國家教育研究院

　　本研究為設計一份適合國小六年級測試的PISA與能力試題，一部分試題（約36％）是從PISA所公告之試題中選取適合國小高年級學生的試題。另一部分（約64％）則根據九年一貫能力指標配合PISA的四個領域內容，以TASA試題研發理念所進行命題。目的是要了解國小六年級學生數學素養與能力之表現與相關，並利用CTT和IRT進行試題量的分析與試題內容質的分析，以了解學生在不同領域、數學素養與能力的成就狀況與錯誤類型分析，提供數學教育學者、教師及行政人員參考。 本研究採立意抽樣，利用紙筆測驗，其中PISA測驗共14題，自編教材測驗A、B卷各12題，以及一份背景變項問卷，受試者包含北、中、南與離島的六年級學生，來自27校54班，有效樣本共1258人。試後分析測驗的信度及試題的難度、鑑別度與選項誘答分析，再以多元計分進行學生能力值估計。 本研究的結果發現： 一、整體試題和PISA試題的能力估計在區域部分，北部顯著高於南部，其餘則沒有差異；另外學童在能力測驗試題上，四個區域皆沒有差異。男生在PISA測驗題表現顯著優於女生，但在整體與能力測驗的表現兩者並無顯著差異。 二、各區域、男女與卷別之能力與素養之相關值：區域中以中部最高為.61，而以南部最低為.54；男女相關值分別為.62與.53，以男生相關值較高；A、B兩卷之相關值分別為.59與.57，以A卷相關值較高。 三、整體、男女、區域國小六年級受試學生在不同內容領域之能力表現，結果發現在空間與形狀部分北部顯著大於南部，而在改變與關係則是北部顯著大於離島，其餘領域內容與區域則沒有顯著差異；男生在數量領域內容的表現顯著高於女生，但其餘三個領域內容則無顯著差異。 四、學生在能力與素養測驗之錯誤類型分析：相同點在空間與形狀的幾何圖形組成要素、位置觀念有混淆；解題中出現單位換算或是乘除中出現小數時造成認知負荷；應用「比和比值」解決問題時，利用比率解決由總量求部分量概念不足。 本研究測驗的結果，PISA+A之 Cronbach 為0.82； PISA+B 之Cronbach為 0.76顯示兩分測驗皆有不錯之信度。

　　The study designs a math test that is appropriate for the sixth grade students to take, in order to understand the performance and relevance of the sixth grade students’ math literacy and ability as well as to provide reference for the math scholars, teachers, and administrative staff. The samples are the sixth grade students from 54 classes in 27 schools, which come from the northern, central, and southern Taiwan and off-shore island. The effective samples are 1258 students. The results of this study are as following: First, in view of the regions about the ability estimation of the overall test and the PISA test, the score in the north is significantly higher than the south. Boys are significant higher than girls on the PISA test. Second, Among different regions, the central region comes to the maximum of .61, while the southern region comes to the minimum of .54. The correlations between boys and girls are .62 and .53. The boys have higher correlation. The correlations between test A and test B are .59 and .57. The test A has higher correlation. Third, The northern region is significantly higher than the southern region on space and shape. The northern region is obviously higher than the off-shore island on change and relationship. Fourth, students are confused about the constituents and positions of geometry in the same point on space and shape. In the process of problem-solving, the students have insufficient cognition about the unit calculation and the decimal figures in multiplication and division. When the students apply “ratio and specific value” to solve problems, they have inadequate concepts about how to use the ratio from the total quantity to calculate the part quantity. The results of this study reliability are that the Cronbach α of PISA+A is 0.82 while the Cronbach α of PISA+B is 0.76, which show that the two tests have good reliability.