{"title":"有理数符号的综合知识预测了儿童的数学成绩和对数值大小的理解","authors":"Lauren K. Schiller , Robert S. Siegler","doi":"10.1016/j.cogdev.2023.101380","DOIUrl":null,"url":null,"abstract":"<div><p>We propose that <em>integrated number sense,</em> the ability to fluidly translate and compare magnitudes within and across notations, is central to understanding of rational numbers. Consistent with this hypothesis, two studies of 6th through 8th grade students (N = 264 and N = 46) indicated that accuracy comparing magnitudes within and across notations predicted overall math achievement and fraction number line and arithmetic estimation accuracy. Cross-notation magnitude comparison accuracy (i.e., fraction vs. decimal, percentage vs. fraction, and percentage vs. decimal) accounted for variance in math outcomes beyond that explained by magnitude representations within individual notations. The findings also revealed a <em>percentages-are-larger bias</em>, in which percentages are perceived as larger than equivalent fractions and decimals in cross-notation comparisons. There were no differences by grade level, suggesting that such number sense does not necessarily develop with age. Explicitly promoting integrated number sense may help improve mathematics instruction.</p></div>","PeriodicalId":51422,"journal":{"name":"Cognitive Development","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Integrated knowledge of rational number notations predicts children’s math achievement and understanding of numerical magnitudes\",\"authors\":\"Lauren K. Schiller , Robert S. Siegler\",\"doi\":\"10.1016/j.cogdev.2023.101380\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We propose that <em>integrated number sense,</em> the ability to fluidly translate and compare magnitudes within and across notations, is central to understanding of rational numbers. Consistent with this hypothesis, two studies of 6th through 8th grade students (N = 264 and N = 46) indicated that accuracy comparing magnitudes within and across notations predicted overall math achievement and fraction number line and arithmetic estimation accuracy. Cross-notation magnitude comparison accuracy (i.e., fraction vs. decimal, percentage vs. fraction, and percentage vs. decimal) accounted for variance in math outcomes beyond that explained by magnitude representations within individual notations. The findings also revealed a <em>percentages-are-larger bias</em>, in which percentages are perceived as larger than equivalent fractions and decimals in cross-notation comparisons. There were no differences by grade level, suggesting that such number sense does not necessarily develop with age. Explicitly promoting integrated number sense may help improve mathematics instruction.</p></div>\",\"PeriodicalId\":51422,\"journal\":{\"name\":\"Cognitive Development\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cognitive Development\",\"FirstCategoryId\":\"102\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0885201423000850\",\"RegionNum\":3,\"RegionCategory\":\"心理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PSYCHOLOGY, DEVELOPMENTAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cognitive Development","FirstCategoryId":"102","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0885201423000850","RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PSYCHOLOGY, DEVELOPMENTAL","Score":null,"Total":0}
Integrated knowledge of rational number notations predicts children’s math achievement and understanding of numerical magnitudes
We propose that integrated number sense, the ability to fluidly translate and compare magnitudes within and across notations, is central to understanding of rational numbers. Consistent with this hypothesis, two studies of 6th through 8th grade students (N = 264 and N = 46) indicated that accuracy comparing magnitudes within and across notations predicted overall math achievement and fraction number line and arithmetic estimation accuracy. Cross-notation magnitude comparison accuracy (i.e., fraction vs. decimal, percentage vs. fraction, and percentage vs. decimal) accounted for variance in math outcomes beyond that explained by magnitude representations within individual notations. The findings also revealed a percentages-are-larger bias, in which percentages are perceived as larger than equivalent fractions and decimals in cross-notation comparisons. There were no differences by grade level, suggesting that such number sense does not necessarily develop with age. Explicitly promoting integrated number sense may help improve mathematics instruction.
期刊介绍:
Cognitive Development contains the very best empirical and theoretical work on the development of perception, memory, language, concepts, thinking, problem solving, metacognition, and social cognition. Criteria for acceptance of articles will be: significance of the work to issues of current interest, substance of the argument, and clarity of expression. For purposes of publication in Cognitive Development, moral and social development will be considered part of cognitive development when they are related to the development of knowledge or thought processes.