科技大學學生數學解題表現與數學社會觀之探究與分析

An Investigation and Analysis of Technological University Students’Mathematical Problem-Solving Performance and Their Views on Mathematics and Society

本研究旨在探究108課綱實施之前科技大學學生的數學解題表現與數學社會觀之關聯。研究工具包含「情境數學評量試題」（Context-Based Assessment-Mathematics [CBA-M]）和「數學與社會觀點問卷」（View on Mathematics and Society [VOMAS]）。其中，CBA-M著重情境式數學問題以評估學生之演算、抽象化、推理、連結與解題能力；VOMAS則從數學本質觀、知識建構觀、數學與生活觀及數學與教育觀四面向分析學生觀點。研究重點在於描繪三所科技大學學生數學解題表現和數學社會觀樣貌，並檢視不同數學解題表現的群組在數學社會觀方面的異同。研究結果顯示，在數學解題表現方面，學生在具固定程序的題目表現相對較佳，但在需建模或非標準解題情境普遍表現偏弱。在數學社會觀方面，不同數學表現的群組在部分數學社會觀的面向上呈現差異，尤其在教育觀方面。學生的數學解題表現與科系專業和他們的數學社會觀有相當程度的關聯。雖不是線性關係，但大致上數學解題表現越好的學生有高比例認為數學是「一種解決科學問題的工具」，主修電資工程的學生越能認識到數學在學校與社會的價值。主修商管學生有高比例認為「不須多讀數學」。本研究結果可作為大學數學素養導向課程設計與批判式數學教育推動之參考，並補充高等教育相關實證研究之不足。

This study investigates the relationship between technological university students’mathematical problem-solving performance and their views on mathematics and society prior to the implementation of Taiwan’s 2019 Curriculum Guidelines. Two research instruments were developed: the Context-Based Assessment in Mathematics (CBA-M) and the Views on Mathematics and Society questionnaire (VOMAS). The CBA-M employs contextualized mathematical tasks to assess students’abilities in computation, abstraction, reasoning, connection, and problem solving. The VOMAS examines students’perspectives across four dimensions: the nature of mathematics, knowledge construction, mathematics and daily life, and mathematics and education. This study aims to characterize both students’mathematical problem-solving performance and their views on mathematics and society, and to explore differences in these views among groups with varying levels of problem-solving performance. The participants were drawn from three technological universities. The results indicate that students performed relatively well on problems involving fixed procedures but showed weaker performance on modeling tasks and non-routine problem-solving situations. Regarding their views on mathematics and society, students with different levels of mathematical performance differed across several dimensions, particularly in educational perspectives. Mathematical problem-solving performance was closely associated with students’academic majors as well as their views on mathematics and society. Although the relationship was not strictly linear, students with higher levels of problem-solving performance were more likely to view mathematics as“a tool for solving scientific problems.”Students majoring in electrical engineering and computer science were more likely to recognize the value of mathematics both in academic contexts and in society. In contrast, a relatively high proportion of business and management majors believed that“there is no need to study much mathematics.”The findings may serve as a reference for the design of mathematics literacy-oriented curricula in higher education and for the promotion of critical mathematics education. This study also contributes empirical evidence to the relatively limited body of research in Taiwan’s higher education context.