Survey On Generalization Strategies Of Middle School Students

It has paid more attention to develop students'algebraic thinking in algebraic teaching. As the core of algebraic thinking, generalization is not only the essential ability to master algebra, but the important thinking method on mathematics. This study tries to examine students' generalization strategies, abilities and cognitive characteristics in solving pattern-based problems in the transitional stage from arithmetic to algebra.This survey on 201 students in an ordinary middle school in Shanghai has some findings. From the aspect of generalization strategies, we find that,1,In linear patterns, students use several strategies which change as the problem representation, discrete or continuous change;2,In nonlinear patterns, students prefer to explore figure to generalize. The false strategies of grade-six students are mainly due to wrong cognition of the figure structure, while grade-seven students due to the false exploration of law of numbers;3,In computational procedure patterns, the sixth grade students prefer to express generalization in words, while seventh grade students in formal language. Both grade focus on number relations but not computational structures in computational procedure.From the aspect of generalization abilities, most difficult is the nonlinear patterns; In linear discrete patterns, figure representation is easier than number representation. Two grades are different in expressing generalization instinctively. The seventh grade students have a deeper understanding in computational procedure patterns and discrete patterns than grade-six students. But in continuous patterns it has little difference.From the aspect of cognitive characteristics in generalization, we find six layers in the process of generalization:1.Finding local commonality, try to make an induction; 2. Defining local commonality, but fail in expressing whatever term; 3. Expressing whatever term by actions performed on numbers; 4. Condensing the number performed actions; 5. Expressing generalization in formal language; 6. developing a schema.