Abstract This study uses mathematical modeling to quantify the impact of learners' needs, motivation, and readiness on teaching effectiveness. It found that active engagement with resources and information leads to meaningful teaching. Teachers used formal assessments and had over ten years of experience. The biggest obstacles were lack of resources and class size. Students recognized their learning demands and evaluated instructional strategies as effective. The study introduced two mathematical models: a linear model and a differential model. The linear model depicts instruction as a function of needs, content, learners, and resources, while the differential model records changes over time. Key terms: Mathematical Modeling, Teaching and Learning and Learners’ needs, readiness and desire Where: Teaching effectiveness (T) is modeled as a function of learner factors (L), needs (N), and a constant factor (C) representing fixed resources and content, such that: T=C⋅L⋅NT = C L NT=C⋅L⋅N where C accounts for infrastructure and teaching materials assumed constant in the analysis. While Learning is a function of readiness, content, resources and desire (Conrad & Donaldson, 2011). Taking content and resources constant, then F (L) is proportional to readiness (R) and desire (D) F (L) = C x R x D ………………………………. ii Where C refers to the constant factors (content and resources) Then combining the teaching and learning equation i and ii: then F (T and L) = C x L x N x R x D This can be interpreted as: C (Bolded) = Factors kept constant (resources and the content) are supposed to be considered in bold, that means they should be as many times as required because of their fundamental roles they play in the process of the teaching and learning. The study has discovered that teaching and learning needs carefully attention from planning to evaluation of educational attainment as it involves complex processes through which some are taken for granted, yet without them the teaching will not be effective. For example content and resources of teaching should always be available according to the learning needs and not focusing to the learners only. Educational planners, curriculum developers and implementers should always take into consideration of reliability of the content, resources and then move to the needs of the learners before executing the teaching and learning.
Shadrack Ernest Mwakalinga (Wed,) studied this question.