Embarrassment in Mathematics Teaching
The day before my 38th birthday, I woke up from a nightmare with my heart pounding. I just dreamed of a math exam. The pool has a water inlet pipe, which can be filled in 5 hours, and a water outlet pipe at the bottom of the pool can be filled in 8 hours. If the inlet pipe and outlet pipe are opened at the same time, how many hours can the empty pool be filled?
Bah, you are crazy. Is it necessary to inject water or discharge water?
One day, my neighbor's children came across a math problem, Cui Ge, with a score of 76 and 23 1 1 plus 13 and 15. What did you say?/Sorry?
I suddenly lost control, shout at top of my voice and cut the crap!
For me, math is a scar, math is a tear, math is an old cold leg, math is rheumatoid, math is femoral head necrosis, math is myocardial ischemia, and math is a stroke. ...
Part of the reason is that due to the influence of "exam-oriented education", some parts of our traditional mathematics teaching are completely divorced from real life, and our students are not allowed to feel the fun and joy brought by mathematics, and they are not allowed to obtain truly valuable and necessary mathematics.
Valuable math? Valuable mathematics should be closely related to students' real life and past knowledge and experience, which is attractive and interesting to them; Valuable mathematics should be suitable for students to contact, understand and master in a limited time. Valuable mathematics should meet the needs of students' life and adapt to the development of students' personality.
Life → Classroom → Life
Life-oriented: liberating students from abstract and virtual textbooks, giving them opportunities to feel nature, society, facts, events, people and processes, and letting them love the world and life in the collision and communication with the real world, so as to acquire knowledge spontaneously and actively.
"Life-oriented mathematics teaching" means that in mathematics teaching, starting from students' life experience and existing life background, mathematics and life are combined to mathematize life problems and make mathematics problems live. It embodies the idea that "mathematics originates from life, resides in life and serves life". In order to stimulate students' interest in learning, we can learn to use mathematical thinking to observe and analyze the real society and solve problems in daily life. Then in mathematics teaching, let students start from familiar life scenes and interesting things, provide students with opportunities for observation and operation, and let them have more opportunities to learn and understand mathematics from the surrounding mathematical things, realize that mathematics is around us, feel the fun and role of mathematics, and experience the charm of mathematics.
The conceptual background of life-oriented classroom teaching;
1. Historical background
4. Future society's requirements for citizens' mathematical literacy.
3. The requirements of students' cognitive psychological development
And:
1. The significance of effective teaching
Professor Wu pointed out that teaching has dual value. Moreover, it is difficult for us to judge whether a certain behavior is effective teaching. She thinks that different types of math classes have different thoughts on effectiveness. With a vivid example, the math class is divided into new teaching, practice class, review class and comprehensive practice class according to the teaching content. The new teaching is like picking pearls, the practical class is polishing pearls, the review class is stringing pearls into beautiful necklaces, and the comprehensive practical activity class is selling necklaces and wearing them around customers' necks.
2. Why should we explore effective teaching?
(1) Teaching is a double-edged sword for students' development.
The negative effects are: imprisoning thinking, suppressing personality and destroying self-confidence.
(2) Our standards
Effective, efficient and beneficial
(3) Our understanding: Effective teaching and student development are the last word.
Teaching is a broken line, always looking for the shortest distance between the starting point and the goal. Each process is a process in which teachers and students choose certain learning materials and learning forms and move from the starting point to the end point through interactive dialogue.
You can think about the following three questions:
What is the teaching goal you want to achieve?
What is the starting point for students?
Where is the distance?
3. Key factors of effective teaching.
(1) Based on the starting point of students;
The starting point of students' learning comes from: life experience, intuitive experience and learning accumulation.
A question worth thinking about: how to understand the starting point of students' learning (through pre-class conversation or through teachers' teaching experience)? What is the starting point for students? How to use students' learning starting point?
(2) Choose valuable learning materials;
A. Valuable learning materials can be divided into two categories according to their nature: presupposition and generation; According to the form, it can be divided into written materials and operational materials; According to the way, it can be divided into teaching situations, teachers' questions and classroom exercises.
A question worth thinking about: how to understand value? (Professor Wu's answer is reasonable, in line with students' cognitive level and has a mathematical structure. Challenge, variation and thinking practice; Learning materials that can be used for various teaching creations. )
B, how to deal with generative learning materials?
The role of generative learning materials is twofold-embarrassing and wonderful.
The reason is the thinking gap between teachers and students. (a) Different levels: the narrowness of teachers and the creativity of students; B. Different angles: mathematical thinking and humanistic thinking. )
C. how to use the wrong resources?
Correctness may be an imitation, but mistakes (meaning careful thinking) are mostly an experience.
When mistakes occur, we should show our experience, guide arguments and discussions, and turn them into favorable learning materials. Is to mobilize the masses to fight the masses.
(3) adopting targeted learning methods;
(4) Using developmental instant evaluation;
An evaluation can be divided into: wrong evaluation, invalid evaluation (repeating students' answers), inefficient evaluation (simple affirmative and negative, compulsory collective evaluation) and developmental evaluation.
B. Developmental real-time evaluation has the following functions: stimulating function, summarizing function and guiding function.
C. Content orientation of developmental evaluation: classify thinking results, reveal thinking process and evaluate learning quality.
D. the expression of developmental evaluation: oral language and body language. (Professor Wu pointed out that research is needed)
Body language includes symbolic body language and descriptive body language.
(5) To achieve the teaching goal of trinity.