民族地区中学壮瑶学生数学认识信念的调查研究
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摘要
学生的数学认识信念是指学生对数学知识和知识认识过程的素朴看法或观点。大量研究表明,学生认识信念深藏在他们的行为表现、认知过程、情感体验的背后,像一只无形的手,指引着学习过程,深刻影响着学习结果。因此,研究学生数学认识信念问题也是数学教育研究的一个重要课题。
本研究以新课程的基本要求与民族地区中学生数学学习现状为立足点,首先通过调查、访谈、个案等研究方法,从民族、性别、学段、年级、班级、地区和学科等角度,试图比较系统地探究民族地区中学壮瑶学生数学认识信念的基本现状,影响民族地区壮瑶学生数学认识信念形成的基本根源。
通过问卷调查、访谈和个案分析,壮瑶学生数学认识信念具有如下基本现状：
(1)就民族而言,壮瑶学生数学认识信念总体及其维度属于中等偏上水平,认识信念总体及其维度在民族上没有显著差异。
(2)就性别而言,壮族女生的信念总体、学习能力和学习速度等信念水平显著或非常显著地高于壮族男生。瑶族女生的知识结构信念水平显著高于瑶族男生。
(3)就学段而言,壮族初中生的学习能力信念水平显著高于壮族高中生,壮族高中生的知识稳定和学习方式信念水平显著高于壮族初中生；瑶族高中生的知识稳定信念水平显著高于瑶族初中生。
(4)就年级而言,随着年级的增长,壮族学生的知识稳定性信念水平呈现升高趋势,且初一年级显著低于高一、高二和高三年级,初二和初三年级显著低于高二和高三年级；随着年级的增长,壮族学生的学习能力信念水平呈现降低趋势,且初三年级显著高于高一、高二和高三年级。瑶族学生数学认识信念总体及其维度在年级上不存在显著差异。
(5)就班级而言,对壮族学生数学认识信念总体水平来说,实验班显著高于中等班和提高班。对壮族学生学习速度信念水平来说,实验班显著高于中等班和提高班。对壮族学生学习方式信念水平来说,实验班显著高于中等班和提高班,中等班显著高于提高班。
对瑶族学生的信念总体水平来说,提高班显著低于实验班和中等班。对瑶族学生的知识结构信念水平来说,提高班显著低于实验班和中等班。对瑶族学生的学习方式信念水平来说,提高班显著低于实验班和中等班。
(6)就地区而言,县城学生的知识稳定维度和学习方式等信念水平显著高于乡镇学生,但乡镇学生的学习能力信念水平显著高于县城学生。
瑶族学生数学认识信念总体及其维度在地区上没有显著差异。
(7)就学科而言,壮族理科学生的数学认识信念总体、知识结构、学习能力和学习方式等信念水平显著高于壮族文科学生。瑶族理科学生数学认识信念总体、知识结构和学习能力等信念水平显著高于瑶族族文科学生。
然后,本研究通过理论思辨和经验总结,进一步从文化差异的视角探究呈现以上特征的文化元素；最后,基于以上研究,提出改善壮族和瑶族学生数学认识信念的教学建议。
The epistemic beliefs about mathematics refer to students'ideas or opinions about mathematical knowledge and cognitive processes. Plenty of foreign studies have shown that students'epistemic beliefs are deeply buried in their behavior, cognitive processes and emotional experiences, guiding their learning process like an invisible hand and influencing their learning outcomes. Therefore, the research into students'epistemic beliefs about mathematics has always been a hot topic in mathematics education research.
Based on the basic requirements of the new curriculum, we try to explore the status quo of Zhuang and Yao students'epistemic beliefs in ethnic areas and the basic causes through ways of questionnaires, interviews and case studies, concerning the differences of their ethnic groups, genders, school stages, grades, classes, areas and subjects. The findings of the research are as follows:
Firstly, from the ethnic point of view, there is no significant difference between Zhuang and Yao students and their epistemic beliefs about mathematics lie at an average level or a little higher than the average.
Secondly, the general epistemic belief of learning ability and learning speed in female Zhuang students are significantly better than those of males. The knowledge structure belief level of female Yao students is higher than those of male Yao students.
Thirdly, school stages have apparent influence on both Zhuang and Yao students. The learning ability of Zhuang students in junior middle schools is higher than that of Zhuang students in senior middle schools while the stability and learning strategy of both Zhuang and Yao students in senior middle schools are better than those in junior middle schools.
Fourthly, as Zhuang students step into a higher grade, their knowledge stability belief level increases while their learning ability belief level decreases. Zhuang students'knowledge stability belief level in Junior One is notably lower than those in senior middle school and learning ability belief level in Junior Three is notably higher than those in Senior Two and Senior Three. However, Yao students do not show significant difference whichever grade they are in.
In terms of classes, the epistemic beliefs about mathematics of Zhuang students in experimental classes are higher than those in middle classes and ordinary classes. Zhuang students'learning ability belief level and learning strategy belief level in experimental classes are higher than those in middle classes and ordinary classes. While the epistemic beliefs about mathematics of Yao students in ordinary classes are notably lower than those in middle classes and experimental classes. Yao students' knowledge structure belief level and learning strategy belief level in ordinary classes are notably lower than those in middle classes and experimental classes.
As far as their living environments are concerned, county Zhuang students show higher epistemic belief level than township students in knowledge stability and learning strategy but township students, but township students show higher level in learning ability. Yao students show no significant difference in general beliefs and dimensions whether they are from county areas or villages.
While considering their subjects, science students of Zhuang people show higher level than liberal arts students in their general epistemic beliefs about mathematics, their knowledge structure, their learning ability and learning strategy. science students of Yao people also show higher level than liberal arts students in their general epistemic beliefs about mathematics, their knowledge structure and their learning ability.
Theoretical Debate
Then, through theoretical debating and experience concluding, this research tries to explore the cultural elements of the above-mentioned from the perspective of cultural difference.
Finally, to improve students' epistemic beliefs about mathematics of Zhuang and Yao people, this research puts forward the following teaching tips.
本研究以新课程的基本要求与民族地区中学生数学学习现状为立足点,首先通过调查、访谈、个案等研究方法,从民族、性别、学段、年级、班级、地区和学科等角度,试图比较系统地探究民族地区中学壮瑶学生数学认识信念的基本现状,影响民族地区壮瑶学生数学认识信念形成的基本根源。
通过问卷调查、访谈和个案分析,壮瑶学生数学认识信念具有如下基本现状：
(1)就民族而言,壮瑶学生数学认识信念总体及其维度属于中等偏上水平,认识信念总体及其维度在民族上没有显著差异。
(2)就性别而言,壮族女生的信念总体、学习能力和学习速度等信念水平显著或非常显著地高于壮族男生。瑶族女生的知识结构信念水平显著高于瑶族男生。
(3)就学段而言,壮族初中生的学习能力信念水平显著高于壮族高中生,壮族高中生的知识稳定和学习方式信念水平显著高于壮族初中生；瑶族高中生的知识稳定信念水平显著高于瑶族初中生。
(4)就年级而言,随着年级的增长,壮族学生的知识稳定性信念水平呈现升高趋势,且初一年级显著低于高一、高二和高三年级,初二和初三年级显著低于高二和高三年级；随着年级的增长,壮族学生的学习能力信念水平呈现降低趋势,且初三年级显著高于高一、高二和高三年级。瑶族学生数学认识信念总体及其维度在年级上不存在显著差异。
(5)就班级而言,对壮族学生数学认识信念总体水平来说,实验班显著高于中等班和提高班。对壮族学生学习速度信念水平来说,实验班显著高于中等班和提高班。对壮族学生学习方式信念水平来说,实验班显著高于中等班和提高班,中等班显著高于提高班。
对瑶族学生的信念总体水平来说,提高班显著低于实验班和中等班。对瑶族学生的知识结构信念水平来说,提高班显著低于实验班和中等班。对瑶族学生的学习方式信念水平来说,提高班显著低于实验班和中等班。
(6)就地区而言,县城学生的知识稳定维度和学习方式等信念水平显著高于乡镇学生,但乡镇学生的学习能力信念水平显著高于县城学生。
瑶族学生数学认识信念总体及其维度在地区上没有显著差异。
(7)就学科而言,壮族理科学生的数学认识信念总体、知识结构、学习能力和学习方式等信念水平显著高于壮族文科学生。瑶族理科学生数学认识信念总体、知识结构和学习能力等信念水平显著高于瑶族族文科学生。
然后,本研究通过理论思辨和经验总结,进一步从文化差异的视角探究呈现以上特征的文化元素；最后,基于以上研究,提出改善壮族和瑶族学生数学认识信念的教学建议。
The epistemic beliefs about mathematics refer to students'ideas or opinions about mathematical knowledge and cognitive processes. Plenty of foreign studies have shown that students'epistemic beliefs are deeply buried in their behavior, cognitive processes and emotional experiences, guiding their learning process like an invisible hand and influencing their learning outcomes. Therefore, the research into students'epistemic beliefs about mathematics has always been a hot topic in mathematics education research.
Based on the basic requirements of the new curriculum, we try to explore the status quo of Zhuang and Yao students'epistemic beliefs in ethnic areas and the basic causes through ways of questionnaires, interviews and case studies, concerning the differences of their ethnic groups, genders, school stages, grades, classes, areas and subjects. The findings of the research are as follows:
Firstly, from the ethnic point of view, there is no significant difference between Zhuang and Yao students and their epistemic beliefs about mathematics lie at an average level or a little higher than the average.
Secondly, the general epistemic belief of learning ability and learning speed in female Zhuang students are significantly better than those of males. The knowledge structure belief level of female Yao students is higher than those of male Yao students.
Thirdly, school stages have apparent influence on both Zhuang and Yao students. The learning ability of Zhuang students in junior middle schools is higher than that of Zhuang students in senior middle schools while the stability and learning strategy of both Zhuang and Yao students in senior middle schools are better than those in junior middle schools.
Fourthly, as Zhuang students step into a higher grade, their knowledge stability belief level increases while their learning ability belief level decreases. Zhuang students'knowledge stability belief level in Junior One is notably lower than those in senior middle school and learning ability belief level in Junior Three is notably higher than those in Senior Two and Senior Three. However, Yao students do not show significant difference whichever grade they are in.
In terms of classes, the epistemic beliefs about mathematics of Zhuang students in experimental classes are higher than those in middle classes and ordinary classes. Zhuang students'learning ability belief level and learning strategy belief level in experimental classes are higher than those in middle classes and ordinary classes. While the epistemic beliefs about mathematics of Yao students in ordinary classes are notably lower than those in middle classes and experimental classes. Yao students' knowledge structure belief level and learning strategy belief level in ordinary classes are notably lower than those in middle classes and experimental classes.
As far as their living environments are concerned, county Zhuang students show higher epistemic belief level than township students in knowledge stability and learning strategy but township students, but township students show higher level in learning ability. Yao students show no significant difference in general beliefs and dimensions whether they are from county areas or villages.
While considering their subjects, science students of Zhuang people show higher level than liberal arts students in their general epistemic beliefs about mathematics, their knowledge structure, their learning ability and learning strategy. science students of Yao people also show higher level than liberal arts students in their general epistemic beliefs about mathematics, their knowledge structure and their learning ability.
Theoretical Debate
Then, through theoretical debating and experience concluding, this research tries to explore the cultural elements of the above-mentioned from the perspective of cultural difference.
Finally, to improve students' epistemic beliefs about mathematics of Zhuang and Yao people, this research puts forward the following teaching tips.
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]Stuart K,Samira M. Culture and personal epistemology:U.S. and Middle Eastern students' beliefs about scientific knowledge and knowing [J]. Social Psychology of Education,2005,8 (4):375-393.
[3]周莹,潘凤珍,唐剑岚.维汉9-12岁儿童数学能力的比较与分析[J].广西师范大学学报,2005,23(2)：60-63.
[4]唐剑岚,周莹,黄国稳.初中生数学认识信念量表的数学模型研究[J].广西师范大学学报,2007,25(3)：1-4.
[5]朱熹,四书集注一大学[M].三秦出版社,1998：8
[6]朱熹,四书集注一论语[M].三秦出版社,1998：85
[7]现代汉语规范用法大词典[M].学苑出版社,2000：1260.
[8]罗竹风主编,汉语大词典(第一卷)[M].汉语大词典出版社,2001：1418.
[9]中国大百科全书(心理学)[M].中国大百科全书出版社,1991：462.
[10] Cooper J.B., McGaugh, J.L.Attitude and related concepts [M].In Gilah:2002.130-132.
[11] Rokeach, M.Beliefs, attitudes and values [M].San Fransisco:Jossey-Bass Inc,113-116.
[12] Richardson. V.The role of attitudes and beliefs in learning to teach [J].Handbook of research on teacher education:102-119.
[13]黄希庭,郑涌.心理学十五讲[M1.北京：北京大学出版社,2005：288.
[14]Schommer, M.. Explaining the epistemological belief system:Introducing the embedded systemic model and coordinated research approach [J]. Educational Psychologist,2004,39(1):19-29
[15] Schoenfeld, A. H.. Exploration of students' mathematical beliefs and behavior [J]. Journal for Research in Mathematics Education,1989, (20):338-355.
[14]Schommer, M.. Explaining the epistemological belief system:Introducing the embedded systemic model and coordinated research approach [J]. Educational Psychologist,2004,39(1):19-29
[15]Schoenfeld, A. H.. Exploration of students' mathematical beliefs and behavior [J]. Journal for Research in Mathematics Education,1989, (20):338-355.
[17]唐剑岚,喻平.学生数学信念：数学教育中一个不容忽视的话题.内蒙古师范大学学报(教育科学版)2007,4.
[18] Muis, K.R... Personal Epistemology and Mathematics:A Critical Review and Synthesis of Research. Review of Educational Research,2004,74(3),317-380.
[19]李燕清,唐剑岚,文琳.民族地区高一学生数学认识信念的调查研究,内蒙古师范大学学报(教育科学版)2011,2.
[20] Braten, I.,& Britt, M.A., Str(?)ms(?), H.I., & Rouet, J.-F. (2011). The role of epistemic beliefs in the comprehension of multiple expository texts:Towards an integrated model.Educational Psychologist,46,48-70.
[21]唐剑岚,周莹,黄国稳.初中生数学认识信念量表的数学模型研究[J].广西师范大学学报,2007,25(3)：1-4.
[22]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.
[22]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(3)：88-91.
[23]彭家威,吕屏.广西旅游招贴设计中的壮族文化语境的营造.包装工程.2011(12)：85--88
[24]玉时阶.试论瑶族文化与瑶族族源的渊源关系[J].学术论坛,2001(6)125-126.
[25]叶澜等,教育理论与实践,高等教育出版社,2000：136
[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]Stuart K, Samira M. Culture and personal epistemology:U.S. and Middle Eastern students' beliefs about scientific knowledge and knowing [J]. Social Psychology of Education,2005,8 (4):375-393.
[3]周莹,潘凤珍,唐剑岚.维汉9-12岁儿童数学能力的比较与分析[J].广西师范大学学报,2005,23(2)：60-63.
[4]唐剑岚,周莹,黄国稳.初中生数学认识信念量表的数学模型研究[J].广西师范大学学报,2007,25(3)：1-4.
[5]朱熹,四书集注一大学[M].三秦出版社,1998：8.
[6]朱熹,四书集注一论语[M].三秦出版社,1998：85.
[7]现代汉语规范用法大词典[M].学苑出版社,2000：1260.
[8]罗竹风主编,汉语大词典(第一卷)[M].汉语大词典出版社,2001：1418.
[9]中国大百科全书(心理学)[M].中国大百科全书出版社,1991：462.
[10]Cooper J.B.,McGaugh,J.L.Attitude and related concepts[M].In Gilah:2002.130-132.
[11]Rokeach,M.Beliefs,attitudes and values[M].San Fransisco:Jossey-Bass Inc,113—116.
[12]Richardson.V.The role of attitudes and beliefs in learning to teach[J].In,Sikula(Ed.),Handbook of research on teacher education:102-119.
[13]黄希庭,郑涌.心理学十五讲[M1.北京：北京大学出版社,2005：288.
[14]Schommer, M.. Explaining the epistemological belief system:Introducing the embedded systemic model and coordinated research approach [J]. Educational Psychologist,2004,39(1): 19-29
[15]Schoenfeld, A. H.. Exploration of students'mathematical beliefs and behavior [J]. Journal for Research in Mathematics Education,1989, (20):338-355.
[14]Schommer, M.. Explaining the epistemological belief system:Introducing the embedded systemic model and coordinated research approach [J]. Educational Psychologist,2004,39(1): 19-29.
[15]Schoenfeld, A. H.. Exploration of students' mathematical beliefs and behavior [J]. Journal for Research in Mathematics Education,1989, (20):338-355.
[16]周莹,唐剑岚,黄国稳.数学教育学报,2008,2.
[17]唐剑岚,喻平.学生数学信念：数学教育中一个不容忽视的话题.内蒙古师范大学学报(教育科学版)2007,4.
[18]Muis, K.R... Personal Epistemology and Mathematics:A Critical Review and Synthesis of Research. Review of Educational Research,2004,74(3),317-380.
[19]李燕清,唐剑岚,文琳.民族地区高一学生数学认识信念的调查研究,内蒙古师范大学学报(教育科学版)2011,2.
[20]Braten, I., & Britt, M.A., Str(?)ms(?), H.I., & Rouet, J.-F. (2011). The role of epistemic beliefs in the comprehension of multiple expository texts:Towards an integrated model. Educational Psychologist,46,48-70.
[21]唐剑岚,周莹,黄国稳.初中生数学认识信念量表的数学模型研究[J].广西师范大学学 报,2007,25(3)：1-4.
[22]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(3)：88-91.
[23]彭家威,吕屏.广西旅游招贴设计中的壮族文化语境的营造.包装工程.2011(12)：85-88.
[24]玉时阶.试论瑶族文化与瑶族族源的渊源关系[J].学术论坛,2001(6)125-126.
[25]叶澜等,教育理论与实践,高等教育出版社,2000：136.
[2]Stuart K,Samira M. Culture and personal epistemology:U.S. and Middle Eastern students' beliefs about scientific knowledge and knowing [J]. Social Psychology of Education,2005,8 (4):375-393.
[3]周莹,潘凤珍,唐剑岚.维汉9-12岁儿童数学能力的比较与分析[J].广西师范大学学报,2005,23(2)：60-63.
[4]唐剑岚,周莹,黄国稳.初中生数学认识信念量表的数学模型研究[J].广西师范大学学报,2007,25(3)：1-4.
[5]朱熹,四书集注一大学[M].三秦出版社,1998：8
[6]朱熹,四书集注一论语[M].三秦出版社,1998：85
[7]现代汉语规范用法大词典[M].学苑出版社,2000：1260.
[8]罗竹风主编,汉语大词典(第一卷)[M].汉语大词典出版社,2001：1418.
[9]中国大百科全书(心理学)[M].中国大百科全书出版社,1991：462.
[10] Cooper J.B., McGaugh, J.L.Attitude and related concepts [M].In Gilah:2002.130-132.
[11] Rokeach, M.Beliefs, attitudes and values [M].San Fransisco:Jossey-Bass Inc,113-116.
[12] Richardson. V.The role of attitudes and beliefs in learning to teach [J].Handbook of research on teacher education:102-119.
[13]黄希庭,郑涌.心理学十五讲[M1.北京：北京大学出版社,2005：288.
[14]Schommer, M.. Explaining the epistemological belief system:Introducing the embedded systemic model and coordinated research approach [J]. Educational Psychologist,2004,39(1):19-29
[15] Schoenfeld, A. H.. Exploration of students' mathematical beliefs and behavior [J]. Journal for Research in Mathematics Education,1989, (20):338-355.
[14]Schommer, M.. Explaining the epistemological belief system:Introducing the embedded systemic model and coordinated research approach [J]. Educational Psychologist,2004,39(1):19-29
[15]Schoenfeld, A. H.. Exploration of students' mathematical beliefs and behavior [J]. Journal for Research in Mathematics Education,1989, (20):338-355.
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