張文華Wen-Hua Chang林原充Yuan-Chung Lin2019-09-052014-6-262019-09-052014http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22GN060045008S%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/104620我國九年一貫課程數學科能力指標關於統計圖表的教學主要是長條圖、折線圖與圓形圖三種圖形，然而國際上的大型數學測驗題目，例如The Programme for International Student Assessment國際學生能力評量計劃，卻包含了不少橫軸與縱軸皆是連續變數且資料變化率不斷在改變的統計圖試題，因此本研究的目的是要了解我國高職一年級學生在九年一貫課程統計圖試題的表現與PISA連續變數統計圖試題之表現之關係，以及其在解PISA連續變數統計圖試題的解題歷程為何與錯誤類型。 本研究採用Pearson相關係數檢驗53名高職一年級學生在九年一貫課程統計圖試題與PISA連續變數統計圖試題兩項測驗之表現的相關性；對12名學生解PISA連續變數統計圖試題實施「放聲思考測驗」，將解題歷程分為「讀題、分析、探索、計畫-執行、驗證」五階段，並根據12位學生在筆試與放聲思考之原案等資料，比對專家解題歷程，以質性分析的方式探討高職一年級學生的解題歷程與錯誤類型。 研究結果發現高職一年級學生在我國九年一貫數學統計圖試題的表現與PISA數學科連續變數統計圖試題的表現有顯著中度正相關；而分析學生放聲思考解PISA連續變數統計圖試題的解題歷程發現： 1.學生閱讀題組情境與統計圖都不夠仔細，且讀題時不習慣在關鍵字做記 號。 2.學生花更多時間於分析階段來重新釐清題目條件與目標的關係。 3.大部分學生解這類題型時沒有經歷探索階段。 4.解答這類題型後學生都沒有做驗證動作。 5.大部分學生都能讀出統計圖的一個點的資料或一段曲線的增、減資料。 6.中成就學生比高成就學生容易粗心讀錯統計圖位置。 7.全部學生都不會使用斜率概念判斷統計圖曲線之資料變化率。 分析高職一年級學生解PISA連續變數統計圖試題發現學生的錯誤類型有： 1.無法理解題目文字敘述或誤解題意。 2.不懂或誤解題目之脈絡情境。 3.只聚焦題目敘述中的數字而忽略其它資訊。 4.粗心讀錯統計圖或粗心沒注意統計圖兩軸代表物。 5.無法將統計圖一段曲線讀成一筆連續資料。 6.無法看懂統計圖一段曲線之連續資料變化率。 7.無法將情境轉化為統計圖曲線之連續資料變化率。In Taiwan, the Grade 1-9 Curriculum for teaching Statistical charts mainly focuses on bar charts, line graphs and pie charts. However, most international mathematic assessments, such as the Programme for International Student Assessment, contain many continuous variable statistical charts, which relate to the horizontal and vertical axis. This research will discuss whether and why the problem-solving process relates to error type when trying to solve these PISA continuous variable statistical chart questions. This research uses Pearson’s correlation coefficient to examine the performance of 53 first-year vocational high school students within the grade 1-9 curriculum on questions related to PISA continuous variable statistical charts. It also looks at 12 students solving PISA continuous variable statistical chart questions and examines the process using the experimental think aloud protocol research method. This divides the process of problem solving into five steps：reading, analysis, exploration, and plan-implement and verification. Then, after the exam, it uses Qualitative Analysis to discuss the problem solving processes and error types of first-year vocational high school students. The research results show a moderate positive correlation in the performances of first-year vocational school students within the grade 1-9 curriculum on their PISA continuous variable statistical chart exam. Through the analysis of think-aloud data from the problem solving process of PISA continuous variable statistical chart, I found： 1.Students are not careful enough when marking the keywords and reading the chart when they were reading the question set context. 2.Students took longer to understand the relationship between question conditions and objectives. 3.Most students do not know how to solve these questions by the exploration method. 4.Students did not normally verify their results after solving the questions. 5.Most students are able to read statistical chart points and curve data showing increase and decrease. 6.The mid-level students make more mistakes than high-level students because of carelessness in solving questions. 7.Students do not know how to use the concept of slope when thinking about the rate of change of the statistical chart curve data. Error types in analysis by first-year vocational school students in PISA continuous variable statistical chart performances are： 1.Not understanding the description of the exam or misinterpreting the questions. 2.Misunderstanding the context of the questions 3.Only focusing on the numbers but ignoring other information in the questions. 4.Making mistakes while reading the statistic chart and not paying enough attention on the unit of the horizontal and vertical axis. 5.Not understanding the statistical chart curve as linear information. 6.Not understanding rate of change of the continuous data on the statistical chart. 7.Not changing context to the rate of change of continuous data on the statistical chart.高職一年級PISA連續變數統計圖解題歷程錯誤類型First-year Vocational High School studentsPISAcontinuous variable statistical chartproblem-solving processesError type