The PGBE Model for Building Students’ Mathematical Knowledge about Percentages

Abstract

<p>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.</p>

Gender Perception of Students in Compulsory Education Regarding Mathematics and Reading

“…Although numerous national and international studies have examined the gender performance of students in mathematics during compulsory education in Kosovo (Mula & Hodnik, 2020;Mullis et al, 2020;Schleicher, 2019), there is a shortage of research on students' gender perception of mathematics in primary and lower secondary schools. These levels are crucial as they represent a critical period in which gendered views about mathematics may emerge, and, if not addressed adequately, have the potential to further expand in the upper grades.…”

Seventh graders’ strategies for shading the percentages of geometric shapes

“…(Kircher, 1926) What percent of 20 is 12? (Guiler, 1946) 88% of $1.75 = $ (Montgomery, 1958) Shading tasks…”

“…(Edwards, 1930) Could you shade 15% of the square for me? (Lembke, 1991) Shade squares in 'b' until 'a' is equal to 150% of 'b' (Montgomery, 1958) Problems Generally, applicational situations embed percent in a context and require the student to extract relevant information, mathematize this information and then solve the problem.…”

“…How many apples fell off during the storm? (Montgomery, 1958) An advertisement for a bicycle says that the price of the bicycle has been reduced by 60% of its regular price. If the sale price of the bicycle is $136, what was the regular price?…”

Elimination of Misconceptions about Percentages with the Cognitive Conflict Approach

“…In order to understand the concept of percentages, students are expected to form their thinking patterns correctly. It is necessary for them to understand the multiple meanings and relationality of percentage (Parker & Leinhardt, Researchers have developed some successful strategies for teaching percentages, such as APOS (Bayraktar, 2020), PGBE (Mula & Hodnik, 2020), RME (Özçelik, 2015), and STEM (Macun, 2019). In addition, some studies have found that students have difficulties dealing with percentages, make mistakes, and have difficulties in understanding and solving problems related to percentages (Koay, 1998;Özbey & Köyceğiz-Gözeler, 2020).…”