| Problem-solving is a basic way in which human beings communicate with the environment. People obtain knowledge and become more intelligent through information communications and problem-solving. The student's learning is also a kind of process of problem-solving. In the context of the course reform of foundational education, the importance of problem-solving in the field of teaching and learning has been thought highly of by many countries. I n their course criterion, the United States, Canada, England, France, Japanese et al plan to train the students the ability of problem-solving. And in their textbooks, there is some content about the principles and subjects of problem-solving. In Chinese, cognitive psychology had achieved many results in many aspects of problem-solving, such as mental mechanism, Problem representations,strategy obtaining,metacognitive supervision etc. However, plenty of educational articles just quote some conclusions from psychology and lack deep researches and demonstrations. Particularly some subjects are in need of practical researches. If we can clarify the main aspects of problem-solving such as representations and strategies, we will make good use of the practical strategies of problem-solving teaching; consolidate the theoretical basis of the researches of teaching and learning; and combine the main idea of psychology and teaching theory, so that guide the practice of teaching. On the basis of previous studies, we studied the core aspect of problem-solving of senior school students and conducted practical teaching in the natural condition. Namely, this is an experimental and theoretical study of representations and strategies of problem-solving. Our purpose is to explore the representation styles, individual differences and the law of strategies applications. Furthermore, according to the conclusions of our researches, strategy training was developed in the natural teaching condition, exploring the effective approaches of teaching and learning, so that we can improve our teaching and learning. This article consists four parts. The first part is the theoretical research about problem-solving. (A) Put forward the main idea of the study. (B) The psychological research of p roblem-solving: Firstly, we defined the meaning of problem and problem-solving. Secondly, we reviewed the studies about the mental mechanism of problem-solving carried on in the earlier period and cognition psychology a research to the secondly and put forward that the occurrence of problem-solving was during the course of cognitive activity that problem-solvers were overcoming some problems. Therefore, the mental process of problem-solving can be divided into two steps, one is comprehending the problem, including retailing the problem and representations. Namely, it is a course of expressing the problem by words and symbols and converting into the internal mental representations of the learners. The other is executive planning,including conducting a plan and the feedback and supervision. The latest development of mental mechanism of problem-solving has shown that problem-solving has already downplayed the stages, and doesn't distinguish the representations from strategies, emphasizing the transformation of the state of representations. Thirdly, we studied the representations during the process of problem-solving. We proposed that the representations should be classified into different types and levels. The classification of the representations is different according to different view. According to the concrete way of use, representations can be classified into: speech, sign, portrait, illustrated manual table, picture, model, concept, principle, method and mathematical formula etc; according to the levels of representations, they can be classified into: external and internal representations, the concrete representations and abstract representations, the physical representations and mental representations. Among them, the different classification method may cross. Fourthly, we studied the strategies of problem-solving. The strategies can be regarded as the special procedure knowledge, and they are the foundation of technique and intelligence. If take no account of the general strategy being metacognitive strategies, just consider specialized strategy knowledge, most studies of strategies concentrate on the differences between experts and apprentices. One point of view is that there is no obvious difference between the reasoning strategies of expert and apprentices. Another view is that the experts choose to set out from the general theory using the positive strategy, theapprentices chooses to set out from the result using the contradictory strategy.(c) We reviewed the subject developmental researches of representations and strategies in problem solving, combining the results of mental mechanism of problem-solving and representations and strategies that is achieved in the general psychology, mathematics, physics and chemistry in recent years, we put forward the basic theoretical assumption of this research: Firstly, there should be a relative stable stage in the continuously changing process of the chemical problem solving. During the simple chemistry problem solving, the stage is obvious. The students mainly experience two main stages, the comprehension and executive plan. In complex chemical problem solving, the stages are misty, the problem-solving process is an alternative development process in which representations transform into each other. The emergence of various representations is not one by one in order, but may be circulative or alternative. Secondly, the classification of different levels is according to the knowledge foundation that the representations are constructed. The classification of different types is according to the concrete way in which representations are used, namely, it is according to the concrete way in which the representations levels are presented. There are four representations levels: partly using the surface characteristics of materials; completely using the surface characteristics; using the surface characteristics and the structure characteristics; completely using the internal representations of the deep structure. The different types of representations are word representations, signrepresentations, schema representations, theory representations, method representations, mathematic representations and so on. And these types of representations may not appear one by one in order, may appear alternately at different stage of problem-solving. But under most circumstances the external representations appear first, after that the internal representations appear. Thirdly, the strategy differences between the students may not be as obvious as the differences between the experts and the apprentices in the chemical problem solving. The poor students probably mainly use the data driven conversing reasoning strategies or tentative reasoning strategies. While excellent students probably mainly use the concept or schema driven positive reasoning strategies or the scene construction strategies. Most students choose the mixture of the positive and conversing reasoning strategies. The second part is a demonstrational study about problem-solving. It consist four experimental studies. The first study: the study of the representations levels and process of problem solving of the senior school students. (A)The differences of representations levels between students of different grades and of different total amount of chemical knowledge. The results show that the total amount of knowledge relates to the scores of classification: X2=80.48,df=3, P﹤O.001, Higher the total amount of knowledge is, higher the categorizing grades are. To the students whose total amount of knowledge are low, the grades relate to the classification score: X 2=6.66, df=2, P ﹤O.05. And the classification scores relate to whether participates are students orteachers: X2=64.02,df=3, P﹤O.001, and the classification scores of the teacher are higher than those of the students. The classification scores correlate with chemical performance, the total score of math and physics, and the performance of problem solving: r=-0.78,r= -0.73,r= -0.74. (B)The results of analyzing the process of simple and complex chemical problem solving show that for the students whose total amount of chemical knowledge are high, there is no significant difference of representations states between different grade in solving simple and complex chemical problems. While for the students whose total amount of chemical knowledge is low, the task performance of high grade students is better than low grade students. We can conclude that the process that presentations change is also the process of problem solving. The differences of representations states are mainly decided by the knowledge that the students grasp in specialized area. The students with high total amount of knowledge can construct internal relation representations from the concept or the theories, and choose simple strategies to solve problems. However, the students with low total amount of knowledge only can establish surface relation representations from the data, and make use of tentatively searching strategies to solve problems. The second study: the study of the representations and strategies of chemical computational problem solving of the senior school students in the same grade. (A) The differences of representations levels and types between students with different total amount of chemical knowledge and different gender. Using MANOVA, the results show that: the interaction of total amountof knowledge and gender is significant. So we tested the significance for total amount of knowledge and gender using unique sums of squares. For the students with low total amount of knowledge, the main effect of gender is significant (Wilks'Λ=0.60). Specifically, there is gender difference in students′word and mathematics representations. Using one-way ANOVA, the results show that for the word representations female students spent more time than male students; for the mathematics representations male students spent more time than female students. For the students with high total amount of knowledge, the main effect of gender is significant (Wilks'Λ=0.67). Specifically, there is gender difference in students′sign representations. Using one-way ANOVA, the results show that male students spent more time than female students. For male students, the main effect of total amount of knowledge is significant (Wilks'Λ=0.28). Specifically, there is amount of knowledge differences in students′theory, method and mathematics representations. Using one-way ANOVA, the results show that students with low amount knowledge spent more time than students with high amount knowledge in the three representations. For female students, the main effect of total amount of knowledge is significant (Wilks'Λ=0.33). Specifically, there is amount of knowledge differences in students′word, sign, theory, method and mathematics representations. Using one-way ANOVA, the results show that students with low amount knowledge spent more time than students with high a mount knowledge in the five representations. And there is interaction between the total amount of knowledge and gender in the sign representations.For the whole time, using two-way ANOVA, results show that the main effect of amount knowledge is significant( F(1,76)=106.39,P﹤0.001), the main effect of gender is significant (F(1,76)=4.36,P﹤0.05) too, and the interaction between amount of knowledge and gender is not significant( F(1,76)=0.25,P﹥0.05). (B) The differences in strategies between students with different amount of knowledge and different gender. Because the data are not normal, we used Mann-Whitney U test. The results show that the scores of the students with high amount of knowledge are higher than the students with low amount of knowledge at positive, lead, monitor, evaluating, computing and inquiring strategies. And the scores of the students with high amount of knowledge are lower than the students with low amount of knowledge at aversive and mixture strategies. There are differences between male and female students at positive, aversive, mixture, computing, inquiring, monitor and evaluating strategies. Specifically, male scored higher than female at all strategies except aversive strategy. There are not differences between male and female students at leading strategies and the rate of accuracy. (C) The differences in mistakes between students with different amount of knowledge and different gender. The results show that the amount of mistakes of students with high amount of knowledge are fewer than the students with low amount of knowledge at representation and strategy mistakes( P﹤0.001). And there are no gender differences at mistakes. The third study: the study of the representations and strategies of chemical inference problem solving of the senior school students in the same grade. (A) The differencesof representations levels and types between students with different total amount of chemical knowledge and different gender. Using MANOVA, the results show that: the interaction of total amount of knowledge and gender is not significant (Wilks'? =0.96). So we tested the main effect of the total amount of knowledge and gender. Namely, we used two-way ANOVA. There is amount of knowledge differences at students′sign, theory, method and mathematics representations. And students with low amount knowledge spent more time than students with high amount knowledge in the four representations. There is gender difference at students′word, sign and mathematics representations. For the word representations female students spent more time than male students; for the sign and mathematics representations male students spent more time than female students. For the whole time, using two-way ANOVA, results show that the main effect of amount knowledge is significant(F(1,76)=153.439,P﹤0.001), the main effect of gender is not significant (F(1,76)=0.18,P>0.05), and the interaction between amount of knowledge and gender is not significant(F(1,76)=0.003,P﹥0.05). (B) The differences in strategies between students with different amount of knowledge and different gender. We used Mann-Whitney U test. The results show that the scores of the students with high amount of knowledge are higher than the students with low amount of knowledge at lead, monitor and evaluating strategies. And the scores of the students with high amount of knowledge are lower than the students with low amount of knowledge at acquiring strategies. There are differences between male and female students at positive, aversive, mixture,computing, inquiring, monitor and evaluating strategies. Specifically, male scored higher than female at all strategies. (C) The differences in mistakes between students with different amount of knowledge and different gender. We used Mann-Whitney U test. The results show that the amount of mistakes of students with high amount of knowledge is fewer than the students with low amount of knowledge at representation, strategy and computation mistakes. There are gender differences at speaking and representation mistakes. And male made more mistakes than female at the two mistakes. The fourth study: the practical study of improving the ability of chemical problem solving of senior school students. Using Mann-Whitney U test, we found that there were significant differences between the experimental class and the control class. Specifically, the scores of the experimental class were higher than those of the control class at immediate speed, delayed speed, immediate balance and delayed balance (P﹤0.001). Using Wilcoxon Signed Ranks Test we found that the scores of immediate tests were higher than those of the delayed tests for both the classes(P﹤0.001). The former four studies supported our hypothesis from different aspects. Just the gender differences were not obvious. The third part is general discussion. We discussed about the results and the future development direction of this study. And we evaluated the creativities and shortcoming, put forward the direction of our study in the future. The fourth part is the conclusions. (A) We suggested that the mental mechanism of chemical problem solving of senior school students is ofstages and do not develop one by one in order.(B)We suggested that there are four levels and six main types of the representations of chemical problem solving of senior school students. The total amount of knowledge, organization of knowledge, the foundation of mathematics and physics, and the cognitive characteristics of the students had effect on the representations, while the grade and gender had no effect on them. The total amount of chemical knowledge of students correlated with the foundation of mathematics and physics, the performance of problem solving, classification scores and representations scores. (C) The senior high school students may mainly use data driven reversing reasoning strategies, concept or schema driven positive reasoning strategies or the mixture of reversing and positive strategies. The students with higher amount of knowledge had high level of cognitive and metacognitive abilities. (D) The amount of representations and strategies mistakes of students with higher amount knowledge was far smaller than the students with lower amount knowledge. While the grade and gender had no effect on the types and amount. (E) Under the natural conditions, combined with the characteristics of the content of teaching, carrying on the strategy training purposely, will promote the abilities of problem solving of the students.
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