エクアドルにおける数学を日常で活用する能力の変化に関する研究 : PISA2003「数学的リテラシー」の項目反応理論による学年差に注目した分析から

抄録

In Ecuador, the student academic achievement is not high. It was revealed by international survey on academic performance for Latin and Caribbean counties called SERCE (the Second Regional Comparative and Explanatory Study), as well as the PISA test which the Municipality of Quito conducted on its own to 282 students of the third year of junior high school in September 2006. As is well known, PISA is international surveys to measure student application ability, and it's constructed by OECD. The result of the PISA test which the Municipality of Quito conducted revealed that the one of the PISA mathematical contents which is "Uncertainty" was the most difficult for the third year students of the junior high school. This fact is usually interpreted as a sign that the "Uncertainty" is the most difficult mathematical content for them to acquire and exert their knowledge and skills. This, however, does not necessarily mean that in the content "Uncertainty" the students will not be able to improve their performance in the near future. In other words, finding out the mathematical content which the students cannot perform highly at this moment is totally different thing from a possibility of improvement of their performance in their future. Then, how can we recognize the mathematical aspect which will be related with the improvement in their performance? To resolve the research question mentioned above, this present study examines differences of the test item difficulty and discrimination between the third year students of the junior high school and the first year students of the senior high school, by making use of the test theory called Item Response Theory (IRT), using the data collected by reconfiguration PISA test of Quito Municipality in February 2010. Sample students were selected from 6 Quito municipal schools who took the PISA test in September 2006, and its number was 514. The study revealed that the mathematical aspects in which the students have possibility to improve their performance are correlated with the degree of the use of mathematical calculation and algorithm. In addition, we got implication that reading ability influences the student mathematical performance improvement.