Problem solving, based on metacognitive learning activities, to improve Mathematical reasoning skills of students

Abstract

Many studies have linked individual weakness in Mathematical reasoning skills with difficulties in Mathematics problem solving. Some other studies found that, a metacognitive process, based on appropriate mathematical thinking, can help a person to solve Mathematical problems more effectively and meaningfully. This study aimed to improve Mathematical reasoning skills of students in a secondary school in Indonesia through a learning strategy, based on a metacognitive process, namely, PMMK. The design and development of PMMK were implemented in five phases. The first phase, the basic information of Mathematical reasoning skills and Metacognitive skills used Mathematical Reasoning Test (UPM) and Self-Monitoring Questionnaire (SMQ), respectively. The results of the basic information were then used in the design and construction phase of PMMK, based on Garofalo and Lester Metacognitive Thinking and Shipman Mathematical Reasoning. Content validity and construction of PMMK which covered probability topics were examined by three assessors of Mathematics education. Overall, the assessors found that, the content, activities, language and design of PMMK qualified for the objectives with a Kappa Agreement =0.65. Moreover, in the implementation and verification phase, the impact of PMMK was conducted on a total of 32 students in grade 11. A comparative analysis, based on UPM score, showed that, PMMK had helped to improve Mathematical reasoning skills of the students highly significantly, with the effect size =79.25%.