This study focused on the teaching of Mathematics to Grade 3 learners and learner underperformance in Mathematics in South Africa and worldwide. A theoretical framework examined the value of social constructivism, behaviourism and connectivism to Mathematics teaching. A comparison was made with Mathematics teaching in primary schools in South Africa, Bangladesh and Mozambique according to the literature. Against this background a qualitative inquiry was conducted in three selected primary schools with a purposeful, convenient sample of five Grade 3 Mathematics teachers in Danielskuil town, North West Province, South Africa Data were gathered by semi-structured individual interviews, non-participatory classroom observation and document analysis to explore theoretical knowledge and teaching approaches of participants, establish strategies to enhance teacher proficiency, identify successes and challenges in teaching Grade 3 Mathematics and factors that impede Mathematics teaching in the selected primary schools. Findings indicated challenges created by lack of physical classroom resources such as stationery, textbooks and learning aids, poor school infrastructure, overcrowded classrooms, discipline problems, teachers' inability to meet the needs of learners with barriers to learning , language barriers , learners' social problems, teachers' lack of Pedagogical Content Knowledge , lack of developmental teacher training and limited stakeholder support from the Department and parents. Successes related to Mathematics intervention programmes, study groups after school and math's clubs. Based on the literature and empirical inquiry, recommendations were made for implementation by Department of Basic Education, schools and teachers improve the learner performance outcomes in Grade 3 Mathematics in primary schools in South Africa. / Curriculum and Instructional Studies / M. Ed. (Curriculum and Instructional Studies)