The use of learning trajectories approach in grade 6 students’ relational thinking skills of the equal sign

• Main Author: Padua, John Carlo
• Format: text
• Language: English
• Published: Animo Repository 2019
• Subjects: Mathematics—Study and teaching (Elementary); Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/7185
• Institution: De La Salle University

This study utilized a mixed method concurrent triangulation design where the proponent developed a learning trajectory plan that includes a mathematical goal, developmental progression, and learning tasks that aimed to improve Grade 6 students’ relational thinking skills towards the equal sign to strengthen their foundation of equality concept as they embark in high school algebra lessons. In the learning trajectory plan, there are six collaborative learning tasks matched to the six levels of relational thinking skills of the equal sign in the developmental progression. The developmental progession serves as the path of learning, while the learning tasks are the paths of teaching. The researcher explored students’ level of relational thinking skills towards the equal sign and their strategies in solving different types of number sentences such as traditional, atypical, and with one or two missing numbers involving addition operation on both sides of the equal sign.The participants of this study consisted of one intact heterogeneous class of 44 Grade 6 students enrolled during the school year 2019 – 2020 at a public elementary school located in Imus City, Cavite. Quantitative and qualitative data were collected in this study using researcher developed and adapted pretest, quizzes, posttest, learning tasks, and students’ reflection to provide necessary information for the completion of the study. Both data were used to corroborate each other and gave a clearer picture and a more detailed analysis and interpretation of the results.Moreover, the learning trajectory plan with a set of collaborative learning tasks administered in this study engaged students cognitively that resulted to a great improvement and changes in their relational thinking skills of the equal sign and strengthened their understanding of the equality concept. There was also a significant change in their level of relational thinking skills towards the equal sign. Outcomes showed that they were able to see equation as a whole and learn the true meaning of equal sign, that is, a represention of the sameness of expressions or quantities on both sides of the equal sign. They were able to use and recognize computational and relational strategies in solving different types of number sentences. By and large, this study showed that the learning trajectory approach is an effective tool in planning collaborative learning tasks to improve students’ relational thinking skills of the equal sign. Lastly, some observations during the conduct of this study were discussed, which should be useful to other mathematics educators, particularly to those who intend to implement learning trajectory approach.