三至九年級學生，數學運算能力等化測量與多向度分析

Multidimensional Test Equating the Arithmetical Abilities of Third to Ninth Grade Students

數學運算能力是學習必備基礎與生活所需技能，在小學階段主要是數字與運算符號的連結，國中階段包含內容知識、代數與函數，內涵廣泛且跨幅大，因此，數學運算能力發展是值得探討的議題。本研究使用數學運算能力測驗，以測驗等化技術進行小學三年級至國中九年級的橫斷資料4,991筆及追蹤測驗511筆縱貫資料分析，使用多向度隨機係數多項洛基模式比較不同階段之數學運算能力發展。研究結果為橫斷資料逐年成長，縱貫追蹤資料僅在使用相同題本之重複測驗中有成長，藉由數學詞彙測驗為參照測驗，發現隨著學生的年級增長，其數學運算能力與數學詞彙能力的關係越強。

Arithmetical ability is a fundamental part of learning and a necessary skill for life. Arithmetical abilities in elementary school are mainly about the connection between numbers and operation symbols, while those in middle school include mathematical computation content knowledge, algebra, and functions with a wide range of content and scope. Therefore, the development of arithmetical abilities is a subject worth exploring. In this study, using a Mathematical Arithmetic Ability Test, 4,991 cross-sectional and 511 longitudinal data were analyzed. These tests equated estimate item parameters and student's arithmetical abilities using multidimensional analysis. The subjects ranged from third graders of elementary school to the ninth graders of junior high school. Multidimensional Random- Coefficients Multinomial Logit Model (MRCMLM) was used to compare the development of arithmetical abilities at different stages. The results revealed that the cross-sectional data grew year by year, while the longitudinal data grew only in the repeated measurement using the same booklet. The mathematical vocabulary test was also used as a reference test to show that the relationship between arithmetical abilities and mathematical vocabulary abilities increases as the grade level advances.