Research On Instruction Based On Task-Design On Promoting Junior Students’ Mathematical Creative Thinking

Cultivating students’ creative thinking is one of the important goals of mathematical education.At present,the research of the education of creative thinking,in accordance with the different levels of attention,can be divided into macro level,medium level and micro level.The macro level focuses on the development of mathematics creative thinking.The medium level is concerned with the development of creative thinking of specific mathematical branches(including algebra,geometry,statistics and probability).The micro level focuses on the creative thinking teaching of a specific class.Existing references show that research of mathematics creative thinking education mostly stay at the macro level,and most of the research results have discipline in general,while the studies of medium level and micro level are relatively fewer.The study here is focusing on the medium level and micro level understand this background.The researchers point out that the cultivating of the mathematical ability should be corresponding to the teaching tasks and the teaching strategies(Stein,2001;Bao jiansheng,Zhou chao,2009).Based on this view,this study bases on the medium level of creative thinking education,namely,algebra,geometry,statistics and probability,respectively discussing the following three questions:(1)What are the behaviors correspond to the junior high school students’ mathematics creative thinking?(2)What are the effective task design strategies to develop students’ mathematical creative thinking?(3)What are the effective teaching strategies for developing students’ creative thinking in mathematics?Among them,the first question is the basis of the following two questions.This study stands on the medium level,implementing qualitative research on all of macro,medium,micro levels of mathematical teaching.First,it takes the mathematical macro level as the entry point and combines the characteristics of different mathematical branches to form the preliminary behavioral analysis framework.Then on the basis of the preliminary behavioral analysis framework on the macro level,initially forming creative task design strategy framework and the teaching strategy framework on the macro level.Then bases on the three frameworks of the macro level to implement case studies on the micro level.On the one hand,case studies can show how to apply three frameworks of the medium level to a specific class,on the other hand,they can in turn modify and improve three frameworks of the medium level.This study only focuses on the initial cycle between the medium and micro levels.On account of the special target of this research(aiming at developing creative thinking quality),Teaching designs consider the perspective of research and teaching at the same time.According to the three frameworks of the medium level,through the analysis of the teaching material analysis,student analysis,combining the opinions of the front-line teachers,selecting a number of creative teaching intervention points for creative tasks in a class to form the design of the whole class,and then implementation of teaching based on the frameworks.During the course of the research,the three frameworks were modified and enriched,and the results were obtained.By two lesson studies in “number and algebra”(“Counting to get 24 points” and “Expressing numbers with letters”),two lesson studies in “graphics and geometric”(“Angle of circumference” and “Equally dividing the areas”),one lesson study in "statistics and probability"(“Variance”),getting three branches of mathematics the refined creative behavior analysis frameworks with the dimension of fluency,flexibility,originality and elaboration(see section 7.1);getting three branches of mathematics the refined creative task design frameworks with the dimension of fluency,flexibility,originality and elaboration(see section 7.2),and refined creative teaching strategy frameworks as well(see section 7.3).The above research results are obtained from the study of first circle between the medium and micro level,which can be further corrected and improved.