Present day Learning Theories and Mathematics Education: Bidirectional Contributions, Bidirectional Challenges

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Current Learning Theories and Mathematics Education: Bidirectional Contributions, Bidirectional Challenges The examination reported here was upheld by the Institute of Education Sciences, U.S. Bureau of Education, through Grant R305H050035 to Carnegie Mellon University. The suppositions communicated are those of the creator and don't speak to perspectives of the Institute or the U.S. Division of Education.

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A Little Personal Background Like numerous agents supported by IES, a large portion of my pre-IES research was hypothetical (Definition: "With no presumable application") IES propelled me to contemplate routes in which the exploration could be connected to essential instructive issues without giving up meticulousness One result has been my momentum look into applying speculations of numerical perception to enhancing low-pay preschoolers' scientific comprehension

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Another result has been to expand my enthusiasm for more extensive issues of use, i.e., instructive arrangement issues This developing enthusiasm for applications drove me to relinquish my customary "simply say no" approach in regards to commissions and boards and acknowledge arrangement to the National Mathematics Advisory Panel (NMAP). Fundamental part was in learning forms assemble The present talk joins points of view picked up from doing the connected research and from taking an interest in the learning forms gathering of NMAP

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Bidirectional Contributions, Bidirectional Challenges Contributions to Mathematics Education from Applying Modern Learning Theories Contributions to Modern Learning Theories from Mathematics Education Applications Challenges to Modern Learning Theories from Mathematics Education Applications Challenges to Mathematics Education from Modern Learning Theories

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Contributions to Mathematics Education from Applying Modern Learning Theories

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Conclusions of NMAP: "9. Empowering comes about have been acquired for an assortment of instructional projects created to enhance the scientific information of preschoolers and kindergartners, particularly those from low-wage foundations. There are compelling systems – got from logical research on learning – that could be given something to do in the classroom today to enhance youngsters' numerical information." "14. Youngsters' objectives and convictions about learning are identified with their science execution. . . At the point when kids trust that their endeavors to learn make them "more intelligent," they demonstrate more prominent constancy in science learning."

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Theoretical Background: The Centrality of Numerical Magnitude Representations An essential issue in numerous cutting edge learning hypotheses includes how information is spoken to In scientific perception, this issue includes the hidden representation of numerical sizes (Dehaene, 1997; Gelman & Gallistel, 2001; Case & Okamoto, 1996) Empirical research shows that straight representations connecting number images with their sizes are vital for an assortment of vital science learning results

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The Number Line Task 71 0 100

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Progression from Log to Linear Representation — 0-100 Range (Siegler & Booth, 2004) Number Presented Number Presented Number Presented

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Second Graders Sixth Graders Median Estimate R 2 log = .95 R 2 lin = .97 Number Presented Number Presented Progression from Log to Linear Representation — 0-1,000 Range (Siegler & Opfer, 2003)

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The Centrality of Numerical Magnitude Representations Linearity of greatness representations associates emphatically and unequivocally crosswise over shifted estimation assignments, numerical extent examination, number-crunching, and math accomplishment tests (Booth & Siegler, 2006; 2008; Geary, et al., 2007; Ramani & Siegler, 2008; Whyte & Bull, 2008).

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Correlations Among Linearity of Magnitude Representations on Three Estimation Tasks (Booth & Siegler, 2006) ** p < .01; * p < .05

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Correlations Between Linearity of Estimation and Math Achievement (Booth & Siegler, 2006) Grade Estimation Task ** p < .01; * p < .05

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** % Correct Sums ** p < .01 Causal Evidence: External Magnitude Representations and Arithmetic Learning (Booth & Siegler, 2008)

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Issue in Mathematics Education: Low-Income Children Lag Behind in Mathematical Proficiency Even Before They Enter School 1. Youngsters differ incredibly in numerical learning when they enter school 2. Numerical information of kindergartners from low-pay families trails a long ways behind that of associates from higher-pay families (ECLS, 2001)

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3. Kindergartners' numerical information emphatically predicts later scientific accomplishment — through basic, center, and secondary school (Duncan, et al., 2007; Jordan et al., 2009; Stevenson & Newman, 1986) 4. Expansive, early, SES related contrasts turn out to be much more professed as youngsters advance through school

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Applying Theory to Educational Problem Might deficient representations of numerical extents underlie low-salary kids' poor numerical execution?

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Applied Goal Raised New Theoretical Question: What Leads Anyone to Form Initial Linear Representation? Tallying background is likely useful and important, yet inadequate Children can tally in a numerical range over a year prior to they can create a direct representation of numerical sizes in that range (Condry & Spelke, 2008; LeCorre & Carey, 2007; Schaffer et al., 1974)

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Playing Board Games Board recreations may assume a significant part in shaping straight representations of numerical sizes Designed to advance collaborations amongst guardians and associates Also furnishes rich encounters with numbers

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Chutes and Ladders

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Key Properties of Board Games Like Chutes and Ladders The more prominent the number a token reaches, the more prominent the Distance that the tyke has moved the token Number of discrete hand developments the youngster has made Number of number names the tyke has spoken Time spent by the tyke playing the amusement Thus, playing number tabletop games gives visuo-spatial, kinesthetic, sound-related, and worldly signals to joins between number images and their extents

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Number Board Game

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Color Board Game

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Effects of Playing the Number Board Game (Ramani & Siegler, 2008) Goal was to research whether playing the number prepackaged game: Improves a wide scope of numerical aptitudes and ideas Produces picks up that stay stable after some time

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Methods Participants : 129 4-and 5-year-olds from Head Start classrooms (mean age = 4.8), 52% African-American Experimental Conditions : Number Board Game (N = 69) Color Board Game (N = 60) Design : Pretest, 4 instructional meetings, posttest, 9 week development.

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Training Procedure : Children play a sum of 20 recreations more than 4 sessions in a 2 week time frame, 15-20 minutes/session Child turns spinner, gets 1 or 2, says while moving token (e.g.) "5, 6" or "blue, red" Feedback and help if necessary Measures : 0-10 Number Line Estimation 1-9 Numerical Magnitude Comparison 1-10 Counting 1-10 Numeral Identification

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Numerical Magnitude Comparison * % Correct M * p < .001

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Counting * Mean Counts Without Error M * p < .001

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Number Line Estimation: Linearity of Individual Children's Estimates * Mean R 2 lin M * p < .001

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Numeral Identification * % Correct M * p < .001

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Percent Correct Addition Answers (Siegler & Ramani, in press) * % Correct M * p < .05

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II. Contributions to Modern Learning Theories from Mathematics Education Applications

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Theoretical Contributions of Number Game Application NMAP Conclusion: "10. The educational programs should at the same time create calculated understanding, computational familiarity, and critical thinking aptitudes. . . These capacities are commonly steady, each encouraging learning of the others." Point to requirement for single hypothesis to incorporate learning of ideas, methods, actualities, and critical thinking Demonstrate need to distinguish regular encounters that fabricate reasonable comprehension

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Illustrate need to recognize focal calculated structures (Case & Okamoto, 1996) Raise question of what other particular exercises add to numerical size representations: Counting objects in column Addition through numbering fingers Conversation about numerical properties Other diversions (e.g., war) Suggest that insufficient division greatness representations somewhat because of absence of encounters that show correlational structure (1/3 + 1/3 = 2/6)

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III. Challenges to Modern Learning Theories from Mathematics Education Applications

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NMAP Executive Summary, p. 32: "There are numerous holes in ebb and flow comprehension of how kids learn polynomial math and the planning that is required before they enter variable based math." Considerable top notch research is accessible with respect to math learning in preschool and initial few evaluations, however far less on later math learning. Speculations and exact studies need to address learning of pre-polynomial math, variable based math, and geometry. Ethicalness of hypothesis based applications: Open up speculations; dodge trap of "more about less and less."

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Conclusion 12 from NMAP: "Trouble with parts (counting decimals and rates) is inescapable and is a noteworthy hindrance to further advance in arithmetic, including polynomial math." Remarkable assention among NMAP individuals and variable based math instructors on significance of divisions for learning polynomial math. Be that as it may, no proof. Requirement for powerful measures of reasonably broad information structures, for example, comprehension of parts, so can examine these relations. Such vigorous measures require better hypothesis of what's integral to (e.g.) understanding portions.

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IV. C

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