학생들의 문제풀이 결과에 따른 방정식 개념들 간의 연결에 관한 연구

Abstract

This research illustrates how well students can solve various types of equations. Equations including but not limited to linear, quadratic, and cubic equations. It also investigates to what extent students can connect one notion of an equation to another. The results of the study read as follows.

First, students can solve linear equations and evaluate the resulting values using transposition. However, they often have difficulty solving linear equations using principles of equality. The students can easily solve linear equations which integer coefficients, but they tend to think it is difficult to evaluate linear equations with fractional coefficients.

Second, when evaluating simultaneous equations, students consider the method of substitution more difficult than solving problems using methods involving addition and subtraction.

Third, it is shown that about 80% of the students are able to solve a quadratic equation using factorization. On the other hand, only 50% of the students solved the problem by making a perfect square expression.

Fourth, the students have more difficulty solving a simultaneous quadratic equation than a simultaneous quadratic equation. They often do not know the solution to cubic equations regardless of the method they use to solve it. Students seem unfamiliar with certain mathematical concepts such as the notion of real roots and imaginary roots.

To conclude, it is necessary to instruct students how to solve equations using a variety of methods such as factorization, perfect square expression and the quadratic formula. It is also essential to analyze students on the results of their problem solving abilities in order to make programs designed for individual students. Last but not least, the instructors should provide students with constructive feedback based on the results of their problem solving assessments.