Pupils Mathematical Factors affecting the level

 Students Mathematical Factors affecting the level of education in Science, Psychology Zhang Guangyu 2004 Instructor: Feng Haiying Abstract: The primary application of the answers to problems, often because of various obstacles to solving the error occurred, it is necessary to answer application questions for students to analyze the impact of factors, and take some corrective strategies. Keywords: students; application problems; problem solving is model can effectively describe the natural phenomena and social phenomena; mathematics for other sciences provide the language, ideas and methods are the basis for all major technology development; mathematics is a culture, his content, ideas, methods, and language is important to modern civilization part of the I. Introduction Applied Maths at the primary stage of mathematics teaching is an important part of solving such problems, can enable students to obtain the relevant mathematical knowledge, but also to develop their mathematical problem solving skills. Mathematical word problems is a combination of practical problems with a question form, which can help students construct mathematical thinking. The teaching of mathematics word problems involving mathematical modeling process, by addressing the subject of these application problems, not only enables students to understand that language processing, mathematical processing and the relationship between conditional reasoning, you can also get a basic understanding of mathematical laws. This article is a variety of students of Applied Problems of reasons to do some analysis and put forward some suggestions. Second, the level of primary school Mathematical individual subjective factors (a) an individual's intelligence, mental ability difference on the impact of application problems answers reflect a person's intelligence as bright. However, to the definition of intelligence, researchers from the perspective of their different kinds of intelligence given the definition, such as the intelligence is Has not yet a universally accepted definition. Our psychology is generally believed that intelligence is a comprehensive mental ability, is to learn to deal with abstract concepts, to handle new situations and solve new problems to adapt to new environments. It embodies the profound things in the reflection of objective, accurate, complete understanding of the extent and the speed and quality of things. It includes attention, observation, memory, imagination, thinking, thinking which is the intellectual force of the heart. Mathematical operations in the marking of students at the right time, many teachers will find that some students are not as careful observation, and misunderstanding; some students in mathematics exercise because the conditions of figure out the relationship between the conditions and problems of the relationship between , leading to the idea of disruption; some students described the exercises can not imagine the appearance of things, so can not answer exercises. Visible, observation, thinking, imagination, a direct impact on the students to solve problems. Students answer word problems, whether it is analysis, reasoning, or the formulation, operation, and both are a reflection of intelligence. To improve students ability to solve problems in mathematics teaching, teachers should pay attention to training and intellectual development of students. (1) Note that students of observation, observation of the formation over time, teachers have a purpose, a conscious observation of the culture to permeate the teaching of various disciplines, and gradually improve their powers of observation. Solve mathematical problem solving in the application, the teacher should pay attention to inspire students to carefully observe, and teach specific methods and skills of observation, careful observation of students to develop good habits. (2) attention to strengthening the ability of students to imagine, there are destinations to the cultivation of imagination, the overall penetration in teaching engineering, mining and play the full potential of the subject material of the imagination factor. Inspire students to start thinking imagination. Problem solving, teachers motivate students to pay attention to evoke memories of life, start thinking, imagination, in-depth analysis, reasoning, problem-solving to find the right way. To fully exploit the intelligence materials (3) to fully tap the intelligence in mathematics textbooks Suhomlinski said: students come to school, not just to obtain a knowledge of the bags, but the main thing is to smarter. Teachers are not limited to the examples on the books, but let students find in understanding the basis of material life, the closely related with the problem of student life organization, making the teaching material taken from life. In the statistical tables, such as teaching, to allow students to collect Shenbian information, data, such as home utilities, telephone bills, school Renshu, the number of vehicle passes a Lukou so. Since the data are collected about the students Qinshou authentic materials of human life, so they produce charts, analysis charts are particularly interested in the natural capacity to learn far more than books, but also cultivate a sense of participation of students, analysis and solve practical problems. 2, thinking, can not meet the quality and level of understanding the problem in a comprehensive, based on the relationship between the number of questions answered correctly applied a key question. Problems in the application which, given the known condition of many forms, some are Syria, some anti-Syrian, and some are known to go through the operation and determine the conditions can get. Unknown link between the given numbers and some direct, while others are indirect, is still some judge to find a solution to the problem. The application of a little more complicated problems, the number of relationships are mostly indirect links exist between the problems and conditions in form of In the answers to word problems, but also requires students to have excellent quality and higher thinking level of abstract thinking. However, the actual situation of the students, the purpose of thinking deeply, flexibility, logical thinking and problem solving necessary for solving the basic capabilities and requirements are not fully compatible. When problem solving performance: quantitative relationship with the examples and description of the same or similar form of direct imitation of the subject; more examples are often the subject of a slight change not quote Luanpeng; comprehensive, thinking on the subject of difficult feelings not start. Teaching various subjects have some systematic, in accordance with the Deep principle of gradual and orderly arrangement. Just behind the front is the foundation of knowledge, knowledge is in front of the back extension and development of knowledge. This provides students with the knowledge of using the migration of the old role, the possibility to try to solve the problem. So, give full play to the role of the old transfer of knowledge, is to ensure that the considerable success of the possibility of trying. Use of state of teaching. Must understand the students have mastered the old knowledge, the original state of knowledge the student teaching, that is, on the basis of old knowledge, old and new knowledge in the connection point to start teaching. Ancient China has been Therefore, the teaching of word problems, teachers should be effective and rational organization of student activities, activation of existing knowledge and experience of the students, guide students to identify problems, to lead the old and new into active participation in the process of the process, become a true discoverers and explorers. Transfer of learning refers to a study on the impact of another study. Transfer of learning in mathematics learning is widespread. For example, the addition of learning will affect the multiplication of the study, the study will affect the rational algebraic learning, the study would affect the function of algebraic learning, the learning plane geometry will affect the three-dimensional geometry of the study, and so on. Moreover, in the mathematical knowledge, skills and abilities also exist between the migration phenomenon. For example, in-depth study with the generation of knowledge, students will gradually equation of knowledge, knowledge and function knowledge of inequality linked organically to form a reasonable chunk of knowledge. In the face of the issues, through which the rational transformation of knowledge to form a reasonable simple solution. For example, solving a quadratic inequality (a ≠ 0), using a quadratic function of the image, into solving a quadratic equation and study the problem of image feature function. This is the mathematical knowledge of the Learning for a typical example of the development of mathematical skills. The moving of mathematics learning of mathematics teaching in the whole system, it is the role of mathematics learning mainly in the following two aspects: (1) to give students a variety of mathematical knowledge for a more extensive and strong links, so that general and systematic form with the stability, clarity and accessibility of mathematical cognitive structure, which can effectively absorb new knowledge of Mathematics and Mathematical gradually to self-generate new knowledge development. Mathematics learning is intended to develop students thinking skills, be able to apply their knowledge to solve problems, which must rely on to achieve transfer of learning mathematics. Mathematical knowledge of the application process, in addressing the current problem, the role of migration that have been organized cognitive structure of mathematics and re-organization, to improve their level of abstraction, making it more complete and enriched to form a stable adjustment mechanism, the mathematical activities in the future to play a better role. (2) is the mathematical knowledge and skills into the key mathematical ability. Mathematics Mathematical ability as an individual psychological characteristics, is a stable, can regulate the activities of the process and the way mathematics psychological structure, which depends on both the formation of mathematical knowledge and skills to master, more dependent on the knowledge and skills of continuous generalization and systematic, that is kind of. Mastery of mathematical knowledge and skills in the course of interaction between old and new knowledge to achieve, so there must migrate, and that kind of mathematical knowledge and skills can be achieved only in migration. Primary Mathematics is a highly systematic disciplines, each of the new knowledge is often an extension of old knowledge and development of knowledge is the basis for follow-up. Keeps the chain of knowledge connected to the old in the new Yun. Such as Two types of checking to be used for Teaching, not only review aliquot of the checking method, but also to 127 ÷ 6 as an example to review more than a few of the division, which focuses on asking: How many? checking business and the division when the only multiply right? how should I do? issue of this series, we discussed. This will be able to successfully master the new rules and checking methods. Thus, in the process of mathematics teaching, we should attach importance to reveal and establish the intrinsic link old and new knowledge from existing knowledge and experience, identify the growing point of knowledge to guide students from the old into the new, the migration of knowledge, while training the thinking of students in order to achieve a deep understanding mastered. (B) an individual's non-intellectual factors, emotional factors, emotional people whether the objective things, the attitude of individual needs arising from the experience is that people are complex, a reflection of mental activity. In real life, meaning it has a broader meaning, including the people most diverse areas of mental life, which we call the affective domain. Emotional education in the field of education that is emotional, it is an education based on certain teaching requirements, through appropriate educational activities to encourage students to positive changes in emotional areas, new emotions, emotional area of the formation of the new process. In mathematics teaching, we not only train students to computing power,UGG boots, logical thinking and spatial imagination, but to nurture students to have good quality of learning psychology, personality and moral qualities and aesthetic qualities, qualities which are indispensable mathematical important components. Good at using emotional education in mathematics teaching, mathematics teaching is not only a higher level of requirements, but also the quality of the current mathematics education. However, the quality of teaching in the traditional view,UGG shoes, knowledge of education or the ability to unilaterally take the absolute center of education, for non-rational, non-logical emotional factors are not given due attention, resulting in many defects, but also set up on the implementation of quality education many obstacles. Therefore, the idea of emotional status and role of education is very urgent and necessary. From a psychological point of view, students in the learning process generally has two mental processes: one feeling - thinking - knowledge of the process; the second is emotional - will - character of the process. The formation and development of intelligent mental process of coordinated development of the two results, simply focus on a particular process will be less effective. Julius • Babanski linked. Because of this, attention, memory, understanding the meaning of something, in this state because of personal feelings of deep and rich together, these feelings intensified to bring the process of understanding and, therefore, more effective and high quality to achieve their goals. quality of the reason for the difference. Currently, in elementary school mathematics teaching is characterized from the The so-called interest is: people seek to understand and get some things and with the positive emotions associated with certain personality tendencies. Show mentality conscious pursuit of the unknown with a strong momentum, and the find and produce surprises and the pursuit of, and further have the desire to want to dedicate their forests. Interest in activities directly affect people's motivation, interest is the mental training of a Primary Mathematics Teaching is no exception, no one's feelings not (and can not have) a love of mathematics and mathematics learning in the pursuit of truth, and to some extent, the teaching of mathematics because its subject is itself there is the boring side, if you pay attention to emotional investment and the introduction of interest is bound to make the students feel that mathematics is difficult to learn and difficult, thus losing confidence in learning mathematics. It is no exaggeration to say that emotion is the lubricant of mathematics teaching in the catalyst. In the study, through classroom observation and written assignments in the field analysis, we found some students not because of poor intelligence, lack of interest only because of the exercise, resulting in a negative mood,Bailey UGG boots, which led to reckless, careless, resulting in problem-solving errors. Can be seen on the problem-solving ability has a significant emotional impact. Once the students love the work, interest on the exercises, it will concentrate on the deep thinking, and find the correct solution. Instead, students will have a negative sentiment on the job, leading to reckless, careless, resulting in misunderstandings. Students work to eliminate negative emotions, to stimulate interest in problem solving, improve problem-solving ability, teaching, teachers work to optimize the structure. Interest in children and give full play to various factors, closely linked to teaching objectives, combined with student practice, designed to close the students real life, the rich meaning of the work interesting exercises to enhance the appeal of exercises to stimulate students interest in solving problems to improve problem-solving capacity. 2, experience and knowledge of the limitations of our dynamic, the development of knowledge in perspective, emphasizing that knowledge is an interpretation of reality, an assumption, it is not an accurate representation of reality, not the ultimate answer to the contrary, It will be with human progress and continue to be and so on, all that knowledge is changing with the deepening understanding of the development. Knowledge does not accurately summarize the law of the world, to address specific problems and can not be used to use, a use for spirit, but rather re-created for specific situations. Knowledge can not exist in the form of entity other than the specific individual, despite signs of human language to express knowledge, so that knowledge has a certain external form, but this knowledge has been recognized relatively common, but that does not mean Learners will have the same understanding of such knowledge, because this understanding is the existing knowledge and experience with learners closely related. Perhaps the view that knowledge does have some extreme, but it is objective knowledge into the learner's subjective factors in order to form the traditional teaching theory a huge challenge, is worth careful consideration. In this view, just a textbook knowledge of phenomena on the assumption that more reliable scientific knowledge contains the truth, but it is not the final correct answer, it is only a correct understanding of reality. These are students accepted prior knowledge, there is no authority for the students to speak, and therefore can not be absolutely correct knowledge as something imposed on students, for students to unconditionally accept, can not be scientists, teachers, textbooks authority to subdue students rely on knowledge to accept the experience of the students themselves to complete, only the students own experience, beliefs, knowledge of the background to analyze reasonable. Students not only for the understanding of new knowledge, but also the analysis of new knowledge, testing and critical, the application of knowledge is not simple to apply, but the creative combination of specific situations need to be selected according to specific scenarios of change. Answer application questions at the right time, the process is quite complicated or even very complicated, require students to have strong problem-solving thinking skills and some skills. In the primary stage, due to the limitations of age, psychological characteristics, some students even have the experience to answer application questions, but because of limited experience and knowledge, not in the psychological make full and necessary preparations, so the application questions situation revealed, for the application of certain terms in question or statement will find it difficult to understand, resulting in barriers to understanding the problem. Example of such a question: There are two ropes, two-thirds of the length of the first and second root of the root are equal. Known to the second rope 2 meters shorter than the first root, find the first number of meters long rope? The terms stimulation patterns are different, students can not understand the meaning of this sentence, but can not be adjusted to the II (one third) Therefore, teachers should strengthen students basic training. Answer application questions in basic training, including: students examine the topic and analysis of mathematical language training, that training students to everyday language into mathematical language, the mathematical relationship from the application questions in the abstract, this is the column type and answer application The key question; students thought of the vastness of the association training, that training students to think through a multi-faceted and consciously pursue problem-solving as many ways of thinking for students to leave enough space; train students to think by analysis Conditions for training, that is based on questions of causality, training students to choose the right according to the conditions of the problem; law students think in an integrated problem of selection training, that training students are given word problems based on the known conditions, to submit the question can be answered; find the standard number of training, that training students to apply the standard number of questions have a clear and correct understanding; find the middle of the issue of training, that training students to find out the application questions in the shelters, etc. . 3, note the limitations of attention, usually refers to the selective attention, that attention is selective processing of certain stimuli while ignoring other stimuli of orientation. It is the mental activity of a certain object point and focused. Note that there are two basic characteristics, one is directional, is a reflection of mental activity have a choice and leave the rest of the object phenomena. Second, concentration, mental activity is to stay in the intensity of the selected object or tension. Mental activity of a certain object point and focus is accompanied by a sense of perception, memory, thinking, imagination and other mental process of a common psychological characteristics, directional characteristics and concentration. Directional performance in the same time as on the many exciting options; concentration showed stimulation of interference suppression. Its production and its scope and duration depends on the characteristics of external stimuli and subjective factors. Primary attention to the development have the following characteristics: (1) dominated by the intention to pay attention to the intention to pay attention to the progressive development of the dominant lower primary students have no intention still plays an important role in attention, and their conscious attention is essentially passive. This is within their nervous system activity related to inhibition has not yet developed. With age, the brain continues to mature, nervous system activity during the gradual coordination of excitation and inhibition together at the same time, because of teaching demands and the training of teachers, students interested in attention and gradually developed. Fourth and fifth graders in the conscious attention largely dominant. (2) specific vivid, visual image of the things that dominated the attention, the attention of the abstract in the development of primary materials, especially the lower grades the level of knowledge and language is very limited, specific image of an important role of thinking, so vivid and specific , the visual image of the things easy for their attention; With the development of student learning activities and knowledge level, as the word-based system and the second signal the development of abstract logical thinking ability, students have a certain level of abstraction Note that the materials have gradually developed. (3) Note that there are significant because emotions are primary school students within the brain and nervous system inhibition has not yet fully developed, the formation of a exciting centers often spread to other activities of the corresponding organs, facial expressions, hand, foot and even the whole body will be with the activity, so pay attention to show marked emotional color. For example, students in the classroom, if they listened attentively, it will show a solemn way; If you hear the happy, smiling faces will be faces lit up, and even danced for joy. Overall, the attention focused on poor students, to maintain attention to the short time, narrow the scope of attention, pay attention to the choice of the direction of trend is often easy to asylum. Therefore, the answers to application questions at the right time, it is difficult steps along the problem solving process to regulate their attention, easy to blindly formulation as the center of attention, understanding the problem and analyze the relationship between the number back at the edge of attention, to check and checking outside or even put attention to unnoticed. This thought process caused by the jump in the procedures, attention to the direction of the bias, note that object omission. For example, students read word problems in right time, attention is often focused on problems in the application of the data (especially data larger more obvious), in the thinking process of problem solving is always eager to out-style, buried calculations, the neglect of analysis of the relationship of the number of interfered with the understanding of the meaning of the questions. 4, the impact of mindset mindset is often used in the form of thinking, the more fixed or even a relative solidification logic, thinking, reasoning, thought content; or someone be named as: a person with a fixed mode of thinking to analyze and solve problems Mindset from another perspective, it can be said that the mindset is the inertia of thinking, or thinking of inertia. Mindset in the people's thinking ability is an important expression of human practices through continuous learning and accumulated experience and form their own unique world of objective knowledge, knowledge of the law means. So obviously the mindset of the individual. Mindset both very positive, but it also has its negative side. It depends on each individual how to deal with their own / and understand their mindset, is a conscious awareness, understanding and using their mindset, or do not know what is the mindset of the law and its advantages and disadvantages. Knowledge of pupils learning in similar, often quick thinking, quick to answer, even students with lower IQ can successfully complete the learning task. Why is this? American psychologist Harold comparison experiments on rhesus monkeys and found that animals in the repeated study of similar topics will find the answers to these problems by a fixed method, after studying similar topics, it will greatly improve the efficiency of solution This phenomenon is known as the mindset. Mindset, once formed, on the one hand to solve similar problems will greatly enhance the speed and capacity - a positive impact. On the other hand will be limited due to fixation, but hamper the detailed analysis of new issues, and even wrong conclusions - negative impact. Why have such negative thinking affected? There are two reasons: First, the mindset that students fail to get rid of proactive interference suppression, so they can not successfully follow the correct way to analyze ideas and solve problems. Second, the mindset that the old idea of flow, keep the old mark in the cerebral cortex is very profound, if without the continued strong new stimulus to be cut off, King is difficult to form new ideas and development of new ideas that must be resolved can not be resolved smoothly. Psychological research shows that students who receive the new knowledge, new problems, often according to a fixed habit of thinking and way of thinking, problem-solving performance when used as a Therefore, students easily get used to the idea of using a rigid or fixed way of thinking to think about issues. The impact of this mindset, resulting in a primary school in the psychological process of thinking. For example, students learn directly described in a simple word problems, word problems are usually described by way of calculation methods should be selected to build a fixed link. The Used to compare As another example, students have some difficulty in the application to answer questions when there is a psychological fear of making mistakes, once a kind of psychological mindset, but also will hinder the students answer questions on the application. Therefore, changes in teaching should pay attention to teaching in the title group, to prevent and overcome the negative effects of mindset. (1) conclusions to be accurate, and experience to complete. Primary school children to learn mathematics is to follow the understanding of the law, according to the country, Deep principle of easy to difficult choreography. Imparting their knowledge is carried out in stages. Single or initial knowledge, mostly incomplete, so in teaching the conclusion to prevent premature or simply summarize the experience, he could feel, and interfere with future learning. (2) to enhance the new stimulation, replacement of old ideas. Fechner famous German scholar in the study that the amount of stimulation and the feeling is directly proportional to the amount of increase or decrease stimulus 10 times, I feel it increase or decrease the amount of 1 times. Some just can not think about the idea of habit, and you have to have a strong new stimulus to be effective in forcing students to the old methods from the old idea come see or transferred to the thinking of new ways. (3) question group teaching, open your mind. Single textbook knowledge-based development, but also causes students to the main causes of mindset. To this end, I received feedback on the new materials processing, often used for teaching problem sets. Select the kinds of questions the basic question is generally the overall title with variant appears, so that students are not stereotyped because of the structure resulting mindset. This is also conducive to vertical linkages of knowledge. (4) analysis of the wrong cases, deepening concepts. The negative effects of mindset persistent, it is not easy in the new post-grant could be overcome completely, it also requires sustained strong stimulation. This requires teacher attention to collecting the wrong case, to collate, analyze, and then feedback to the students. To prevent and overcome the negative mindset is, its methods and means as well. In teaching as long as we take a positive attitude and effective measures, will enable students to get a negative mindset to overcome the maximum, and to eliminate and overcome in this to help students learn to master the correct way to broaden the problem-solving ideas, form a good quality of thinking so as to promote optimization of classroom teaching. 5, the perception of roughness in psychology, I feel that the human brain directly on the sensory organs of the things that reflect the individual properties. Has many individual properties of objective reality, these individual attributes reflected in the human brain is feeling. Sense in human life has a very important role. First of all, the feeling is that people start to understand the world. By feeling, people can not only know the color of external things, lightness, odor, hardness and other properties, but also understand their state of the body, such as hunger, thirst, so as to effectively carry out self-regulation. Information obtained by means of feeling, people can be more complex perception, memory, thinking and other activities, to better reflect the objective world. Secondly, the feeling is important to maintain normal mental protection activities. Experimental results show that the early ontogeny in animals to sensory deprivation, sensory function of the animals would have serious defects; humans can not long endure all or part of sensory deprivation. Sensory deprivation causes confusion in people's thought processes, hallucinations, attention can not concentrate, or even a serious psychological disorder. Any kind of feeling, reflects the individual properties of things, when we put on the individual properties of different things to be comprehensive, they produced a comprehensive reflection of things, this is the perception. Perception of the human brain is directly on the sense organs, a reflection of the whole thing, is the organization of sensory information and interpretation process. Daily life, we seldom realize that the feeling of isolation, because of things we always put together a variety of sensory information, and according to their own experience to explain things. In other words, we are usually in the form to reflect the perception of things. For example, we see red, not red from the concrete things, but the red flag, red, or red flowers, red, red red car, etc.; to hear, we are always perceived as the words sound, water sound or sound of a car such as a meaningful voice. Feel the process is the phenomenon of children's understanding of things and the basis of quality characteristics. One relationship is established the basis for comparison in mathematics. Perceptual activity is the first mathematical concept formation. Activities in the perception of object shape, size and number were compared, and the experience of these activities with children compared to past experience. Therefore,UGG boots cheap, organizations accumulate experience of children, teach them to use recognized standards and to compare the most reasonable approach is very important. Steering children experience, on the one hand to recommend them from their familiar graphic features to identify and call out the same graphics, and can include them quadrangle, on the other hand has a rectangular shape recommended for children to find objects. This type of specific work will enhance children's understanding of the quadrilateral. Fully understanding the problem, to grasp the whole subject is a prerequisite to answer application questions. Fully understanding the problem begins with the senses of the subject as a whole - part - whole fine, the perception of repeated activities, and therefore recognize the problems in the text, words, conditions and problems, thus effectively taking the thinking process of the material - the number of relevant relationships . As students a rough sense of things, and they often lose the basis for understanding the problem and objectives, but also affected the overall grasp of the subject. For example, understanding the problem, often the and so on. Therefore, teaching problem-solving steps to strengthen the analysis in strict accordance with the habits and thought the quality of training, to mental and non-intellectual factors play their respective advantages. 6, lack of self-examination, self-adjustment of the sense of self-evaluation of students is the student learning process of their own self-observation, the results of the study and analysis of the process of self-judgment, is a self-examination behavior. Guide students to self-evaluation, not only the reproduction and reinforcement of knowledge, but also to enable students to develop good study habits is the beginning of self-education is conducive to the development of student subjectivity. Therefore, guiding students to self-evaluation, is to enhance the students to reflect on the wisdom of a good entry point. The researchers believe that self-assessment to guide students may take the following three main forms: (1) self-evaluation of individual students. When students complete the exercises or to answer a question, allow students to think, judge, think about their own problem-solving process in the success and shortcomings, to develop self-examination, self-regulation awareness. Enable students to evaluate themselves, both knowledge representation, while the ability of the students and methods of their own comprehensive reflection, new understanding and evaluation of self, the formation of self-reflective consciousness of thought and action. (2) group peer assessment. Usually groups of four, the teacher can in the classroom on an issue or situation of the students organizing students to group discussions, so that each student has the opportunity to express their views, you can evaluate yourself, others can be evaluated.