東華大學圖書館 |

Cognitive Supports for Analogical Reasoning in Rational Number Understanding.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Cognitive Supports for Analogical Reasoning in Rational Number Understanding./
作者:	Yu, Shuyuan.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2022,
面頁冊數:	134 p.
附註:	Source: Dissertations Abstracts International, Volume: 84-04, Section: A.
Contained By:	Dissertations Abstracts International84-04A.
標題:	Mathematics education. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30003991
ISBN:	9798351438818

Cognitive Supports for Analogical Reasoning in Rational Number Understanding.
Yu, Shuyuan.

Cognitive Supports for Analogical Reasoning in Rational Number Understanding. - Ann Arbor : ProQuest Dissertations & Theses, 2022 - 134 p.

Source: Dissertations Abstracts International, Volume: 84-04, Section: A.

Thesis (Ph.D.)--The Ohio State University, 2022.

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.Specifically, Chapter 1 examined the debated role of integers in the development of fractions, and whether the comparison of integers and fractions on number lines facilitates a better schema for fraction magnitudes representation. Study 1 explored the developmental trajectory of 177 3rd-to-5th graders' representation of integer and fraction estimates. With age, children's estimates of integers and fractions became more coherent, and representational coherence predicts fraction proficiency. To further investigate whether comparison leads to schema generation, Study 2 assigned 100 third-to-fifth graders to an Alignment condition, where children estimated fractions and integers on aligned number lines, or to a No Alignment condition. Results showed that spatial alignment between integers and fractions on number lines facilitated a better understanding of fractional magnitudes, and increased children's fraction estimation accuracy to the level of college students.Chapter 2 further examined whether better schemas of fraction knowledge representation help explicit analogical reasoning. Study 3 examined whether knowledge of terms matters in a simple classical 4-term analogy task by asking 321 adults and children to complete 4-term analogy tasks featuring letters, lines, integers, or fractions. Performance was lowest for fractions, and strongly impacted by educational background. To further establish the causal link that training conceptual knowledge of fractions facilitates proportional analogies, Study 4 administered an educational intervention focusing on either Conceptual Knowledge, Procedural Knowledge, or Both to 343 3rd-to-5th graders. Children with poor pretest magnitude knowledge were more likely to fail analogical reasoning, and training on conceptual knowledge that fractions denote magnitudes improved children's analogies. These findings indicate that knowledge of fractional magnitudes is important to proportional analogy. Analogies require domain-specific knowledge, not merely the maturation of domain-general cognitive abilities.Finally, Chapter 3 explored whether supports that help children's quantitative reasoning (number lines) might also help political partisans. Political ideology leads educated adults - especially the highly numerate - to selectively reason about numbers that support their beliefs ('motivated numeracy'). Study 5 asked 1000 adults to interpret fictional data, in the table or number-line format, about politically neutral or controversial issues. We found data presented in number-line formats yielded greater accuracy than table formats controlling for numeracy skills, regardless of whether the true interpretation of data affirms, neutral to, or disaffirms participants' political outlooks. Solving table problems after number-line problems yielded greater accuracy compared to solving table problems first, suggesting the number-line practice is educational. Results imply that researchers should use number-line to communicate policy-relevant data, especially on politically divisive issues.Together, these studies indicate that analogies can play an important role in rational number learning, with the help of number lines as schemas. These studies aim to shed light on best practices in STEM education curriculum and science communication.

ISBN: 9798351438818Subjects--Topical Terms:

641129
Mathematics education.
Subjects--Index Terms:

Number line estimation

Cognitive Supports for Analogical Reasoning in Rational Number Understanding.
LDR:05053nmm a2200469 4500 001 2400956
005 20241007100316.5
006 m o d
007 cr#unu||||||||
008 251215s2022 ||||||||||||||||| ||eng d
020 $a 9798351438818
035 $a (MiAaPQ)AAI30003991
035 $a (MiAaPQ)OhioLINKosu1657958603433209
035 $a AAI30003991
035 $a 2400956
040 $a MiAaPQ $c MiAaPQ
100 1 $a Yu, Shuyuan. $3 3771018
245 1 0 $a Cognitive Supports for Analogical Reasoning in Rational Number Understanding.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2022
300 $a 134 p.
500 $a Source: Dissertations Abstracts International, Volume: 84-04, Section: A.
500 $a Advisor: Opfer, John E.
502 $a Thesis (Ph.D.)--The Ohio State University, 2022.
520 $a Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.Specifically, Chapter 1 examined the debated role of integers in the development of fractions, and whether the comparison of integers and fractions on number lines facilitates a better schema for fraction magnitudes representation. Study 1 explored the developmental trajectory of 177 3rd-to-5th graders' representation of integer and fraction estimates. With age, children's estimates of integers and fractions became more coherent, and representational coherence predicts fraction proficiency. To further investigate whether comparison leads to schema generation, Study 2 assigned 100 third-to-fifth graders to an Alignment condition, where children estimated fractions and integers on aligned number lines, or to a No Alignment condition. Results showed that spatial alignment between integers and fractions on number lines facilitated a better understanding of fractional magnitudes, and increased children's fraction estimation accuracy to the level of college students.Chapter 2 further examined whether better schemas of fraction knowledge representation help explicit analogical reasoning. Study 3 examined whether knowledge of terms matters in a simple classical 4-term analogy task by asking 321 adults and children to complete 4-term analogy tasks featuring letters, lines, integers, or fractions. Performance was lowest for fractions, and strongly impacted by educational background. To further establish the causal link that training conceptual knowledge of fractions facilitates proportional analogies, Study 4 administered an educational intervention focusing on either Conceptual Knowledge, Procedural Knowledge, or Both to 343 3rd-to-5th graders. Children with poor pretest magnitude knowledge were more likely to fail analogical reasoning, and training on conceptual knowledge that fractions denote magnitudes improved children's analogies. These findings indicate that knowledge of fractional magnitudes is important to proportional analogy. Analogies require domain-specific knowledge, not merely the maturation of domain-general cognitive abilities.Finally, Chapter 3 explored whether supports that help children's quantitative reasoning (number lines) might also help political partisans. Political ideology leads educated adults - especially the highly numerate - to selectively reason about numbers that support their beliefs ('motivated numeracy'). Study 5 asked 1000 adults to interpret fictional data, in the table or number-line format, about politically neutral or controversial issues. We found data presented in number-line formats yielded greater accuracy than table formats controlling for numeracy skills, regardless of whether the true interpretation of data affirms, neutral to, or disaffirms participants' political outlooks. Solving table problems after number-line problems yielded greater accuracy compared to solving table problems first, suggesting the number-line practice is educational. Results imply that researchers should use number-line to communicate policy-relevant data, especially on politically divisive issues.Together, these studies indicate that analogies can play an important role in rational number learning, with the help of number lines as schemas. These studies aim to shed light on best practices in STEM education curriculum and science communication.
590 $a School code: 0168.
650 4 $a Mathematics education. $3 641129
650 4 $a Curriculum development. $3 684418
650 4 $a Elementary education. $3 641385
650 4 $a Quantitative psychology. $3 2144748
650 4 $a Early childhood education. $3 518817
650 4 $a Education. $3 516579
653 $a Number line estimation
653 $a Proportion reasoning
653 $a Mathematical development
653 $a Analogical reasoning
653 $a Numerical cognition
653 $a Progressive alignment
653 $a Rational numbers
690 $a 0632
690 $a 0515
690 $a 0524
690 $a 0727
690 $a 0518
690 $a 0280
710 2 $a The Ohio State University. $b Psychology. $3 1267002
773 0 $t Dissertations Abstracts International $g 84-04A.
790 $a 0168
791 $a Ph.D.
792 $a 2022
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30003991