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Author: YEE-HO GENTHEW. LEUNG
Publisher:
ISBN: 9781361079768
Category :
Languages : en
Pages :
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Book Description
This dissertation, "An Evaluation of a Teaching Approach to Improve Students' Understanding of Mathematical Induction" by Yee-ho, Genthew, Leung, 梁以豪, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: ABSTRACT "Mathematical Induction" is not a new mathematics topic in Hong Kong secondary school Mathematics curriculum. Dubinsky & Lewin (1986), (Dubinsky 1986, 1989) provided a theoretically based instructional method, using computer experiences, in teaching MI. These three papers was a beginning of a theory for teaching MI based on the genetic epistemology of Jean Piaget. Dubinsky & Lewin (1986) worked out a genetic decomposition of MI to describe the required construction process for learning it. Dubinsky (1986,1989) designed and improved an instructional method for teaching MI which based on students' computer experiences. He claimed that the method is well developed and it can be used for teaching. Although this instructional method is remarkable, it entirely depends on students' computer experience. Can we have a similar instructional method which is independent of computer experience? Movshovitz-Hadar (1993) posted ten classroom activities to enhance students' understanding in MI. I found some of these activities are suitable for formulating an instructional method. I decided to take some of these 10 activities and some self-designed activities to form a new instructional method. The main purpose of the study is to do an evaluation on this computer independent teaching approach. The overall performance on the evaluations suggests that this teaching approach was effective in bringing students to the concept of Mathematical Induction. I hope that it could be developed until we can use it in any ordinary classroom even ii where there are no computer facilities. Also, there were various examples of reflective abstraction in the interview. Students built up the concept from one schema to another. It reflected that the genetic decomposition proposed by Dubinsky & Lewin (1986) is a reasonable way to meditate the construct of Mathematical Induction. iii DOI: 10.5353/th_b3551612 Subjects: Induction (Mathematics) - Study and teaching (Secondary) - China - Hong Kong
Author: YEE-HO GENTHEW. LEUNG
Publisher:
ISBN: 9781361079768
Category :
Languages : en
Pages :
Get Book Here
Book Description
This dissertation, "An Evaluation of a Teaching Approach to Improve Students' Understanding of Mathematical Induction" by Yee-ho, Genthew, Leung, 梁以豪, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: ABSTRACT "Mathematical Induction" is not a new mathematics topic in Hong Kong secondary school Mathematics curriculum. Dubinsky & Lewin (1986), (Dubinsky 1986, 1989) provided a theoretically based instructional method, using computer experiences, in teaching MI. These three papers was a beginning of a theory for teaching MI based on the genetic epistemology of Jean Piaget. Dubinsky & Lewin (1986) worked out a genetic decomposition of MI to describe the required construction process for learning it. Dubinsky (1986,1989) designed and improved an instructional method for teaching MI which based on students' computer experiences. He claimed that the method is well developed and it can be used for teaching. Although this instructional method is remarkable, it entirely depends on students' computer experience. Can we have a similar instructional method which is independent of computer experience? Movshovitz-Hadar (1993) posted ten classroom activities to enhance students' understanding in MI. I found some of these activities are suitable for formulating an instructional method. I decided to take some of these 10 activities and some self-designed activities to form a new instructional method. The main purpose of the study is to do an evaluation on this computer independent teaching approach. The overall performance on the evaluations suggests that this teaching approach was effective in bringing students to the concept of Mathematical Induction. I hope that it could be developed until we can use it in any ordinary classroom even ii where there are no computer facilities. Also, there were various examples of reflective abstraction in the interview. Students built up the concept from one schema to another. It reflected that the genetic decomposition proposed by Dubinsky & Lewin (1986) is a reasonable way to meditate the construct of Mathematical Induction. iii DOI: 10.5353/th_b3551612 Subjects: Induction (Mathematics) - Study and teaching (Secondary) - China - Hong Kong
Author: Yee-ho Leung (Genthew)
Publisher:
ISBN:
Category : Induction (Mathematics)
Languages : en
Pages : 122
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Book Description
Author: Dr. Matthew Yip
Publisher: Mathewmatician
ISBN:
Category : Education
Languages : en
Pages : 4
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Book Description
Author: Stacy A. Brown
Publisher:
ISBN:
Category : Induction (Mathematics)
Languages : en
Pages : 846
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Book Description
This dissertation examines how students' understandings of proof by mathematical induction evolved during an 8-week teaching experiment. The design of the experiment was informed by a theoretical perspective that is a synthesis of two complementary theories: the Theory of Didactical Situations (Brousseau, 1997) and the Necessity Principle, Harel's (1998) theory of intellectual need. This study provides an account of how the proof schemes and ways of understanding of a cohort of students progressed through three stages: pre-transformational, restrictive transformational, and transformational, as they worked through a series of proof by mathematical induction appropriate tasks. It also reports on the various didactical and epistemological obstacles the students encountered at each stage. Harel's (1998) Dual Assertion and Harel and Sowder's (1998) proof schemes are used to explain the students' ways of acting in terms of two coexisting schemes, the students' ways of thinking and ways of understanding. The results of the study indicate that the students' conceptions of what constitutes a convincing argument changed in response to a series of shifts in the students' understandings of generality.
Author: Maria Teresa Tatto
Publisher: Springer Nature
ISBN: 3030440478
Category : Education
Languages : en
Pages : 168
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Book Description
This book reports on an innovative study into the first five years of mathematics teaching: FIRSTMATH. For the first time, the study has developed a viable methodology to analyze the knowledge, skills, and dispositions of beginning mathematics teachers as well as instruments to explore the contexts where they work. The book provides a step by step account of this exploratory (proof-of-concept) research study, using a comparative and international approach, and introduces readers to the challenges entailed. The FIRSTMATH study promises the development of methods and strategies to make it possible for teacher educators and future teachers to examine (and improve on) their own practices in an important STEM area.
Author: Francis Howard Hildebrand
Publisher:
ISBN:
Category : Induction (Mathematics)
Languages : en
Pages : 288
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Book Description
Author:
Publisher: Disha Publications
ISBN: 9392552599
Category :
Languages : en
Pages : 201
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Book Description
Author: Carol A. Tomlinson
Publisher: ASCD
ISBN: 0871205122
Category : Education
Languages : en
Pages : 128
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Book Description
Offers a definition of differentiated instruction, and provides principles and strategies designed to help teachers create learning environments that address the different learning styles, interests, and readiness levels found in a typical mixed-ability classroom.
Author: Randall E. Groth
Publisher: SAGE Publications
ISBN: 1452256020
Category : Education
Languages : en
Pages : 513
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Book Description
Teaching Mathematics in Grades 6 - 12 by Randall E. Groth explores how research in mathematics education can inform teaching practice in grades 6-12. The author shows preservice mathematics teachers the value of being a "researcher—constantly experimenting with methods for developing students' mathematical thinking—and connecting this research to practices that enhance students' understanding of the material. Ultimately, preservice teachers will gain a deeper understanding of the types of mathematical knowledge students bring to school, and how students' thinking may develop in response to different teaching strategies.
Author: Alan H. Schoenfeld
Publisher: MAA Press
ISBN:
Category : Education
Languages : en
Pages : 86
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Book Description
This book provides the means for improving instruction, and describes the broad spectrum of mathematical skills and perspective students should develop. The curriculum recommendations section shows where to look for reports and course resources that will help in teaching. Extensive descriptions of advising programmes that work are included, along with suggestions for teaching that describe a wide range of instructional techniques.
