The Research On The Sixth Grader’s Algebraic Thinking In Dealing With Word Problems

In February1994, NCTM（the National Council of Teachers of Mathematics）passed a report titled“Algebra for Everyone”, which pointed out that all middle highschool students should have the opportunity to learn the basic ideas and methods ofalgebra. That report also established the importance of Algebraic thinking in juniorhigh school mathematics teaching.But the fact is that the students have difficulty in switching their thinking froman arithmetic way to a symbolic one, which is so obvious when the seventh gradersstart to learn algebra but can not understand the algebraic signs. Luckily, thatproblem can be solved by the teaching of word problems during the sixth grade anddeveloping the students’ algebraic thinking in that phase. But there is barely anyresearch on the process of students’ thoughts development in that field..We willstudy the impact of students’ different ways of thinking on their learning of wordproblems through the research on the process of switching from arithmetic thinkingto an algebra one in dealing with this kind of problems.In order to analyze the actual thinking process of the6th graders when dealingwith the word problems, I have developed the four following analysis dimensions:Dimensionⅰ, arithmetic dimension; Dimensionⅱ, the dimension betweenarithmetic and algebra; Dimensionⅲ, the dimension of elementary algebraicthinking; Dimensionⅳ, the relatively proficient algebraic dimension.The students can easily solve the simple word problems with only arithmeticthoughts; the method of assuming an unknown number k or a unit is on thedimension between arithmetic and algebra thinking, on which the teacher can guidethe students to carry out the normative algebraic thinking by instead of unfoundedguessing; the students can solve the word problem of specific mode, formula orgraphic on the dimension of elementary algebraic thinking；on the algebraicdimension, the students can establish an equation with unknown numbers accordingto the equivalent relationship in the word problems, establishing a mathematicalmodeling independently with the changing requirements. The research effectively shows the developing process of the6th graders’algebra thoughts. Meanwhile, the idea of using four dimensions provides us withreference of how to improve the students’ capability of word problems, which alsoprovides ideas for the research on how to plan suitable teaching strategies from thestudents’ algebra thinking.