Teaching Study On 6^th Graders' Mathematical Communicating Reasoning Competency

On the one hand,as a prominent research topic recognized by worldwide mathematics education field,mathematical reasoning had always been put emphasis on by mathematics educators and front-line practitioners of mathematics education.On the other hand,the rapid development of current society put new demands on talent cultivation.Especially the ability to cooperate and communicate with others had become increasingly important.Thus,traditional talent cultivation had been unable to meet fast social development currently.Cultivating learners'mathematical communication ability was the"microcosm"of the new talent cultivation conception in the discipline of mathematics education.Therefore,mathematical reasoning and mathematical communication were the hotspots of mathematics educators nationally and internationally.Mathematical communicating reasoning was a concept generated by the integration of mathematical reasoning and mathematical communication,which could be defined from two perspectives of“process/activity”and“compentency”respectively.In the article,“mathematical communicating reasoning”was defined as a“compentency”,which refered to the ability of individuals/studnents can clearly and precisely construct viable arguments to support their own reasoning,can use succinct mathematical language to expound their own reasoning and to critique the reasoning of others systematically,reasonably and accurately.This article aimed at exploring the task design and teaching strategies for promoting the development of 6^th graders'mathematical communicating reasoning competency through teaching intervention.This paper aimed at investigating the following two research questions?RQ?:1.What's the current status of mathematical communicating reasoning competency of 6^th graders in China?Concretely,?1?what kinds of major problems/errors existed in the communicating reasoning process of 6^thh graders??2?the reasons why 6^th graders had those above-mentioned problems/errors??3?what's the development features of 6^th graders'mathematical communicating reasoning competency??1?what's the overall development features of 6^th graders'mathematical communicating reasoning competency??2?what's the local development features of 6^th graders'mathematical communicating reasoning competency?2.Through teaching intervention,?1?whether it was effective to avoid the problems/errors 6^th graders had in the process of'communicating reasoning??2?if 6^thh graders'mathematical communicating reasoning competency could be improved significantly?In theory,this paper sorted out relevant literatures nationally and internationally,clarified and enriched the definition of mathematical communicating reasoning competency.The relationship between mathematical communicating reasoning competency and several similar concepts was clarified.6^th graders'mathematical communicating reasoning competency evaluation framework?scale?based on SBAC was developed.In addition,rating scales of total three mathematical communication reasoning competency tests were builed.Based on relevant empirical researches worldwidely,the teaching strategies of effectively improving students'mathematical justification,mathematical reasoning ability and mathematical communication ability were sorted out.The following two technical lines were developed according to two research questions in this paper.The test survey method was conducted to solve research question one.Qualitatively analyzed the answers of 306 6^th graders'mathematical communicating reasoning competency tests to explore existing problems/errors in their communicating reasoning process.Reasons why 6^th graders had those above-mentioned problems/errors?focuse on teaching?were further explored through the qualitative analysis of 12 sixth-grade learners interview contents in total.Finally,based on the quantitative analysis of 306 6^th graders'mathematical communicating reasoning competency tests?SGMCRCT?,the development characteristics of their communicating reasoning competency were summarizedTeaching interventions and classroom observation were conducted to solve research question two.Total 52 students in the experimental class were conductd a one-month teaching interventions.Then,a total of 52 test sheets?SGMCRCPos?were distributed to all learners in the experimental class after interventions were completed.In addition,11 Students accepted follow-up interviews after each intervention.Through the qualitative analysis of the researcher's classroom observation notes and students'interview contents,whether the teaching interventions were able to effectively avoid the errors of 6^th graders in the process of mathematical communicating reasoning was proved.Accoring to the quantitative analysis of the test scores of students in the experimental class,whether teaching interventions in the article effectively improved6^th graders'mathematical communicating reasoning competency.In summary,empirically,this study initially explored the development status and teaching strategies of 6^th graders'mathematical communicating reasoning competency in China.The results showed that?1?the overall development level of 6^th graders'mathematical communicating reasoning competency was generally low,and they had many difficulties in the process of mathematical communicating reasoning.?2?Teaching interventions were helpful to avoid the errors in 6^th graders'process of mathematical communicating reasoning effectively.The mathematical communicating reasoning competency performance of experimental class students resulted in a statistically significant improvement.Therefore,the teaching interventions in this study were able to effectively improve 6^th graders'mathematical communicating reasoning competency.