The PGBE Model for Building Students’ Mathematical Knowledge about Percentages

Abstract

This research study presents the PGBE model for teaching and learning percentages with students of Grade 7 when their cognitive development enables the conceptual understanding of percentages as proportional statements, and offers the possibility for more effective matching of them with fractions and decimal numbers. The abbreviation PGBE presents the interrelation of the poster method and three instructional models through which different types of students’ mathematical knowledge about percentages can be built. Hence, P stands for the poster method through which the recognition of students’ previous knowledge about percentages can be done, G represents different grids that can be used for building concrete type of knowledge about them; B signifies the bar model for developing students’ proportional understanding of percentages, and E represents the extended bar model for fostering students’ principled-conceptual understanding of percentages. The effectiveness of the implementation of the PGBE model is assessed by organizing two cycles of piloting and conducting the experimental method with 263 students of ten Grade 7 classes. The results of the study show that the implementation of the PGBE model has had an impact on the learning of students, stimulating an in-depth learning and a long lasting knowledge about percentages for this cohort of students.