The chapter explores the diverse interpretations related to the learning of mathematics for learners at lower grade levels. At the core of understanding the dynamics of teaching and assessment of mathematics tasks for lower grade learners lie the general perceptions on the subject and how these have shaped educator and learner approaches to the subject as well as associated nuances of cognitive development. The chapter also explores how educators deal with inclusivity in the context of the curriculum and cognitive capabilities of learners in teaching and assessment. Different interpretations to assessments are also explored. A different approach to assessment that locates learners on a continuum of current proficiency is advocated. A flexible teaching philosophy is proposed which rather than cut the class into a pass/fail dichotomy, acknowledges each learner's right to progress in particular through the use of targeted teaching for challenged learners.