初中代数学习困难生认知特征及干预措施的研究
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摘要
学习困难生是指智力和身体发育正常，但学习成绩明显低于同年级学生的异质群体。学习困难的成因及教育干预措施一直受到研究者们的关注。有关这方面的研究大致可分为三个层面：神经生理层面、心理层面和社会环境层面。由于神经机能缺陷与特定的学习困难难以一一对应，又由于社会环境层面的因素对学习活动的影响并非直接，所以心理层面的研究，尤其认知特征的研究备受青睐。在学习困难生的认知特征研究方面，也由于研究者的视角不同而呈现观点纷纭，各执己见的态势。有的研究者关心学习困难生的一般认知能力的缺陷，有的研究者关注学习困难生元认知的缺陷，也有的学者重视学习困难生的与解决问题相关的知识结构——图式的缺陷。在此基础上提出的教育干预措施也千差万别。所以，我们有必要对影响学生学习水平的各认知成分和认知因素进行整合研究，以期更全面描述和分析学习困难生的认知特征，更准确把握学习困难的成因，为学习困难的教育干预提供更坚实的理论基础和实证依据；并在此基础上探讨更有效的学习困难的教育干预措施。
研究一，以鞍山市一所中等水平的学校67中初二年级的106名学生为被试，对他们在代数学习过程中反映一般认知能力、元认知能力和图式水平的17项指标以及中等难度问题解决水平和较高难度问题解决水平进行测试。使用SPSS10.0软件和LISREL8.0软件对数据进行统计分析。在此基础上建构代数学习中学生认知因素与问题解决水平关系的理论结构模型，进而全面描述和分析代数学习困难生的认知特征，准确推断代数学习困难的成因。
研究二，根据研究一的结果设计不同的图式教学方式，以大连市35中初二年级的144名学生和鞍山市67中初二年级的104名学生为被试，进行多种图式教学与正常教学的对比研究，探讨更适合代数学习困难生的教育干预方式，也可以从实际教学的角度佐证研究一建构的理论模型。
研究三，在研究一、二的基础上，以庄河第九中学初三年级的109名学生为被试，探讨代数学习困难生规则使用有效性低是来源于规则提取困难还是规则应用困难。一方面可进一步佐证研究一、二的结果，另一方面可更深入探讨代数学习困难的成因，以期更好地把握代数学习困难教育干预的重点。
通过以上研究得出下列结论：
1、影响代数学习的认知因素有四种：第一，图式水平，包括六个子因素：陈述性知识表述全面性和表征准确性，程序性知识自动化，程序性知识可逆性，程序性知识全面性，知识的组织性。第二，低级认知加工能力，包括四个子因素：心算水平和效率，空间表象水平和效率。第三，辨别和再认能力，包括三个子因素：知觉速度，语文记忆能力，图形记忆能力。第四，高级认知加工能力，包括四个子因素：状态元认知能力，推理能力，工作记忆能力和数字记忆能力。其中图式水平可作为独立的认知因素存在。
2、四种认知因素与代数问题解决水平关系的理论结构模型的拟合状况良好。结构方程的标准化解显示：无论在中等难度问题解决中，还
是在较高难度问题解决中，四种认知因素对问题解决水平的解释率均达
到81%。在中等难度和较高难度问题解决中，图式水平的作用效果都非
常明显(只0.01)，对代数问题解决水平有非常高的预测力。在较高难
度问题解决中，高级认知加工能力有一定的作用效果(只0.10)，对较
高难度代数问题解决水平有一定的预测力。
3、对代数问题解决水平有显著和一定预测力的两种认知因素中，
不同的认知成分的预测力也有大有小。在中等难度问题解决中，知识组
织性、陈述性知识表征准确性、程序性知识可逆性对代数问题解决水平
有较大的预测作用。在较高难度问题解决中，陈述性知识表述全面性、
程序性知识可逆性和状态元认知能力对代数问题解决水平有较大的预
测作用。
4、图式水平低，推理能力差，状态元认知水平低，空间表象能力差，
心算水平低，语文记忆能力差是代数学习困难生的认知特征。
5、图式水平对代数问题解决水平有明显的预测作用，代数学习困难
生的图式水平明显低于中等生和优等生，针对程序性知识全面性、组织
性设计的图式教学和针对陈述性、程序性知识全面性和知识组织性设计
的图式教学效果明显。可见，图式水平低是代数学习困难的主要成因。
高级认知加工能力对代数问题解决有一定的预测作用，代数学习困难生
的状态元认知水平和推理能力都低于中等生和优等生。可以推断，推理
能力差和状态元认知水平低是代数学习困难的成因。
6、在代数学习困难的集体千预中，图式教学没有取得立竿见影的效
果。但只要教师努力引导和帮助学生建立合理的问题中心图式，图式教
学的远期效果非常明显。规则中心图式和综合图式在不干扰优等生和中
等生学习的前提下，能显著提高学习困难生的学习成绩。所以，在课堂
教学中，规则中心图式教学和综合图式教学是代数学习困难教育干预的
较为理想的方式。样例中心图式对优等生的学习有一定的干扰作用，所
以，样例中心图式教学可作为代数学习困难的个体干预方式，推广到课
堂教学中还需要进一步的研究。
7、改变图式特征是代数学习困难教育干预的重点。在六种图式?
Students with learning difficulties is a generic term that refers to a heterogeneous group whose intelligence and body develop normally, but whose academic achievement level is significantly lower than the others in the same group. Researchers have paid much attention to the causes and intervention methods for a long time. The interrelated studies can be generally divided into three divisions: nerve-function level, psychology-education level and social environment level. Because the disorder in nerve function can' t be corresponding to specific learning difficulty and the social environment impacts on learning process indirectly, the study at psychological level, especially on cognitive features of learning difficulties is highly valued. Some researchers regard defects of general cognitive abilities; some researchers focus on meta-cognition, and some researchers value the defects of schema that refers to the knowledge structure related with problem solving. On the base of these different findings, the educat
ional intervention methods are various. Therefore, this study intents to integrate cognitive compositions and cognitive factors influencing academic performance, then to describe and analyze cognitive features of learning difficulties overall, have an accurate grasp of the causes of learning difficulties. Findings above would be helpful to improve strong theory foundation and experiment evidence, and to put forward the more effective intervention methods.
In the first study, 106 students in grade two of Anshan NO. 67 middle school were tested on 17 indices which reflect general cognitive abilities, meta-cognition and schema level, and tested on solving moderate difficult level problems and high difficult level problems. On the data analysis by SPSS10. 0 and LISREL8.0, the theory structure model about relation between cognitive factors and problem-solving level in algebra study was built and examined. Further, to describe the cognitive features of learning difficulties overall and deduce the accurate causes of learning (! i rfi(;Li].ties.
In the second study, based on the first study' s finding.'-,, different schema teaching methods were designed and were contrasted with normal teaching method. In this study, Ss were M4 students in grade two of Dalian NO. 35 middle school and 104 students in grade two of Anshan NO. 67 middle school. The purpose of this study was to find educational intervention methods which are more fit for students with algebra learning difficulties, and to provide a supplemental evidence for the theory model built in the first study.
In the third study, Ss were 109 students in grade three of Zhuanghe NO. 9 middle school. Based on the first and the second study, this study' s purpose was to explore that low rule-efficiency in solving algebra problem is whether because of rule-applying difficulty or rule-retrieving difficulty. Findings coming through this study can provide a supplemental evidence for the first study findings and the second findings on one hand. On the other hand, we can grasp the focal point of educational intervention for students with algebra learning difficulties.
The major findings in the above three studies are as followings:
l.The cognitive compositions affecting middle school students' algebra study can be explained by four cognitive factors. The first factor is Schema level which comprises overall expressing and correctly representing of declarative knowledge, overall handling, adversely handling and automatic using of procedure knowledge, and organizing of knowledge. The second is low cognitive processing ability that comprises mental arithmetic level and efficiency, space image level and efficiency. The third is discrimination-recognition ability which comprises consciousness speed, language and literature memory ability, and figure memory ability. The fourth is high cognitive processing ability that comprises reasoning ability, meta-cognitive ability, working memory ability and digit memory ability. Schema level can be regarded as one independent cognitive fact
研究一，以鞍山市一所中等水平的学校67中初二年级的106名学生为被试，对他们在代数学习过程中反映一般认知能力、元认知能力和图式水平的17项指标以及中等难度问题解决水平和较高难度问题解决水平进行测试。使用SPSS10.0软件和LISREL8.0软件对数据进行统计分析。在此基础上建构代数学习中学生认知因素与问题解决水平关系的理论结构模型，进而全面描述和分析代数学习困难生的认知特征，准确推断代数学习困难的成因。
研究二，根据研究一的结果设计不同的图式教学方式，以大连市35中初二年级的144名学生和鞍山市67中初二年级的104名学生为被试，进行多种图式教学与正常教学的对比研究，探讨更适合代数学习困难生的教育干预方式，也可以从实际教学的角度佐证研究一建构的理论模型。
研究三，在研究一、二的基础上，以庄河第九中学初三年级的109名学生为被试，探讨代数学习困难生规则使用有效性低是来源于规则提取困难还是规则应用困难。一方面可进一步佐证研究一、二的结果，另一方面可更深入探讨代数学习困难的成因，以期更好地把握代数学习困难教育干预的重点。
通过以上研究得出下列结论：
1、影响代数学习的认知因素有四种：第一，图式水平，包括六个子因素：陈述性知识表述全面性和表征准确性，程序性知识自动化，程序性知识可逆性，程序性知识全面性，知识的组织性。第二，低级认知加工能力，包括四个子因素：心算水平和效率，空间表象水平和效率。第三，辨别和再认能力，包括三个子因素：知觉速度，语文记忆能力，图形记忆能力。第四，高级认知加工能力，包括四个子因素：状态元认知能力，推理能力，工作记忆能力和数字记忆能力。其中图式水平可作为独立的认知因素存在。
2、四种认知因素与代数问题解决水平关系的理论结构模型的拟合状况良好。结构方程的标准化解显示：无论在中等难度问题解决中，还
是在较高难度问题解决中，四种认知因素对问题解决水平的解释率均达
到81%。在中等难度和较高难度问题解决中，图式水平的作用效果都非
常明显(只0.01)，对代数问题解决水平有非常高的预测力。在较高难
度问题解决中，高级认知加工能力有一定的作用效果(只0.10)，对较
高难度代数问题解决水平有一定的预测力。
3、对代数问题解决水平有显著和一定预测力的两种认知因素中，
不同的认知成分的预测力也有大有小。在中等难度问题解决中，知识组
织性、陈述性知识表征准确性、程序性知识可逆性对代数问题解决水平
有较大的预测作用。在较高难度问题解决中，陈述性知识表述全面性、
程序性知识可逆性和状态元认知能力对代数问题解决水平有较大的预
测作用。
4、图式水平低，推理能力差，状态元认知水平低，空间表象能力差，
心算水平低，语文记忆能力差是代数学习困难生的认知特征。
5、图式水平对代数问题解决水平有明显的预测作用，代数学习困难
生的图式水平明显低于中等生和优等生，针对程序性知识全面性、组织
性设计的图式教学和针对陈述性、程序性知识全面性和知识组织性设计
的图式教学效果明显。可见，图式水平低是代数学习困难的主要成因。
高级认知加工能力对代数问题解决有一定的预测作用，代数学习困难生
的状态元认知水平和推理能力都低于中等生和优等生。可以推断，推理
能力差和状态元认知水平低是代数学习困难的成因。
6、在代数学习困难的集体千预中，图式教学没有取得立竿见影的效
果。但只要教师努力引导和帮助学生建立合理的问题中心图式，图式教
学的远期效果非常明显。规则中心图式和综合图式在不干扰优等生和中
等生学习的前提下，能显著提高学习困难生的学习成绩。所以，在课堂
教学中，规则中心图式教学和综合图式教学是代数学习困难教育干预的
较为理想的方式。样例中心图式对优等生的学习有一定的干扰作用，所
以，样例中心图式教学可作为代数学习困难的个体干预方式，推广到课
堂教学中还需要进一步的研究。
7、改变图式特征是代数学习困难教育干预的重点。在六种图式?
Students with learning difficulties is a generic term that refers to a heterogeneous group whose intelligence and body develop normally, but whose academic achievement level is significantly lower than the others in the same group. Researchers have paid much attention to the causes and intervention methods for a long time. The interrelated studies can be generally divided into three divisions: nerve-function level, psychology-education level and social environment level. Because the disorder in nerve function can' t be corresponding to specific learning difficulty and the social environment impacts on learning process indirectly, the study at psychological level, especially on cognitive features of learning difficulties is highly valued. Some researchers regard defects of general cognitive abilities; some researchers focus on meta-cognition, and some researchers value the defects of schema that refers to the knowledge structure related with problem solving. On the base of these different findings, the educat
ional intervention methods are various. Therefore, this study intents to integrate cognitive compositions and cognitive factors influencing academic performance, then to describe and analyze cognitive features of learning difficulties overall, have an accurate grasp of the causes of learning difficulties. Findings above would be helpful to improve strong theory foundation and experiment evidence, and to put forward the more effective intervention methods.
In the first study, 106 students in grade two of Anshan NO. 67 middle school were tested on 17 indices which reflect general cognitive abilities, meta-cognition and schema level, and tested on solving moderate difficult level problems and high difficult level problems. On the data analysis by SPSS10. 0 and LISREL8.0, the theory structure model about relation between cognitive factors and problem-solving level in algebra study was built and examined. Further, to describe the cognitive features of learning difficulties overall and deduce the accurate causes of learning (! i rfi(;Li].ties.
In the second study, based on the first study' s finding.'-,, different schema teaching methods were designed and were contrasted with normal teaching method. In this study, Ss were M4 students in grade two of Dalian NO. 35 middle school and 104 students in grade two of Anshan NO. 67 middle school. The purpose of this study was to find educational intervention methods which are more fit for students with algebra learning difficulties, and to provide a supplemental evidence for the theory model built in the first study.
In the third study, Ss were 109 students in grade three of Zhuanghe NO. 9 middle school. Based on the first and the second study, this study' s purpose was to explore that low rule-efficiency in solving algebra problem is whether because of rule-applying difficulty or rule-retrieving difficulty. Findings coming through this study can provide a supplemental evidence for the first study findings and the second findings on one hand. On the other hand, we can grasp the focal point of educational intervention for students with algebra learning difficulties.
The major findings in the above three studies are as followings:
l.The cognitive compositions affecting middle school students' algebra study can be explained by four cognitive factors. The first factor is Schema level which comprises overall expressing and correctly representing of declarative knowledge, overall handling, adversely handling and automatic using of procedure knowledge, and organizing of knowledge. The second is low cognitive processing ability that comprises mental arithmetic level and efficiency, space image level and efficiency. The third is discrimination-recognition ability which comprises consciousness speed, language and literature memory ability, and figure memory ability. The fourth is high cognitive processing ability that comprises reasoning ability, meta-cognitive ability, working memory ability and digit memory ability. Schema level can be regarded as one independent cognitive fact
引文
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