Teachers’ Pedagogical Content Knowledge on Learners’ Mathematical Competencies in Junior Schools in 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, critical thinking, 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 and critical thinking within Webuye-East and Webuye-West sub-counties. The study was guided by four objectives: assessing the level of PCK of mathematics teacher, determining the relationship between PCK and learners’ problem-solving and critical thinking competencies, and identifying contextual challenges affecting PCK application. Grounded in Vygotsky’s Social Interaction Theory, the research employed a descriptive survey 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 by simple random sampling to obtain 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). Findings revealed that teachers possessed a high level of PCK (M = 4.2, SD = 0.5 on a 5-point scale). A Pearson correlation analysis showed a moderate positive relationship between PCK and critical thinking (r = 0.38, p = 0.015) and a weaker but significant correlation with problem-solving (r = 0.23, p = 0.022), leading to rejection of the null hypotheses. However, contextual challenges hindered PCK effectiveness, including resource shortages (78% of schools lacked manipulatives), infrastructure gaps (65% had overcrowded classrooms), and limited professional development (only 55% of teachers had been retooled). The study concludes that while PCK enhances competency-based learning, systemic barriers limit its impact.The study recommend that: Continuous  retooling to enhance teacher PCK that leads to improvement in achievement of learners’ problem solving and critical thinking competencies, Enhancing PCK by adopting new technology that supports learner development of critical thinking competence and the Education stakeholders and the Ministry to provide resources for enhancement of teacher capacity, infrastructure in schools for better learner outcome. These findings benefit the Ministry of Education in policy making, teacher trainers in curriculum reviews, and schools in optimizing instructional practices.