Editor's note
In the special period of the whole nation's epidemic prevention, in order to support the exchange of learning and learning among the educational practitioners, the educational reform and innovation undertaking of the state and schools is not stopped. The four WeChat ILEAD official account is launched:
"Teaching innovation in the new era" for College Teachers
"Student centered administrative support" for college student workers and teaching management service personnel
◆ responding to the "future oriented online education" of non-stop classes
◆ voice of education and Development Alliance launched for "education and development personnel"
If you like these columns, you are welcome to recommend them to your colleagues and friends.
In the ongoing fifth Xipu national university teaching innovation competition, there are many excellent teachers and competitors and cases. In order to share and display these teaching innovation cases and provide learning and communication opportunities for a wide range of education innovators, Xipu ilead will select some cases from the fifth competition, and invite the corresponding competition investigators to share the research insights and evaluation of the competition in the form of voice or video.
Higher mathematics is the foundation for engineering students to master and use professional course knowledge. This course has a high degree of abstraction and calculation, strict logic and extensive application. It is a very important but difficult course to learn.
This issue shares the team of Zhang Xiaoping, a teacher of Nanjing University of technology. With the method of flipped classroom teaching of higher mathematics and the driving force of application-oriented teaching ideas, we pay attention to the mutual penetration and collaborative innovation of content, fully combine classroom teaching with mathematics subject competition, and form the "teaching" of extracurricular hierarchical progression based on the "foundation improvement expansion" mode of knowledge points in class The cooperative innovation training mode of "learning competition practice" can effectively improve students' ability of comprehensive application of mathematics and innovation.
Teaching team: Zhang Xiaoping, Ma Shujian, Jiao Juncai
Dialogue Investigator
In order to let more teachers who are keen on teaching innovation have the opportunity of in-depth exchange of innovation cases, the fifth Xipu national university teaching innovation competition has set up a comprehensive research link to investigate each participating teacher on the spot.
Guo Ruixin, a researcher from China Pharmaceutical University, went to Nanjing University of technology on December 27, 2019 to investigate the innovation practice of Zhang Xiaoping's team.
Guo Ruixin (third from the right) field survey Zhang Xiaoping's team
Click on the voice below, and listen to Guo Ruixin, the researcher of the competition, about the experience, harvest and perception of the survey.
Teaching innovation practice sharing
Course teaching objectives
1. Through the discussion and explanation of flipped classroom, we can stimulate the enthusiasm of students' active learning and cultivate their initiative, collaborative creativity and independent learning ability.
2. Through the comprehensive analysis of problems, improve students' ability to solve problems, develop students' exploration ability and innovation ability, so as to improve students' communication ability, communication ability and cooperation spirit.
Mathematics flipped classroom in a hierarchical and progressive way
Through the teaching form of flipped classroom of higher mathematics, taking mathematics subject competition as the platform, taking college students' innovation and entrepreneurship projects and various subject applications as the practice, Zhang's team organically integrates the contents of higher mathematics course teaching and mathematics subject competition, students' Extracurricular self-organized learning, and forms a relatively perfect course evaluation system.
On the basis of the hierarchical progressive mode of "foundation improvement expansion" of knowledge points in class, the "teaching competition practice" mode of extracurricular hierarchical progressive is formed, which pays attention to the mutual penetration and collaborative innovation of contents, explores the "back feeding" role of students' mathematics learning and competition, fully combines classroom teaching with mathematics subject competition, effectively improves students' comprehensive innovation quality, and realizes From the learning of advanced mathematics to the participation of various competitions in mathematics, students can realize the hierarchical and progressive application in the innovation and entrepreneurship projects of college students and various disciplines.
The learning objectives of students
Classroom teaching design
Basic level - guided teaching
The content of higher mathematics basically includes concepts, theorems, formulas, examples and applications, among which concepts are the basis of new knowledge points and are essential for the follow-up related learning. However, because most of the concepts of higher mathematics are abstract and obscure, it is very difficult for students to understand them, especially to grasp the connotation and extension of concepts in depth. There are also some theorems and formulas that are very abstract and difficult to understand, which requires teachers to teach in class, so that the traditional teaching methods of "teaching" and "teaching" can play a full role, guide students to firmly grasp the theoretical knowledge points, and prepare for the follow-up flipped learning. At the same time, it also clarifies the key and difficult points of teaching, so that students can have a clear idea and do a better job of self-learning in flipped classroom.
Promotion level - flipped classroom
Classroom flipping, group discussion, classroom discussion and group report are combined to set different topics. Based on Moodle online, QQ group, superstar learning platform and other communication tools, students establish group online learning group according to flipping group, discuss independently, communicate in time, form group report, report in class and carry out discussion.
How to arouse the enthusiasm and participation of students is a great challenge for every teacher. It's really not easy to ensure the participation of every student. With the guidance teaching as the foreshadowing, the teaching content, key and difficult points, teaching purposes, etc. are more clear. All the plans for teaching are more transparent, so that you know what I know, the interaction in the classroom will not be cold, and the participation of students will be higher, so that they can ask questions and answer questions.
Teacher Zhang divided the class into 10 groups, combined with the teacher's guided teaching, according to the teaching content and problems in autonomous learning to determine the problems to be explored in the classroom, and each group discussed topics in advance for class explanation.
At the same time, in order to encourage the students to participate actively, while flipping the explanation of each group in the classroom, other groups will be given bonus points for the discussion, which is conducive to other groups to participate in the discussion and improve the participation and enthusiasm of the discussion.
Through group discussion after students choose their own topics, students give questions in class, other groups take the initiative to answer questions, answer questions and explain questions, so that each student can go to the platform to explain, exercise language expression ability, enhance the learning atmosphere, and better grasp what they have learned.
For higher mathematics, we should pay attention to the mastery of basic concepts, theorems and formulas, at the same time, we should focus on the application and expansion of knowledge points, and internalize knowledge transfer to solve practical problems. Through the dialogue between teachers and students, students and students, independent exploration or group cooperation, put forward problems, discuss problems, solve problems, and lay a good foundation for the follow-up competition and various practical applications.
Student flipped classroom scene
Development level - stage summary
Stage summary is an essential part of the hierarchical progressive model of higher mathematics, such as stage test and mind mapping.
The content of advanced mathematics is complex and abstract, and the learning cycle is long. It can be reviewed once a chapter or a month. We can also test the learning effect by stages according to the limit, derivative, integral and other knowledge modules, and detect the problems in time to consolidate the learning results.
Mind mapping is an effective graphic thinking tool to express divergent thinking, which is simple but extremely effective. For the course of higher mathematics, which has many knowledge points, abstract theory, strong logicality and emphasizes comprehensive discrimination and application, students use the technique of paying equal attention to graphics and text to show the contents of each chapter with the hierarchical diagram of mutual subordination and correlation, carry out systematic review, clarify the logical structure of the whole content, and make the knowledge system clear.
Thinking map of advanced mathematics drawn by students
Through various teaching links, students are gradually trained to have abstract thinking ability, logical reasoning ability, spatial imagination ability, calculation ability and self-study ability. In addition, special attention should be paid to training students to have the ability to analyze and solve problems by comprehensively using the knowledge they have learned, cultivate and develop students' exploration ability and innovation ability, and improve students' communication ability, communication ability and cooperation ability Spirit.
Extracurricular teaching expansion
Teaching level competition level practice level
Through the exercise of flipped classroom, a group of excellent students are selected and cultivated. First, they take part in the college students' higher mathematics competition. Then, the excellent students in the mathematics competition class take part in the school's mathematics modeling elective class to strengthen the training of mathematics application ability. After the selection of "Zhongdan Cup" mathematical modeling competition, we participated in the National College Students' mathematical modeling competition, and selected the students with rich experience to participate in the Xiaomei competition, laying the foundation for the excellent results of the American Mathematical modeling competition.
Let students from the foundation to improve, from learning to competition, from higher mathematics examination competition to mathematical modeling competition, from domestic mathematical modeling to international mathematical modeling competition, from mathematics to the application of the whole professional learning, from independent learning to comprehensive ability improvement. The students' learning level by level, ability level by level, and achievements level by level increase, which promotes the students to achieve excellent results in higher mathematics learning, mathematics subject competition and practical innovation projects.
The foundation and guarantee of the hierarchical and progressive model classroom
The foundation and guarantee of teaching innovation design
◆ advanced concept -- Constructing flipped classroom teaching based on network information environment
● students study in groups;
● teachers' layered guidance, students' pre class learning and classroom interaction between teachers and students;
● overall tracking and comprehensive evaluation;
● practice innovation activities.
◆ perfect resources - establish a set of online and offline teaching resources suitable for our school
● online: online teaching resources are established based on Moodle online teaching and super star learning platform of Nanjing University of technology;
● offline: prepare digital teaching materials, and students can directly watch the micro class video by scanning the two-dimensional code in the teaching materials;
● integration of online and offline, paper and electronic interaction.
Online teaching resources
◆ the method of fusion - form online and offline fusion of "preview, discussion, explanation, detection and sharing"
Online and offline fusion teaching process
◆ comprehensive evaluation: develop a set of comprehensive evaluation index system in combination with hierarchical and progressive mode
A set of practical comprehensive evaluation index system is constructed by the way of students' self-evaluation, teachers' evaluation, inter group evaluation and intra group evaluation.
Comprehensive evaluation index system of Higher Mathematics
Student learning outcomes
1. Excellent performance in Advanced Mathematics
Compared with the situation that students generally have difficulties in understanding abstract concepts at the beginning of the course and can't grasp them in time, on the basis of the teacher's guided teaching, after the flipped classroom is carried out, students' learning enthusiasm is improved, the classroom actively participates, and the teaching effect is obvious. After half a semester's study, the average score of unified papers and papers in the whole school at the end of the term is more than 10 points higher than that in the next semester, and the average score of papers in multivariate function part is more than 15 points higher than that in the next semester.
2. Outstanding subject competition
Every year, there are about 60-80 students participating in various disciplines competition training and competitions. In the past two years, students have won various awards in national, provincial and school level competitions. Among them, there are prizes in the college students' mathematical modeling competition, the United States competition, the college students' mathematical competition and other competitions.
3. Students' comprehensive ability has been improved
From the beginning of the flipped classroom, students need teachers to help them answer questions, correct errors, reinterpret, and then