Asiala, Anne Brown, David DeViries, E. Dubinsky, David Mathews, Karen Thomas
Over the past several years, a community of researchers has been using and re ning a particular framework for research and curriculum development in undergraduate mathematics education. The purpose of this paper is to share the results of this work with the mathematics education community at large by describing the current version of the framework and giving some examples of its application. Our framework utilizes qualitative methods for research and is based on a very speci c theoretical perspective that is being developed through attempts to understand the ideas of Piaget concerning reective abstraction and reconstruct them in the context of college level mathematics. Our approach has three components. It begins with an initial theoretical analysis of what it means to understand a concept and how that understanding can be constructed by the learner. This leads to the design of an instructional treatment that focuses directly on trying to get students to make the constructions called for by the analysis. Implementation of instruction leads to the gathering of data, which is then analyzed in the context of the theoretical perspective. The researchers cycle through the three components and re ne both the theory and the instructional treatments as needed. In this report the authors present detailed descriptions of each of these components. In our discussion of theoretical analyses, we describe certain mental constructions for learning mathematics, including actions, processes, objects, and schemas, and the relationships among these constructions. Under instructional treatment, we describe the components of the ACE teaching cycle (activities, class discussion, and exercises), cooperative learning and the use of a mathematical programming language. Finally, we describe the methodology used in data collection and analysis. The paper concludes with a discussion of issues raised in the use of this framework, followed by an extensive bibliography.
{"title":"A Framework for Research and Curriculum Development in Undergraduate Mathematics Educationjpeg","authors":"Asiala, Anne Brown, David DeViries, E. Dubinsky, David Mathews, Karen Thomas","doi":"10.1090/cbmath/006/01","DOIUrl":"https://doi.org/10.1090/cbmath/006/01","url":null,"abstract":"Over the past several years, a community of researchers has been using and re ning a particular framework for research and curriculum development in undergraduate mathematics education. The purpose of this paper is to share the results of this work with the mathematics education community at large by describing the current version of the framework and giving some examples of its application. Our framework utilizes qualitative methods for research and is based on a very speci c theoretical perspective that is being developed through attempts to understand the ideas of Piaget concerning reective abstraction and reconstruct them in the context of college level mathematics. Our approach has three components. It begins with an initial theoretical analysis of what it means to understand a concept and how that understanding can be constructed by the learner. This leads to the design of an instructional treatment that focuses directly on trying to get students to make the constructions called for by the analysis. Implementation of instruction leads to the gathering of data, which is then analyzed in the context of the theoretical perspective. The researchers cycle through the three components and re ne both the theory and the instructional treatments as needed. In this report the authors present detailed descriptions of each of these components. In our discussion of theoretical analyses, we describe certain mental constructions for learning mathematics, including actions, processes, objects, and schemas, and the relationships among these constructions. Under instructional treatment, we describe the components of the ACE teaching cycle (activities, class discussion, and exercises), cooperative learning and the use of a mathematical programming language. Finally, we describe the methodology used in data collection and analysis. The paper concludes with a discussion of issues raised in the use of this framework, followed by an extensive bibliography.","PeriodicalId":415007,"journal":{"name":"Colección Digital Eudoxus","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134413682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 2000 syllabus revisions took into account the need to include the process of history. In alignment with the change in the syllabus, assessment changed and pupils were expected to answer a compulsory source-based question. This research project is constructed to study Singapore teachers characterisation of historical interpretation and enquiry four years after the new syllabi was implemented.
{"title":"Singapore teachers' characterisation of historical interpretation and enquiry: enhancing pedagogy and pupils' historical understanding","authors":"Doreen Tan","doi":"10.18546/HERJ.04.2.09","DOIUrl":"https://doi.org/10.18546/HERJ.04.2.09","url":null,"abstract":"In 2000 syllabus revisions took into account the need to include the process of history. In alignment with the change in the syllabus, assessment changed and pupils were expected to answer a compulsory source-based question. This research project is constructed to study Singapore teachers characterisation of historical interpretation and enquiry four years after the new syllabi was implemented.","PeriodicalId":415007,"journal":{"name":"Colección Digital Eudoxus","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131890761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Solve It! is a research-based instructional program for students who have difficulty solving mathematical word problems. Many of these students require particular help in understanding and using cognitive processes and self-regulation strategies that underlie effective and efficient problem solving. This article underscores the need to improve students' mathematical problem solving, describes the theoretical framework for the instructional program, reviews the research on Solve It!, presents an overview of the program, and discusses several practical issues related to its implementation. This mathematical problem-solving program has been successful for students with mathematical learning disabilities and, therefore, can be used in inclusive, general education classrooms as well as special education classes.
{"title":"Solve It! Strategy Instruction to Improve Mathematical Problem Solving . Learning Disabilities Research & Practice.","authors":"Marjorie Montague, C. Warger, Thelma H. Morgan","doi":"10.1207/SLDRP1502_7","DOIUrl":"https://doi.org/10.1207/SLDRP1502_7","url":null,"abstract":"Solve It! is a research-based instructional program for students who have difficulty solving mathematical word problems. Many of these students require particular help in understanding and using cognitive processes and self-regulation strategies that underlie effective and efficient problem solving. This article underscores the need to improve students' mathematical problem solving, describes the theoretical framework for the instructional program, reviews the research on Solve It!, presents an overview of the program, and discusses several practical issues related to its implementation. This mathematical problem-solving program has been successful for students with mathematical learning disabilities and, therefore, can be used in inclusive, general education classrooms as well as special education classes.","PeriodicalId":415007,"journal":{"name":"Colección Digital Eudoxus","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130973069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1996-04-01DOI: 10.1111/J.1949-8594.1996.TB10220.X
C. Stuessy, Gilbert L. Naizer
An innovative teacher preparation course which integrates methods of teaching elementary mathematics and science was the context of this study. The course was developed as a prototype for the Teachers As Reflective Problem Solvers model for the preparation of elementary mathematics and science teachers. Data from 35 preservice elementary teachers' performance-portfolios were analyzed to reveal patterns of change in their reflections and problem-solving performance during the semester. Many of the students' reflections changed from task-focused learning to broader teaching applications. No relationship was discerned between changes in students' reflections and changes in their levels of problem-solving performance, although both increased during the semester. A significant correspondence was found, however, between students' perceptions of their problem-solving abilities and their actual performance in solving teaching problems in integrated mathematics and science contexts.
{"title":"Reflection and problem solving: Integrating methods of teaching mathematics and Science. School Science and Mathematics.","authors":"C. Stuessy, Gilbert L. Naizer","doi":"10.1111/J.1949-8594.1996.TB10220.X","DOIUrl":"https://doi.org/10.1111/J.1949-8594.1996.TB10220.X","url":null,"abstract":"An innovative teacher preparation course which integrates methods of teaching elementary mathematics and science was the context of this study. The course was developed as a prototype for the Teachers As Reflective Problem Solvers model for the preparation of elementary mathematics and science teachers. Data from 35 preservice elementary teachers' performance-portfolios were analyzed to reveal patterns of change in their reflections and problem-solving performance during the semester. Many of the students' reflections changed from task-focused learning to broader teaching applications. No relationship was discerned between changes in students' reflections and changes in their levels of problem-solving performance, although both increased during the semester. A significant correspondence was found, however, between students' perceptions of their problem-solving abilities and their actual performance in solving teaching problems in integrated mathematics and science contexts.","PeriodicalId":415007,"journal":{"name":"Colección Digital Eudoxus","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127435013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1992-05-06DOI: 10.1111/J.1949-8594.1992.TB15582.X
R. Mayes
{"title":"The Effects of Using Software Tools on Mathematical Problem Solving in Secondary Schools. School Science and Mathematics.","authors":"R. Mayes","doi":"10.1111/J.1949-8594.1992.TB15582.X","DOIUrl":"https://doi.org/10.1111/J.1949-8594.1992.TB15582.X","url":null,"abstract":"","PeriodicalId":415007,"journal":{"name":"Colección Digital Eudoxus","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115426182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Treatment of Refutations: Aspects of the Complexity of a Constructivist Approach to Mathematics Learning","authors":"N. Balacheff","doi":"10.1007/0-306-47201-5_5","DOIUrl":"https://doi.org/10.1007/0-306-47201-5_5","url":null,"abstract":"","PeriodicalId":415007,"journal":{"name":"Colección Digital Eudoxus","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114628260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this paper is to present classroom-tested geometry activities based on the van Hiele geometric thinking levels using dynamic geometry applications. The other ideas behind the activities include teacher questioning, active student participation, and studentcentered decision-making. During the lessons student teachers engaged in self-exploration and reinvention of geometric relations. It was evident from the episodes that students raised their level of geometric thinking by building on their current geometric understanding.
{"title":"Geometric Explorations with Dynamic Geometry Applications based on van Hiele levels","authors":"S. Olkun","doi":"10.1501/0003625","DOIUrl":"https://doi.org/10.1501/0003625","url":null,"abstract":"The purpose of this paper is to present classroom-tested geometry activities based on the van Hiele geometric thinking levels using dynamic geometry applications. The other ideas behind the activities include teacher questioning, active student participation, and studentcentered decision-making. During the lessons student teachers engaged in self-exploration and reinvention of geometric relations. It was evident from the episodes that students raised their level of geometric thinking by building on their current geometric understanding.","PeriodicalId":415007,"journal":{"name":"Colección Digital Eudoxus","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114536762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantum Mechanics, Mathematics, Cognition and Action","authors":"M. Mugur-Schächter, A. V. Merwe","doi":"10.1007/0-306-48144-8","DOIUrl":"https://doi.org/10.1007/0-306-48144-8","url":null,"abstract":"","PeriodicalId":415007,"journal":{"name":"Colección Digital Eudoxus","volume":"92 21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128866154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-0-387-71575-9_5
Albrecht Heeffer
{"title":"Learning Concepts Through the History of Mathematics","authors":"Albrecht Heeffer","doi":"10.1007/978-0-387-71575-9_5","DOIUrl":"https://doi.org/10.1007/978-0-387-71575-9_5","url":null,"abstract":"","PeriodicalId":415007,"journal":{"name":"Colección Digital Eudoxus","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115831868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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