problem solving skills. Participants’ inhibitory skills were measured using Stroop and Go/No-Go tasks with numerical and non-numerical stimuli. Finally, non-symbolic number sense was measured using two different versions of a numerosity comparison task that differed in the stimulus generation protocols (Panamath; Halberda, Mazzocco & Feigenson, 2008, https://doi.org/10.1038/nature07246; G&R, Gebuis & Reynvoet, 2011, https://doi.org/10.3758/s13428-011-0097-5). We find that performance on the Panamath task, but not the G&R task, related to measures of calculation and applied problem solving but not arithmetic fluency, even when controlling for inhibitory control. One possible explanation is that depending on the characteristics of the stimuli in the numerosity comparison task, the reliance on numerical and non-numerical information may vary and only when performance relies more on numerical representations, a relation with math achievement is found. Our findings help to explain prior mixed findings regarding the link between non-symbolic number sense and math and highlight the need to carefully consider variations in numerosity comparison tasks and math measures.

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38

Rowland, Tim. "Mathematics in ‘the news’: number theory and number sense." Mathematical Gazette 106, no. 567 (October 12, 2022): 467–73. http://dx.doi.org/10.1017/mag.2022.119.

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Time spent in national pandemic ‘lockdowns’ and ‘tiers’ for most of 2020 has created an opportunity to revisit some ideas previously committed to paper, but unfinished. I now return to one of them, to continue and share the line of thought, if not to complete it.

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39

d'Errico, Francesco, Luc Doyon, Ivan Colagé, Alain Queffelec, Emma Le Vraux, Giacomo Giacobini, Bernard Vandermeersch, and Bruno Maureille. "From number sense to number symbols. An archaeological perspective." Philosophical Transactions of the Royal Society B: Biological Sciences 373, no. 1740 (January 2018): 20160518. http://dx.doi.org/10.1098/rstb.2016.0518.

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How and when did hominins move from the numerical cognition that we share with the rest of the animal world to number symbols? Objects with sequential markings have been used to store and retrieve numerical information since the beginning of the European Upper Palaeolithic (42 ka). An increase in the number of markings and complexity of coding is observed towards the end of this period. The application of new analytical techniques to a 44–42 ka old notched baboon fibula from Border Cave, South Africa, shows that notches were added to this bone at different times, suggesting that devices to store numerical information were in use before the Upper Palaeolithic. Analysis of a set of incisions on a 72–60 ka old hyena femur from the Les Pradelles Mousterian site, France, indicates, by comparison with markings produced by modern subjects under similar constraints, that the incisions on the Les Pradelles bone may have been produced to record, in a single session, homologous units of numerical information. This finding supports the view that numerical notations were in use among archaic hominins. Based on these findings, a testable five-stage scenario is proposed to establish how prehistoric cultures have moved from number sense to the use of number symbols. This article is part of a discussion meeting issue ‘The origins of numerical abilities’.

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40

Porter, Laura. "Focus on Family: From Number Rhymes to Number Sense." Childhood Education 91, no. 6 (November 2, 2015): 492–94. http://dx.doi.org/10.1080/00094056.2015.1114819.

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41

Bray, Wendy S., and Laura Abreu-Sanchez. "Using number sense to compare fractions." Teaching Children Mathematics 17, no. 2 (September 2010): 90–97. http://dx.doi.org/10.5951/tcm.17.2.0090.

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Third-grade teachers found that giving particular attention to the use of realworld contexts, mental imagery, and manipulatives brought success to problem solving as students moved from using models to reasoning.

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42

Schneider, Sally B., and Charles S. Thompson. "Incredible Equations Develop Incredible Number Sense." Teaching Children Mathematics 7, no. 3 (November 2000): 146–68. http://dx.doi.org/10.5951/tcm.7.3.0146.

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43

Sukma, Y., S. Somakim, and I. Indaryanti. "Students’ number sense on fraction problems." Journal of Physics: Conference Series 1882, no. 1 (May 1, 2021): 012055. http://dx.doi.org/10.1088/1742-6596/1882/1/012055.

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44

Dougherty, Barbara J., and Terry Crites. "Applying Number Sense to Problem Solving." Arithmetic Teacher 36, no. 6 (February 1989): 22–25. http://dx.doi.org/10.5951/at.36.6.0022.

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NCTM's Commission on Standards for School Mathematics (1987) has identified problem solving and number sense as important components of an effective mathematics program. This emphasis is generating attempts to understand the problem-solving process better and to incorporate the results into classroom practice. In keeping with the thrust, this article discusses the interrelationships between problem solving and number sense in light of difficulties experienced by students participating in the problem-solving process.

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45

Sun, Kathy L., Erin E. Baldinger, and Cathy Humphreys. "Number Talks: Gateway to Sense Making." Mathematics Teacher 112, no. 1 (September 2018): 48–54. http://dx.doi.org/10.5951/mathteacher.112.1.0048.

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46

Sowder, Judith, Bonnie Schappelle, and Diana Lambdin. "Research into Practice: Number Sense-Making." Arithmetic Teacher 41, no. 6 (February 1994): 342–45. http://dx.doi.org/10.5951/at.41.6.0342.

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In Everybody Counts, a document from the National Research Council (1989), we are told that the major objective of elementary school mathematics should be to develop number sense. This strong statement, if taken seriously, can change the way many—but not all—teachers teach mathematics in elementary school.

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47

Diezmann, Carmel M., and Lyn D. English. "Developing young children's multidigit number sense." Roeper Review 24, no. 1 (September 2001): 11–13. http://dx.doi.org/10.1080/02783190109554118.

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48

Burr, David C., Giovanni Anobile, and Roberto Arrighi. "Psychophysical evidence for the number sense." Philosophical Transactions of the Royal Society B: Biological Sciences 373, no. 1740 (January 2018): 20170045. http://dx.doi.org/10.1098/rstb.2017.0045.

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It is now clear that most animals, including humans, possess an ability to rapidly estimate number. Some have questioned whether this ability arises from dedicated numerosity mechanisms, or is derived indirectly from judgements of density or other attributes. We describe a series of psychophysical experiments, largely using adaptation techniques, which demonstrate clearly the existence of a number sense in humans. The number sense is truly general, extending over space, time and sensory modality, and is closely linked with action. We further show that when multiple cues are present, numerosity emerges as the natural dimension for discrimination. However, when element density increases past a certain level, the elements become too crowded to parse, and the scene is perceived as a texture rather than array of elements. The two different regimes are psychophysically discriminable in that they follow distinct psychophysical laws, and show different dependencies on eccentricity, luminance levels and effects of perceptual grouping. The distinction is important, as the ability to discriminate numerosity, but not texture, correlates with formal maths skills. This article is part of the discussion meeting issue ‘The origins of numerical abilities’.

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49

Huang, Yi-Huei, Hsu-Jung Lin, Li-Yu Lin, and Chuan-Chin Chiao. "Do cuttlefish have fraction number sense?" Animal Cognition 22, no. 2 (January 2, 2019): 163–68. http://dx.doi.org/10.1007/s10071-018-01232-3.

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50

Baroody, Arthur J., Michael Eiland, and Bradley Thompson. "Fostering At-Risk Preschoolers' Number Sense." Early Education & Development 20, no. 1 (February 6, 2009): 80–128. http://dx.doi.org/10.1080/10409280802206619.

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