實施以臆測爲中心的教學探討四年級學生臆測思維歷程與主動思考能力展現之行動研究

Action Research on Implementing Conjecturing-centered Instruction to Investigate Fourth Graders' Conjecturing Thinking Processes and Active Thinking Abilities

蕭淑惠(Shu-Hui Hsiao)

《數理學科教學知能》 第2冊 (2010/07) Pp. 68-80

https://doi.org/10.6614/pck.2010.2.68

摘要

本研究旨在發展以臆測活動爲中心的數學教學活動，實施於國小四年級數學課室中，除了分析教師教學和學生學習時所遭遇的難題之外，還要觀察學生數學臆測思維歷程和主動思考能力的展現情形。 研究設計是以行動研究法之「規畫」、「行動」、「觀察」和「反省」四個階段來進行研究，總共進行兩個循環，歷時三個月。研究對象爲彰化縣某國小四年級班級，全班24位學生採異質分組方式分成四大組，主要觀察學生有六位（3男3女）。在以臆測爲中心的數學解題活動主要經由「進入」、「攻擊」和「回顧」三個解題階段，引導學生提出一個一般化的規則、檢驗規則，並修正自己的想法，讓學生在不斷猜測、檢驗、相信或反駁的過程中逐步建構自己的數學概念。收集的研究資料包括：課室錄影、臆測思維歷程檢核表、主動思考能力觀察表、半結構性晤談、學生學習文件記錄、教學日誌和研究者反思紀錄。 研究結果發現，在以臆測爲中心的活動中有五種促發學生提出猜想的誘因；四年級學生臆測思維歷程包含觀察、提出猜想、檢驗和推廣等四大基本要素；不同學習表現的學生在基礎、整合和問題解決等不同思考層次中的表現不盡相同。據此獲致的研究結論如下：（一）生活化的故事情境能有效促發學生的主動思考；（二）教學者應針對課堂上不同參與程度的學生給予適當的支持；（三）教師善用提問技巧可幫助建立學生正向的數學學習態度；（四）透過臆測活動體認數學知識發展的歷程。

關鍵字

臆測 ； 臆測思維歷程 ； 主動思考能力

並列摘要

This dissertation aimed at developing the conjecturing-centered instruction activities and implementing them in a fourth grade classroom to investigate the pupils' conjecturing thinking processes and active thinking abilities. The research design was based on action research method which analyzing involved four steps: planning, acting, observing and reflecting. The study was conducted through two circles which lasted for three months. The research subjects were 24 four-grade pupils which were divided into four groups, while the main observed subjects were three boys and three girls. They carried on mathematical reasoning and resolving by means of ”entry step”, ”attack step” and ”review step” in the conjecturing-centered mathematical activities. The instructor led the pupils to pose a general rule, test that rule, and then revise a conjecture accordingly. The pupils constructed their conceptions gradually in the circle that consisted of posing a conjecture, testing it, believing it, or rejecting it. The collected data included videotapes, conjecturing thinking processes checklists, active thinking abilities observational notes, semi-structured interviews, students' learning files, instructional journals, and researcher's reflective records.
The results evinced several findings in the conjecturing-centered instruction. First, there were five factors that stimulated the pupils to bring up conjectures. Second, the fourth graders' conjecturing thinking processes consisted of observation, conjectures suggesting, verification and generalization. Third, the pupils that emerged different performance had different manifestations in basic thinking, reorganizing thinking and problem solving thinking. The conclusions were declared as follows: (1) real life related problems would stimulate active thinking effectively; (2) the instructor should supply different pupils with different assistances; (3) the instructor could help pupils build positive attitudes by using questions appropriately; (4) the pupils would experience the development of mathematical knowledge in the conjecturing-centered activities.

並列關鍵字

conjecturing ； conjecturing thinking processes ； active thinking abilities