• School Mathematics
• /
• v.9 no.1
• /
• pp.141-160
• /
• 2007

The purpose of this paper was to evaluate how students apply prior knowledge or experience in solving algebra word problems from the chain of signification-based perspective. Three middle school students were evaluated in this case study. The results showed that the subjects formed similarities in the process of applying knowledge needed for solving a problem. The student A and C used semi-open-end formulas and closed formulas as solutions. They then formed concrete shape for each solution using the chain of signification that was applied for solution by forming procedural similarity. At this time, the chain of signification could be the combination of numbers, words, and pictures (such as diagrams or graphs) or just numbers or words. On the other hand, the student C who recognized closed formulas and her own rule as a solution method could not formulate completely procedural similarity due to many errors arising from number information. Nonetheless, all of the subjects showed something in common in the process of coming up with a algorithm that was semi-open-end formula or closed formula.

• Journal of Educational Research in Mathematics
• /
• v.17 no.1
• /
• pp.67-90
• /
• 2007

The purpose of this study is to understand students' thinking process in the algebra problem solving, on the base of the works of Vinner(1997a, 1997b). Thus, two middle school students were evaluated in this case study to examine how they think to solve algebra word problems. The following question was considered to analyze the thinking process from the similarity-based perspective by focusing on the process of solving algebra word problems; What is the relationship between similarity and the characteristics of thinking process at the time of successful and unsuccessful problem solving? The following results were obtained by analyzing the success or failure in problem solving based on the characteristics of thinking process and similarity composition. Successful problem solving can be based on pseudo-analytical thought and analytical thought. The former is the rule applied in the process of applying closed formulas that is constructed structural similarity not related with the situations described in the text. The latter means that control and correction occurred in all stages of problem solution. The knowledge needed for solutions was applied with the formulation of open-end formulas that is constructed structural similarity in which memory and modification with the related principles or concepts. In conclusion, the student's perception on the principles involved in a solution is very important in solving algebraic word problems.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2001.10a
• /
• pp.222-225
• /
• 2001

This paper describes design and performance test of dual-mode horn antenna for HAPS (High Altitude Platform Station) in 47.2 - 47.5 GHz and 47.9 - 48.2 GHz bands. To obtain the optimal geometry parameters of it. the conical section is represented by a stepped transition composed of a set of cylindrical waveguide sections. For each step. the corresponding generalized scattering matrix is calculated. The elements of the matrices at the open end of the horn, are calculated by the rigorous formulas of the factorization method. To verify the theoretical results, a horn breadboard was manufactured for the medium frequency of 47.7 GHz and its radiation beam patterns were measured. The calculated and theoretical results are in good agreement.