Topic
Number sense
About: Number sense is a research topic. Over the lifetime, 959 publications have been published within this topic receiving 27120 citations. The topic is also known as: number meaning.
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01 Jan 2010
TL;DR: Section I Teaching Mathematics: Foundations and Perspectives teaches Mathematics in the Era of the NCTM Standards chapter 1 exploring What It Means to Do Mathematics and developing Understanding in Mathematics.
Abstract: Section I Teaching Mathematics: Foundations and Perspectives chapter 1 Teaching Mathematics in the Era of the NCTM Standards chapter 2 Exploring What It Means to Do Mathematics chapter 3 Developing Understanding in Mathematics chapter 4 Teaching Through Problem Solving chapter 5 Planning in the Problem-Based Classroom chapter 6 Building Assessment into Instruction chapter 7 Teaching Mathematics Equitably to All Children chapter 8 Technology and School Mathematics Section II Development of Mathematical Concepts and Procedures chapter 9 Developing Early Number Concepts and Number Sense chapter 10 Developing Meanings for the Operations chapter 11 Helping Children Master the Basic Facts chapter 12 Whole-Number Place-Value Development chapter 13 Strategies for Whole-Number Computation chapter 14 Computational Estimation with Whole Numbers chapter 15 Algebraic Thinking: Generalizations, Patterns, and Functions chapter 16 Developing Fraction Concepts chapter 17 Computation with Fractions chapter 18 Decimal and Percent Concepts and Decimal Computation chapter 19 Proportional Reasoning chapter 20 Developing Measurement Concepts chapter 21 Geometric Thinking and Geometric Concepts chapter 22 Concepts of Data Analysis chapter 23 Exploring Concepts of Probability chapter 24 Developing Concepts of Exponents, Integers, and Real Numbers appendix A Principles and Standards for School Mathematics: Content Standards and Grade Level Expectations appendix B Professional Standards for Teaching Mathematics: Teaching Standards appendix C Guide to Blackline Masters References Index
1,300 citations
TL;DR: There are large individual differences in the non-verbal approximation abilities of 14-year-old children, and that these individual Differences in the present correlate with children’s past scores on standardized maths achievement tests, extending all the way back to kindergarten.
Abstract: Human mathematical competence emerges from two representational systems. Competence in some domains of mathematics, such as calculus, relies on symbolic representations that are unique to humans who have undergone explicit teaching. More basic numerical intuitions are supported by an evolutionarily ancient approximate number system that is shared by adults, infants and non-human animals-these groups can all represent the approximate number of items in visual or auditory arrays without verbally counting, and use this capacity to guide everyday behaviour such as foraging. Despite the widespread nature of the approximate number system both across species and across development, it is not known whether some individuals have a more precise non-verbal 'number sense' than others. Furthermore, the extent to which this system interfaces with the formal, symbolic maths abilities that humans acquire by explicit instruction remains unknown. Here we show that there are large individual differences in the non-verbal approximation abilities of 14-year-old children, and that these individual differences in the present correlate with children's past scores on standardized maths achievement tests, extending all the way back to kindergarten. Moreover, this correlation remains significant when controlling for individual differences in other cognitive and performance factors. Our results show that individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense. Further research will determine whether early differences in number sense acuity affect later maths learning, whether maths education enhances number sense acuity, and the extent to which tertiary factors can affect both.
1,220 citations
TL;DR: The number domain is a prime example where strong evidence points to an evolutionary endowment of abstract domain-specific knowledge in the brain because there are parallels between number processing in animals and humans.
786 citations
TL;DR: Key findings from the small body of research on mathematics difficulties (MD) relevant to early identification and early intervention are highlighted and the presence of reading difficulties seems related to slower progress in many aspects of mathematics.
Abstract: This article highlights key findings from the small body of research on mathematics difficulties (MD) relevant to early identification and early intervention. The research demonstrates that (a) for many children, mathematics difficulties are not stable over time; (b) the presence of reading difficulties seems related to slower progress in many aspects of mathematics; (c) almost all students with MD demonstrate problems with accurate and automatic retrieval of basic arithmetic combinations, such as 6 + 3. The following measures appear to be valid and reliable indicators of potential MD in kindergartners: (a) magnitude comparison (i.e., knowing which digit in a pair is larger), (b) sophistication of counting strategies, (c) fluent identification of numbers, and (d) working memory (as evidenced by reverse digit span). These are discussed in terms of the components of number sense. Implications for early intervention strategies are explored.
775 citations
TL;DR: It is shown that number acuity improves with age in typically developing children, establishing for the first time a clear association between dyscalculia and impaired "number sense", and may open up new horizons for the early diagnosis and rehabilitation of mathematical learning deficits.
636 citations