| 摘要: | 本研究目的為分析德國2003年出版的Lambacher Schweizer Mathematik（LSM）教科書。在量化分析方面，利用統計認知分析表、圖表理解分析表將教學例題予以歸類，瞭解德國統計教育著重或涵蓋哪些認知內容。在質性分析方面，瞭解統計相關單元的知識內容、教學活動、題目佈題方式與情境，以獲得德國統計課程編排脈絡的統整了解。
根據量化分析結果，在統計認知的各層次中，德國LSM教科書於統計知識佔比最多，而統計推論、統計思考兩層次共佔比3成以上，且各子類目皆佔有一定的題數。在圖表理解的各層次中，解讀、繪製圖表相關能力佔較高的比例，但識別以何種圖像表達數據與批判反思能力仍佔2成以上。另外，質性分析結果顯示，德國LSM統計課程的教學脈絡為六年級學習建構與報讀圖表，七年級分析圖表上的數據；六年級須畫出指定的統計圖，七年級則須自行選擇符合呈現數據特性的統計圖。本研究亦針對題目的內容分析，將教科書中例題分為數學內容、跨領域思維、統計素養相關題型。
為將德國LMS教科書的統計課程與臺灣教科書進行比較，本研究引用李健恆與楊凱琳對臺灣國中教科書之內容分析結果（2012）。比對結果顯示，雖然德國的統計課程學習年齡於11至12歲，較早於臺灣的14歲，但是德國於統計認知各層次中皆有一定比例的題目量，而且有與機率、速率與百分比等數學主題或跨領域學科建立統整性連結。
相對而言，國內教科書的統計主題相關內容，大多著重於基本統計知識的了解、公式套用與簡易的統計量計算、圖表的繪製及直接讀取資訊中的數據。我國的教科書應增加屬統計推理與統計思考的教學內容，提高題目情境與生活週遭經驗的連結，以培育具備統計素養的學生。本研究之結果提供國內統計課程設計者參考，並期望對數學教科書中統計單元的設計與編輯有所助益。
;The purpose of this study is to analyze the statistics contents in Lambacher Schweizer Mathematik (LSM) textbook which was published in Germany in 2003. We classify the topics by using the statistical cognitive analysis table and the graph-chart comprehension analysis table. Therefore, we can use quantitative and qualitative analysis methods to understand what the Germany statistics education focus on. We also investigate how knowledge contents, teaching activities, problem-solving situations of the statistics related units are implemented to integrate the context of the German statistics curriculum.
According to the results of quantitative analysis, the LSM textbook accounts for the largest portion of statistical knowledge among all dimensions of statistical cognition. But the portions of statistical reasoning and statistical thinking still sum up to more than 30%, and each subcategory has a certain number of teaching examples. Among dimensions of graph-chart comprehension, the ability to interpret and graph-chart have higher portions, but of the graphical presentation and critical reflection abilities still account for more than 20%. In addition, the results of the qualitative analysis show that the teaching context of the German statistics curriculum is the construction and comprehension of graph-chart for the sixth grade study, the analysis of the graph-chart for the seventh grade; the statistical graph-chart are designated to the sixth graders, while the seventh graders must choose appropriate graph-charts which suit the purpose. For the content analysis of the topic, the examples in the textbook are categorized into mathematical content, cross discipline thinking, and statistical literacy related questions.
In order to compare textbooks between German and Taiwan on statistical cognition and graph-chart comprehension, we cite the work of Kin-Hang Lei and Kai-Lin Yang (2012). According to the results, although statistics is taught earlier in German (11 and 12 years old) than in Taiwan (14 years old), the proportion of statistical knowledge in the statistical cognition dimension is still higher in Germany. Furthermore, the teaching examples of LSM textbook establish integrated links with mathematical topics such as rate and percentage or cross disciplinary subjects.
On statistics content and statistical topics, most Taiwanese textbooks focus on the understanding of basic statistical knowledge, formula application, simple statistical calculation, graph-chart drawing and direct reading of information in the statistic chart. Therefore the study recommends that textbook editors increase the content of statistical reasoning and statistics thinking. In order to cultivate students with statistical literacy, we should often link problem situation with experience of life.
The results of this study also provide Taiwan statistics course designers as a reference. We also expect to contribute to the design and editing of statistics units in mathematics textbooks. |
