A Survey And Research On The Relationship Between Number Sense And Metacognition Of 6^th And 8^th Students

Number sense is important to people's life and study, it not only helps people know and use number, but also help people solve problems related to number quickly. Since the early eighties of last century, the NCTM had proposed to develop their students'number sense, and then other countries and regions had also offered to train and develop students'number sense, China also proposed to develop students'number sense in Standard Course on Mathematics for Full-time Education--- Experimental Draft.Number sense refers to people's general sense that helps them choose an efficient strategy to solve the problem, based on the understanding and thinking of number and operation. In this study, the author discusses number sense in five dimensions: 1. understanding basic number meanings; 2. recognizing the relative magnitude of numbers; 3.representing numbers in various ways; 4. understanding the role of operation in numbers; 5. choosing and deciding appropriate strategies to solve problems, and deciding the reasonableness of results.Through questionnaire and interview, this research focuses on two problems:First, the level of number sense and metacognition in the 6th and the 8th grade students in Changchun and Taonan; Second, the relationship between number sense and metacognition.The findings are as follows:1. The general condition of of 6th and 8th students'number sense:The majority of 6th and 8th students are used to solving problems by ways of conventional calculation, while only a minority can do it through number sense. Therefore, the students'performance of number sense should be improved.There is an extremely significant difference in every dimension of students'number sense in different grades; the overall trend is that in a higher grade, the number sense increases. That is to say, as students'knowledge, life experience and mind condition develop, their number sense grows as well. At the same time, the math education promotes the development of number sense.In the comparison of the five dimensions, students from both grades perform better in understanding basic number meanings, expressing numbers in varied ways and understanding the functions of operation; but poorer in recognizing the relative magnitude of numbers and choosing and deciding appropriate strategies to solve problems, and deciding the reasonableness of results.2. The condition of metacognition 6th and 8th studentsThe metacognition level of students from both grades level is almost the same, and there is no significant difference on the whole or in any dimension, but the differences are great among individuals and the 6th's is greater than 8th's. Moreover, the poorest performance is metacognitive monitoring.3. The relationship between number sense and metacognition of 6th and 8th studentsIn grade 6, number sense and metacognition are in positive linear relation. That is to say, a student will be good at using number sense to solve problems with numbers if he possesses a good metacognition, but the low metacognition student can't. However, the effect is not obvious. In grade 8, there is no linear relation between number sense and metacognition. That means, whether students use number sense or not is hardly related to metacognition. By comparing the two grades, we can find that the relationship between number sense and metacognition doesn't increase with the higher grade.