[논문]수학 및 과학 간 지적 자원의 사용: 이론적 모형에 대한 실증 연구

최경미; 서경운; 황지현

doi:10.7468/mathedu.2020.59.4.405

수학 및 과학 간 지적 자원의 사용: 이론적 모형에 대한 실증 연구
A theoretical model for the utilization of intellectual resources between science and mathematics: An empirical study 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.59 no.4, 2020년, pp.405 - 420

최경미 (버지니아대학교) , 서경운 (서울대학교) , (아이오와대학교) , 황지현 (강원대학교)

초록
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학생들이 수학과 과학을 배울 때 개발 및 사용하는 지적 자원의 이론적 모형을 구성하였다. 9,300명의 미국 4학년 학생들의 수학 과학 성취도 평가의 응답을 통계적으로 분석하여 이 이론적 모델을 검증하였다. 그 결과는 이론적 모형이 타당함을 보여주며, 4학년 학생들의 과학 학습에서 인식적 실천은 수학 학습에서 인식적 실천의 발달에 영향을 준다.

There have been mixed reports about the idea of utilization of resources developed from one discipline across disciplinary areas. Grounded with the argument that critical thinking is not domain-specific (Mulnix, 2012; Vaughn, 2005), we developed a theoretical model of intellectual resources (IR) that students develop and use when learning and doing mathematics and science. The theoretical model shows that there are two parallel epistemic practices students engage in science and mathematics - searching for reasons and giving reasons (Bailin, 2002; 2007; Mulnix, 2012). Applying Confirmatory Factor Analysis and Structural Equation Model to the data of 9,300 fourth grade students' responses to standardized science and mathematics assessments, we verified the theoretical model empirically. Empirically, the theoretical model is verified in that fourth graders do use the two epistemic practices, and the development of parallel practices in science impacts the development of the two practices in mathematics: A fourth grader's ability to search for reasons in science affects his or her ability to search for reasons in mathematics, and the ability to give reasons in science affects the same ability use in mathematics. The findings indicate that educators need to open ideas of sharing development of epistemic practices across disciplines because students who developed intellectual resources can utilize these in other settings.

주제어

표/그림 (6)

표 [Table 1] Descriptions of the Selected Science and Mathematics Cognitive (Mullis et al., 2009)
그림 [Fig. 1] Hypothesized structural equation model for CFA and SEM
그림 [Fig. 2] Results for the SEM. CFI=.952; TLI=.918; and SRMR=.031
표 [Table 2] Model fit information of the hypothesized model
표 [Table 3] Standardized and unstandardized factor loading for the CFA model
표 [Table 4] Results from the structural equation modeling Direct plus Indirect Effects

AI 본문요약
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제안 방법

Given the current demands to use innovative pedagogical approaches in the teaching and learning of STEM where epistemic practices related to inquiry are emphasized, the theoretical model we established and empirically verified with fourth grade students' data has the potential to help in examining different pedagogical approaches that build on the reasoning factors identified in this study.
The ITBS science test were composed of one section with 34 multiple-choice items while the mathematics tests had three sections: concepts and estimation, problem solving and data interpretation, and computation. We decide to exclude the mathematics computation section due to the nature of the items in that section: They are to measure simple computation skills (Iowa Testing Program, 2014).
Researchers echoed that model evaluation in CFA/SEM is different from the traditional hypothesis tests like t tests, and it is significant to use other possible goodness-of-fit measure to evaluate global model fit (Chen, Currna, Bollen, Kirby, & Paxton, 2008). The decision about model fit should not be made with a single way, so we did not reject our hypothesized model solely due to RMSEA. Focusing on the other indices showing acceptableness of our model, we could consider several reasons about poor fit of RMSEA.
With the assumption that critical thinking (cognitive processing) skills acquired in one discipline (science in this study) can be utilized in another disciplinary learning setting (mathematics), it is hypothesized that the cognitive resources required for making inferences in Science (abductive inference and deductive inference in science) are utilized in making of inferences in Mathematics (inductive inference and deductive reasoning in mathematics). This study addresses this question, first, by conceptually establishing common features of cognitive resources in each of the disciplines in the Cognitive Framework established by TIMSS, and then to demonstrate the possible linkages and/or relationships with empirical data. As such, the model shown in [Fig.

대상 데이터

The data set includes 9,300 students' responses to 34 science items and 60 mathematics items.
The data were fourth grade Iowa students' responses to the Iowa Tests for Basic Skills (ITBS) mathematics and science items collected in each year from 2006 to 2009.

데이터처리

We evaluated the fit of the hypothesized model based on the following indices as operationalized in Mplus 7.2 in conjunction with MLR estimation: Comparative Fit Index (CFI), the Tucker-Lewis fit index (TLI), the standardized root mean square residual (SRMR), and the 90% confidence interval of the root mean square error of approximation (RMSEA). Values above .

성능/효과

It should be noted that the science resources were affecting mathematical resources with different magnitudes. That is, the direct effect of abductive inference in science was higher for mathematical inductive inference than deductive inference in mathematics while the total effect of abductive inference on two mathematical inferences is reversed due to a large indirect effect on deductive inference. Conversely, the higher direct effect of deductive inference in science was observed in deductive inference in mathematics than in the inductive inference, the pattern of which was maintained even after adding a relatively large indirect effect on inductive inference (0.
We decide to exclude the mathematics computation section due to the nature of the items in that section: They are to measure simple computation skills (Iowa Testing Program, 2014). Types of skills we are interested for this study were cognitive processing skills, not simple computation skills, when solving mathematics problems. The data set includes 9,300 students' responses to 34 science items and 60 mathematics items.

후속연구

For example, one of the possible reason is using MLR instead of maximum likelihood (ML) because CFA/SEM with MLR showed poorer fit than that with ML. Also, we might need to attend to diagnostics for possible reasons of model misfit in further research. It is also possible to follow other researchers' suggestions that "the use of precise numerical cutoff points for RMSEA should not be taken too seriously" (Chen et al.

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