{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/79744"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/79744","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Development of Conceptual and Procedural Knowledge in Preschoolers' Addition and Subtraction","abstract":"Learning in some domains requires the learner to construct relations between conceptual and procedural knowledge. However, we still do not have full knowledge about the underlying processes. Understanding of this issue will help researchers not only in building theories of knowledge acquisition but also in designing appropriate instruction. Two questions were investigated in this research: What is the knowledge basis that young children depend on to discover two arithmetic principles and to invent computational procedures? The first purpose of these questions was to understand how young children acquire these conceptual and procedural components with little intervention, and the second purpose was to explore the developmental relations between conceptual and procedural knowledge. Thirty-five and 36 children, between 2½ and 3½ years of age, participated in the first study and the second study, respectively. Each child was individually interviewed with three tasks: quantification, principle, and computation tasks. Four general findings were obtained from the two studies. First, the development of either of the principles in the more general form does not require knowledge of quantification. Second, there were mixed findings about the initial development of the principles, and none of them was conclusive at this point. Third, for both of the principles, the emergence of the general principle precedes the computational procedures for small numbers. Nevertheless, the development of the computational procedures for the simplest problems does not seem to rely on the general principles, at least not both of them. Although further evidence about the initial relations between quantification and the principles and between the principles and the procedures is needed, the results and discussion have two implications for the developmental relations between conceptual and procedural knowledge. First, two conceptually related components of conceptual and procedural knowledge may not always entail the same functional relation in development. Second, it follows from the first implication that the iterative improvement model proposed by Rittle-Johnson and colleagues may not always be true.","abstract_html":"Learning in some domains requires the learner to construct relations between conceptual and procedural knowledge. However, we still do not have full knowledge about the underlying processes. Understanding of this issue will help researchers not only in building theories of knowledge acquisition but also in designing appropriate instruction. Two questions were investigated in this research: What is the knowledge basis that young children depend on to discover two arithmetic principles and to invent computational procedures? The first purpose of these questions was to understand how young children acquire these conceptual and procedural components with little intervention, and the second purpose was to explore the developmental relations between conceptual and procedural knowledge. Thirty-five and 36 children, between 2½ and 3½ years of age, participated in the first study and the second study, respectively. Each child was individually interviewed with three tasks: quantification, principle, and computation tasks. Four general findings were obtained from the two studies. First, the development of either of the principles in the more general form does not require knowledge of quantification. Second, there were mixed findings about the initial development of the principles, and none of them was conclusive at this point. Third, for both of the principles, the emergence of the general principle precedes the computational procedures for small numbers. Nevertheless, the development of the computational procedures for the simplest problems does not seem to rely on the general principles, at least not both of them. Although further evidence about the initial relations between quantification and the principles and between the principles and the procedures is needed, the results and discussion have two implications for the developmental relations between conceptual and procedural knowledge. First, two conceptually related components of conceptual and procedural knowledge may not always entail the same functional relation in development. Second, it follows from the first implication that the iterative improvement model proposed by Rittle-Johnson and colleagues may not always be true.","abstract_has_math":false,"creators":["Liao, Hsin-Mei"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Education","degree_department":null,"school":null,"contributors":["Perry, Michelle"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T19:53:20Z","date_published":"2015-09-25T19:53:20Z","updated_at":"2026-07-22T22:26:12Z","subjects":["Education, Educational Psychology"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3086228"],"render_values":[{"text":"(MiAaPQ)AAI3086228","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/79744","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Perry, Michelle"]},{"key":"dc:creator","label":"Author","values":["Liao, Hsin-Mei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T19:53:20Z","10000-01-01","2002"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Education"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Education, Educational Psychology"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/79744","(MiAaPQ)AAI3086228"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Learning in some domains requires the learner to construct relations between conceptual and procedural knowledge. 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First, the development of either of the principles in the more general form does not require knowledge of quantification. Second, there were mixed findings about the initial development of the principles, and none of them was conclusive at this point. Third, for both of the principles, the emergence of the general principle precedes the computational procedures for small numbers. Nevertheless, the development of the computational procedures for the simplest problems does not seem to rely on the general principles, at least not both of them. Although further evidence about the initial relations between quantification and the principles and between the principles and the procedures is needed, the results and discussion have two implications for the developmental relations between conceptual and procedural knowledge. First, two conceptually related components of conceptual and procedural knowledge may not always entail the same functional relation in development. 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First, the development of either of the principles in the more general form does not require knowledge of quantification. Second, there were mixed findings about the initial development of the principles, and none of them was conclusive at this point. Third, for both of the principles, the emergence of the general principle precedes the computational procedures for small numbers. Nevertheless, the development of the computational procedures for the simplest problems does not seem to rely on the general principles, at least not both of them. Although further evidence about the initial relations between quantification and the principles and between the principles and the procedures is needed, the results and discussion have two implications for the developmental relations between conceptual and procedural knowledge. First, two conceptually related components of conceptual and procedural knowledge may not always entail the same functional relation in development. 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