Error Analysis Of Grade Eight Students’ Congruent Triangles Reasoning And Proving Learning

The mathematical thinking of grade eight students is in a period of transition from the image thinking to empirical abstract logical thinking. Students in the leap period have great potential and strong plasticity. The geometry learning of students during this period will have a profound impact on subsequent geometry learning. This paper chooses congruent triangles reasoning and proving as research content, because it’s the beginning of strict proving learning of grade eight students besides it’s abundant educational value. Therefore, congruent triangles teaching should be more discreet.In this paper, we use the research methods of students testing, students and teachers interviews in the overall analysis of typical errors in congruent triangles reasoning and proving, which are summarized as the following five aspects:(1) students do not fully understand judgment theorems of congruent triangles;(2) the standard graphic sets;(3) visual impairment, lack the ability of space imagination;(4) lack of multiple representation ability, i.e. the mathematical language, natural language and graphs transformation has not reached the level of automation;(5) the lack of reasoning and proving rigor.According to the above analysis, we put forward five teaching strategies:(1) pay attention to the "process-concept" duality of geometric concept, develop the students’ ability of space imagination;(2) the strategy of multiple contact;(3) variant teaching and breakthrough the thinking sets;(4) pay attention to the analysis “thinking process” of geometric reasoning and proving, lay emphasis on both plausible reasoning and deductive reasoning;(5) emphasizes students’ rigor, form the good habit of reasoning and proving.