高中生数学认识信念的初步研究
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摘要
学生数学认识信念是西方国家关注了近三十年的研究课题,而我国在该领域的研究刚起步,尽管诸如“数学观”的相关研究较多,但从研究理论与方法的取向上,仍有待进一步拓展。高中生的数学认识信念较少受关注,基于此,有必要以此为切入点进行比较系统的研究。
本研究基于调查、个案等研究试图探究高中生数学认识信念的层面差异及其对数学学习产生的影响。研究得到如下结论:
1.在总体信念及各维度上均无性别差异,总体信念上存在显著的城乡差异、学科差异。在总体信念及知识结构、学习能力、学习方式维度上存在极其显著的年级差异,随着年级升高,总体信念及各维度的认识却逐步走向消极。
2.高一优、中、后进各层次学生在总体信念及其维度均无显著差异;高二各层次学生在总体信念及知识结构上差异极其显著,高三各层次学生在总体信念及学习能力上差异显著。高一、高三成绩与信念认识水平均不呈线性变化,高二大体上呈线性变化。
3.年级与城乡在总体信念上存在显著的交互效应。
4.总体信念均与消极情感、积极情感、兴趣、高二、高三成绩呈极其显著的正相关并能对其有效预测。各维度在对消极情感、积极情感、兴趣、高二成绩的预测中,知识结构最具预测力。
5.普遍认同数学的实用价值,能对知识质疑,重视对知识的理解,解决问题需循序渐进,学好数学主要取决于后天因素,对知识的判断要靠深层的思维活动。掌握知识普遍以“会做题、考试过关”为衡量标准。
6.学科特点、升学压力可能导致消极的信念或出现信念与学习行为并不完全一致的情形。随着学习经验的不断增加,学生的数学认识信念趋向建构性、辩证性。
基于上述研究,最后本研究对如何培养学生有效的数学信念提出一些建议。
Student’s epistemic beliefs about mathematics has been researched in western education nearly thirty yeas, and in our country we begin to study it just now. There are more correlate researched such as“Mathematics idea”,but the tropism of research’s theory and method need to more develop.We few give senior students' epistemc beliefs our attention.On this basis,we make a systematic research of senior students' epistemc beliefs in our country.
Based on investigate and case research we try to explore the difference of senior students' epistemc beliefs and the factor of beliefs about mathematics on learning.The conclusions are as follows:
There are no significant gender differences in each dimension and the whole beliefs,but there is significant town differences in the whole beliefs. There are significant grade differences in the whole beliefs and Simple Knowledge, Fixed Ability , and Fixed manne.Along with grade hoist, whole beliefs and each dimension congnition become eliminate.
There are no significant differences in whole beliefs and each dimension in administrative levels student Grade One; There are significant differences in the whole beliefs and Simple Knowledge in Grade Two, and there are significant differences in the whole beliefs and Fixed Ability in Grade Three.Between Grade One, Grade Three’s achievement and beliefs cognition are no linearity chance,but Grade Two is differ.
There are significant grade and town alternation domino offect in the whole beliefs.
There is a significant positive-correlation between the whole beliefs and negative sensibility, protagonist sensibility,interest, Grade One, Grade Three’s achievement, and it can directly efficiency predict.In each dimension , Simple Knowledge is most directly efficiency predict negative sensibility, protagonist sensibility,interest, Grade One, Grade Three’s achievement.
More students identify with mathematics’s practicality value, oppugn knowledge,regard understand,solve problem need to in proper sequence,emulate good mathe lie on the day after tomorrow factor,estimate knowledge need to deep thinking.Mastery knowledge’s purpose is“do exercise,past exam”.
Subject characteristic, enter a higher school press may result in negative beliefs or beliefs and study behavior are imperfection consistent. Along with study experience hoist, Student’s epistemic beliefs about mathematics become constructive and dialectic.
Based on above research, at the end of this article we provide some some considerations for teaching to cultivate availability student’s epistemic beliefs about mathematics.
本研究基于调查、个案等研究试图探究高中生数学认识信念的层面差异及其对数学学习产生的影响。研究得到如下结论:
1.在总体信念及各维度上均无性别差异,总体信念上存在显著的城乡差异、学科差异。在总体信念及知识结构、学习能力、学习方式维度上存在极其显著的年级差异,随着年级升高,总体信念及各维度的认识却逐步走向消极。
2.高一优、中、后进各层次学生在总体信念及其维度均无显著差异;高二各层次学生在总体信念及知识结构上差异极其显著,高三各层次学生在总体信念及学习能力上差异显著。高一、高三成绩与信念认识水平均不呈线性变化,高二大体上呈线性变化。
3.年级与城乡在总体信念上存在显著的交互效应。
4.总体信念均与消极情感、积极情感、兴趣、高二、高三成绩呈极其显著的正相关并能对其有效预测。各维度在对消极情感、积极情感、兴趣、高二成绩的预测中,知识结构最具预测力。
5.普遍认同数学的实用价值,能对知识质疑,重视对知识的理解,解决问题需循序渐进,学好数学主要取决于后天因素,对知识的判断要靠深层的思维活动。掌握知识普遍以“会做题、考试过关”为衡量标准。
6.学科特点、升学压力可能导致消极的信念或出现信念与学习行为并不完全一致的情形。随着学习经验的不断增加,学生的数学认识信念趋向建构性、辩证性。
基于上述研究,最后本研究对如何培养学生有效的数学信念提出一些建议。
Student’s epistemic beliefs about mathematics has been researched in western education nearly thirty yeas, and in our country we begin to study it just now. There are more correlate researched such as“Mathematics idea”,but the tropism of research’s theory and method need to more develop.We few give senior students' epistemc beliefs our attention.On this basis,we make a systematic research of senior students' epistemc beliefs in our country.
Based on investigate and case research we try to explore the difference of senior students' epistemc beliefs and the factor of beliefs about mathematics on learning.The conclusions are as follows:
There are no significant gender differences in each dimension and the whole beliefs,but there is significant town differences in the whole beliefs. There are significant grade differences in the whole beliefs and Simple Knowledge, Fixed Ability , and Fixed manne.Along with grade hoist, whole beliefs and each dimension congnition become eliminate.
There are no significant differences in whole beliefs and each dimension in administrative levels student Grade One; There are significant differences in the whole beliefs and Simple Knowledge in Grade Two, and there are significant differences in the whole beliefs and Fixed Ability in Grade Three.Between Grade One, Grade Three’s achievement and beliefs cognition are no linearity chance,but Grade Two is differ.
There are significant grade and town alternation domino offect in the whole beliefs.
There is a significant positive-correlation between the whole beliefs and negative sensibility, protagonist sensibility,interest, Grade One, Grade Three’s achievement, and it can directly efficiency predict.In each dimension , Simple Knowledge is most directly efficiency predict negative sensibility, protagonist sensibility,interest, Grade One, Grade Three’s achievement.
More students identify with mathematics’s practicality value, oppugn knowledge,regard understand,solve problem need to in proper sequence,emulate good mathe lie on the day after tomorrow factor,estimate knowledge need to deep thinking.Mastery knowledge’s purpose is“do exercise,past exam”.
Subject characteristic, enter a higher school press may result in negative beliefs or beliefs and study behavior are imperfection consistent. Along with study experience hoist, Student’s epistemic beliefs about mathematics become constructive and dialectic.
Based on above research, at the end of this article we provide some some considerations for teaching to cultivate availability student’s epistemic beliefs about mathematics.
引文
[1]唐剑岚. 学生数学认识信念的研究述评[J]. 数学教育学报,2007,16(1):29～33.
[2]刘儒德,陈红艳. 论中小学生的数学观[J]. 北京师范大学学报(社会科学版),2004,(5):39～43.
[3] Hofer B K, Pintrich P R.. The development of epistemological theories: Beliefs about knowledge and knowing and their relation to learning. Review of Educational Research, 1997, 67(1):88～140.
[4] King, P. M., Kitchener, K. S.. Reflective judgment: Theory and research on the development of epistemic assumptions through adulthood. Educational Psychologist, 2004, 39(1): 5～18.
[5] Schommer, M.. Explaining the epistemological belief system:Introducing the embedded systemic model and coordinated research approach. Educational Psychologist, 2004, 39(1): 19～29.
[6] Kitchener, R.. Folk epistemology: An introduction. New Ideas in Psychology, 2002,20(2): 89～105.
[7] Muis, K.R.. Personal Epistemology and Mathematics: A Critical Review and Synthesis of Research. Review of Educational Research, 2004,74(3):317～380.
[8] Erkki Pehkonen ,Anu Pietil?. On Relationships between Beliefs and Knowledge in Mathematics Education, http://www.dm.unipi.it/~didattica/CERME3/proceedings/tableofcontents_cerme3.html.
[9] Hofer B K.. Epistemological understanding as a metacognitive process: Thinking aloud during online searching. Educational Psychologist, 2004, 39(1): 43～55.
[10] Schoenfeld, A. H.. Exploration of students' mathematical beliefs and behavior. Journal for Research in Mathematics Education, 1989, (20):338～355.
[11] McLeod, D. B.. Research on affect and mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning, New York: Macmillan,1992:575～596.
[12] Schoenfeld, A. H.. Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning, New York:Macmillan,1992:334～370.
[13]喻平, 唐剑岚. 个体认识论的研究现状与展望(J). 心理科学进展,2006,(4) .
[14] Kloosterman, P., Raymond, A. M., Emenaker, C.. Students' beliefs about mathematics: A three-year study. The Elementary School Journal, 1996, 97(1): 39～56.
[15] Mason, L.. High school students' beliefs about math, mathematical problem solving, and their achievement in math: A cross-sectional study. Educational Psychology, 2003,(23): 73～85.
[16] Eccles,J.S.,Wigfield,A.,Harold,R.D.,Blumenfeld,P..Age and gender differences in children’s self～and task perceptions during elementary school. Child Development,1993,(64):830～847.
[17] Schommer, M., Duell,O., Hutter,R.. Epistemological Beliefs, Mathematical Problem～Solving Beliefs, and Academic Performance of Middle School Students. The Elementary School Journal, 2005, 105(3):289～304.
[18] Schoenfeld, A. H.. Exploration of students' mathematical beliefs and behavior. Journal for Research in Mathematics Education, 1989, (20):338～355.
[19] Hiebert, J., Carpenter, T.P.. Learning and teaching with understanding. In D.A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan, 1992: 65～97.
[20]Schommer, M., Grouse, A., Rhodes, N.. Epistemological beliefs and mathematical text comprehension: Believing it is simple does not make it so. Journal of Educational Psychology, 1992, 84(4): 435～443.
[21] Lerch, C. M.. Control decisions and personal beliefs: their effect on solving mathematical problems. Journal of Mathematical Behavior, 2004(23):21～36.
[22] Mason,L.,Scrivani,L..Enhancing students’ mathematical beliefs:an intervention study, Learning and Instruction,2004,14(2):153～176.
[23] Francisco, J. M. Students’ reflections on their learning experiences: lessons from a longitudinal study on the development of mathematical ideas and reasoning,Journal of Mathematical Behavior ,2005,24(1):51～71.
[24] Schoenfeld, A. H.. When good teaching leads to bad results: The disasters of "well～taught" mathematics classes. Educational Psychologist, 1988, 23(2):145～166.
[25] Bendixen, L. D., Rule,D.C.. An Integrative Approach to Personal Epistemology: A Guiding Model. Educational Psychologist, 2004,39(1): 69～80.
[26] Louca, L., Elby, A., Hammer, D., Kagey, T.. Epistemological resources: Applying a new epistemological framework to science instruction. Educational Psychologist, 2004,39(1):57～68.
[27] Schraw, G., Sinatra, G. M.. Epistemological development and its impact on cognition in academic domains. Contemporary Educational Psychology, 2004,29(2):95～102.
[28] Siegler, R. S., Crowley, K.. The microgenetic method: A direct means for studying cognitive development. American Psychologist, 1991,46(6): 606～620.
[29]辛自强,林崇德. 微观发生法:聚焦认知变化(J).心理科学进展,2002,(2):206～212.
[30] Burr, J. E., Hofer, B. K.. Personal epistemology and theory of mind: Deciphering young children’s beliefs about knowledge and knowing. New Ideas in Psychology, 2002,20(2):199～224.
[31]林崇德. 试论发展心理学与教育心理学研究中的十大关系(J).心理发展与教育,2005,(1):1～6.
[32] 荆其诚,张航.时代精神与当代心理学(J).心理科学进展,2005,(2):129～138.
[33]Chan K, Elliot R G.. Exploratory study of Hong Kong teacher education students' epistemological beliefs: Cultural perspectives and implications on beliefs research. Contemporary Educational Psychology, 2003, 27(3): 392～415.
[34] 杨善朝,张军舰. 统计软件应用基础[M]. 桂林:广西师范大学出版社,2001:55～203.
[35] 吴明隆. SPSS 统计应用实务-问卷分析与应用统计[M]. 北京:科学出版社,2003:23～170.
[36] 王林全. 数学课程要帮助学生形成正确的学科观念[J]. 数学通讯,2000,5:6～7.
[37]吕松军. 高师院校数学系学生数学观发展研究[D]. 长沙:湖南师范大学,2004.
[38]白芸. 质的研究指导[M]. 北京:教育科学出版社,2002:2～134.
[39]陈向明. 教师如何做质的研究[M]. 北京:教育科学出版社,2001:9～30.
[40]刘儒德,陈红艳. 小学生数学学习观调查研究[J]. 心理科学,2002,(2):194～197.
[41]王婷婷. 关于我国高中生认识论信念的初步研究[D]. 上海:华东师范大学,2004.
[42]李宏,吴颖康,李士锜. 关于中学生信念和数学学习行为调查[J]. 数学教育学报, 2001,10(3):88～91.
[43]黄毅英. 数学观研究综述[J]. 数学教育学报,2002,11(1):1～5.
[44]涂荣豹, 宋晓平. 中国数学教学的若干特点[J]. 课程·教材·教法,2006,26(2):43～46 .
[45]罗润生,申继亮,王孟成. 影响高中生数学学业成绩的主因素分析[J]. 数学教育学报,2006,15(2):57～60.
[46]刘晓伟. 消解与建构[J]. 课程·教材·教法,2007,27(2):26～30.
[47]孙杰远. 现代数学教育学[M]. 桂林:广西师范大学出版社,2004:375～382.
[48]胡中锋,黎雪琼,刘桂秋. 论新课程评价中质的评价与量的评价整合[J]. 课程·教材·教法,2006,26(2):3～7.
[49]叶尧城. 高中数学课程标准教师读本[M]. 武汉:华中师范大学出版社,2003:1～11.
[2]刘儒德,陈红艳. 论中小学生的数学观[J]. 北京师范大学学报(社会科学版),2004,(5):39～43.
[3] Hofer B K, Pintrich P R.. The development of epistemological theories: Beliefs about knowledge and knowing and their relation to learning. Review of Educational Research, 1997, 67(1):88～140.
[4] King, P. M., Kitchener, K. S.. Reflective judgment: Theory and research on the development of epistemic assumptions through adulthood. Educational Psychologist, 2004, 39(1): 5～18.
[5] Schommer, M.. Explaining the epistemological belief system:Introducing the embedded systemic model and coordinated research approach. Educational Psychologist, 2004, 39(1): 19～29.
[6] Kitchener, R.. Folk epistemology: An introduction. New Ideas in Psychology, 2002,20(2): 89～105.
[7] Muis, K.R.. Personal Epistemology and Mathematics: A Critical Review and Synthesis of Research. Review of Educational Research, 2004,74(3):317～380.
[8] Erkki Pehkonen ,Anu Pietil?. On Relationships between Beliefs and Knowledge in Mathematics Education, http://www.dm.unipi.it/~didattica/CERME3/proceedings/tableofcontents_cerme3.html.
[9] Hofer B K.. Epistemological understanding as a metacognitive process: Thinking aloud during online searching. Educational Psychologist, 2004, 39(1): 43～55.
[10] Schoenfeld, A. H.. Exploration of students' mathematical beliefs and behavior. Journal for Research in Mathematics Education, 1989, (20):338～355.
[11] McLeod, D. B.. Research on affect and mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning, New York: Macmillan,1992:575～596.
[12] Schoenfeld, A. H.. Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning, New York:Macmillan,1992:334～370.
[13]喻平, 唐剑岚. 个体认识论的研究现状与展望(J). 心理科学进展,2006,(4) .
[14] Kloosterman, P., Raymond, A. M., Emenaker, C.. Students' beliefs about mathematics: A three-year study. The Elementary School Journal, 1996, 97(1): 39～56.
[15] Mason, L.. High school students' beliefs about math, mathematical problem solving, and their achievement in math: A cross-sectional study. Educational Psychology, 2003,(23): 73～85.
[16] Eccles,J.S.,Wigfield,A.,Harold,R.D.,Blumenfeld,P..Age and gender differences in children’s self～and task perceptions during elementary school. Child Development,1993,(64):830～847.
[17] Schommer, M., Duell,O., Hutter,R.. Epistemological Beliefs, Mathematical Problem～Solving Beliefs, and Academic Performance of Middle School Students. The Elementary School Journal, 2005, 105(3):289～304.
[18] Schoenfeld, A. H.. Exploration of students' mathematical beliefs and behavior. Journal for Research in Mathematics Education, 1989, (20):338～355.
[19] Hiebert, J., Carpenter, T.P.. Learning and teaching with understanding. In D.A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning, New York: Macmillan, 1992: 65～97.
[20]Schommer, M., Grouse, A., Rhodes, N.. Epistemological beliefs and mathematical text comprehension: Believing it is simple does not make it so. Journal of Educational Psychology, 1992, 84(4): 435～443.
[21] Lerch, C. M.. Control decisions and personal beliefs: their effect on solving mathematical problems. Journal of Mathematical Behavior, 2004(23):21～36.
[22] Mason,L.,Scrivani,L..Enhancing students’ mathematical beliefs:an intervention study, Learning and Instruction,2004,14(2):153～176.
[23] Francisco, J. M. Students’ reflections on their learning experiences: lessons from a longitudinal study on the development of mathematical ideas and reasoning,Journal of Mathematical Behavior ,2005,24(1):51～71.
[24] Schoenfeld, A. H.. When good teaching leads to bad results: The disasters of "well～taught" mathematics classes. Educational Psychologist, 1988, 23(2):145～166.
[25] Bendixen, L. D., Rule,D.C.. An Integrative Approach to Personal Epistemology: A Guiding Model. Educational Psychologist, 2004,39(1): 69～80.
[26] Louca, L., Elby, A., Hammer, D., Kagey, T.. Epistemological resources: Applying a new epistemological framework to science instruction. Educational Psychologist, 2004,39(1):57～68.
[27] Schraw, G., Sinatra, G. M.. Epistemological development and its impact on cognition in academic domains. Contemporary Educational Psychology, 2004,29(2):95～102.
[28] Siegler, R. S., Crowley, K.. The microgenetic method: A direct means for studying cognitive development. American Psychologist, 1991,46(6): 606～620.
[29]辛自强,林崇德. 微观发生法:聚焦认知变化(J).心理科学进展,2002,(2):206～212.
[30] Burr, J. E., Hofer, B. K.. Personal epistemology and theory of mind: Deciphering young children’s beliefs about knowledge and knowing. New Ideas in Psychology, 2002,20(2):199～224.
[31]林崇德. 试论发展心理学与教育心理学研究中的十大关系(J).心理发展与教育,2005,(1):1～6.
[32] 荆其诚,张航.时代精神与当代心理学(J).心理科学进展,2005,(2):129～138.
[33]Chan K, Elliot R G.. Exploratory study of Hong Kong teacher education students' epistemological beliefs: Cultural perspectives and implications on beliefs research. Contemporary Educational Psychology, 2003, 27(3): 392～415.
[34] 杨善朝,张军舰. 统计软件应用基础[M]. 桂林:广西师范大学出版社,2001:55～203.
[35] 吴明隆. SPSS 统计应用实务-问卷分析与应用统计[M]. 北京:科学出版社,2003:23～170.
[36] 王林全. 数学课程要帮助学生形成正确的学科观念[J]. 数学通讯,2000,5:6～7.
[37]吕松军. 高师院校数学系学生数学观发展研究[D]. 长沙:湖南师范大学,2004.
[38]白芸. 质的研究指导[M]. 北京:教育科学出版社,2002:2～134.
[39]陈向明. 教师如何做质的研究[M]. 北京:教育科学出版社,2001:9～30.
[40]刘儒德,陈红艳. 小学生数学学习观调查研究[J]. 心理科学,2002,(2):194～197.
[41]王婷婷. 关于我国高中生认识论信念的初步研究[D]. 上海:华东师范大学,2004.
[42]李宏,吴颖康,李士锜. 关于中学生信念和数学学习行为调查[J]. 数学教育学报, 2001,10(3):88～91.
[43]黄毅英. 数学观研究综述[J]. 数学教育学报,2002,11(1):1～5.
[44]涂荣豹, 宋晓平. 中国数学教学的若干特点[J]. 课程·教材·教法,2006,26(2):43～46 .
[45]罗润生,申继亮,王孟成. 影响高中生数学学业成绩的主因素分析[J]. 数学教育学报,2006,15(2):57～60.
[46]刘晓伟. 消解与建构[J]. 课程·教材·教法,2007,27(2):26～30.
[47]孙杰远. 现代数学教育学[M]. 桂林:广西师范大学出版社,2004:375～382.
[48]胡中锋,黎雪琼,刘桂秋. 论新课程评价中质的评价与量的评价整合[J]. 课程·教材·教法,2006,26(2):3～7.
[49]叶尧城. 高中数学课程标准教师读本[M]. 武汉:华中师范大学出版社,2003:1～11.