浅谈初中数学分层教学几种教学模式

　 初中数学分层教学的几种教学模式

　寿阳四中 常智斌

　 自古以来，便有提倡“因材施教”，宋代朱熹在《论语》的注解中指出：“孔子教人，各因其材。”我们在初中数学分层教学课题研究过程中进一步深刻认识到分层教学有利于调动每位学生的成长动力，有利于班级整体的和谐发展。另一方面，建构主义认为，学习者的知识不是通过教师讲授得到的，而是学习者在一定的社会文化情境下，以自己的背景经验和知识结构为基础，主动地探索、发现、总结、实践的反复过程，是自己建构知识的过程。依据上述观点，我们在反复实践中构建了以下两种初中数学分层教学模式：

　 一、新授课分层教学模式：

　 教学流程：情景引入，导学展示 分层练习，合作互助

　 分层检测，反馈小结

　 1.情景引入，导学展示

　 “导学”即引导学生思考、探究预设的问题或自学课本例题。“展示”可以是口头回答提问、小组内讲解或作业本、黑板上书面表达。通过问题情景引入新课后，让学生独立思考、自主学习，按老师指导的方式展示,教师引导学生对展示过程中暴露的问题进行必要的反思纠正，此环节以学生自主学习、展示讲解为主。

　 2.分层练习，合作互助

　 操作程序如下：

　 (1)分解学习目标，让学生先完成对应层次的习题，再选做其他习题；(2)多数同学完成后，让学生在小组内互相检查，有问题时共同分析矫正或请教老师。也可以抽部分同学在黑板上板书，再分析讲解；(3)自我纠错，小组成员互相复查，达到共同把关、合作共赢的目的。

　 教师把握时机，合理组织，及时调控。重点关注合作互助的落实情况和疑难问题的处理。教师也可以给出参考答案，让学生对照答案互相检查。对普遍存在的问题及时引导学生分析，或教师做必要的讲解(重点关注B层),以澄清认识误区，扫除学习中的障碍。

　 3.分层检测，反馈小结

　 以分层测试的方式完成课堂作业，以检查学生对于新的知识掌握的情况。教师在学生测试过程中就开始有针对性地批阅部分同学的作业，再组织小组内互批，查找问题，指导及时纠错、小结。课堂中没批改完成时课后由小组长组织批阅，并写出作业情况分析交老师审阅。（或者收齐作业本交老师继续批阅）。

　 此模式的主要特点：在教学过程中，始终以学生为中心，充分发挥学生学习的主动性,考虑到学生学习的差异，注重分层要求，分层指导,适合新授课的教学。

　 二、练习课分层教学模式：（以一次函数分层练习课为例）

　 教学流程：精编题组，先练后教 小结提升，当堂测试

　 分层批阅，纠错过关

　 教学关键：通过学生全面参与学习（分层次要求），达到每个学生在学习中有不同的发展。

　 1.精编题组，先练后教

　 操作程序如下：

　 (1)情景引入本节课学习内容、学习方式、要求，同时分发导学案或课件呈现练习题（提前设计好分层练习题,合理选择习题的呈现方式是前提）；(2)教师巡视,指导学生完成对应习题，有针对地指导C层和A层部分同学；(3)让学生在组内分层展示，C层同学先讲解，再B层，然后A层，有问题时集体纠正或互教。教师注意倾听学生的交流，对部分小组进行指导,收集共性问题；(4)抽部分学生在全班范围内分析讲解重难点问题，教师评判或补充讲解。

　 “先练”是高效、自主、独立学习，练习内容分层要求（C组:1～5.B组:5～6.A组：5～7.)，或者统一练习内容，但提出不同的层次要求。“后教”是学生分层讲解、互教或教师评判、点拨、补充讲解。教师的课堂辅导重点关注C层，面向全班的课堂讲解重点关注B组，通过兴趣小组的方式强化A层。

　 2.小结提升，当堂测试

　 操作程序如下：

　 (1)结合前面研究过的习题，梳理基础知识要点，归纳数学思想方法，构建知识体系，达到复习强化本章核心内容的目的。例如（以一次函数分层练习课为例）：师生小结强调以下几方面内容：① 一次函数有关概念；②一次函数图象；③一次函数的性质；④会用待定系数法确定一次函数解析式；⑤会用一次函数解决实际问题，能用函数观点看方程（组）与不等式。

　 (2)让学生以考试的方式先完成对应层次的必做习题，有时间再选做其它习题。（C组:1～5.B组:1～6.A组：4～7.)

　 (3)小组长按教师约定的要求收齐作业本。

　 “小结”可在小组内进行，也可面向全班进行，尽量先C、B层，后A层，先学生，后老师。按时交作业，培养学生的学习速度，提高效率，养成竞争意识和当堂完成作业的习惯。

　 3.分层批阅，纠错过关

　 操作程序如下：

　 (1)测试过程中教师批阅指导小组长（培养小老师，为学生的组内批阅准备）。(2)组织各小组在组内互批，指导及时督促纠错过关。(3)教师查阅学生作业情况，并做相应处理。

　 课堂中没批改完成时课后由小组长组织其它时间批阅，并督促纠错过关，并写出作业情况、纠错过关情况分析交老师审阅，或者收齐作业本交老师继续批阅、督促纠错。本环节可在课内进行，也延伸到课外。

　 此模式主要特点：在练习、小结、检测、批阅的过程中梳理基础知识，强化解题能力，达到反思提高的目的。分层次要求，成功调动学生的学习主动性和积极性。

　 总之，我们体会到以上两种教学模式切合教学实际，具有可操作性和实践价值。但我们应依据教学内容实际灵活选择教学模式，或在此基础上做适当的调整。另外，先对学生进行分组分层，备课时对教学内容、习题分层次设计，选择好教学内容（或习题）的呈现方式（学生现有资料、导学案、课件），这些都是我们成功实施分层教学的前提条件。

　Manufacturing transformation and development planning1 comprehensive strength of the manufacturing industry to upgradeRelying on good traffic conditions and location advantages of the industrial base, the manufacturing industry comprehensive strength steadily, the total size of the total, technical level, economic benefits and so on in the country has become the cornerstone of the precedent, the city's economic and social development and an important support. "12th Five-Year" period, the total industrial added value, the average annual growth rate of dada%, the amount of the total amount of investment of the city's industrial enterprises with an average annual growth rate%, above scale industrial enterprises realized a total profit of the average annual growth rate of%.xx years, the city's above scale industrial output mode billion yuan output value of over 80 billion yuan of industrial dada to 8, above scale industrial added value billion yuan, industrial growth. Added value accounted for GDDP%, the resident population per capita GDP reached million, ranked second in XXX Province, the national large and medium-sized cities in the forefront.2 continuous optimization of industrial structureThe benefit oriented, high end orientation and the direction of intensive development, gradually increase efforts to promote the transformation of industrial structure adjustment and optimization of industry has made remarkable achievements. As to XX, machinery, textile, petrochemical, metallurgy and electronics and other 55 pillar industries above scale industrial output value at current prices billion yuan, accounting for the proportion of for the high-tech industry output value accounted for%. The proportion of above scale industrial output value reached%, one percentage point increase over 2010. Sensor network innovation shows the construction of the demonstration zone to promote the smooth, emerging industry gradually expand the scale of production is expected to total output average growth rate, new energy, new materials, energy saving and environmental protection, Internet of things, the rapid development of microelectronics and other emerging industries, has become an important field of XX industrial transformation and upgrading.3 innovation capacity significantly improvedSeize the new round of the wave of technological innovation brings plenty of historical opportunity, in-depth implementation of innovation driven development strategy for the manufacturing industry's innovation and transformation and upgrading provides a strong intellectual support for the.Xx year, R & D expenditure accounting for the main business service income ratio reached%, among the province's first patent. The application amounted to 224197, the right amount of invention patents reached 5480, 000 people obviously patent has reached 25, are located in the forefront of the province of.Xx has a provincial engineering technology research centers heart 506, country, provincial high technology research key laboratory 10, International cooperation base, 9 national, provincial, foreign R & D center 41, provincial and international technology transfer center 8, selected "research research institutions" key enterprises XX 84. Tsinghua University, South, Fudan University, Harbin Institute of technology, Huazhong University of science and technology, Northeastern University and other colleges and universities have been set up in the XXX Research Institute.4 green manufacturing results significantly"XXX water crisis", energy saving and environment protection increasing pressure, vigorously promote the green, low-carbon, circular ring production mode, adhere to energy-saving emission reduction, the implementation of energy control, improve the energy source utilization rate of.Xx years, the city unit of GDP energy consumption decreased 20%, increase the added value of industrial energy consumption per ton standard coal / million. "" 12th Five-Year "period, the cumulative unit of GDPP energy consumption decreased percent, energy consumption consumption value XX lowest decline of XX south, South first. The elimination of backward production capacity can work orderly, shut down 8823 enterprises, 852 enterprises for rectification of family, eliminate backward production capacity of cement 75 million 770 thousand Tons, dyeing 244 million 600 thousand meters, 100 thousand tons of chemical fiber, Leather 3 million standard sheets, paper million tons, 2 million 280 thousand tons of steel, 106 battery Wanqianqian KVA, 200 thousand tons of steel casting, resolve the production capacity of 3 million 370 thousand tons, cement production capacity of 710 thousand tons, completed ahead of schedule into "12th Five-Year" planning objectives.5 enterprise vitality is increasingThe emergence of a number of key enterprises in the industry a lot of industries, some have developed into the world class level leading enterprises and leading enterprises. The key point of enterprises in technological innovation, product development, market development, has played an important leading role for.Xx and other aspects of social responsibility, listed 15 companies around the "top 500 enterprises Chinese" listed 221 companies "Chinese manufacturing enterprise 500 strong", all year for nine consecutive years, ranking first in the province. The city's domestic and foreign listed enterprises amounted to 94, ranked in the prefecture level city in the forefront. The integration of military and civilian combined to accelerate, the number of the city's participation in scientific research and production of weapons equipment industry the advantages of private enterprises Year after year, through the confidential qualification certification enterprises ranked 22 in the province.Two 6 integration steadily intoAs a national integration of the two test area, has been to two of the depth of financial integration and enhance the core competitiveness of enterprises as an important starting point, to accelerate the transformation of development mode. The information of all business to achieve the city's more than 80% large-scale enterprises, a total of at or above the provincial level demonstration pilot enterprises, 250 enterprises, including 22 national. Fusion demonstration of 4 enterprises, the provincial demonstration integration of the two test, Park 8. Baidu and Alibaba, Pakistan, Chinese manufacturing network, China network library and so on enterprises to carry out in-depth cooperation, support enterprises with the development of electronic commerce, there have been 4 enterprises selected for the national e-commerce service integrated innovation pilot .In a comprehensive summary of the "12th Five-Year" achievement at the same time, should also see some problems still exist in the development of XX manufacturing industry, difficulties and contradictions, need to be solved in the "Shisansanwu" period. The main is: not many major industrial projects, lack of a group with strong power, high output level large projects the industrial economic growth. Lack of weak industrial products to the intermediate product, the added value is not high. The emerging industry is small, difficult to support the city's economic growth. Science and technology innovation ability is not strong, high dependence on foreign technology, high level talent shortage. Excess capacity in some industries, some enterprise production and management difficulties. These difficulties all Urgent need to be addressed in the future development of the exhibition.1 from the global perspective, a new round of scientific and technological revolution and the rise of industrial change, to bring significant strategic opportunities for the transformation of the XXX industryThe development mode of the industry will undergo profound changes. When a new round of technological revolution in the application of the new generation of information technology integration as the core feature, "Internet plus" has become an important direction of industrial development. The high-end, smart, green, as the service has become a new trend of industrial development; the Internet network to break the constraints of time, the world famous enterprises and enterprises to achieve global collaborative design and production; intelligent manufacturing technology in the design, development, application, manufacturing and other aspects of the daily trend of generalization deepening; based on fusion, and services, new formats and new model into a platform for the new form of industry.The industrial division of labor and competition face remodeling. Europe and other developed countries to implement the "re industrialization strategy, trying to consolidate its leading position; emerging economies have focused on the implementation of catch-up strategy, competition to seize the high-end manufacturing areas to accelerate the end of a space for one person. To developed countries" reverse transfer, emerging countries rely on information the comparative advantage of labor resources, to attract international investment led shunt. Significant changes in Global trade investment system, the United States actively promote the TPP and TTIIP as the core of the trade and investment heavy order reconstruction, the future of China's foreign trade and absorbing the international direct investment is facing greater pressure.At present, the development of the XX industry development level in the nation, with the foundation and conditions follow a new round of revolution of science and technology revolution and industry industry, to seize the great opportunities in grasping the concept of development, innovation, production mode and format to change the strain, the first action, to create new competitive advantages of industry competition. At the same time. Despite the change of international trade and investment will lead to industrial growth slowed to put XXX of export-oriented industries, jobs and social challenges, increase the risk of wind, but also bring down forced backward industries and low added value of industry chain, promote industrial restructuring and upgrading opportunities.2 from across the country, China's economic development has entered a new normal norm, put forward urgent requirements of development quality and efficiency of quality industry in XX CityThe industrial economy is facing multiple conversion speed, structure and power. China's economic development has entered a new norm, is to form a higher division of advanced, more complex, more reasonable structure can decrease the growth rate of stage evolution. It may lead some challenges to There's no telling war, a variety of factors, constraints tightening, road development the traditional expansion gets narrower. Must take the innovation as the new engine driven by economic development, speeding up the drive to convert from elements of the scale of investment driven development to the development of innovation driven development based principal.The supply and demand of the market environment has changed greatly. Different from the demand side, the grade and residents' demand structure has undergone significant changes, the basic medium has been close to the level of developed countries, the individuality has become the competitiveness of products to reflect the heavy, large quantity of products demand is gradually being customized by small batch of personality replace. See from the aspect of supply, supply of existing products can not meet the rapid escalation of market demand, the lack of effective supply, supply mode and become the deep level reason of industrial economic downturn. Through product innovation arousing potential consumer market, stimulate investment demand, increase effective supply, has It has become an important direction to boost China's industrial economy.Industrial transformation and upgrading by elements to resource constraints more urgent. I China's per capita fresh water, arable land, forest resources is only the world average level of 28%, 40%, 25%%, oil, iron ore, copper and other important mineral resources per capita reserves respectively for the world average level%. 117%, 17%, the traditional industry has been difficult to support resources and high energy consumption. The long-term accumulation of environmental conflicts are concentrated, serious pollution of the atmosphere pollution has become a national environmental and social problems, water pollution, soil pollution is more prominent, increasingly, the industry restructuring and development to put forward urgent Pray.To deepen the reform, formation and development of new power will be the "13th Five-Year" industrial development in China. The theme of the next five years, XX industry development must establish the new ideas of thinking, to adapt to and guide the new norm as macro logic of industrial development, breaking the current resource bottleneck was completed, speed, actively and steadily. The structural change, multiple motive etc... to make good use of the big deployment of national level of the market and institutional environment of product of positive influence, seize the opportunity to expand the space of domestic development, focus on structural optimization, attention to enhance the quality, focus on environmental improvement, fully activate the development of energy industry xx, Provide continuous power for industrial upgrading.3 from the city to see, XX course of economic development, natural endowment and location, determine the XX must take industrial strong city roadRaise the level of independent innovation opportunities of the industrial structure of.Xxx is two, three, and a "heavy chemical characteristics of industrial scale manufacturing characteristic is apparent, especially in the equipment manufacturing sector, in the province and even the whole country has comparative advantage. To firmly firmly grasp the national independent innovation demonstration in South XX area XX sensor network innovation demonstration zone construction in a major strategic opportunity, perfect the system of innovation incentive mechanism, increasing the field of manufacturing and innovation investment, enhance the innovation output, stimulated to stimulate innovation and vitality, enhance innovation and lead development ability.The critical period of building a modern industry to develop new heights. From now until 2020, XXX should strive to build a "new Qiang Fu makall" XX, a high level of comprehensive well-off well-off society. The manufacturing industry is still an important force to promote sustained and healthy economic and social development xxx not indispensable, is to promote the XX economy jumped to a higher level basic support. To accelerate industrial restructuring and upgrading, stronger advanced manufacturing industry, fostering the growth of strategic emerging industries, accelerate the development of modern service industry, push to promote the establishment of innovation ability, quality benefit, structure reasonable layout, sustainable development and international competitive production A new system of industry, revitalize the vibration XX industry glory on the new starting point.Full integration into the national strategy of regional development gold period.Xx geographical advantages are obvious, and the historical and cultural heritage, has strong strong industrial strength and potential development of..xx should be fully docking "The Belt and Road Road, the Yangtze River economic belt, the Yangtze River Delta region a major strategic integration area, strengthen the strong docking with Shanghai, enhance with XXX, XX and even the entire north Yangtze River Basin industrial collaboration, open economy, to a higher level of development, and actively promote international industrial cooperation, the formation of a higher level and wider domain opening pattern.The next five years, XX must be the quasi future trend direction, continue to play in the field of manufacturing characteristics and advantages, will revive the industry itself as XX wind is the center of economic development as task, promote the industrial structure from low-end to high-end forward end, to create new heights of development of modern industry.Comprehensive implementation of the party's eighteen and eighteen session of the 33, fourth, Fifth Plenary Session spirit, foster innovation, harmony, green, open, sharing development idea, firm not to shift industries of City Road, take the initiative to melt into the global industrial division system, comprehensive implementation of the "made in China" and 2025 "XX the platform for action, to the depth of information technology and industrialization integration as the main line, in order to improve the quality and efficiency of economic development benefits as the center, and actively develop new industries, new technologies, new formats and new models, and vigorously promote industrial intelligent, green color, services, high-end development, and to build in emerging industries for the pilot to guide. As the main body of modern manufacturing, modern service industry as the support of the new modern industrial system, the XX to create a domestic first-class, internationally influential manufacturing city, revitalize the vibration XX industry glory in the new starting point for the construction of "the economy is strong, rich people, beautiful environment, social civilization degree is high" the new XX solid solid strong industrial base.Accelerate the innovation development, the implementation of talent drive. Firmly adhere to the development on the basis of innovation, and vigorously promote the comprehensive innovation in science and technology innovation as the core of the nucleus, since the focus on enhancing the capability of independent innovation, get rid of institutional system obstacles, to maximize the liberation and shock to stimulate innovation and vitality, accelerate the formation of innovation as the main leading and support the economic system and mode of development. Strengthening of "talent is the first resource" the idea, focus on the development of needs and direction of innovation, efforts to consolidate the foundation of science and education, optimize the talent environment, to create a high level of innovation of new talents for sustained economic and social healthy development continued to provide strong support.Play to the market mechanism, the transformation of government function. Focus on the decisive role of the market in resource allocation and better play the role of government, strengthen the supply of supply side reform, improve the quality and efficiency of the supply system, co-ordinate the use of economic, legal, policy and means, strengthen the guide and regulate the industry, promote the optimization the upgrading of the industrial structure industry. The implementation of negative list management clear, to further eliminate the obstacles of scientific development system, continuous development and promotion to stimulate the vitality of market players.Grasp the direction of development, firmly adhere to guidance. Based on the basis of the existing industry system and development, accurately grasp the main direction of holding a new round of technological revolution and the industrial revolution leather, strengthen strategic planning and forward-looking deployment, increase investment in innovation, enhance innovation output, stimulate a new vitality, stronger in advanced manufacturing industry, fostering the growth of strategic emerging industries, accelerate the development of producer services, promote industrial system to the reasonable structure, development, agglomeration, clear competitive advantage in the direction of development.To promote energy conservation, improve the ecological benefits. Firmly establish the concept of green development, unswervingly walk the green development, development cycle, low carbon development, increase energy conservation and pollution remediation efforts in resource saving, environment friendly, basis to improve the efficiency rate of the ecosystem, improve the quality and efficiency of development, strengthen the sustainable development the ability to force.Optimization of space layout, and promote regional cooperation. With the layout of concentration, land intensive, industrial cluster, cluster development oriented, optimize industrial park space layout, cultivate advantageous industry clusters, the formation of industrial development is relatively concentrated, production integration of the city space layout good interaction between elements, through the integration of resources. Expand the market space, improve the regional influence and competitiveness.To 20220when the Terminal level when installed on the line number (Word) should be arranged from top to bottom. 6.4.4 cable core must be completely loose and straight, but not damage the insulation and core. Core bundle of the same plate vertically or horizontally arranged

　Manufacturing transformation and development planning1 comprehensive strength of the manufacturing industry to upgradeRelying on good traffic conditions and location advantages of the industrial base, the manufacturing industry comprehensive strength steadily, the total size of the total, technical level, economic benefits and so on in the country has become the cornerstone of the precedent, the city's economic and social development and an important support. "12th Five-Year" period, the total industrial added value, the average annual growth rate of dada%, the amount of the total amount of investment of the city's industrial enterprises with an average annual growth rate%, above scale industrial enterprises realized a total profit of the average annual growth rate of%.xx years, the city's above scale industrial output mode billion yuan output value of over 80 billion yuan of industrial dada to 8, above scale industrial added value billion yuan, industrial growth. Added value accounted for GDDP%, the resident population per capita GDP reached million, ranked second in XXX Province, the national large and medium-sized cities in the forefront.2 continuous optimization of industrial structureThe benefit oriented, high end orientation and the direction of intensive development, gradually increase efforts to promote the transformation of industrial structure adjustment and optimization of industry has made remarkable achievements. As to XX, machinery, textile, petrochemical, metallurgy and electronics and other 55 pillar industries above scale industrial output value at current prices billion yuan, accounting for the proportion of for the high-tech industry output value accounted for%. The proportion of above scale industrial output value reached%, one percentage point increase over 2010. Sensor network innovation shows the construction of the demonstration zone to promote the smooth, emerging industry gradually expand the scale of production is expected to total output average growth rate, new energy, new materials, energy saving and environmental protection, Internet of things, the rapid development of microelectronics and other emerging industries, has become an important field of XX industrial transformation and upgrading.3 innovation capacity significantly improvedSeize the new round of the wave of technological innovation brings plenty of historical opportunity, in-depth implementation of innovation driven development strategy for the manufacturing industry's innovation and transformation and upgrading provides a strong intellectual support for the.Xx year, R & D expenditure accounting for the main business service income ratio reached%, among the province's first patent. The application amounted to 224197, the right amount of invention patents reached 5480, 000 people obviously patent has reached 25, are located in the forefront of the province of.Xx has a provincial engineering technology research centers heart 506, country, provincial high technology research key laboratory 10, International cooperation base, 9 national, provincial, foreign R & D center 41, provincial and international technology transfer center 8, selected "research research institutions" key enterprises XX 84. Tsinghua University, South, Fudan University, Harbin Institute of technology, Huazhong University of science and technology, Northeastern University and other colleges and universities have been set up in the XXX Research Institute.4 green manufacturing results significantly"XXX water crisis", energy saving and environment protection increasing pressure, vigorously promote the green, low-carbon, circular ring production mode, adhere to energy-saving emission reduction, the implementation of energy control, improve the energy source utilization rate of.Xx years, the city unit of GDP energy consumption decreased 20%, increase the added value of industrial energy consumption per ton standard coal / million. "" 12th Five-Year "period, the cumulative unit of GDPP energy consumption decreased percent, energy consumption consumption value XX lowest decline of XX south, South first. The elimination of backward production capacity can work orderly, shut down 8823 enterprises, 852 enterprises for rectification of family, eliminate backward production capacity of cement 75 million 770 thousand Tons, dyeing 244 million 600 thousand meters, 100 thousand tons of chemical fiber, Leather 3 million standard sheets, paper million tons, 2 million 280 thousand tons of steel, 106 battery Wanqianqian KVA, 200 thousand tons of steel casting, resolve the production capacity of 3 million 370 thousand tons, cement production capacity of 710 thousand tons, completed ahead of schedule into "12th Five-Year" planning objectives.5 enterprise vitality is increasingThe emergence of a number of key enterprises in the industry a lot of industries, some have developed into the world class level leading enterprises and leading enterprises. The key point of enterprises in technological innovation, product development, market development, has played an important leading role for.Xx and other aspects of social responsibility, listed 15 companies around the "top 500 enterprises Chinese" listed 221 companies "Chinese manufacturing enterprise 500 strong", all year for nine consecutive years, ranking first in the province. The city's domestic and foreign listed enterprises amounted to 94, ranked in the prefecture level city in the forefront. The integration of military and civilian combined to accelerate, the number of the city's participation in scientific research and production of weapons equipment industry the advantages of private enterprises Year after year, through the confidential qualification certification enterprises ranked 22 in the province.Two 6 integration steadily intoAs a national integration of the two test area, has been to two of the depth of financial integration and enhance the core competitiveness of enterprises as an important starting point, to accelerate the transformation of development mode. The information of all business to achieve the city's more th