The main foci of the study are to understand how grade seven students solve the word problems of linear equations of one variable, and the respective errors and misconception. Also, the study investigated the possible causes of the errors and misconception. Qualitative and quantitative methods were used in the study. Researcher collected and categorized different types of errors and misconception, and outlined the distribution through descriptive statistics. Worksheet and quiz used in the study were constructed by several secondary school mathematics teachers. Based on these assessing tools, a screening test was designed. 75 students participated in this part of the study, their responses were analyzed. An interview test paper of several word problems were then constructed with items based on the errors and misconception, from problems with highest error rate and problems with most number of different errors, given by the students in the screening test. Nine students were selected to participate in this second part of the study. All of them were asked to report their verbal protocols when they worked on the test paper. Case study was done in this part. The study found that 47% of students committed several kinds of errors and misconception, mainly on three types of word problems: (1) distribution problems, (2) ratio problems, and (3) speed problems. In the screening test, there were seven types of errors and misconception found: (1) confusion on inverse relationship, (2) misinterpretation on the words, (3)miscomprehension on the problems, (4) unable to keep the “equal” relationship between the two sides of the equation, (5) confusion among similar concepts,(6) misuses of concepts, and (7) errors in formula application. In the interview test, there were four types of errors and misconception found: (1) unable to keep the “equal”relationship between the two sides of the equation,(2) unit confusion,(3) applying addition and subtraction for ratio calculation, and (4) measurement unit confusion. In general, word problems are quite difficult for students. To conclude from error rate, errors or misconception, the difficulties may be attributed to (1) students’ prior knowledge, (2) students’ problem schemes, and (3) students’ ability to comprehend the problems. Finally, researcher suggests that teachers could consider (1) students’organization of prior knowledge, (2) students' problem scheme establishment and problem category recognition, and (3) how to apply situation models for assistance when they teach word problems of linear equations of one variable.

本研究的主要目的是了解澳門初一學生在一元一次方程的應用題的解題情況和錯誤概念類型，以及探討初一學生在一元一次方程的應用題產生錯誤概念的原因。本研究利用質與量的研究方法。在量的研究方法上，研究員對澳門初一學生學習一元一次方程應用題的錯誒類型進行量化的統計，從而了解學生出現錯誤的分佈情況。爲了收集學生解應用題的錯誤類型，本研究經由幾名有經驗的數學老師編制此單元的工作紙及小測卷，通過工作紙和小測卷的作答分析，編制出一份篩選性測驗卷，向75 名學生進行施測，再通過此卷的作答分析學生的錯誤概念類型。在質的研究方法上，通過篩選性的測驗卷分析錯誤概念類型，從中找出錯誤率最高，又或者同一题目的解題的錯誤方法最多的題目，把這些類型的題目編制成一份面談測驗卷，再利用這份測驗卷向選定的九名學生作解題的放聲思考，然後進行原案分析，這樣可更深入了解學生學習一元一次方程的應用題時產生錯誤概念的原因。 硏究發現學生解答應用題的錯誤率頗高，約有47%學生在解題時犯上多種的錯誤，犯錯最多的題型是分配問題、比例問題和行程問題:在篩選性測驗出現很多不同的錯誤概念，主要分爲七種錯誤概念類型:1.關係的逆轉;2.錯誤理解文字的意思:3.誤解題意:4.方程左右兩邊沒有等量的關係;5.相近的概念知識混淆;6.錯誤知識概念的運用;7.錯誒公式的運用;在面談測驗中，找到四種錯誤概念類型:1.方程左右兩邊沒有等量的關係;2.物體的混淆:3.以加减法計算比值;4.長度單位混淆;總括來說，因爲應用題對學生來說是比較困難的單元，所以出現解題錯誤率高和錯誤的類型多的情況。無論從錯誤率、錯誤類型還是錯誤概念去探討，所得出導致這些問題的原因，都可歸納為學生先備知識不足、缺乏基模知識、沒法理解題目和沒有解題的參照方法。最後，研究員建議從「先備知識的整合和組織」「問題模型建立和問題類型的辨認」和「利用情境教學協助學生建立情境模型」這三個方面，去幫助學生學習一元一次方程的應用題。