Influence of Teachers’ Pedagogical Content Knowledge on Learners’ Mathematical Problem-Solving Competence in Junior Schools Bungoma County, Kenya

Education is a critical equalizer, and every learner deserves quality, differentiated instruction. Kenya’s Competency-Based Education (CBE) aims to nurture holistic learners equipped with problem-solving and other essential competencies. However, the effectiveness of CBE depends heavily on teachers’ Pedagogical Content Knowledge (PCK)—their ability to tailor instruction to diverse learners while mastering subject matter. Despite its importance, little research has examined how PCK influences competency development in junior schools, particularly in rural settings like Webuye. This study bridges that gap by investigating the relationship between teachers’ PCK and learners’ achievement in problem-solving in Webuye-East and Webuye-West sub-counties. The objective of the study was to determining the relationship between PCK and learners’ problem-solving competence. Grounded in Vygotsky’s Social Interaction Theory, the research employed a descriptive survey research design. The target population included heads of institution, mathematics teachers, Grade 8 learners from all 149 junior schools in the two sub-counties. A sample of 686 respondents was selected—373 learners, 206 mathematics teachers and 107 head of institutions. Data was collected via questionnaires, interviews, learner assessment tests, and lesson observations. Validity was ensured through expert review, and reliability was confirmed using Cronbach’s alpha (α > 0.7). A Pearson correlation analysis showed a weaker but significant correlation with problem-solving (r = 0.23, p = 0.022), leading to rejection of the null hypothesis. The study concluded that while PCK enhances competency-based learning, systemic barriers limit its impact. Recommendations include: Continuous teacher retooling to align PCK with CBE demands. Adoption of learner-centered approaches (e.g., collaborative learning and integration of technology) to strengthen problem-solving. deficits. These findings benefit the Ministry of Education in policy making, teacher trainers in curriculum reviews, and schools in optimizing instructional practices.