學生解決基準量問題的經驗類型層次

Students' Experiential Reality in Solving the Norming Problems

馬秀蘭(Hsiu-Lan Ma)

《高雄師大學報：自然科學與科技類》 21期 (2006/12) Pp. 19-36

https://doi.org/10.7060/KNUJST.200612.0019

摘要

本文目的乃是探討國民小學六年級學童在解決基準量問題時的經驗類型層次，並檢查學生單位化、基準化能力，以及探究該能力與學生解題瞭解之關係。本文發現如下：
(一)學生在解決時間、面積的「基準量」問題時，會在情境中找尋經驗的存在，他們依個人注意力取捨方向的不同，而表現出不同的經驗類型層次；有的只從事「經驗」層次中的「辨識」活動，有的達「察覺」階段，有的已達「瞭解」階段；
(二)成功的解題者在解決基準量問題時，皆具有「單位化」與「基準化」之能力；他們會依自己的觀點去選擇解題可用之「基準量」；
(三)學生對時間、面積的「單位化」與「基準化」能力可幫助學生解題成功，然而該能力對學生是否能瞭解解題相關過程中的關係或運算，不見得是一個保證。因此即使學生在解題時選擇相同的「基準量」，他們也可能表現出不同的經驗類型。例如當學生解題活動的有效可能是意外碰上的「辨識」活動，或是活動的有效雖是預期已知，但也只是經驗類型重新表現的「察覺」時，這些成功的解題者在該解題情境中皆是無法形成概念瞭解的知識。

關鍵字

基準量 ； 經驗 ； 察覺 ； 瞭解

並列摘要

The purpose of this paper was to explore the experiential reality while the sixth graders solved norming problems. The abilities of unitizing and norming were examined. In addition, it studied the relationship between the abilities and understanding to problem solving. The findings were as follows:
1. The students looked for the existence of experience in mathematical situation in time and area. They responded to special types of experiences based on the differences of personal attention. Some only involved in the ”recognition” activity, some arrived at the level of awareness, and others already reached to the level of understanding.
2. The successful solvers had the abilities of unitizing and norming while solving the norming problems. They had their own viewpoints to select their reference unit to solve those problems.
3. The students could use the thought of unitizing and norming about time and area to help figure out what to do when they solved problems. Among them some students had difficulty in understanding the relationship or operation related to that procedural. The problem solvers could respond to varied types of experiences, even though they chose the same reference unit. For example, a problem solver did not have a conceptualized understanding while his/her experiential reality was the ”recognition” activity which was valid and run into accidence, or ”awareness” which was valid and known already to expect.

並列關鍵字

norming ； experience ； awareness ； understanding

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