在數學臆測教學下學生數學創造力的展現

本研究的目的是在探究數學臆測任務中，五年級學生所展現的數學創造力。本研究的個案班級導師是進行臆測活動長達六年時間的國小教師，此班級學生多為第一年接觸數學臆測教學。研究中的資料蒐集，主要來自研究者擔任研究助理期間拍攝的科技部計畫資料，以及臆測教學專書中的案例。學生數學創造力的評分架構是參照Leikin(2013)的評分方式，該架構以數學思維方式的流暢性、變通性及原創性來評估學生的數學創造力表現。　　初步研究結果發現：(1) 兩臆測任務中，學生提猜想的原創性表現較弱，顯示學生提猜想時，比較容易注意到數據表面的共通現象，但多數學生有能力提出不同類型的猜想；(2) 高分組創造力學生能看見更多資料中的規律、差異和相似性並提出數學猜想。而低分組創造力學生提出的猜想以低原創性為主，但有能力解讀數據間的關係；(3) 臆測任務中學生猜想的原創性分數與創造力分數之間具高相關，顯示臆測任務是評量數學創造力的有效工具，因為它與創造「有用的新產品」此數學創造力定義相匹配；(4) 造例數據類型多寡及學生數學先備知識可能會影響猜想的變通性表現。但同構的造例數據，不會因組織分類方式影響學生形成個人猜想的創造力表現；(5) 兩臆測任務中，學生猜想的流暢性、變通性、原創性沒有顯著差異，但分數乘法任務中學生猜想創造力的品質較梯形面積任務佳。

關鍵字

數學臆測任務；數學創造力；評量工具

並列摘要

The objective of this study was to investigate the mathematical creativity 5th graders showed in mathematics conjecturing tasks. The participants of this research include an elementary school homeroom teacher who has been conducting conjecturing instructions for six years and the students mostly involved in mathematical conjecturing instructions for the first time. The data of this research was mainly collected by the researcher who photographed the information when he worked as the research assistant in Ministry of Science and Technology and partly from the cases in the books of conjecturing instructions. The criteria of students’ mathematical creativity refers to Roza Leikin (2013) scoring methods, with the framework of assessing students’ performance of mathematical creativity based on the fluency, flexibility and originality of their mathematical way of thinking. 　　The preliminary research findings are as follows: (1) In two mathematical conjecturing tasks, the majority of the students is those who with low flexibility and low originality. It shows that most students focus on common phenomenon of surface data when they formulate the conjecturing. Nonetheless, most students have the ability to formulate different types conjecturing. (2) Students with high creativity can see more regularity, difference and similarity in the data, and therefore formulate mathematical conjecturing, while those who with low creativity formulate conjecturing with low originality yet are able to interpret the relationship between data. (3) In the task, the originality score of conjecturing has high correlation with creativity score, which shows conjecturing tasks are an effective tool in evaluating mathematical creativity for it matches the definition of “creating useful new products”. (4) The number of example data types and students’ prior knowledge might affect the flexibility of conjecturing performance. However, the example data of the same type do not affect students’ personal performance of conjecturing creativity even with different grouping methods. (5) In these two conjecturing tasks, there is no significant difference in students’ creativity performance of conjecturing formulation. Still, in the task of fractional multiplication, the quality of students’ conjecturing creativity outdid that in the task of trapezoidal area.