After students spend approximately 12 years of formal math learning from high school, they bring a store of enormous “learned” mathematics factual knowledge to face the challenges and prepare for college/tertiary level learning. However, research has shown that early tertiary-level students struggle to learn college mathematics. The ability to think mathematically and use this learned factual knowledge (mathematical thinking) to solve higher-order thinking skills (HOTS) problems is essential to tertiary education. Thus, do these high school leavers have access to previously learned factual knowledge and use it effectively in solving these HOTS problems? This sequential research design study was conducted among 640 high school leavers who received an A in their national examination. In the first phase, the researchers investigated their mathematical thinking ability, followed by interviews with selected students on the difficulties and challenges they faced in solving the underlying problems. The findings showed that these students lack the ability to effectively use the previously learned factual knowledge from school mathematics to solve mathematical thinking problems. Secondly, they lack the habitual mind to check their answers after deriving a solution to a given problem. Thirdly, most rarely used heuristics to devise a strategy to solve fundamental math problems. Although the expectation of the school math curriculum over the last decade has been re-engineered towards “teaching students to think,” this expectation has yet to be fulfilled. Thus, university educators must do more to guarantee that high school leavers can deconstruct their mathematical knowledge and reconnect it with the underpinnings and linkages of college mathematics requirement.