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Alternative TitleDevelopment of Approximate Number System Acuity and its Relationship with Mathematical Ability in Primary-School Students
Thesis Advisor施建农
Degree Grantor中国科学院研究生院
Place of Conferral北京
Degree Discipline心理学
Keyword近似数量系统 数学能力 交叉滞后回归分析 智力
Abstract在日常生活和科学研究中,数学有着不可替代的作用,从小培养学生的数学能力具有重要的意义。特殊领域观点 (Domain-Specific Approach)认为,个体数学能力的差异是由数量表征能力的个体差异性导致的。近期研究发现,近似地表征较多数量信息的近似数量系统(Approximate Number System, ANS)与数学能力有紧密的相关关系。但目前文献中对近似数量系统的研究主要集中在婴幼儿和成人阶段,较少涉及小学生群体,对于近似数量系统在小学阶段是如何发展的尚不清楚。同时,近似数量系统与数学能力相关关系的实验结果差异性很大,而对于两者之间是否有因果关系存在很大争议。
1. 研究了一、三、五三个年级的小学生近似数量系统敏锐度,发现三个年级近似数量系统敏锐度整体上呈现先下降后上升的趋势,出现“三年级效应”。
2. 研究了一、三、五三个年级的小学生近似数量系统敏锐度与数学能力的相关关系,发现在三个年级中两者的相关系数(0.22~0.47)均非常显著,且三个年级的相关系数没有显著差异(ps>.05)。
3. 追踪了三、四、五三个年级小学生的近似数量系统敏锐度和计算能力在一年内三个时间点的变化。研究发现,两者之间存在显著的相关关系,且相关关系的显著度不随时间变化(0.33-0.34)。综合运用交叉滞后回归分析和潜变量增长曲线模型对两者相关关系的因果方向性进行了系统研究。潜变量增长曲线模型的结果显示,小学生近似数量系统敏锐度的初始状态能正向预测计算能力的初始状态(路径系数为0.47),小学生计算能力的初始状态对近似数量系统敏锐度的变化速率起着负向预测作用(路径系数为-0.32)。将近似数量系统作为随时间变化的协变量后,潜变量增长曲线模型的结果显示近似数量系统敏锐度能正向预测计算能力(路径系数为0.08;χ2=3.92, df=7, RMSEA=0, CFI=1, TLI=1.04,SRMR=0.04)。交叉滞后回归分析的结果显示,T2 近似数量系统敏锐度可以解释T3 计算能力变异的25%。这些结果表明,小学生近似数量系统敏锐度可以正向预测其计算能力。
4. 研究了智力在近似数量系统敏锐度与数学能力的关系的调节作用,发现智力在小学生近似数量系统敏锐度与计算能力关系中的调节作用显著(t=2.57,p<.05);智力在小学生近似数量系统敏锐度与期末数学成绩关系中的调节作用也显著(t=-3.39, p<.001)。
Other AbstractMathematical ability and quantities information are very important, and closely related to our daily life and science. Specific-domain approach found that individual differences of representation of quantities are strongly correlated with different levels of mathematical ability. Recent studies reported that Approximate Number System (ANS), which represents the approximate number of items in visual or auditory arrays without verbally counting, has a strong connection with mathematical ability. However, the literature mainly focuses on the ANS acuity of pre-school children and adults, and how ANS acuity develops in the primary-school period still remained unclear. Moreover, inconsistent results exist on the relationship between ANS acuity and mathematical ability and the causal direction of this relationship still remained unexplored.
To address the above questions, the thesis focuses on the developmental curve of ANS acuity of primary-school students, the causal relationship between ANS acuity and mathematical ability, and the role of intelligence in this relationship. We used a longitudinal study in our work. On one hand, we tracked the development of ANS acuity and arithmetic ability of 3rd, 4th and 5th grade students through one-year period; on the other hand, the ANS acuity and arithmetic ability of 1st, 3rd and 5th
grade students were systematically studied. The collected data were analyzed using latent growth curve modeling and cross-lagged analysis and latent structural equation. Structure equation model was used to investigate the role of intelligence played in the relationship between ANS acuity and mathematical ability.
The results are as follows:
1. Systematically investigated the ANS acuity of 1st, 3rd and 5th grade students and found that the ANS acuity first increases at 3rd grade and then decreases at 5th
2. Studied the relationship between ANS acuity and arithmetic ability of 1st, 3rd
and 5th grade students, and found that the correlation coefficients of ANS acuity and arithmetic ability were significant at all three grades (0.22-0.47)and the differences between any two of them were not significant (ps > 0.05).
3. Studied the development of ANS acuity and arithmetic ability of 3rd, 4th and 5th grade students through one year at three time points. Cross-lags regression analysis showed that T2 approximate number system acuity can explain 25% of T3 calculation’s variation. Furthermore, Latent growth curve model showed that initial approximate number system acuity played a significant positive role on the initial calculation(path coefficient was 0.47), The initial calculation played a negative role on the change rate of approximate number system acuity (path coefficient was-0.32). Taking approximate number system acuity as a time-varying covariate, the results showed that approximate number system acuity could predict calculation(path coefficient was 0.08,χ2= 13.92, df = 7, RMSEA = 0, CFI = 1, TLI = 1.04, SRMR = 0.04).
4. Intelligence was a moderator in the relationship of approximate number system acuity and calculation (t = 2.57, p <. 05). Also, Intelligence was a moderator in the relationship of approximate number system acuity and mathematical achievement (t = -3.39, p <. 001).
Subject Area发展与教育心理学
Document Type学位论文
Recommended Citation
GB/T 7714
何云凤. 小学生近似数量系统敏锐度的发展及其与数学能力的关系[D]. 北京. 中国科学院研究生院,2016.
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