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Maths Teaching

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					Maths Teaching
With the deepening of the curriculum reform, the traditional teacher talk, students
listen, teachers ask students to answer as the center of the classroom teaching by the
relentless impact, the impact of the efforts of a large, under the new curriculum, can
not find feeling of teaching. To change this embarrassing situation, in order to develop
students ability to explore the awareness and practice of classroom teaching model as
the goal came into being.
First, the "problem-centered" theory based on mathematics
1, in the "teaching" and "learning" this
contradiction,      the     contradiction     lies     the     main       aspects     of
"learning" that learners take the lead role in internal, which is
the basis for studying behavior change. Behavioral changes caused by the starting
point for students in the learning process is a "problem", said
Mr. renowned educator Tao, "thousands and thousands of inventions,
starting in asking" the question is the starting point of thinking, the
problem is the heart of thinking , teaching Consciousness ignore the problem, ignore
student learning along the "problem" to begin thinking of wings,
also ignored the contradiction between the main aspects of teaching and learning.
2, the mathematics learning as a dynamic and creative human activities, mainly as a
kind of exploration activities, which include "Try - Explore -
Improvement" dynamic process, the new curriculum standards is based on
the view , advocated the mathematical activities "self-exploration and
cooperation in the exchange process to truly understand and master the basic
mathematical knowledge and skills, mathematical ideas and methods, access to a wide
range of mathematical activities in experience." Student thinking in
mathematics is sometimes aware of the existence of mathematical problem started, the
start, the students explore the discovery, autonomous learning, cooperation and
exchange, and the beginning of critical acceptance.
3, depending on the learning for learners in their own way, take the initiative to
construct an internal mental representation of the process of learning so much
emphasis initiative, social and situational; we have stressed from the context to find
math problems, posing problems, but also to the self- explore solutions to problems
and to solve problems to find new problems.
Second, the "problem-centered" classroom teaching students
math problem awareness and behavior
Problem awareness-raising activities that students felt in some of the problems
difficult to resolve the doubts generated when a doubt, confusion, explore the
psychological state, this state of mind positive thinking will inspire students to
continue to raise questions, solve problems. So, yes, the problem is the starting point
of thinking, there is no question of thinking is superficial and passive. Activities in
primary schools, only to make students aware of the existence of a felt need to ask
"why"?                                 "What?"
"How?" To arouse students thinking of spark, and this sense of
the more intense, more active student thinking on the more profound cause of the
more wealthy.
Awareness of the behavior of the performance issues:
Curiosity. Curiosity is the source of the problem is a typical example of problem
awareness. Teaching, curiosity will drive students to the emerging situation and
respond to new changes, identify problems, the root, stir the desire to explore and
promote innovation.
Doubt. Another suspected problem awareness an important behavior. No doubt can
not see the truth, only those with critical and skeptical attitude to have queried further
requesting different, will have to ask questions of desire and impulse to raise new
questions about the concept of breaking and innovative.
Confusion. Sense of confusion is also a manifestation of the problem. Students
appeared in a confused situation in the state, showing heart and not want to pass, I
express freely their opinion, but less than, in fact, a kind of
"outrage", "but can not speak," the state, a
little coaching, they suddenly see the light under can ask or answer a question.
To train students in problem awareness, teachers should delve into cognitive,
scientific organization teaching content as far as possible the problem Wei Yi Shi
nurtured students create a supportive environment, some of Tansuo Jinkenengji
students, guess space to permit students to be problem consciousness Zhubu culture.
Third, the "problem-centered" objectives of mathematics
teaching model features
In the "problem-centered" classroom teaching role and
influence, students in the study to reflect the thinking of active, able to challenge
boldly and actively ask questions, and can seriously question themselves, conscious of
the problem; Mathematics increased interest in learning, studying and living in the
mathematical perspective is good at observing and analysis; better training in
mathematics learning. Careful attention to the views of others; After pondering
express their views and interact with others; to cooperate with students to cultivate the
spirit of cooperation; to integrate into the collective being, to share with others the joy
of success.
Fourth, the "problem-centered" process of teaching
Students: challenge questions, the whole process of self-study and implement
Mathematical context set
Mathematical problem
To solve mathematical problems
Focus on math application
Teachers guide: stimulate interest and reflection throughout the whole process of
Fifth, the "problem-centered" model of the implementation of
the mathematics classroom strategies
Seriously study related to teaching theory and the "Primary Mathematics
Curriculum Standards" (trial version), and firmly establish under the
guidance of the theory of "problem-centered" classroom
organization awareness, understanding model requirements and strive to implement
the purpose of "to problem-centered "teaching mathematics
classroom theory into concrete reality of the behavior of teaching process.
(A), set the mathematical context
Student learning environment, can be interpreted as students to engage in learning
activities, create learning behavior of the environment or background, it can provide
students to think of space and the background to produce a feeling of experience,
which induces students to submit Wen Ti and final resolution of a kind of stimulus
events and information materials, context is also passed the information carrier.
Students explore the initiative often comes from a good problem situation, a good
problem situation, they often have "a ripple" effect, so that
students feel excited heart, can actively participate, independently explore.
1, with practice and the creation of life problem situation
Although people often say: "Mathematics comes from life, but also applies
to life." However, because the content of the traditional teaching seriously
divorced from reality, the students already had on the mathematics of the dull,
mysterious, difficult to understand, tired of the impression. The new standards
emphasize learning mathematics curriculum to student life to understanding the basis
of background, emphasizing the learning of mathematics close contact with real life,
so give teachers made it clear that teaching should be good at life from a familiar
background of the students to create situations so that students feel that math on your
side, inspire self-exploration.
2, contact the creation of knowledge known to extend the problem situation
Teaching on the student's knowledge as the basis of the original, create 知
识 develop and extend, for students to explore the problem situation, Ze primary
mathematics teaching in the main line, Ji Tong Guo situation properly to provide
incentives to shock the suspect, cited thinking, Yinfazizhu exploration, Let each
student learning in the process of experience "perceived problem,
independent thinking, problem-solving" process, enabling students to study
math self-experience, self-discovery, self-perception.
3, contact the creation of an open physical problem situation
Open mathematical problem is clearly opposed to those conditions, the conclusion to
determine the purposes of the closed nature of the problem, it can give students a
broader space of thinking. As the teaching process is a special understanding of the
process, that process of discovery and practice. Teachers should pay attention to
design and open mathematical problems, and carefully arrange the development of
students and structure-based level. Cognitive activity of students basically have to
depend on the specific physical or pictures, or tour of duty in life to start as a
cognitive activity.
4, contact the development of the creation of innovative problem situation for students
Innovation is an inexhaustible motive force of a nation. Middle School Mathematics
Learning Innovation Awareness not only in the process in the quest for new
knowledge and, more widely present in the new knowledge development and
comprehensive use of the process. Therefore, pay special attention to teaching
students with new learning to overcome the end, that is, developing awareness of
innovation awareness end. Take on new knowledge of different methods and
knowledge to explore the comprehensive use of students awareness of innovation as
another new level, in order to achieve the innovative sense of students in the
classroom is always through. The same time students still need to carefully create
innovative problem situation.
(B), mathematical problem
?"Creating context" aims to enable students to function in
situations under the proposed mathematical problems, teachers and traditional
teaching speaking, listening, teachers ask students to answer, teachers standing
"to teach" point of view of teaching to the default, then let the
students thinking along the pre-set direction, finish the new knowledge from old
knowledge to the whole process, which is precisely to curb the problem courses.
Therefore, a mathematical problem, in the classroom teaching students through the
learning process is particularly important. First of all, to raise awareness and give
students the opportunity of posing problems. Sense from a perspective that people
engage in an activity automated psychological tendency, in the primary school
mathematics teaching, teachers should determine the objectives of teaching, teaching
programs, creating teaching situation and a series of teaching behavior consciously
posing problems for students provide time and space.
Second, to guide the observation, students raised close to mathematical problems. The
new curriculum emphasizes course content, teaching design should and social
progress, technological development, the students with real life contact, stress
everywhere in life have a maths, mathematics on the student side, stressed the Ba
mathematics of life issues, from life Zouxiang Mathematics , the mathematical
problems of everyday life back to life from the mathematics. For example, a Year
"study mathematics, mathematical," the teaching, guide
students to observe the classroom environment that "classroom of students
and more teachers," or classroom on the left three potted plant on the right
with two potted plant, "together a number of potted plant? "and
other mathematical problems, and to better train students in mathematical perspective
to observe our environment, found that mathematical problem, posing problems.
Third, a clear requirement for students to make good mathematical problem. Teaching,
although teaching is often stimulating situations, but teachers still need to explicitly
ask students to make mathematical problems. For example, in the first year,
"recognize objects" in the teaching of teachers require students
to come up with a cuboid: "ask someone to come up with a bag from a
school with such an object shaped like a look, feel, find anything, can be make the
mathematical problem? " Students through observation and operation, the
proposed "that the object has 6 faces, the shape is long; every two Egyptian
side there is a straight line with; shape they looked very square" and other
valuable mathematical problems . Summarized the issues raised by the students arrive,
like this "object is called a long rectangular square." Because of
the clear requirements of teachers, students not only posing problems, but also vividly
reflected the student's self-inquiry learning, new learning methods,
embodied in the classroom teaching colors.
(C), solve the problem.
Learning methods are accepted and found two: the acceptance of learning, the
learning content is based on findings presented in the form directly to the students and
is the recipient of knowledge; in discovery learning, the learning content is a problem
or indirectly the presentation of the students are discoverers of knowledge, both
learning methods has its own value, is a complementary relationship to each other.
However, too much emphasis on traditional ways of learning to accept and master the
neglect of discovery and inquiry learning into mere passive acceptance, memory
process. Transforming learning method is to change the status of this study, the
learning process of speculation, discovery, exploration and other activities emerged in
the learning process as students found more problems, ask questions, problem-solving
(D), focus on math application
When teaching the students experienced in the situation in question, under the control
of the problem to solve the problem and in order to promote student mastery of
knowledge and the formation of skills, teaching students to attach great importance to
the application of mathematical knowledge to design new knowledge in the learning
process stage after the end of practice and a comprehensive new lesson exercises. The
design should not only pay attention to practice the form of colorful, but also pay
attention to the stairs to the degree of difficulty so that students master the knowledge
into a line of vertical, horizontal piece, and establish a new cognitive structure.