手持式图形计算技术的新发展不仅继承了原有图形计算技术强大的代数运算、函数绘图、程序编制等功能，更在屏幕显示、界面导航、操作方式、功能应用以及学习支持服务五个方面的性能上有了整体的提升，极大地增强和扩展了手持式图形计算技术在我国数学教育中的适用性和应用性。数学教学的核心任务是培养学习者的数学思维，数学高阶思维作为较高层次的数学思维已成目前数学教学改革的核心诉求，但由于常规课堂教学技术手段的落后，无法为学习者开展分析、评价、创新等数学高层次思维发展提供支持，因此，长期以来，数学高阶思维的培养目标很难在教学中落实。手持式图形计算技术的新发展使我们看到了解决数学教学中长期存在的初中学习者数学高阶思维培养缺失问题的契机。虽然手持式图形计算技术已进入我国数学教育领域十几年，但已有的研究更多关注在手持式图形计算技术本身。本研究立足于教育技术领域，从促进学习者数学高阶思维发展的视角系统地开展了手持式图形计算技术与数学教学整合的理论与实践研究，实现了数学思维发展、技术应用、数学教学三者的深度整合。具体包括以下三部分研究内容： （1）从数学教学的角度构建手持式图形计算技术促进初中生数学高阶思维发展的教学模型并对教学进行初步设计在大量文献研究的基础上，本文采用理论演绎和专家、教师访谈的方法提出了对数学高阶思维发展过程的认识框架，为在数学教学中开展对学习者数学高阶思维培养的教与学活动提供了指导。在相关思维发展理论、建构主义理论、分布式认知理论、信息技术与课程深层次整合理论的指导下，本文构建了“手持式图形计算技术环境下的以数学高阶思维发展为导向的数学问题探究式教学模型”，此“模型”以推动数学高阶思维活动过程作为目标导向、以手持式图形计算技术作为促进数学高阶思维发展的认知工具、以数学问题探究式教学作为数学高阶思维培养的载体、以思维发展共同体作为个体学习者数学高阶思维发展的外界环境。在“模型”的指导下本文对“模型”所涵盖的四类教学进行了初步的设计，在教学理念和教学设计层面将数学高阶思维发展、手持式图形计算技术的应用以及初中数学进行了有机的整合。（2）从数学教学实践的角度考察教学理念和教学模型的的合理性、可行性和有效性教学模型最终需要数学教学实践的检验才会具有真实的理论价值。本文选择了4所具有手持式图形计算设备的实验学校，分别在4个初二年级开展了四类促进数学高阶思维发展的实践教学研究，为期1年半，具体分为前期培训准备阶段，中期教学适应阶段和后期正式实施阶段。在此过程中，主要运用行动研究法，研究者提出教学设计原型并与教师实施讨论，教师实施教学时研究者进行课堂观察，教学结束后开展师生访谈和调查等，并在课后运用口语报告法、测验法等获得研究数据。本文从每一类教学案例中选择一个有代表性的，根据课堂实录和访谈，从师生的课堂行为、技术行为以及所存在的问题三个角度对课堂教学的合理性和可行性进行了具体的分析。运用口语报告实验、测试、问卷等数据从学生的思维发展过程、思维发展结果、学习态度转变以及教师教学理念转变四个层面分析和验证了课堂教学的有效性。根据实践的过程和结果，本文进一步对教学理念及教学模型进行了修正，使其更具有合理性和可行性。（3）从应用策略的角度构建手持式图形计算技术促进初中生数学高阶思维发展的策略体系恰当而富有智慧的手持式图形计算技术的教学应用策略是顺利开展课堂教学活动、高效发挥技术威力的关键因素，因此本文运用案例研究法和师生访谈法从所实施的7个典型案例教学中提炼出手持式图形计算技术的10条具体应用策略，并结合数学高阶思维发展的规律及技术的特色构建了手持式图形计算技术促进初中生数学高阶思维发展的策略体系。实践研究表明，本文所提出的教学理念和教学模型具有一定的合理性、可行性，手持式图形计算技术的运用对学生的数学高阶思维表现出有益的影响和促动，本研究实施的教学使学生的学习态度和教师的观念转变发生了积极的变化，说明了教学理念和教学模型指导下的教学实践在整体上是有效的。本文的创新点：第一，从促进学习者数学高阶思维发展的视角系统探讨了手持式图形计算技术与数学教学的整合，突破了以往的单纯以技术出发的研究视角，以一种更系统、更深入的研究视角将信息技术的优势与数学教学的变革统整于数学高阶思维发展这一核心目标下，实现了信息技术、数学教学和数学高阶思维发展的全面整合，体现了信息技术与数学课程整合的深层发展。第二，本文从思维发展过程的教学可操作化角度对数学高阶思维过程进行了阐释，已有的研究更多是从心理学上的数学思维过程，或数学思维结果以及形式的角度来认识，在很大程度上实现了数学高阶思维在数学教学中的可操作性，本文进而以此为目标导向创新性的构建了一套利用手持式图形计算技术促进学习者数学高阶思维发展的数学教学理念体系——手持式图形计算技术环境下的以数学高阶思维发展为导向的数学问题探究式教学模型，既充分整合了数学思维理论、建构主义理论、信息技术与课程整合理论以及分布式认知理论的先进思想，又丰富和发展了相关指导理论的内涵。第三，通过创新性的教学实践研究，本文系统地、明确地提炼出了教学实践中手持式图形计算技术对数学高阶思维发展的促进作用以及应用方式，并在此基础上进行了理论提升，以数学高阶思维发展为主线提出了一套利用手持式图形计算技术促进初中生数学高阶思维发展的策略体系，将手持式图形计算技术的优势与学习者数学高阶思维的发展两者进行了系统而明确的结合，为教师开展手持式图形计算技术环境下的教学实践提供更系统的、操作性更强的方法指引。

Development of Handheld Graphing Calculating Technology (HGCT) succeed the intrinsic function of algebraic calculus, function plotter and programming of intrinsic Graphing Calculating Technology, and promote comprehensively the performance of screen display, user interface, operating mode, function application and learning support service, which strengthen and broaden its application in Chinese Mathematics Education. The new proficiency brought by the development of HGCT give us the chance to make up for the training omission of Higher Order Thinking Skills (HOTS) in Mathematics Education for students in junior high school. Though the application of HGCT has been carried out in Chinese Mathematics Education for more than ten years, little research has been done on the integration between HGCT and Mathematics Education from angle of view of essence of Mathematics Education. All existing research focused on HGCT itself. Herein, this research start out from view of the integration of the develop of mathematical thinking, application of HGCT and Mathematics Education, cut in from the training of HOTS, comprehensively study the theory and practice for integration of HGCT and Mathematics Education for students in junior high school.（1）Build the teaching theory and teaching pattern of promoting the develop of mathematics HOTS for students in junior high school. Based upon plenty of literature review, we construct the general framework of mathematics HOTS, and analyze possible promoting effect of the new development and potential application of HGCT for the integration of HGCT and mathematics education. Thus we found the strategy to promote mathematics HOTS by HGCT, i.e dividing the general definition of mathematics HOTS into four periodic objectives related to mathematics contents and types of deep understanding, problem solving, innovative construction and rational evaluation. Then based upon the constructivism and distributed cognition theory, we proposed the teaching theory and teaching pattern of promoting the development of mathematics HOTS for students in junior high school, integrated the develop of mathematical HOTS, application of HGCT and Mathematics Education in junior high school.（2）Investigate the reasonability, feasibility and validity of the teaching theory and teaching pattern from the view of mathematics education practice. New teaching theory and teaching pattern should be proved effective by mathematics education practice. We select five experimental schools with handheld graphing calculating devices, and carried on teaching research for promoting the development of mathematics HOTS in second-year junior high school students for half past one year, which including the period of preliminary training work, medium-term adaptive phase and late stage of formal implementation. Action research method was adopted to carry out the research. The researcher proposed the original teaching theory and teaching pattern and discussed with teachers, did classroom observation when teachers implement teaching process, and collected research data by verbal protocol method, measurement method after class. We selected a representative teaching case from every type, and analyzed in detail the reasonability and feasibility of classroom teaching from classroom behavior, technical behavior of teachers and students and existent problems based upon classroom record and interview. And we analyzed and checked the validity of classroom teaching from the process and results of thinking development, change of learning attitude for students and teaching concept for teachers, using verbal protocol method, measurement method and questionnaire. We further rectified the teaching theory and teaching pattern to more reasonable and feasible based upon the practice process and results.（3）Construct the strategy of promoting the development of mathematics HOTA for students in junior high school by HGCT from the view of application. Suitable and intelligent application strategy is the key issue to carry out instructional activity in classroom by fulfilling the potential of HGCT. We constructed strategy of promoting the development of mathematics HOTS for students in junior high school by HGCT, and refined detailed application strategy combined with development law of mathematics HOTS and advantages of HGCT from seven teaching cases using case study. In connection with the reasonability and comprehensiveness of the strategy, we interviewed in-depth five teachers by interviewing method, and improved correspondingly.Innovation of this research:（1）Innovation of research perspective. This research start out from view of the integration of information technology, Mathematics Education and develop of mathematical thinking, , cut in from the training of HOTS, comprehensively study the integration of HGCT and Mathematics Education for students in junior high school. First this research angle breakthrough the view of pure HGCT, pure mathematical or pure thinking, unify the application of information technology and reformation of Mathematics Education to the develop of mathematical thinking, which benefit to the integration. Second, Higher Order Thinking Skills (HOTS) in Mathematics Education is a new concept proposed in this thesis, which distinguish and criticize from the lower level and one sidedness in traditional Mathematics Education, and provide direction for the deep integration of information technology with Mathematics Education, boosting to a higher and in-depth level of platform. （2）Innovation of theory perspective: This research proposed the teaching theory and teaching pattern of promoting the develop of mathematical HOTS by HGCT with the guidance of related thinking theory, constructivism theory, distributed cognition theory and theory for information technology and curriculum integration, combing with development law of mathematics HOTS and advantages of HGCT. This result for theory synthesized related thinking theories and proposed innovative knowledge about mathematical thinking stages from view of Mathematics Education, enriching mathematical thinking theory. The value of promoting the develop of mathematics HOTS by HGCT enriched the intension of cognitive tools, embodying the development in distributed cognition theory. This research probes into the integration of HGCT with mathematics teaching from view of mathematics HOTS, elevates the theoretical level of information technology and curriculum integration, enriches the intension of theory for information technology and curriculum integration in mathematics.（3）Innovation of practice perspective: This research put the innovative proposed teaching theory and teaching pattern into teaching practices, promoted the innovation of mathematics teaching practices by changing teaching concept for teachers, learning attitude for students and new technical methods, and refined the practice results into the strategy of promoting the development of mathematics HOTS for students in junior high school by HGCT, which provides systemic and targeted method for teaching practice using HGCT by following teachers.