Developing students\u27 mathematical understanding on linear equations in two variables using a UbD unit plan

The purpose of the study was to identify the instrumental understanding and relational understanding (procedural and conceptual knowledge) developed by the students through paperand- pencil exercises and performance task after the implementation of a unit plan inspired by the Understanding by Design, and the students perceptions of their skills and proficiency before and after the implementation of the unit plan. The UbD unit plan was validated by eleven professional teachers. It was then carried out in a heterogeneous class of 40 students in a private laboratory school in Manila. The study used both qualitative and quantitative methods of research. The quality of the students answers for both written exercises and performance task and the advice of the validators supported the qualitative analysis of the students developed instrumental understanding and relational understanding (procedural and conceptual knowledge) through written exercise and performance task and students perceptions of their skills and proficiency before and after the implementation of the unit plan. Descriptive statistics supported the quantitative analysis of determining if there are significant differences between the perceptions of the students on their skills and proficiency before and after the implementation of the unit plan. Results showed that the students have developed almost all the instrumental understanding, the rate of the students who developed relational understanding (procedural knowledge) was remarkably high, and the results on the students developed relational understanding (conceptual knowledge) were promising. The z-statistic for differences between two proportions at 95% confidence showed that there are minimal significant differences between the students perceptions of their skills and proficiency before and after the implementation of the UbD unit plan, and between the number of students who perceived that they could perform a certain skill and the number of students who were able to carry out the skill. The study recommends the following: engagement to more real world problems for the students to see the significance of studying mathematics and reinforcement of meaningful performance task as another means to gauge students understanding