題型對學生數學表現水準之影響─以相似形為例 Effects of Item Type on Student Mathematics Performance: Similar Figures as an Example

Abstract

本研究的目的為探討不同題型對試題難度、試題鑑別度及九年級學生數學表現水準的影響，研究者以相似形的能力指標作為測驗內容，設計相同的題目敘述之選擇題、填空題及計算說理題，並編製成含有六題共同題的三種試卷，以進行測驗等化之用。每份試卷分別有361、411及378位的受試者，合計1,150位的受試者。研究設計採用共同題不等組設計，並以同時校準法（concurrent calibration method）進行測驗等化。本研究分別用單向度二參數部分計分模式與多向度潛在迴歸模式（multidimensional latent regression model），進行試題難度、鑑別 度及學生在不同題型下所表現之能力參數的估計，並將學生在各題型中的能力估計值排序換算為百分等級。研究結果發現：一、選擇題的平均難度最低，計算說理題的平均難度最高；二、選擇題的平均鑑別度最低，計算說理題的平均鑑別度最高；三、單向度模式分析發現，有69.04%的學生在三種題型能力估計值的PR值（百分等級）相差20以上；四、多向度潛在迴歸模式分析發現，有12.61%的學生在三種題型能力估計值的PR值相差15以上。研究結果顯示，測驗題與學生的數學表現水準有關，而且主要有兩種不同型態的影響。文末針對兩類學生在不同題型較具優勢的原因，做進一步的討論。 This study investigated the influence of item type on the difficulty and discriminatory power of items and on ninth graders’ mathematics performance. Researchers tested similar figures as competence indicators; three tests were designed with multiple-choice items, completion items, and essay items that corresponded to the same stem, and six common items were equated for each test. The tests were administered to 1,150 students, with 361, 411, and 378 receiving different kind of three tests. The tests were equated using a common-item, nonequivalent group design and the concurrent-calibration method. The difficulty and discriminatory power of items and the ability parameters of the students taking the tests with different item types were estimated with a unidimensional two-parameter partial-credit model and a multidimensional latent regression model. The estimates of the students’ ability parameters were converted to percentile ranks (PRs). The following are the results of the study: (1) The average difficulty of the multiple-choice items was the lowest, and that of the essay items was the highest. (2) The average discriminatory power of the multiple-choice items was the lowest, and that of the essay items was the highest. (3) For 69.04% of the students, the values of three item types differed by 20 or more in PR. (4) Finally, the multidimensional latent regression model revealed that, for 12.61% of the students, the values of three item types differed by 15 or more in PR. The results indicate that item type is related to student mathematics performance through two main types of effect. The researchers further investigated why some students’ performance on the completion and essay items was superior to that on the multiple-choice items and why some students’ performance on the multiple-choice items was superior to that on the essay items.

Keywords

• 相似形
• 測驗等化
• 試題反應理論
• 題目類型
• similar figure
• test equating
• item-response theory
• item type