Issa Ndungo

This conceptual paper refines and expands the Geometry Pedagogical Improvement Cycle (GeoPIC), a framework designed to improve the teaching and learning of geometry. Rooted in the Van Hiele Theory of Geometric Thinking, GeoPIC was initially developed to integrate the strengths of both Conventional Van Hiele Phased Instruction and its technology-enhanced variant while addressing their contextual limitations. Building on prior empirical findings, the paper deepens the framework’s theoretical foundations, clarifies its six instructional phases, and illustrates how it aligns with the principles of Competency-Based Curriculum (CBC). Additionally, it offers brief, practical classroom scenarios to illustrate the application of each phase. The refined framework provides a dynamic, adaptive, and learner-centered instructional approach that facilitates progression through Van Hiele levels while accommodating diverse classroom contexts.

Numbers speak, not just in exams or bank accounts, but in every corner of school life. They whisper through attendance registers, shout from report cards, and sit quietly in budget plans and timetables. Whether you become a classroom teacher, a school administrator, or a national policy officer, you will meet numbers every day. This course, Numeracy Skills in Education, is designed to help you understand numbers and, more importantly, use them effectively. In Uganda’s education system, educators are called not only to teach but also to lead, plan, report, and justify their actions. This involves interpreting enrollment trends, analyzing test results, planning budgets, designing teaching schedules, and making data-driven decisions that impact real learners in actual schools. Numeracy is not just for mathematicians; it is a professional survival skill for every educator. Yet, for many students entering this course, numbers may feel distant, complicated, or even intimidating, especially for those whose paths have not emphasized mathematics. That’s why EMT1101 begins not with formulas, but with purpose. It invites you to view numeracy not as abstract arithmetic but as a powerful language for solving problems, making informed decisions, and enhancing lives. You will begin by revisiting basic mathematical operations and reasoning, learning to estimate, round, and organize data in ways that are relevant to your everyday tasks. From there, you will explore how school variables, such as attendance, performance, income, and dropout rates, relate to one another, and how we can model and predict these relationships. You will delve into logical thinking and argumentation, enabling you to construct sound decisions, explain them clearly, and apply them effectively in school settings. The course will also prepare you to read and interpret trends in school data, enabling you to recognize when performance is slipping or when a program is effective. You will build timetables and budgets, estimate activity costs, and allocate resources. You'll learn how to collect and analyze data, write clear reports, and maintain records that strengthen school planning and accountability. Finally, you will grapple with the uncertainty of real-life school situations using probability and decision-making tools that guide action when outcomes are not guaranteed. Throughout the course, you will not just learn about numeracy, you will live it, through realistic examples, school-based scenarios, and tasks drawn from the Ugandan context. You’ll begin to see how a simple graph can tell the story of a school, how a well-structured timetable can save a teacher from burnout, and how a carefully made decision can change a learner’s future. This course does not aim to make you a mathematician. It aims to make you an empowered educator, someone who is confident with numbers, comfortable with logic, and courageous in decision-making. With these skills, you will not only understand your school better, but you will also be prepared to lead it, support it, and transform it.

This study compared shifts in learners’ attitudes under two instructional strategies: technology-enhanced Van Hiele phased instruction (TVHPI) and conventional Van Hiele phased instruction (CVHPI). A quasi-experimental design was used with 245 learners in the CVHPI group and 238 learners in the TVHPI group. Owing to non-normal data distribution, non-parametric tests were applied. The Wilcoxon signed-rank test revealed significant improvements in attitudes from pre-test to post-test in both groups (p < 0.001), with CVHPI showing a strong effect (rβ = 0.970) and TVHPI demonstrating an even larger shift (rβ = 0.998). Further analysis using the Mann–Whitney U-test and a difference-in-differences model confirmed that TVHPI led to a greater positive change in attitudes than CVHPI. These findings extend the Van Hiele theory beyond its traditional focus on geometric reasoning by demonstrating its potential to influence learners’ attitudes positively, an effect that is further amplified through integrating technology, such as GeoGebra, into phased instruction. Thereby supporting technology-enhanced, learner-centred approaches aligned with Uganda’s Competency-Based Curriculum.