國小二年級學童數學加減法文字題錯誤分析

Error Analysis of Addition and Subtraction Word Problems for Second-Grade Students

研究目的
本研究目的為分析國小二年級學童的加減法文字題錯誤情形，包括解題錯誤與教材題型占比及解題歷程的關連，並探究部分原因。
研究設計／方法／取徑
首先統計國小二年級數學教材（南一版）的加減法文字題，在課本中有61題，課後練習（習作、隨堂演練及兩次期中評量）有143題。再以臺北市某公立國小二年級18位課後照顧班學童為對象，每週二次收集其課後練習（習作、隨堂演練及兩次期中評量）的解題表現。全學年共收集342題解題錯誤案例，並計算各題型之錯誤率。以內容分析及半結構訪談部分學童，分析其解題歷程錯誤類型。
研究發現或結論
課後練習的平均錯誤率為13.3%，其中單步驟題平均錯誤率為11.8%（0-50.0%），兩步驟題平均錯誤率為19.8%（0-29.6%）。從教材題型占比來看，單步驟題中占比高的題型多為基礎題型（改變類與合併類），錯誤率較低；占比低的題型答題時受到語意結構影響，錯誤率較分散。兩步驟題的各類題型占比均低（0-6.6%），與錯誤率無明顯關連。從解題歷程來看，題意理解錯誤在單步驟題占31.3%，兩步驟題占36.5%，可能原因包括逆推困難、關鍵字解題、題意複雜與多餘訊息。計算執行錯誤在單步驟題占68.7%，兩步驟題占63.5%，可能原因包括進位、借位錯誤、位值概念錯誤、大數減小數、運算錯誤、寫錯或漏寫數字等。
研究原創性／價值
本研究提供更具生態效度之解題錯誤資料，能真實反應學童於教材各類題型的課堂學習成果，並回答教材題型占比與錯誤率之關係。
教育政策建議與應用
教師可透過各類表徵或提問以促進學童理解題意，並要求正確書寫與直式計算以減少計算執行錯誤。教材應盡量呈現各類題型並提供適當練習題數。

Research Purpose
This study aimed to analyze errors made by second-grade elementary school children in solving addition and subtraction word problems. We also investigated the correlation between errors and the proportion of problems in textbooks, problem-solving processes, and underlying reasons.
Research Design/Method/Approach
First, we tallied 61 word problems from textbooks and 143 word problems from after-school math practices (including math assignments, in-class exercises, and two midterm assessments) by the Nan-I publisher. Then, 18 second-grade students from an after-school care class at a public elementary school in Taipei City were recruited twice a week for after-school math practice. A total of 342 word problem errors were collected throughout the school year, and the error rates for each problem type were calculated. Content analyses of error problems were conducted and semi-structured interviews were held with selected participants to analyze the types of errors in their problem-solving processes.
Research Findings or Conclusions
The average error rate of after-school math practices was 13.3%, with 11.8% for one-step problems (range 0-50.0%) and 19.8% for two-step problems (range 0-29.6%). Regarding the proportion of problem types in textbooks and after-school math practices, word problem types with a high proportion were mainly basic problem types (change and compare), which had lower error rates. Meanwhile, problem types with a low proportion had a more dispersed error rate, owing to semantic structure influences. The proportion of various types of two-step problems remained low (0-6.6%), and showed no correlation with the error rate. In terms of the problem-solving process, errors in the representational process accounted for 31.3% of single-step problems and 36.5% of two-step problems. These errors included difficulties in making reversible inferences regarding the part-whole operation, using keyword strategies to solve problems when experiencing difficulty in semantic translation, grappling with the complexity of more extended two-step problems, and dealing with extraneous information from problem sets. Errors in the solution process accounted for 68.7% of one-step problems and 63.5% of two-step problems, which could be attributed to errors in carrying, borrowing, place value concepts, subtracting the smaller from larger number, miscalculation, incorrect copied numbers, or number omission.
Research Originality/Value
This study provides greater ecological validity of problem-solving error data, which can genuinely reflect students’learning outcomes on various types of problems in textbooks and shed light on the connections between the percentage of problems in textbooks and error rates.
Educational Policy Recommendations and Applications
to help students understand the problem statements. Encouraging accurate written expressions and vertical calculations can minimize calculation errors. Providing textbooks with diverse problem types and sufficient practice exercises can support effective learning.