Analysis of Slow Learners in the Calculation of Symbolic Fractions and Development of an Online System to Support them

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Slow learners do not learn the calculation of symbolic fractions easily even if they have enough skills to calculate numerical fractions. The suspected reason is that symbolic calculations depend on several mathematical rewriting rules, which are usually hidden in black boxes at numerical calculations, and the slow learners cannot use the rules properly. They can calculate numerical fractions automatically according to a few patterns they have learnt from experience and without thinking of the mechanism of the calculating steps.We have been developing a Web-based online exercise system to support such slow learners in symbolic calculation. The system analyzes the input symbolic expressions sent by the students, categorizes the calculating errors into careless mistakes, fatal errors, and other errors. The fatal errors are mostly caused by incorrect rewriting rules that look similar but are not equal to any mathematical rewriting rules, and show that the student do not calculate upon mathematical rules. The system has two special Web pages: step-by-step instruction page and the explanation page. The instruction page shows one step of the calculation to the student according to the selected rewriting rule. By using this page, the student is accustomed to use rewriting rules in his/her symbolic calculation. The explanation page shows itself when the student makes a fatal error on his/her calculation in the exercise page. It explains that the exact calculating step is lead by an incorrect rule, and shows a numerical counter example to show the incorrectness.Slow learners who used the system showed better recognition than other students in the post-test, which demonstrates the effectiveness of the method and the system developed in this project.