Planning and evaluation of a learning model for deepining studentsʹ understanding of percentagesMula, Melinda (Avtor) Hodnik, Tatjana (Mentor) percentageAlthough percentage is one of the most ubiquitous mathematical concepts that applies widely in school and real-life situations and students are aware about benefits in learning it, there are evidences showing that a considerable number of students struggle to solve different percentage problems. The criticism is mainly addressed to teachers for being focused on mastering students’ skills for calculating percentages and not so much on building students’ principled-conceptual knowledge about percentages, as an effective and sustainable investment for solving percentage problems from various contexts. This study addressed the necessity to develop a new learning model for teaching and learning percentages in Grade 7, when students’ cognitive development ensures the conceptual understanding of percentages as proportional statements and offers the possibility for more effective matching of them with students’ prior knowledge about multiplicative structures, such as fractions and decimal numbers. This study explores various instructional models that are acknowledged for maximizing the development of a certain type of students’ mathematical knowledge about percentages and their effective interrelation into a learning model for facilitating students’ in-depth understanding of percentages. As the intention behind designing the new learning model was interventionist and process oriented for improving the introduction of percentages, the design research method based on teaching experiment was used for designing it. This method offered the possibility to use the inductive approach in designing two Hypothetical Learning Trajectories (HLTs), pilot them consecutively as teaching experiments in two different classrooms and refine them into a new learning model (the PGBE model) for teaching and learning percentages. The abbreviation PGBE presents the interrelation of main methods and instructional models for developing four types of students’ mathematical knowledge related to percentages, such as: P for the poster method for recalling students’ intuitive knowledge about them, G for different patterns of grids for building concrete type of knowledge about percentages, B for bar model for developing students’ procedural knowledge for calculating percentages and E for extended bar model that fosters students’ principled-conceptual understanding of percentages. The effectiveness of the implementation of the PGBE model in students’ learning of percentages was assessed through two cycles of piloting and the empirical study conducted with 473 students of Grade 7 classes of ten different schools in three municipalities, analysis of the knowledge and retention tests results, classroom observation protocols, teachers’ reflective diaries, students’ exit cards, and semi-structured interviews with teachers. Piloting offered the possibility to assess the effectiveness of the interrelation of different research-based instructional models into the development path of the HLT 1 and HLT 2 and the social interaction between teacher and students, and also between students themselves during their implementation. The feedback from consecutive piloting of both HLTs was used to finalize the PGBE model. Even though the piloting was done twice, the effectiveness of the implementation of PGBE model was assessed by organizing the experimental method and conducting statistical analysis of students’ results in the knowledge test and retention test on percentages. Students’ results in the knowledge test and retention test fulfilled the assumptions of the parametric tests, so the independent t-test was used to perform statistical analysis of students’ results in both of them, whereas for performing statistical analyses of students’ results in the knowledge test on percentages related to four types of mathematical knowledge a Mann-Whitney U test was used. The statistical analysis of students’ results shows that students of the experimental group outperformed students of the control group in 26 out of 28 items of the knowledge test, and in 21 out of 28 items of the retention test. This indicator proves that students of the experimental group outperformed their counterparts in 92.9 % of all items of the knowledge test and in 75 % of all items of the retention test conducted two months later. In particular, students’ results of the experimental group are higher in 16 out of 22 items of the retention test that are related to the highest levels of students’ mathematical knowledge about percentages. All these indicators regarding the knowledge test and retention test prove that the implementation of the PGBE for teaching and learning percentages had impacted the learning of students of Grade 7, since it influenced their in-depth learning and a long-lasting knowledge about percentages. As a result of this research study, the implementation of the PGBE model for deepening students’ understanding of percentages is recommended. This learning model supports students in gaining a deeper understanding about percentages, in mastering their computational skills, and sophisticating their mathematical thinking and reasoning about percentages and other similar mathematical concepts, such as fractions and decimal numbers.20202020-08-20 04:07:37Doktorska disertacija118096COBISS_ID: 25514499sl