High stakes international assessments of mathematics, such as Trends in International Mathematics and Science Study (TIMSS) (Thomson et al., 2012), have placed a premium on students’ ability to apply previously acquired knowledge when reasoning and solving problems in new contexts. Far transfer of mathematical knowledge from the known to the unknown calls for understandings that are deep and wide. Two questions emerge from this hypothesis. First, what is the nature and quality of mathematical knowledge that can drive far transfer in students’ mathematical problem-solving performances? Second, teachers and their teachings are critical factors in the learning process; therefore, how can teachers better support their students’ learning? In this chapter, I attempt to analyse these questions from a cognitive perspective and draw on research findings from my own work in mathematics and that of others to throw light on these issues.