海峡两岸高中教材函数习题比较研究
摘要
随着高中新课标的推进与实施，高中数学新教材投入使用后引起教育界的广泛关注。台湾于2018年开始正式实施十二年国民教育改革，统一编写了基础教育阶段的数学教材。习题作为数学教材的重要内容，是反映数学课程难度的重要指标。研究两地数学教材习题的比较有助于彼此取长补短，为今后数学课程改革和考试评价提供借鉴，又能对数学的教学改进提供一定的实践参考价值。
本文以翰林版与新人教版中指数函数与对数函数的习题作为研究对象，采用文献分析法、比较研究法、定性与定量的研究方法。从宏观上对两地课程标准及函数内容进行比较；从微观上对函数习题进行表层结构（数量、题型、呈现方式）和深层结构（习题层次性、核心素养、难度和例习题难度的一致性）的比较。研究结果显示：
第一，大陆《新课标》较台湾《纲要》在函数内容的要求方面更为详尽；大陆《新课标》在要求数学核心素养方面具有针对性，而台湾《纲要》则具全局性；在教材的章节编排和内容设置方面，两岸教材的设计方式不同。
第二，两岸高中函数习题的表层结构比较结果显示，在数学习题的题量、题型和呈现方式三个方面，两版教材习题表现出题量差异明显，题型侧重方面和呈现方式不一致的特点。
第三，在两岸高中函数习题的深层结构比较中，两版教材习题的层次性具有差异；在数学核心素养的表现上，翰林版习题侧重直观想象素养的培育，而新人教版习题更关注数学运算素养；在习题难度比较中，新人教版习题在“背景”和“知识综合”的难度因素上较翰林版低，在“数学认知”、“运算”和“推理”的难度因素上较翰林版高；在例习题难度一致性比较中，两版教材函数练习题均在“运算”、“推理”、“数学认知”、“知识综合”四个难度因素上高于例题。
班主任会议根据结论提出如下建议：丰富习题问题背景，融入现实生活元素；重视核心素养的落实，培育数学建模素养；适当增加知识点的宽度和广度，注重知识的联系性；合理设置例习题难度，重视知识之间的衔接；例习题设置应突出课程标准的要求，体现一致性。
关键词：中国大陆；中国台湾；函数习题；比较研究
A Comparative Study Of Function Exercis Of High School Textbooks On Both Sides Of The Taiwan Straits
Abstract
With the promotion and implementation of the new curriculum standard in nior high school, the new mathematics textbook in nior high school has aroud widespread concern in the educational
field after being put into u. Taiwan Province officially implemented the 12-year national education system in 2018 and uniformly compiled mathematics textbooks for the basic education stage. As an important content of mathematics textbook, exerci is an important index reflecting the difficulty of mathematics curriculum. The rearch on the exercis of mathematics textbooks in mainland and Taiwan Province can help each other learn from each other. It not only provides reference for the future mathematics curriculum reform and examination evaluation, but also provides some practical reference value for the improvement of mathematics teaching.
This paper takes the exercis of exponential function and logarithmic function in mathematics textbooks published by Hanlin Press and People's Education Press as the rearch object, and literature analysis, comparative rearch, qualitative and quantitative rearch methods are ud. It takes the broad view to compare curriculum standards and function contents between the mainland and Taiwan Province. The surface structure (quantity, type and prentation) and the deep structure (the level of exerci, key competencies, consistency between difficulty of exercis and difficulty of examples) of function exercis are compared from the micro level. The results are as follows:
Firstly, the new curriculum standard of mainland China is more detailed than the outline of Taiwan Province in terms of function content requirements. The new curriculum standard in mainland China
pays attention to training students' mathematics key competencies, while the outline in Taiwan Province has overall significance. In terms of chapter arrangement and content tting of teaching materials, the design of teaching materials on both sides of the Taiwan Straits are different.
Secondly, the results of the comparison of the surface structure of the high school function exercis on both sides of the strait show that the two editions of the textbook exercis show obvious differences in the number of questions, the focus of the question types and the inconsistency of the prentation methods in terms of the number, type and prentation of the
mathematics questions.
Thirdly, in the deep structure comparison of function exercis in high school textbooks on both sides of the Taiwan Straits, there are differences in the levels of exercis in the two editions of textbooks. In the expression of mathematics key competencies, the exercis in textbook of Hanlin version focus on the cultivation of intuitive imagination. And the exercis in textbook of the new PEP version pay more attention to mathematical operation. In the comparison of the difficulty of exercis, the difficulty factors of "background" and "knowledge synthesis" in the textbook of new PEP version are lower than tho in the textbook of Hanlin version. The difficulty factors of "mathem
atical cognition", "operation and reasoning" in the textbook of new PEP version are higher than tho in the textbook of Hanlin version. In the comparison of the consistency between the difficulty of examples and exercis, the four difficulty factors of "operation and reasoning", "mathematical cognition" and "knowledge synthesis" of exerci are higher than tho of examples on both sides of the Taiwan Straits.
According to the conclusion, the following suggestions are put forward：enriching the background of problem solving and integrating elements of real life into teaching; paying attention to the implementation of key competencies and cultivate mathematical modeling competencie; properly increasing the width and breadth of knowledge points, and paying attention to the connection of knowledge; reasonably tting the difficulty of example and exercis and attaching importance to the connection between knowledge; the tting of examples and exercis should highlight the requirements of curriculum standards and reflect consistency.
上蔡中学
Keywords: Mainland China;TaiwanProvince; Function exercis; Comparative rearch
目录
隘的读音第1章绪论 (1)
1.1问题提出 (1)
1.2研究意义 (2)
第2章概念界定与相关研究 (4)
2.1概念界定 (4)
2.1.1数学函数 (4)
2.1.2习题难度 (4)
2.2相关研究 (5)
2.2.1关于函数习题比较的相关研究 (5)
2.2.2关于数学习题难度的相关研究 (7)
2.2.3文献评述 (10)
第3章研究设计 (11)
3.1研究目的 (11)
3.2研究对象 (11)
3.3研究方法 (11)
3.3.1文献研究法 (11)
3.3.2比较研究法 (12)
3.3.3定性与定量研究法 (12)
3.4研究工具 (12)
3.4.1数学习题核心素养测评工具 (12)
点球大赛3.4.2数学习题难度测评工具 (13)
翩字组词3.5研究过程 (18)
第4章两地课程标准及函数内容的比较 (19)
4.1两版课程标准的相应要求比较 (19)
4.1.1两版课程标准函数部分相应要求比较 (19)
皮卡丘的简笔画4.1.2两版课程标准核心素养的相应比较 (20)
4.2两版教材“指数函数与对数函数”内容比较 (21)
4.2.1章节安排的比较 (21)
4.2.2内容设置的比较 (23)
4.3小结 (24)
第5章两地高中函数习题的比较研究 (26)
5.1两地高中函数习题表层结构的比较 (26)
5.1.1两地高中函数习题数量的比较 (26)
5.1.2两地高中函数习题题型的比较 (27)
5.1.3两地高中函数习题呈现方式的比较 (31)
5.2小结 (32)
5.3两地高中函数习题深层结构的比较 (33)
5.3.1两地高中函数习题层次性的比较 (33)
乾乾意思是什么
5.3.2两地高中函数习题核心素养的比较 (35)
5.3.3两地高中函数习题难度的比较 (39)
5.3.4两地高中函数例习题难度一致性的比较 (46)
5.4小结 (57)
第6章结论与建议 (58)
6.1主要结论 (58)
6.1.1 两地课程标准与函数内容的比较分析结论 (58)
6.1.2两地高中函数习题的比较分析结论 (58)
6.2思考与建议 (59)
6.3不足与展望 (61)
促销策略
致谢 (62)
参考文献 (63)
