Development and Validation of Numerical Reasoning Test for Grade 7~8 Students

doi:10.12139/j.1672-0628.2024.03.013

Abstract

Abstract:

In the present study, items of numerical reasoning were developed for Grade 7 and Grade 8 students in China, which was based on the subscale numerical reasoning of the Differential Aptitude Test from America. Twenty-two items were included in the initial test. More than 7500 7th and 8th grade students participated in the study. After exploratory factor analysis, confirmatory factor analysis and Rasch analysis, the final instrument consisted of 18 items with good reliability and validity, which showed no gender differential item functioning. It suggests that the test is an effective and reliable tool for assessing 7th and 8th grade students’ numerical reasoning. The test can be used to identify underachieving students who have a high numerical ability. In addition, it can be used to screen for students with mathematical learning difficulties that caused by insufficient numerical reasoning ability. Therefore, the application of the test is helpful for educators to provide assistance to students who need help.

Key words: numerical reasoning, Rasch analysis, reliability, validity

摘要：

参考美国成熟的鉴别能力倾向测验中分维度数字推理能力的题目设置，编制适用于国内7～8年级学生的数字推理能力测验，初始测验共包含22道题目。选取初中七、八年级共计7500余名学生为被试。经过探索性因素分析、验证性因素分析以及基于Rasch模型对测量工具的质量进行分析之后，最终的数字推理能力测验由18道题目组成，该测验的内部一致性信度、分半信度、结构效度、效标效度都达到了心理测量学的标准，并且在性别上不存在项目功能差异，表明该测验可以有效地测量初中7～8年级学生的数字推理能力，该测验可用于甄别出数字推理能力与学业成绩不匹配的学生，以及筛查出是否因数字推理能力不足导致的数学学习困难学生，帮助一线教育工作者有针对性地对学生进行干预和指导。

关键词: 数字推理, Rasch模型, 信度, 效度

Shouying ZHAO, Rongrong REN, Wei CHEN, Bangjun MU. Development and Validation of Numerical Reasoning Test for Grade 7~8 Students[J]. Studies of Psychology and Behavior, 2024, 22(3): 387-394.

赵守盈, 任蓉蓉, 陈维, 牟帮军. 7～8年级学生数字推理能力测验的编制及信效度验证[J]. 心理与行为研究, 2024, 22(3): 387-394.

Figures/Tables 6

References 0

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类型		样本一 (八年级)	样本二
类型		样本一 (八年级)	七年级	八年级
性别	男	155(48.3%)	1880(51.9%)	1795(51.0%)
性别	女	166(51.7%)	1743(48.1%)	1722(48.9%)
是否寄宿	走读	130(40.5%)	1739(48.0%)	1746(49.6%)
是否寄宿	寄宿	191(59.5%)	1874(51.7%)	1774(50.4%)
是否独生	独生子女	179(55.8%)	1690(46.6%)	1778(50.5%)
是否独生	非独生子女	142(44.2%)	1926(53.2%)	1735(49.3%)
样本总量		330	7180
有效样本量		321	7143
样本回收率		97.3%	99.5%

类型		样本一 (八年级)	样本二
类型		样本一 (八年级)	七年级	八年级
性别	男	155(48.3%)	1880(51.9%)	1795(51.0%)
性别	女	166(51.7%)	1743(48.1%)	1722(48.9%)
是否寄宿	走读	130(40.5%)	1739(48.0%)	1746(49.6%)
是否寄宿	寄宿	191(59.5%)	1874(51.7%)	1774(50.4%)
是否独生	独生子女	179(55.8%)	1690(46.6%)	1778(50.5%)
是否独生	非独生子女	142(44.2%)	1926(53.2%)	1735(49.3%)
样本总量		330	7180
有效样本量		321	7143
样本回收率		97.3%	99.5%

题号	因子载荷	题号	因子载荷
Q1	0.51	Q10	0.40
Q2	0.41	Q11	0.39
Q3	0.49	Q12	0.56
Q4	0.58	Q13	0.50
Q5	0.55	Q14	0.54
Q6	0.62	Q15	0.53
Q7	0.67	Q16	0.43
Q8	0.56	Q17	0.46
Q9	0.46	Q18	0.42
第一因子特征值	4.69	第二因子特征值	1.32

题号	因子载荷	题号	因子载荷
Q1	0.51	Q10	0.40
Q2	0.41	Q11	0.39
Q3	0.49	Q12	0.56
Q4	0.58	Q13	0.50
Q5	0.55	Q14	0.54
Q6	0.62	Q15	0.53
Q7	0.67	Q16	0.43
Q8	0.56	Q17	0.46
Q9	0.46	Q18	0.42
第一因子特征值	4.69	第二因子特征值	1.32

题号	难度估计值	Infit MNSQ	Outfit MNSQ	点测量相关系数	题号	难度估计值	Infit MNSQ	Outfit MNSQ	点测量相关系数
Q1	−0.59	0.94	0.87	0.47	Q10	0.45	1.13	1.20	0.38
Q2	−1.27	0.97	0.90	0.40	Q11	0.09	1.09	1.11	0.40
Q3	−0.11	0.93	0.89	0.51	Q12	−1.33	0.89	0.76	0.45
Q4	0.29	0.96	0.96	0.50	Q13	0.61	1.07	1.10	0.43
Q5	−1.22	0.92	0.83	0.44	Q14	1.07	0.96	0.99	0.51
Q6	0.52	0.93	0.91	0.53	Q15	0.90	1.07	1.12	0.43
Q7	−0.47	0.85	0.75	0.54	Q16	0.48	1.03	1.05	0.46
Q8	−1.19	0.88	0.81	0.46	Q17	0.38	1.07	1.09	0.43
Q9	0.33	1.04	1.08	0.44	Q18	1.07	1.17	1.25	0.37