能力指標系統的重組及表現標準適切性評估之研究

Abstract

能力指標系統的重組及表現標準適切性評估之研究 --以數學領域能力指標為例 研究者：杜佳真 中文摘要 本研究以九年一貫課程數學領域暫行綱要為例，瞭解能力指標系統發展的程序，並透過實徵的方式進行「數與量」和「代數」主題的重組以及第一、二階段表現標準適切性的評估。本研究的研究目的有七項： 1. 瞭解九年一貫課程數學領域暫行綱要發展的程序。 2. 瞭解九年一貫課程數學領域暫行綱要的內涵以及指標系統建構時的理念。 3. 瞭解九年一貫課程數學領域課程綱要和暫行綱要觀點的差異。 4. 以九年一貫課程數學領域暫行綱要的內涵為基礎，重新陳述「數與量」和「代數」主題軸的能力指標系統。 5. 以模糊得懷術來評估由研究者所重組的九年一貫課程數學領域能力指標暫行綱要「數與量」和「代數」主題軸的能力指標系統的適切性。 6. 瞭解我國學生在第一、二階段的「數與量」和「代數」主題軸之數學能力表現。 7. 透過標準設定的程序來評估由研究者重組之第一、二階段「數與量」和「代數」主題軸之數學基本能力表現標準的適切性。

本研究分為「研究一」、「研究二」與「研究三」三部份進行。 在「研究一」中，研究者透過質性分析的方式來瞭解暫行綱要發展的內涵和程序，並分析九年一貫課程數學領域暫行綱要和課程綱要觀點的差異。結果發現：暫行綱要發展歷程匆促，尚未考量到指標的呈現形式和檢視學生的表現結果，而暫行綱要和課程綱要的觀點從對於基本能力表現界定的差異，衍生出標準高低的爭議等不同看法。 「研究二」由研究者針對暫行綱要「數與量」和「代數」主題軸，進行重組和專家模糊得懷術適切性評估。主要邀集8位專家代表進行2次評估後，專家建議把表現標準融入指標內容中進行陳述，在本研究所重組的88項指標細項中，有46項通過7.5的門檻值，而有35項指標細項介於6.0-7.5之間，低於6.0的有7項。 「研究三」利用Angoff（1971）所提出的表現標準設定程序和得懷術技術，針對「數與量」和「代數」主題軸的第一、二階段表現標準適切性進行評估。經過15位專家代表進行3次評估問卷，結果發現：第一階段能力指標所指陳的學生表現標準較合乎我國學生的實徵結果，第二階段能力指標所指陳的表現標準較為簡單。 然後依據本研究過程整理出能力指標系統發展的四階段程序，作為未來能力指標系統發展的參考。 最後，本研究分別對「能力指標系統發展程序方面」、「能力指標系統發展技術層面」、「能力指標系統執行層面」以及「未來研究」等四方面提出建議。研究者衷心建議能力指標系統的發展能有更周延審慎的規劃和整合，同時進行適切性的評估，讓能力指標系統能發揮最大的效益。Evaluation on reorganization of competence indicator system and applicability of performance standard：An example from research on competence indicator system of mathematics

Chia-Chen Tu

Abstract:

The temporary Curriculum Guidelines of Mathematics for grade 1-9 was used as subject of this study. It was intended to (1) better understand the procedure for development of competence indicator system, (2) reorganize the themes of “number and quantity” and “algebra” through fuzzy Delphi method, and (3) evaluate the applicability of performance standard at stage one and two. The purposes of this study are seven folds as described below: 1. To understand the procedure in developing the temporary Curriculum Guidelines of Mathematics for Grade 1-9. 2. To understand the essence of the temporary Curriculum Guidelines of Mathematics for Grade 1-9 and the intents in developing indicator system. 3. To understand the differences between the new Curriculum Guidelines of Mathematics for Grade 1-9 and the current temporary Guidelines. 4. To reorganize competence indicator system with new emphasis on the main themes of “number and quantity” and “algebra” based on the essence of temporary Curriculum Guidelines of Mathematics for Grade 1-9. 5. To evaluate the applicability of competence indicator system with fuzzy Delphi method. 6. To understand the performance of Taiwanese students in mathematics at stage one and two with “number and quantity” and “algebra” as main themes. 7. To evaluate the applicability of basic performance standard in mathematics at stage one and two reorganized by the researcher with “number and quantity” and “algebra” as main themes through performance standard setting procedures.

The study was carried out along three parts of research to meet the objectives. A brief description of each research including its approach and result are mentioned as follows:

Study one: the researcher tried to understand (1) the essence and procedure of how the temporary Curriculum Guidelines have been developed through qualitative analysis, and (2) the conceptual difference between the original Curriculum Guidelines of Mathematics for Grade 1-9 and the current temporary Guidelines. The results showed the temporary guidelines were developed hastily without taking into account of how the indicator should have been displayed and of the response from students. The difference in definition of basic performance led to disputes on issues such as how to set up the reasonable criteria.

Study two: This research set out to evaluate the applicability of reorganizing temporary Curriculum Guidelines with “number and quantity” and “algebra” as main themes by fuzzy Delphi method. A panel of eight experts was invited to conduct such evaluations twice. The conclusion from experts suggested including statement in the incorporation of performance standard into indicators. With 88 items of indicator reorganized in this research, 46 items were rated above the threshold of 7.5, 35 items were rated between 7.5 and 6, and 7 items were rated below 6.

Study three: This research was carried out to evaluate the applicability of performance standard at stage one and two with “number and quantity” and “algebra” as main themes with performance standard setting procedure proposed by Angoff (1971) and Delphi method. Three separate evaluations conducted by 15 experts showed that competence indicator of stage one could better corroborate with existing data on the performance standard of students in Taiwan. The competence indicator of stage two was less challenging in addressing the performance standard.

The procedure to develop competence indicator system in four stages was also compiled in this study as reference to similar efforts in the future.

In conclusion, this study offered advises on development of competence indicator system in the aspects of procedure, technicality, execution and future research. Researcher of this study sincerely suggests the development of competence indicator system to be more thoroughly planned and integrated with appropriate evaluation to achieve its best efficacy.