The Relationship Between Deductive Reasoning And Different Mathematical Abilities Of Senior Primary School Students

Mathematical ability is the ability to acquire,process and preserve mathematical information,and is the basic ability of individuals to understand the world,which affects their decisions and behaviors.As the core ability of cognitive development,deductive reasoning and mathematical ability have been considered to be closely related.However,there is relatively little research on the relationship between deductive reasoning and mathematical ability.The existing researches have not reached a consensus.Knowledge can be generally divided into three kinds: factual knowledge,procedural knowledge and conceptual knowledge.According to the classification of mathematical knowledge,this study divides mathematical ability into three different types: mathematical ability dependent on factual knowledge,mathematical ability dependent on procedural knowledge and mathematical ability dependent on conceptual knowledge.It has been found that deductive reasoning is significantly related to mathematical ability dependent on procedural knowledge,but the relationship between deductive reasoning and mathematical ability dependent on factual knowledge and conceptual knowledge gives inconsistent results.Based on previous studies,this study proposes the procedure-dependent hypothesis,that is,deductive reasoning is uniquely correlated with the mathematical ability dependent on procedural knowledge,but independent of the mathematical ability dependent on factual knowledge and conceptual knowledge.A total of three studies were designed to test the procedure-dependent hypothesis,all of which used transitive reasoning to measure deductive reasoning ability and used SPSS26.0 for statistical analysis of the data.In study 1,256 sixth graders were tested.The mathematical ability dependent on procedural knowledge is measured by arithmetic,and the mathematical ability dependent on conceptual knowledge is measured by numerical reasoning.Relevant research results show that deductive reasoning is significantly correlated with both arithmetic and numerical reasoning.Regression analysis showed that after controlling for age and gender,general intelligence,spatial ability and other cognitive factors,deductive reasoning is significantly correlated with arithmetic,but has nothing to do with numerical reasoning.In Study 2,271 sixth graders were tested.The mathematical ability dependent on procedural knowledge is measured by exact computation,and the mathematical ability dependent on conceptual knowledge is measured by approximation computation.The results of relevant studies showed that deductive reasoning was significantly correlated with both exact computation and approximation computation.Regression analysis showed that after controlling for age and gender,general intelligence,spatial ability and other cognitive factors,deductive reasoning was significantly correlated with exact computation,but not with approximation computation.In Study 3,242 sixth graders were tested.The mathematical ability dependent on procedural knowledge is measured by complex exact computation,and the mathematical ability dependent on factual knowledge is measured by simple exact computation.The results show that deductive reasoning is significantly correlated with both complex exact computation and simple exact computation.Regression analysis showed that after controlling for age,gender,general intelligence,spatial ability and other cognitive factors,deductive reasoning is significantly correlated with complex exact computation,but not with simple exact computation.Through the above studies,the following conclusions are drawn:Deductive reasoning is uniquely correlated with mathematical ability dependent on procedural knowledge,but not with factual knowledge and conceptual knowledge.