國小高年級學童數感特徵暨數感動態評量發展之探討

The development and validity of the computerized dynamic number sense assessment system

林素微(Su-wei Lin)

指導教授 ： 林世華 ； 洪碧霞

國立臺灣師範大學/教育學院/教育心理與輔導學系/博士(2002年)

摘要

本研究的主要目的在發展電腦化數感動態評量系統以探討目前國小高年級學童的數感特徵，希望可以了解目前高年級學童的數感表現概況並且提供數感教學與測量的參考。本研究將數感定義為情境中數的覺知與推理，在真實化克漏字式的數學問題情境中，學生對多個未知數量合理值的選擇和判準的能力。研究內容包含電腦化數感評量工具的研發及其初步應用信效度議題的探討。對於本研究的558位高年級常模樣本而言，數感評量的測驗難度適中偏易，平均答對比率為.69，題目的難度來源包含考生對於題目情境的熟悉程度、考生所需同時處理的未知數，以及未知數所涉及潛在的變項數及變項間的關聯等因素的影響。研究中將數感評量問題區分為三個難度層次，以答對率70%為精熟水準之決定依據，在本研究高年級學童中，有14.5%的學童無法通過最低難度層次，其基本的數感相當薄弱。而有32%左右的學童屬於數感表現水準1，這類學童對於日常生活中習見、而且未知數量資訊不太複雜的情境數學合理性推估的表現不錯，但對於較不習見且數運作較複雜的情境掌握度則仍待加強。而36%左右的學童屬於表現水準2，僅有17%的學童具有全面靈敏的數量合理性推估表現。而數感表現較高的學生，平均作答思考時間較長，數感愈好的學生，對於題目難度也有較佳的後設覺察，他們普遍較能隨題目的難度而調整自己的作答時間。就常模而言，數感表現和數學能力測驗、數量估算評量的相關在.47左右，呈現中度的正相關。具體而言，本研究所研發的電腦化數感評量，題目情境真實而題型新穎，內容結構明晰、難度大致適切，利於後續的擴充發展。
根據常模在數感評量的測驗結果，研究進一步編輯適性的電腦化數感動態評量系統，動態評量系統主要分成第一階段數感表現水準區辨、第二階段介入、以及第三階段後測三部分。研究中另擇取147位五年級學童進行動態評量系統效益探討。結果顯示，動態提示系統運作適性而有效，整個動態評量系統對於學生具有協助與區辨的效益。其後測與數學能力測驗、數量估算等學習表現變項的相關明顯皆高於常模在靜態測驗的結果，顯示動態評量系統對於學習表現的預測力比靜態測驗高。以前、後測、進步幅度、以及前測加進步幅度等不同評量依據進行歸類，結果顯示，納入中介後，數感與數學能力的關連明顯提昇，即後測歸類的組別變項對於數學能力解釋力最強，顯示動態介入後所測量的表現水準和數學整體學習表現具有較強的關聯。整體而言，對於數感這類教育文化中學生尚未具有充分、公平學習經驗的變項，動態評量是較佳的評量取向，得以更有效探討該變項的構念、預測效益與重要性。本研究以電腦化克漏字式的數學問題情境為數感的構念做了操作性的界定，初步信效度結果顯示，該界定所評定的學生有關數量合理值的覺知與推理能力與在校數學成績及標準化的一般數學能力有中度的相關，而動態評量取向也靈敏的提昇了該構念的效標關連效度。

關鍵字

數感 ； 動態評量

並列摘要

The purpose of this study was to develop a computerized dynamic number sense assessment system (CDNSA) to investigate the issues of elementary students’ number sense. Number sense is the ability of awareness and reasoning for the relationships between the numbers, which were embedded in the context or situation. The students’ number sense can be enriched by meaningful experiences and the performance is situated in specific content or context. Based upon the operational definition, this research developed the closed item type about actual mathematical problem contexts to investigate the students’ number sense. The major tasks included were (1) building up a static computerized number sense assessment (CNSA); (2) developing the adaptive computerized dynamic number sense assessment system (CDNSA) by which to promote the students’ number sense.
Around 558 fifth and sixth grade students were stratified sample as norm group for CNSA. Three difficulty levels were developed to assess the students’ number sense. The study estimated that there were around 14.5% students who were unable to demonstrate the basic number sense and there around 17% students could perform number sense sensitively. The results showed that the three difficulty levels of CNSA could discriminate different ability levels groups successfully. It suggested that there were discriminative power in CNSA for distinguishing different number sense degrees. The correlation coefficients between CNSA and the Computerized Adaptive Mathematic Ability Test (CAMAT) and the Computerized Estimation Test (CET) were around .47s for the norm group.
Another 147 fifth students were stratified as the intervention study’s sample. The results suggested that hint system of CDNSA could promote the students’ number sense efficiently and adaptively and the CDNSA could promote and discriminant the students’ number sense successfully. The correlation coefficients between the intervention study’s post test of CDNSA and CAMAT and CET were higher than the coefficients between CNSA and the two tests of norm sample. Number sense was a new and important focus in our mathematics education. For this new strand, the students not yet had sufficient learning experience; it could be unfair to assess the students’ number sense by traditional assessment format. In order to having a deep and better understanding the relationship of number sense and general mathematic ability, the dynamic assessment was a workable and productive assessment approach.