Primary Mathematics self-study activities to explore strategies

[Abstract] refers to self-exploration activities in question as the carrier to take the initiative to explore the characteristics of the learning activities used in elementary school Mathematics to explore their own learning, not only conducive to the development and enhancement of students' potential, but also help students to fully develop, to stimulate explore the motivation, create a harmonious atmosphere, practice-oriented activities, guide the effective organization, attention to quality of training is to explore effective strategies to explore the main activities.

[Keywords] Primary Mathematics self-inquiry learning strategies
Self-exploration activity refers to the problem as a carrier to take the initiative to explore the characteristics of the learning activities to explore their own learning activities help students develop and enhance the potential, help students to fully grow, help students life-long desire to learn and ability to form, and promoting the development of student's personality, so in Mathematics teaching in primary schools should pay attention to explore their own learning activities, and actively explore the "self-inquiry learning" an effective strategy to better promote the development of students.

An incentive to stimulate exploration activity is the premise of self-exploration
Learning motivation for students to explore their own activities, intrinsic motivation, it can effectively lead students to actively participate in inquiry-based learning activities. Clever set of problem situations can effectively lead students to explore the motivation for this reason, according to math teacher learning content, the use of practical applications of Mathematics or the use of new knowledge and existing cognitive structures to create awareness of the issue of conflict situations, the students into eager to explore the situation.

For example, in teaching "a rectangular area calculation", the teacher with the school repair lawn to create an instance of problem situation: the students, our school to beautify the campus, school repair in a 20 meters long, 15 meters wide, rectangular lawn, in order to budget funds , one must calculate how much of this lawn area. Students, do you have any way to help schools calculate the area of ​​the lawn it? real problem so that students feel the value of Mathematics learning, greatly induce the motivation to explore the area of ​​a rectangle, actively engaged in inquiry learning.

Two create a harmonious atmosphere is the basis of self-exploration activities
Democracy, equality and harmonious learning environment is the foundation of student creativity. Democracy and relaxed learning environment, equality pleasant learning atmosphere, helping to eliminate the psychological burden of student learning, to stimulate their creative passion, so that they dare, dare, dare, dare to show, willing to create.

For example, in teaching "digit by digit", the teacher first to create a shopping scenario: the school to purchase books, to the Xinhua bookstore purchase a popular science books, a set of 12, each $ 24. Q: Can pose any problems? How-column? When students list the 24 × 12, the teachers let go and encourage students to think first, then team, the way to see which group more? the encouragement of teachers, students actively use their brains, the creation of a number of ways. classified briefing about the following categories: First, the two-digit by digit by one digit into the number of calculations (such as 24 × 12 = 24 × 3 × 4 or 24 × 12 = 24 × 2 × 6, the second is the two-digit by digit by digit into a dozen and a whole number, then add (such as 24 × 12 = 24 × 10 +24 × 2, Third two-digit by digit into two digits are then added together by a number (eg 24 × 12 = 24 × 8 +24 × 4, four is to use multiplication to multiply into even the meaning of plus five is the use of two number calculated by a number of vertical vertical knowledge transfer directly calculated to not make any evaluation of teachers, let students talk about their ideas, then guide them to make more in the mutual exchange of evaluation, they feel connected with Addition trouble with even the multiplier is not universal, to 12 and then split into two numbers multiplied, which split into a dozen and a whole number by both universal and convenient, and calculations and the vertical split into 12 10 and 2 to take the written form is only different, essentially the same for a large number of calculations with the vertical is more convenient because of the whole learning process, students in an equal, democratic and harmonious atmosphere, they dare to think, say, created a lot of good ways to solve new problems, truly construct their own knowledge.

Three practice-oriented activities are an important way of self-exploration activities
"Let the students do hands-on math, instead of ear mathematics." Any knowledge to learn the best way to discover through their own practice, because it found that Li Jie deepest, and most easy to grasp the inherent laws of nature and contact, so teaching to give students sufficient practice space, so that each student has the opportunity to participate in activities, in the hands of Research study, hands-on learning, exploration and innovation in practice.

For example, in teaching "angles of a triangle", the first teacher on the blackboard to show the different types of triangle (a right triangle, acute triangle, obtuse triangle, to enable students to guess, how many degrees angles of a triangle? Different types of angles of a triangle and the same? available any way to verify? and then allow students to small groups, each with different types of out of school with bags of triangles, each depicting a triangle study to be undertaken in the group after the first exchange, then as a team reporting in the amount used to explore some ways in some ways to fight the use of scissors, and some methods used to fight off, concluded that "any and all angles of a triangle equal 180 °". explore The practice not only enable students to experience the knowledge acquisition process, deeply understand and master the knowledge, but also the development of student thinking and improve the learning mathematics.

Four effective organization is self-guided exploration activities to ensure
Although the emphasis on inquiry-based learning activities, student self-exploration, but not rich knowledge and experience of students, especially students in lower grades, so teachers need to explore learning activities carefully organized guide.

1. Provide inquiry-based learning materials
The so-called inquiry-based learning materials is a teacher in the organization of materials to give the students left a relatively broad space to think, so that students can observe, experiment, speculation, try, reasoning, communication potential to be developed to explore the ability to be innovative full play.

For example, in teaching "rectangular, square perimeter", the teacher re-teaching materials, first to produce a set of triangular, square, trapezoid, parallelogram, rectangle, hexagon, five-pointed star geometry such as to enable students to review the circumference of the sense, based on several optional group as a unit to carry out search planes graphic graphics perimeter calculations. From the report, the students choose a square, hexagonal, star of the most graphic reason is: to facilitate the calculation, are available multiplied by the side of method, to calculate the circumference of the number of edges. Also choose the triangle, trapezoid, and the calculation methods are be connected to the plus side, while the choice parallelogram, rectangle algorithm to diversify, and some with even add some first added to the side by 2, and some adjacent side first and then take the sum of 2 and then Teachers guide for the appropriate comparison algorithm, requires students to calculate the circumference of the above graphics based on different methods to classify upgrade because of the lesson provided rich material to explore the idea of ​​opening up students to participate in a wide range of each student's potential have been developed to explore the capabilities and innovation capabilities have been improved.

2. Granted an appropriate method of inquiry
Need for new knowledge to explore appropriate ways, students in lower grades because of the limitations of experience, so in self-exploration activities to guide students to be granted the right way.

Common method of inquiry are: First operation found that the organization operating activities of students, in operation in the perception, measurement, fight put, thinking to solve problems, such as knowledge of geometry to learn more use of this method. Second, try to explore that let students try, try to explore, discover, and then get through the exchange of knowledge, teaching most of the transport calculation method has been applied. Third, verify the conjecture, that let the students make conjecture based on existing knowledge and experience, and then verified through a variety of ways. Fourth, observe induction, that is, first observed example, through a more integrated analysis, the inductive generalization. three basic nature of mathematics, law and other laws of the five operators have adopted this method to explore the knowledge. Fifth analog associations, such as integer multiplication by a sense of association to decimal, fractional multiplication meaning of course to explore the issues and sometimes several at the same time explore ways to use and only to guide teachers in teaching students to explore the importance of learning, students explore the ability to continue to improve.

3. Give the necessary guidance to explore
Self-exploration study guide does not negate the positive role of teachers, when students encounter difficulties in the exploration activities do not go exploring, when lost in the process of inquiry, the teacher should be given proper guidance and timely, but teachers too far if the boot or boot properly, will result in the failure to explore here the most important thing is to consider the guidance of the "degree" and "opportunity." Links to free download http://www.hi138.com guide "degree" of certainty depends on the students ability to explore and teaching materials, must be based on existing knowledge and experience of students was higher than the existing knowledge and experience, the problem set in the zone of proximal development of students for the first time in more difficult knowledge to explore the former to provide some of the learning background, and give guidance on methods and strategies such as teaching "the divisor is a decimal division," teachers provide students with life experience first, the background: her mother go to farms to buy food, cabbage price 0.5 yuan, 1.25 yuan to buy my mother cabbage, and asked to buy several kilograms of cabbage? lists for students to explore their own after the formula 1.25 ÷ 0.5 how to calculate because of the students with the "yuan, jiao and fen" in the background and knowledge of their background and to buy food, and some students took 0.5 yuan, 1.25 yuan into 0.5 and 12.5 angle, and some converted into 50 points and 125 points, and then use integer division of communication into, to problem-solving purposes. Also explore the results for some problems not immediately, teachers can guide students to a large problem into progressive layers of small issues to explore, and for the difficulty is not, and can direct students to explore.

Guide is also very important to grasp the timing to guide the timing points: probe-guided, exploration in the guide, after the probe guide. Probe-guided exploration is the former without first guide, students can not start when coupled with guidance such as the calculation is in front of decimal division example. explore the opportunity to be elected to guide the students to explore the difficulties, do not go to explore, the teacher should give guidance. coping strategies: First, pre-class full default, the class smart response to the second, when students explore lost direction, to mention ancillary issues, such as the problem of the past learned what problems linked? How do you know this is right? there is no other possibility? Third, the span is too large to explore the problem, teachers should be given to add some sub-problems guide. After the main probe to guide the inquiry process to guide students to reflect on their own, focusing on mathematical thinking from the lessons that explore the process clear, principled, master mathematical way of thinking, to improve the ability to explore.

Five focus to explore the quality to develop is to improve the ability to explore fundamental
Self-inquiry learning activities most important purpose is to train students to explore innovation, while exploring innovative ability in addition to master the necessary knowledge and methods of the most fundamental thing is to train students to dare to explore, dare to express their independent views, the courage to Zhiyiwennan quality. To this end, teachers should pay attention to teaching students to explore the quality of training.

1. Independent views of the students to cherish
The so-called "independent opinion" is that students in mathematical problem solving in the individual mathematical problems through their own independent thinking and arrive at a unique understanding and insights and it reflects the student a sense of innovation and good quality of thinking, therefore, teachers in teaching Students must value the independent opinion to protect the enthusiasm of the students.

For example, teaching "to take business approximation", the introduction of teacher talk: the summer to buy popsicles, the retail price of each $ 2 the wholesale price of a box (30 50, see these two messages, you most want to know? Health: most want to know the wholesale price of each Popsicle much cheaper price than zero? Teacher: That first of all need to know? Health: need to know the wholesale price of each Popsicle's price? Teacher: We first try to calculate the wholesale price of each Popsicle price, calculated after the report. when reporting a Health said: I calculated the price of each Popsicle ... ... 1.666 million, and before the students finished, B students wait to stand up and say: No, the minimum of RMB unit is the "points" should be 1.66 yuan or 1.67 yuan. teachers do not comment and continue to inspire: there are different opinions? C Chan said: I think it should be 1.7 million, because the market does not use "points" of the. Students rushes to open the debate and finally teachers for Summary: Students views are justified, in fact, the values ​​of our business according to the different needs of different emulated, such as popsicles just calculated the price, if accurate to "points" that percentile, with rounding to take, approximately equal to 1.67 yuan, if accurate to the "corner", that very position, with the rounding method to take, equivalent to about 1.7 yuan ... ... in this piece of teaching, because teachers respect students to express their independent views of the classroom atmosphere was very lively, with good results.

2. Question the ability of students
Learning from the Si, Si in the suspect, the suspect then induced to explore, to discover the truth. Jiuyuan Song renowned scholar has pointed out: "To learn is undoubtedly suffering, doubt there into a small doubt a small forward, a big doubt great progress." Ancient Greek philosophy Home Aristotle once said: "Since the surprise and doubt start thinking." Therefore, students questioned the ability to get to the bottom so that students develop habits to help students explore the capacity of the formation.

For example, teaching "angle of understanding" in the corner with activities to explore the angle deviates from the size and angle on both sides of the relationship between the size, the teacher asked: What you say? Unexpectedly, a student stood up and asked: Teacher, I activities on both sides pull into a corner after the straight line or corner is not it? a ripple, students have open discussion, some say, some say it is not, and some expect the teacher to say in this time, teachers are not immediately given to judge, and guide the students to determine their own definition of angle about: the activities on both sides pull into a corner meets corner after a straight line features? discussion after the students finally understand activity on both sides pull into a corner after a line is still the angle, further deviates from, or angle above fragment, a casual teacher, "What to say?" not only active in the student's thinking, expand knowledge and, more important is to develop the students Zhiyiwennan quality.

Promote self-inquiry learning is a new curriculum approach to learning, it helps to mobilize the students enthusiasm and initiative to help students construct their own knowledge, more conducive to students' mathematical thinking skills, problem-solving skills and emotional the comprehensive development of attitudes and values, but it also has some limitations, not all questions need to explore, not all of the content can effectively explore, and inquiry learning time-consuming, random big, which we should draw attention.

References
[1] full-time compulsory Education. Mathematics curriculum standards (trial version [S]. Beijing: Beijing Normal University Press, 2001.7 (1st edition
[2] Zhou Yuren. Primary Mathematics Teaching [M]. Beijing: China Renmin University Press, 1999
[3] (the United States] DA Grouse. Mathematics Teaching and Learning Research Handbook [M]. Shanghai: Shanghai Education Publishing House, 1999
[4] Zhu Dejiang. Mathematics teachers pedagogical content knowledge (PCK's training strategy [J]. Teaching magazine, 2010 (4 Links to free download http://www.hi138.com