Teachers’ Use of Assure Model Instructional Design on Learners’ Problem Solving Efficacy in Secondary Schools in Bungoma County, Kenya

Mathematical problem-solving skills are a critical competency for secondary school learners, yet many students struggle with applying conceptual knowledge to real-world scenarios. This study investigated the effect of the ASSURE instructional design model on learners' mathematical problem-solving efficacy in secondary schools within Bungoma County, Kenya. Grounded in John Dewey's Cognitive Constructivism Theory, the research employed a descriptive survey design to examine four key dimensions: teachers' analysis of learners' entry behavior, utilization of instructional resources, teacher-learner engagement, and classroom evaluation approaches. The study population comprised principals, mathematics teachers, and Form Three students from 53 public secondary schools in Bungoma North Sub-County. A sample of 280 teachers and 378 students was selected from categorized schools (extra-county, county, and sub-county tiers). Data was collected using questionnaires, student tests, and principal interviews. Instruments were validated through pilot testing, and data was analyzed using descriptive statistics, presented in tables, charts, and text. Key findings revealed that teacher responsiveness to learners' prior knowledge significantly enhanced instructional outcomes (β = 0.37, *p* < .05), though diagnostic assessments were underutilized (56.7% of teachers rarely conducted them). Customized instructional materials improved problem-solving skills (β = 0.37, *p* < .001), while excessive reliance on technology had a negative impact (β = −0.31, *p* < .001). Student-led explanations of problem-solving processes were highly effective (β = 0.55, *p* < .001), whereas teacher modeling (β = −0.33, *p* < .001) and unstructured group work (β = −0.19, *p* = .02) were counterproductive. A notable perception gap emerged in assessment practices: 93.2% of teachers rarely used formative assessments, yet 69.9% of students believed their progress was regularly monitored. Based on these findings, the study recommends targeted teacher training in diagnostic assessments and differentiated instruction to address diverse learning needs. It advocates for strategic technology integration (e.g., GeoGebra) aligned with Bloom's Taxonomy and structured collaborative learning protocols (e.g., defined roles, rubrics) to enhance group work. These recommendations support Kenya's Competency-Based Curriculum (CBC), highlighting the ASSURE model's potential to improve instructional design and problem-solving competency. The study underscores the need for systemic reforms in teacher professional development and evidence-based assessment practices to bridge gaps between teaching strategies and learning outcomes in mathematics education