國中生數學符號素養的創造思考表現

Abstract

本研究透過根據PISA數學問題解決形成、應用和詮釋三過程的具體活動設計題目，探討在此三過程中，台灣國中生在符號及其運算中的數學創造思考表現。研究對象兼採立意及方便抽取樣，為在台灣北部和南部各取兩所中等程度以上的國中，在其中32個8年級班級中隨機抽取的210位學生參與研究，其中男生104位，女生106位。研究採問卷調查法，並根據從兩個角度評估學生的創造思考：，一是為學生回答答案的特質；二是，另一為創造思考中基於流暢性、變通性和與獨創性三項的傳統指標，為此，。題目設計與傳統研究創造思考所設計的題目有兩大差異，一為題目乃素養導向試題，二為題目提供了可創造無限多種答案的解答空間以激發學生的創造思考。設計的開放性題目允許學生提出多種可能的創意答案。研究結果顯示，當題目設計強調激發學生鼓勵創造性思考維時，大多數學生能夠提出多個適當且多樣的答案。特別是在形成階段過程的題目中，超過80%的學生能提出三個不同的適當答案。然而，當題目限制使用特定、難度較高的數學物件時，學生的數學難度的增加會影響學生提出創造性答案的能力，尤其是當題目限制使用特定數學物件時，這一點在應用過程中的表現尤為明顯，顯示出學生在面對更高挑戰時，創造作答表現明顯力的展現可能會受限。不論在哪一個在數學過程中，學生的創造思考表現皆依序為流暢性、變通性和獨創性的順序下降。針對流暢性思考，學生在各數學過程中的表現差異不大；針對變通性思考，學生在詮釋階段過程的表現最佳；針對獨創性思考，學生在形成階段過程的表現最佳。此外，在詮釋過程中，雖然大部分學生能提供至少兩個可接受的答案，但創造出第三個或更多答案的學生比例顯著下降，指出表示這一過程對學生而言可能的創造思考可能更具挑戰性。另一個重要發現是，當學生被鼓勵提出具有高差異度和獨特性的答案時，許多學生展現了出色的結合式創造思考能力，提出了遠超預期的創新解答。研究透過K-means群集分析將學生依各數學過程分群，還發現，研究結果顯示，不論是整體學生或分群學生，男女性別對各數學過程中學生學生的整體創造思考表現以及高低數學創造性思考群集上並皆無顯著影響差異。This study, based on the three processes of formulate employ, and interpret from PISA mathematical problem-solving, designs tasks to explore the mathematical creative thinking performance of Taiwanese junior high school students in the context of symbols and their operations. The study employs both purposive and convenient sampling, selecting two moderately performing junior high schools each from northern and southern Taiwan. From 32 eighth-grade classes, 210 students were randomly selected to participate. The research uses a questionnaire survey method and evaluates students' creative thinking from two perspectives: the characteristics of students' answers and three indicators of creative thinking—fluency, flexibility, and originality. The task design differs from traditional creative thinking research in two major ways: the tasks are competence-oriented and provide a solution space that allows for infinite answers to stimulate students' creative thinking. The results show that when the task design emphasizes stimulating students' creative thinking, most students can propose multiple appropriate answers. Particularly in the formation process tasks, over 80% of students were able to propose three different appropriate answers. However, when tasks limited the use of specific, more challenging mathematical objects, students' performance was significantly constrained. In any mathematical process, students' creative thinking performance decreased in the order of fluency, flexibility, and originality. For fluency, there was little difference in students' performance across the various mathematical processes. For flexibility, students performed best in the interpretation process, and for originality, students performed best in the formation process. Additionally, in the interpretation process, although most students could provide two acceptable answers, the proportion of students who created a third answer significantly decreased, indicating that this process might be more challenging for students' creative thinking.

Another important finding is that when students are encouraged to propose highly diverse and unique answers, many students exhibited outstanding combinatory creative thinking abilities, presenting innovative solutions beyond expectations. Using K-means cluster analysis to group students by each mathematical process, the results show that, regardless of the overall or clustered students, there were no significant gender differences in students' creative thinking performancein any mathematical process.