Indefinite integral automatic analysis mechanism research and development—Using integrals involving quadratic square roots as an example☆
Introduction
Unfortunately, “for the overwhelming majority of students, the calculus is not a body of knowledge, but a repertoire of imitative behavior patterns [1]”. Although many calculus students are successful in performing procedural tasks in calculus, their understanding of underlying concepts is lacking [2], [3]. Therefore, this study evaluated the use of the knowledge structure theory to determine the conceptual structure map of items, and then utilize Bayesian network analysis to develop the computerized diagnostic testing system of integrals, to propose four Bayesian network models to compare the recognition rates. to provide easy understanding of the students’ learning situation to instantly detect student error types and, engage in subsequent remedial teaching.
Section snippets
Purposes
The purposes of this study are: (1) to use the experts’ knowledge structure to determine the conceptual structure map of items, (2) to build an “indefinite integral” online test system, and (3) to diagnosis and analyze the effectiveness of indefinite integral's computerized responses.
Content quiz
However, Calculus is formed forms a bridge between basic mathematics and science.
Basic calculus including limits, derivative function, integral and infinite series constitutes the majority of modern university
The experts’ knowledge structure
A knowledge structure was created by domain experts and practicing university teachers. The experts’ knowledge structure was shown in Fig. 4.
According to each node of the experts’ knowledge structure, the researcher worked out one corresponding constructed response item of the paper-pen pre-trial.
Constructed-Response items present an item stem and require examinees to construct a response from scratch [4].
There were three trigonometric substitutions useful in integrals with different forms. In
Results and discussion
In recent years, Bayesian Network has become an important modeling method for decision making problems of real-world applications [14]. This study regarded the ``indefinite integral'' of university Calculus as the scope of the study, to build a computerized diagnostic test, based on Constructed-Response items and combined with BN, which had multiple-choice and Constructed-Response items. The automatic analysis system was developed with the hope that, through this system, teachers could provide
Conclusions
Conclusions of this study were: (1) to establish the experts'knowledge structure to determine the conceptual structure map of items as Fig. 2, (2) to build an “trigonometric substitution of indefinite integral about integrands involving quadratic square root”online test system, and (3) to diagnosis and analyze the effectiveness of indefinite integral's computerized responses. In this study, these recognition rates of model 2 to 4 were 0.8217, 0.8502 and 0.8710, respectively. However,
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