Study On Developing A Instructional Model For Teaching Through Problem Solving

Teachers are the key to the quality of education, and teachers" development depends on teacher education. Since21century, the cultivation of innovative talents has gradually become the focus of education in China. In order to change traditional mathematics teaching and learning and cultivate students’ ability of innovation and practice, the Mathematics Curriculum Standard for Compulsory Education (Published in2011) puts forward "Four Bases" and "Four kinds of Competence". In the Long-term Education Reform and Development Program of China, innovative training model is promoted. And heuristics, discussion, participation and exploration teaching method are encouraged to help students’ learning. Teachers are the key to implement these policies and cultivate innovative talents. However, traditional teaching model is still very common in math classroom as the result of the traditional views about education and teachers’ professional competence. Students in math classroom do not have enough time and opportunity to explore and cooperation. The above requirements above and the status quo of math teaching have given great challenges to teachers who grew up in traditional education. Therefore, how to improve the quality of math teachers has become the hot issue of current teacher education.The author studied teaching through problem solving seriously during studied in Canada as a joint PhD student. Teaching through problem solving is leaded by the ill-structured problems that designed by teachers or found by students. Students try to solve problems through cooperation and exploration in the situation and contruct new knowledge and mathematical skills. It changes traditional teaching and learning method, gives students enough space to explore, cultivates creative and practical competence. Teaching through problem solving, which satisfies the basic requirements of the Mathematics Curriculum Standard and the Long-term Education Reform and Development Program, is an innovative teaching strategy and teaching training method. However. how to use this strategy to enhance teachers’professional development, especially preservice teachers, is a problem that deserve to exploration.Using literature analysis, micro-experiment, survey, comparative study, classroom observation and statistical analysis, this study firstly abstracts a TTPS Model in Canada through classroom observation and points out its deficiency. Secondly, based on the related theories, key concepts and needs of Chinese education, this study adjusts the TTPS Model and gains a new TTPS Model which emphases on learners’critical reflection and creation. Then in order to verify its feasibility, the study uses micro-experiment and survey. In the experiment which aims to verify the feasibility of this model and propose suggestions for adjustment, the study implements two similar teaching plan in China and Canada respectively, and then compares Chinese results to Canadian’s and traditional teaching case. The core question of this study is:how to construct an instructional model for teaching through problem solving (TTPS Model) in preservice teacher education? There are three sub-questions:(1) how to construct a TTPS Model in preservice teacher education?(2) What is the difference between this model and traditional teaching model?(3) What is the difference between the implementation of this model in China and Canada?The Conclusion of the study is as follows.1. Constructing a new TTPS Model for preservice teacher education. This model consists of cognitive and operative ingredients which both correspond to each other. There are five stages: Awareness—find or propose a reality problem; Experience—analyze, explore and solve the problem; Critize—reflection in group; Scheme—form initially knowledge; Creation—conclusion in group. If new problems are found in the last stage, then a new cycle is begun. From Creation to Awareness, it is the process of "Stage Reduction". Therefore, the cognitive or operative sequence is a cycle. If there is no new problem found in group conclusion, then the teaching goes into the final step, that is, teachers’ summary and assessment and students’ reflection in their diary. In TTPS Model, students are the centre of teaching; instructors are outside the classroom exploration or in the exploration. There are two basic requirements for implementing this model.(1) From the inner part, instructors should have good professional literacy, and students should have solid mathematics foundation and know what TTPS Model is. Besides, from the perspective of knowledge, the TTPS Model only works for some topics that are suitable for exploring.(2)From the outside part, instructional resources and the support from schools are needed.2. There are three features of the new TTPS Model for preservice teacher education. Firstly, composite exploration structure in teaching with problem as its clue of teaching. Secondly, the exploration in class takes "teaching problem space" as its core experience reinventing knowledge, and merge exploration, heuristics and reflection together. Thirdly, pre-service teachers play a role as teacher and student. These three features are the base of the TTPS Model and also the significant differences between the TTPS Model and other teaching models. The Model for preservice teacher education has three advantages.(1) This model exceeds the existing models for teaching through problem solving and three stages model about teachers" learning and behavior.(2) This model shows some key concepts of "problems, practicing, reflection, reinventing and creation".(3) This model connects theory and practicum.3. The TTPS Model break through the traditional teaching models in the following aspects.(1) Using problems to stimulate learners to explore initiatively which changes passive learning to active learning.(2) The roles of instructors have changed from lecturers to guides, organizers and explorers.(3) The communication in the classroom includes several styles but not just "teach-listen and learn".(4) Using TTPS Model to teach impacts positively on learners’thinking about teaching and their learning attitude, and promote the practice-oriented teaching in pre-service math teacher education.4. There are four characteristics in Chinese classroom using TTPS Model:1) emphasizing on "standard" and "unity" in the teaching;2) paying much attention to the connection of different parts;3) much time is spent on the instructor’s conclusion;4) pre-service teachers answer instructors’ questions but do few reflection. The commonality in using the TTPS Model in Chinese and Canadian pre-service teacher education and the consistency of Chinese and Candidan learners" understandings about this model illustrates the rationality and feasibility of this model. These differences also show the necessity and urgency to change the teaching model in pre-service teacher education in China.The innovative aspects of this study are:based on the existing theory and practice in other countries, the study constructs TTPS Model which merges cognitive and operative perspectives, and proposes some concepts such as composite exploration structure, teaching problem space; then use micro-experiment and survey to verify the feasibility of this model in the pre-service teacher education in China. The results of them illustrate that the model could increase learners’interst, cultivate their creative ability and stimulate their self-exploration.Limited by reasearch time, condition and capacity, there are some limitations in this study:1) the model is verified by a micro-experiment instead of several large scale experiment and adjustment;2) the sample in the survey is very small which might lead errors in results;3) two topics about "measurement" which are similar in content and complexity has to be taught in the experiment because of the differences of math textbooks in China and Canada.In the following studies two aspects will be done. Firstly, some large scale experiment will be implemented according to "constructing—verifying—adjusting—verifying—adjusting— spreading", and much feedbacks will be gained for further verifying, adjusting and spreading the model. Secondly, develop some curriculum related to the TTPS Model for pre-service math teachers.