• The Mathematical Education
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• v.49 no.2
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• pp.161-174
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• 2010

The purpose of the study is to analyze various types of errors appeared in true-false proof problems of matrix and to find out correction method. In order to achieve this purpose, error test was conducted to the subject of 87 second grade students who were chosen from D high schoool. It was shown from this test that the most frequent error type was caused by the lack of understanding about concepts and essential facts of matrix(35.3%), and then caused by the invalid logically reasoning (27.4%), and then caused by the misusing conditions(18.7%). Through three hours of correction lessons with 5 students, the following correction teaching method was proposed. First, it is stressed that the operation rules and properties satisfied in real number system can not be applied in matrix. Second, it is taught that the analytical proof method and the reductio ad absurdum method are useful in the proof problem of matrix. Third, it is explained that the counter example of E=$\begin{pmatrix}1\;0\\0\;1 \end{pmatrix}$, -E should be found in proof of the false statement. Fourth, it is taught that the determinant condition should be checked for the existence of the inverse matrix.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.75-81
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• 1996

Polynomial measurement error model(MEM) with one predictor is considered. It is briefly mentioned that Chan and Mak's generalized least squares estimator(GLSE) can be derived more easily if Hermite polynomial concept is applied. It is proved that GLSE derived using new procedure is equivalent to the estimator obtained from corrected score function. Finally, much simpler proof of the asymptotic behavior of GLSE than that of Chan and Mak is provided. Much simpler formula of asymptotic covariance matrix of GLSE is a part of that proof.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.985-987
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• 1998

This paper presents a stability proof for the nonlinear feedback linearization-full order observer-based sliding mode controller (NFL-FOO-based SMC). The closed-loop stability is proved by a Lyapunov function candidate using an addition form of the sliding surface vector and the estimation error.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.976-978
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• 1998

This paper presents the stability proof of a nonlinear feedback linearization-reduced order observer/sliding mode controller (NFL-ROO/SMC). The closed-loop stability is proved by a Lyapunov function candidate using an addition form of the sliding surface vector and the estimation error.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.979-981
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• 1998

This paper presents a stability proof for the nonlinear feedback linearization-observer/sliding mode model following controller (NFL-O/SMMFC). The separation principle is derived, and the closed-loop stability is proved by a Lyapunov function candidate using an addition form of the sliding surface vector and the estimation error.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.988-990
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• 1998

This paper presents the stability proof of a nonlinear feedback linearization-reduced order observer-based sliding mode controller (NFL-ROO-based SMC). The closed-loop stability is proved by a Lyapunov function candidate using an addition form of the sliding surface vector and the estimation error.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.991-993
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• 1998

This paper presents a stability proof for the nonlinear feedback linearization-observer-based sliding mode model following controller (NFL-O-based SMMFC). The closed-loop stability is proved by a Lyapunov function candidate using an addition form of the sliding surface vector and the estimation error.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.55-68
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• 2008

In this paper, we investigated difficulties that middle school students face in the teaming process of proof, and then inquired how does learning of proof using GSP ease students' difficulties. Throughout the inspection, we identified that students have difficulties in understanding process of premise and conclusion, use of notation, process of reasoning. And we identified, throughout learning process of proof using GSP, students can be feedbacked for their guess or reasoning, generalize the special case to general properties and have attitude checking ideas needed in proof by themselves.

• School Mathematics
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• v.6 no.1
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• pp.59-90
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• 2004

This study has been established with two purposes. The first one is to development the learning-teaching model for enhancing students' creative proof capacities in the domain of demonstrative geometry as subject content. The second one is to aim at experimentally testing its effectiveness. First, we develop the learning-teaching model for enhancing students' proof capacities. This model is named the generative-convergent model based instruction. It consists of the following components: warming-up activities, generative activities, convergent activities, reflective discussion, other high quality resources etc. Second, to investigate the effects of the generative-convergent model based instruction, 160 8th-grade students are selected and are assigned to experimental and control groups. We focused that the generative-convergent model based instruction would be more effective than the traditional teaching method for improving middle school students' proof-writing capacities and error remediation. In conclusion, the generative-convergent model based instruction would be useful for improving middle grade students' proof-writing capacities. We suggest the following: first, it is required to refine the generative-convergent model for enhancing proof-problem solving capacities; second, it is also required to develop teaching materials in the generative-convergent model based instruction.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.973-975
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• 1998

For a nonlinear feedback linearization-full order observer/sliding mode controller (NFL-FOO/SMC), the separation principle is derived, and the closed-loop stability is proved by a Lyapunov function candidate using an addition form of the sliding surface vector and the estimation error.