高低年級數學臆測教學的規範之比較

本研究之目的主要探討高年級與低年級的臆測教學的規範之比較，研究者目的是在臆測教學課室下，探討國小高年級與低年級建立的臆測教學的規範在內容、建立策略、建立時機與建立者上面有何異同。臆測教學包含了五個階段: 造例、提出猜想、效化、一般化和證明五個階段，而本研究主要觀察臆測教學的前三階段。本研究採用個案研究法，以班級教師為研究對象，需要進入到班級觀察臆測教學的過程，為了避免研究者主觀推論，因此使用錄音、錄影及觀察筆記的方式記錄研究對象在課堂上課、討論的情形，分析蒐集的資料，探究現象發生的原因及所蘊含的意義。研究者將關注數學臆測活動進行時，不同教師臆測教學的規範有何不同，透過分析教師與學生間的對話內容探討兩位教師在提升論證能力之臆測教學的規範間的差異性，研究架構依據林碧珍(2019)的數學臆測與數學論證關係圖為基礎加以修改來探討規範的內容、策略、時機、建立者四個層面。初步研究結果發現：（1）造例階段時，低年級常為師生以意義式在偶發時建立規範；高年級常為師生以討論式在初始時建立規範（2）提出猜想階段時，低年級常為教師以告知式在偶發時建立規範；高年級常為教師以告知式在初始時建立規範（3）效化階段時，低年級常為教師以告知式在偶發時建立規範；高年級常為師生以告知式在偶發時建立規範。

關鍵字

數學臆測；臆測教學的規範

並列摘要

The purpose of this research is to explore the comparison of the norms in conjecturing teaching between the higher and lower grades. The researcher's purpose is to discuss what is the difference between the higher and lower grades of elementary schools in establish strategies, and the establishment time and the creator.Conjecture teaching includes five stages: making an example, proposing a conjecture, effectiveness, generalization, and proof. This research mainly observes the first three stages of conjecture teaching. This research adopts a case study method, with class teachers as the research object. It is necessary to enter the process of class observation and conjecture teaching. In order to avoid subjective inferences by researchers, recordings, recordings, and observation notes are used to record the facts of the research in class and discussion, and to analyze the collected data to discuss the reasons and significance of the phenomenon. The researchers will pay attention to the differences in the norms in conjecturing teaching of different teachers when the mathematics conjecturing activities are carried out. By analyzing the content of the dialogue between teachers and students, they will discuss the differences between the two teachers' norms in conjecturing teaching to enhance the demonstration ability. The research framework is based on Lin (2019) mathematical conjecture and mathematical argumentation diagram was modified based on the four levels of the content, strategy, timing, and creator of the specification. The finding of the study indicates that (1) At the stage of making a case, teachers and students in the lower grades often set up norms in a meaningful way at the occasional occasion; in the higher grades, they often set up norms at the initial stage for teachers and students in a discussion style. (2) At the stage of conjecturing, In the lower grades, teachers often use the informative style to establish norms when occasional; the higher grades often use the informative style to establish norms at the beginning (3) In the stage of effectiveness, the lower grades often use the informative style to establish norms when occasional; the higher grades often establish norms for teachers and students in an informative manner when occasionally.