Mathematics problem solving skill acquisition: Learning by problem posing or by problem solving

Problem posing is an instructional method where students are asked to create problems based on the given information, then solve them. While in an instructional method of problem solving, students learn by solving given problems. The aim of this study was to test: (1) the differences of efficacy between learning by problem posing and the problem solving method of individual and small group instruction strategies; (2) the interaction effect of learning methods and grouping strategies.With regard to the independent variables, problem solving skill or cognitive load, a quasi experiment with post-test-onlynon-equivalent control group design was used. Year 7 contextual mathematics problems were tested in this experiment, and one hundreds students, who had sufficient prior knowledge, participated. A 2 by 2 anova was employed for data analysis. The results showed that: (1) problem posing method was significantly more effective than problem-solving method; (2) there was no significant difference in efficacy between individualized instruction and small group instruction strategies; (3) the interaction between learning methods and grouping strategies, where it is more likely that learning problem posing was better than problem solving for individual instruction.