上海七年级学生“平行”概念表征与转译的调查研究——基于数学核心素养的视角
|
摘要
基于数学表征与转化的能力水平划分框架,通过文献梳理数学概念表征的内涵与可测的表征类型,在参考与改进国外已有测评样例的基础上,设计了关于七年级学生对"平行"概念的表征与转译的测试题.施测结果显示,上海七年级学生对平行概念的操作性定义理解较好,对平行概念标准形式下的表征有着良好的识别表现;但在进行不同表征形式存在单向性的转译问题,对非标准形式下的概念表征辨识则表现出较大的认知困难.基于此,从关注核心素养发展的角度提出有针对性的概念教学建议.
Based on the framework of competency levels of mathematical representation and translation,after reviewing the literatures,we designed a test on the representation and translation of parallel conception for Grade 7 students,which followed similar tests used in researches of geometrical conceptual representation,and made this investigation in a middle school of Shanghai.As presenting in the result,Grade 7 sample students had a good understanding on the operational definition of parallel conception,as well as how they perform in the recognition of standard representation.However,Grade 7 students also got difficulties in translating different presentation forms and recognizing the nonstandard representation of parallel conception.Then several instructional suggestions were come up from the perspective of core Competencies of School Mathematics at the end.
Based on the framework of competency levels of mathematical representation and translation,after reviewing the literatures,we designed a test on the representation and translation of parallel conception for Grade 7 students,which followed similar tests used in researches of geometrical conceptual representation,and made this investigation in a middle school of Shanghai.As presenting in the result,Grade 7 sample students had a good understanding on the operational definition of parallel conception,as well as how they perform in the recognition of standard representation.However,Grade 7 students also got difficulties in translating different presentation forms and recognizing the nonstandard representation of parallel conception.Then several instructional suggestions were come up from the perspective of core Competencies of School Mathematics at the end.
引文
[1]CHRISTOPHER H.Representations as basis of cognitive processes[C]//Annual Conference on Artificial Intelligence.Berlin,Heidelberg:Springer,1996:99-101.
[2]MARY H,KOZHEVNIKOV M.Types of visual-spatial representations and mathematical problem solving[J].Journal of Educational Psychology,1999,91(4):684.
[3]CAI J F,LESTER F K.Solution representations and pedagogical representations in Chinese and US classrooms[J].The Journal of Mathematical Behavior,2005,24(3):221-237.
[4]DANIEL H.Qualitative representation of spatial knowledge[M].Berlin:Springer Science&Business Media,1994:13-23.
[5]National Council of Teachers of Mathematics(NCTM).Principles and standards for school mathematics[M].Reston,VA:NCTM,2000:17-21,65-71.
[6]National Council of Teachers of Mathematics(NCTM).Principles to actions:ensuring mathematical success for all[M].Reston,VA:NCTM,2014:24-29.
[7]徐斌艳.数学学科核心能力研究[J].全球教育展望,2013,42(6):67-74,95.
[8]徐斌艳.关于德国数学教育标准中的数学能力模型[J].课程·教材·教法,2007,27(9):84-87.
[9]徐斌艳,朱雁,鲍建生,等.我国八年级学生数学学科核心能力水平调查与分析[J].全球教育展望,2015,44(11):57-67,120.
[10]谢海燕,姜慧慧,张晋宇,等.我国八年级学生数学表征能力的调查研究[J].基础教育,2016,13(1):65-70.
[11]WING-KWONG.Using computer-assisted multiple representations in learning geometry proofs[J].Educational Technology&Society,2011,14(3):43-54.
[12]HAGAR G,LINCHEVSKI L.To see or not to see:analyzing difficulties in geometry from the perspective of visual perception[J].Educational Studies in Mathematics,2010,74(2):163-183.
[13]DAVID M.Vision:a computational investigation into the human representation and processing of visual information[J].The Philosophy and the Approach,1982(79):213-219.
[14]唐剑岚.国外关于数学学习中多元外在表征的研究述评[J].数学教育学报,2008,17(1):30-34.
[15]GERALD A G,KAPUT J J.A joint perspective on the idea of representation in learning and doing mathematics[M]//STEFFE L P,NESHER P,COBB P,et al.Theories of Mathematical Learning.Mahwah,NJ:Erlbaum,1996:397-430.
[16]罗新兵.数形结合的解题研究:表征的视角[D].上海:华东师范大学,2005:10.
[17]KEES H.Representing contextual mathematical problems in descriptive or depictive form:design of an instrument and validation of its uses[J].Studies in Educational Evaluation,2016(50):22-32.
[18]DUVAL R.A cognitive analysis of problems of comprehension in a learning of mathematics[J].Educational studies in Mathematics,2006,61(1-2):103-131.
[19]PARZYSZ B.Representation of space and students'conceptions at high school level[J].Educational Studies in Mathematics,1991,22(6):575-593.
[20]中华人民共和国教育部.义务教育数学课程标准(2011年版)[M].北京:北京师范大学出版社,2011:5-6.
[21]MARSHALL A,SUPERFINE A,CANTY R.Star students make connections[J].Teaching Children Mathematics,2010,17(1):38-47.
[22]唐剑岚.概念多元表征的教学设计对概念学习的影响[J].数学教育学报,2010,19(2):28-33.
[2]MARY H,KOZHEVNIKOV M.Types of visual-spatial representations and mathematical problem solving[J].Journal of Educational Psychology,1999,91(4):684.
[3]CAI J F,LESTER F K.Solution representations and pedagogical representations in Chinese and US classrooms[J].The Journal of Mathematical Behavior,2005,24(3):221-237.
[4]DANIEL H.Qualitative representation of spatial knowledge[M].Berlin:Springer Science&Business Media,1994:13-23.
[5]National Council of Teachers of Mathematics(NCTM).Principles and standards for school mathematics[M].Reston,VA:NCTM,2000:17-21,65-71.
[6]National Council of Teachers of Mathematics(NCTM).Principles to actions:ensuring mathematical success for all[M].Reston,VA:NCTM,2014:24-29.
[7]徐斌艳.数学学科核心能力研究[J].全球教育展望,2013,42(6):67-74,95.
[8]徐斌艳.关于德国数学教育标准中的数学能力模型[J].课程·教材·教法,2007,27(9):84-87.
[9]徐斌艳,朱雁,鲍建生,等.我国八年级学生数学学科核心能力水平调查与分析[J].全球教育展望,2015,44(11):57-67,120.
[10]谢海燕,姜慧慧,张晋宇,等.我国八年级学生数学表征能力的调查研究[J].基础教育,2016,13(1):65-70.
[11]WING-KWONG.Using computer-assisted multiple representations in learning geometry proofs[J].Educational Technology&Society,2011,14(3):43-54.
[12]HAGAR G,LINCHEVSKI L.To see or not to see:analyzing difficulties in geometry from the perspective of visual perception[J].Educational Studies in Mathematics,2010,74(2):163-183.
[13]DAVID M.Vision:a computational investigation into the human representation and processing of visual information[J].The Philosophy and the Approach,1982(79):213-219.
[14]唐剑岚.国外关于数学学习中多元外在表征的研究述评[J].数学教育学报,2008,17(1):30-34.
[15]GERALD A G,KAPUT J J.A joint perspective on the idea of representation in learning and doing mathematics[M]//STEFFE L P,NESHER P,COBB P,et al.Theories of Mathematical Learning.Mahwah,NJ:Erlbaum,1996:397-430.
[16]罗新兵.数形结合的解题研究:表征的视角[D].上海:华东师范大学,2005:10.
[17]KEES H.Representing contextual mathematical problems in descriptive or depictive form:design of an instrument and validation of its uses[J].Studies in Educational Evaluation,2016(50):22-32.
[18]DUVAL R.A cognitive analysis of problems of comprehension in a learning of mathematics[J].Educational studies in Mathematics,2006,61(1-2):103-131.
[19]PARZYSZ B.Representation of space and students'conceptions at high school level[J].Educational Studies in Mathematics,1991,22(6):575-593.
[20]中华人民共和国教育部.义务教育数学课程标准(2011年版)[M].北京:北京师范大学出版社,2011:5-6.
[21]MARSHALL A,SUPERFINE A,CANTY R.Star students make connections[J].Teaching Children Mathematics,2010,17(1):38-47.
[22]唐剑岚.概念多元表征的教学设计对概念学习的影响[J].数学教育学报,2010,19(2):28-33.