初探運用ChatGPT建置國中會考數學解題家教

Abstract

本研究以108課綱國中教育會考數學科試題為例，設計能引導學生解題之人工智慧。希望能幫助學生進行課後的自主學習，能在無需教師介入的情況下，完成對試題的練習，經由與人工智慧的對談，加強其對於解題所用到之數學概念的理解。本研究以Polya的解題歷程四部分做為人工智慧進行解題引導的解題架構，並以蘇格拉底詰問法進行對學生的引導對談。為建置此人工智慧，本研究分兩部分，第一部分為探討人工智慧在108課綱國中教育會考數學科試題之解題表現與錯誤類型，第二部分為探討如何建置108課綱國中教育會考數學科解題家教。主要研究結果如下：ㄧ、在未經訓練之情況下，GPTs的國中教育會考數學科成績平均分數為56分，其中各年的得分所對應之等級標示為B或B+。二、GPTs在學生答對率較高、數與量主題類別、代數主題類別、無附圖且與圖形無關等類型之題目能有較高的答對率。三、GPTs在學生答對率較低、空間幾何主題類別、有附圖之圖形問題等類型之題目有較低的答對率。此發現與過往研究指出AI在視覺與空間推理上的限制相符。四、經過訓練後，GPTs能進行解題引導，但仍存在不穩定性，尤其是面對其答對率較低的題目時，較有可能出現錯誤。

This study uses the mathematics questions from the Comprehensive Assessment Program for Junior High School Students under the 108 Curriculum Guidelines as examples to design an AI that can guide students in problem-solving. This study uses Polya’s four-step problem-solving framework and applies the Socratic method for AI-guided problem solving, and utilizes it to conduct guided dialogue with students. To develop this AI tutor, the research is divided into two parts. The first part explores the performance and error types of AI on the Comprehensive Assessment Program for Junior High School Students math questions under the 108 Curriculum. The second part investigates how to build an AI-based math tutor for these questions.1. The mean score of GPTs without prior training on the Junior High School Mathematics Comprehensive Assessment Program was 56 points, with a performance level corresponding to a B or B+ grade in the different years.2. GPTs showed greater accuracy on questions with higher student success rates, questions related to magnitude and algebra, and questions without diagrams and unrelated to geometric figures.3. GPTs showed lower accuracy on questions with lower student success rates, spatial geometry questions, and questions involving diagrams. This is consistent with previous research showing the limits of artificial intelligence in visual and spatial reasoning.4. After the training, GPTs was able to guide the students to solve the problems; however, there was still some instability, especially in the face of questions with low accuracy rates, and its was still prone to errors, especially when dealing with questions on which its accuracy was low.