Working Memory, Analogical Reasoning And The Second Year Pupils' Mathematical Word Problem Solving

The psychological research on the problem solving is a hot topic of cognitive psychology research in recent years. However, studies of relationship between working memory and the pupils' mathematical word problem solving are relatively insufficient in China. This study uses 72 primary school students in grade two as the subjects exploring the influence of working memory and analogical reasoning on solving the mathematical word problems in primary schools.The content of the study includes the following factors' influences on the arithmetic word problem solving: working memory capacity of the second year students; the speed of the different system of working memory and executive function; the developing feature of analogical reasoning ability and influence of different types of analogical reasoning. In addition, the relationship between the classification, the presentation formats of mathematical problem and the problem solving is included in this article.A couple of tasks including digit span memory, dot memory , digit span working memory, visuo-spatial working memory and Stroop experiment are used to investigate working memory. Language analogical reasoning and graph analogical reasoning are examined via the primary school students' reasoning ability test and Raven's standard progressive matrices. Three mathematical-word-problem questionnaires for the primary school students were compiled by the author and had been proved with satisfying internal consistency of reliability. The results of the research reveal that:1.The capacity of the working memory influences the mathematical word problem solving of the second year students .Specifically, the proficient group has better working memory capacity than the below proficient group on the digit span memory and digit span working memory, whereas no statistically significant difference of dot memory and visuo-spatial working memory between the two groups has been detected.2.There is no statistically significant difference of the collecting speed of the different working memory system between the two groups.3.There is no statistically significant difference of the executive function in implementation function between the two groups. 4.The second year students' ability on different kinds of language analogical reasoning relationship indicates unbalance. In general, they are relatively good at contrast and function, moderate at cause and effect, and the subordinate relations, and relatively poor at the relationship between the whole and the part and of the same kind.5.The pupils who have normal ability in word problem do far better than those disabled ones in language analogical reasoning and graph analogical reasoning.6.The second year students work much better on the mathematical word problems of one step than those of two steps. Among the problems of one step, the comparative ones are the most difficult, the equalized ones ranking the second and those of adding up some figures is the easiest.7.The visual or audio presentation format of the mathematical word problems implicates insignificant influence on the two groups' response of the problems solving. Nevertheless, they have great influence on their accuracy and the audio presentation has greater influence on the below proficient students than the presentation of sight.8.There is no sex difference of the students on working memory, analogical and the word problem solving.