Mathematics textbooks are regarded as important components of mathematics intended curriculum in each country. However, how much a teacher uses them in their classroom varies from countries to countries. In China, the problems presented in textbooks usually can't meet the needs of teachers’ teaching practice, and teachers need to look for more problems from other resources for use. Therefore, this survey compares the difficulty levels of the problems presented in mathematics textbooks and those used in mathematics classrooms in secondary schools, in order to provide some advice on the development of our mathematics textbooks. This paper mainly focuses on the analysis of difficulty between problems in the chapter of “Pythagoras Theorem" presented in mathematics textbooks and those used in classrooms in a secondary school in China. We observe three teachers classrooms and record problems they use in their teaching. Firstly, we compare the number of problems and the number of worked examples presented in mathematics textbooks and those used in classroom practice of the three teachers. It is found that the number of the problems used in classroom practice is as 3~5 times as those presented in mathematics textbooks, and nearly half of the worked examples used in classrooms are from materials other than textbooks. Secondly, we make a comparative analysis of difficulty levels between problems presented in textbooks and those used in classroom practice using a difficulty model which developed by Bao JianSheng (2002) includes five aspects(i.e. Inquisition, Background, Calculation, Reasoning, Knowledge). The result shows that the problems used in classroom are more difficult than those presented in textbooks in all the five aspects, and especially place a great emphasis on “Two basics". Thirdly, based on students’ response to problems, we further analyze the features of difficulty levels of the problems used in a lesson both from a theoretical and empirical perspective. The problems used in classroom teaching are elaborately arranged by teachers, and they're presented from the easiest to the most difficult. However, the problems for homework are from other reference books, and they are not presented strictly in such an order. Finally, we survey the three teachers individually about how they select problems during lesson plan period, the frequencies they select problems from different materials, how they use problems presented in textbooks, and why they do so. The teachers survey reveal that textbook and reference books are two most frequent resources they select problem from, but they usually deal with the problems in class and don't use them for homework. There are no new problems presented in Teachers' Guide so it contributes little to the selection of problems. In addition, from a discussion about the ongoing mathematics education reform in China, we put forward some advice on the development of mathematics textbook. Key words: mathematics textbooks; classroom teaching; mathematics problems; difficulty levels; secondary mathematics; Pythagoras Theorem

數學教科書是各國數學期望課程的一個重要體現，但是，各國數學老師實際教學中對教科書依賴程度不盡相同。在我國，教科書包含的問題通常不能滿足實際教學需要，教師需要從教科書以外的材料中尋找可以用作教學的問題。因此，本研究對我國數學教科書中包含的問題和教師教學使用問題的難度進行比較分析，旨在為改進我國數學教科書編寫帶來一定啓示。 本論文主要對初中數學教科書中“畢氏定理”這一單元呈現的問題與該單元教學時老師實際使用問題的難度特徵進行了研究。我們以三位不同教齡的老師作爲調查對象，搜集了他們在教學該單元時實際使用的問題。 首先，我們對教科書中這一單元的問題和實際教學中使用的所有問題、例題的數量進行了比較分析，結果顯示，三位老師實際教學中使用的問題是教科書問題數量3~5倍，教學中重要的例题也有近1/2來自教科潜以外的其它材料。 其次，我們利用鮑建生(2002)建立的由“探究、背景、運算、推理、知識含量”五個難度因素構成的綜合難度模型，對教科書中這一單元呈現的問題和實際教學中使用的問題(主要是補充問題)難度進行了比較分析，結果顯示，老師實際教學使用問題(主要是補充習題)在五個難度因素上的水平均大於教科書問題，並且明顯的強化了對“雙基”的要求。在量化分析的基礎上。我們進一步以教師一課時使用的問題為例，結合學生對問題的作答情況，分別從理論和實際兩個維度對實際教學使用問題的難度特徵進行了質性分析，研究顯示，老師在課堂教學中使用的問題是經過老師精心設計的，基本按照由易到難的順序呈現;而課後作業題來自一些現成教輔材料，沒有嚴格的按照這個順序呈現。 最後，我們對老師在備課時如何選擇問題、從不同來源中選擇問題的頻率、 如何使用教科書中的問題以及他們這樣選擇教學問題的原因進行了調查，結果顯示，同步教輔材料是教師選擇各類教學問題最為頻繁的來源，老師往往會在課堂中就處理完教科書中的問題，與教科書配套的教師用書沒有提供新的問题，因而對老師選擇教學問題的參考意義不大。 最後，本文結合當今數學課程改革的實施情況，對我國數學教科書的編寫提出了一些建議。 關鍵字:數學教科書；課堂教學；問題；難度；初中；畢氏定理