The Cognitive Gap in the Mathematical Thinking Abilities of High School Leavers for College: Are they ready?

After students spending approximately 12 years of formal math learning from high school, they bring a store of enormous "learned" mathematics factual knowledge with them to face the challenges and prepare for college/tertiary level learning. However, research has shown that early tertiary level students face a struggle in learning college mathematics. The ability to think mathematically and use this learned factual knowledge (mathematical thinking) to solve higher order thinking skills (HOTs) problems is an essential requirement of tertiary education. Thus, do these high school leavers have the accessibility of the 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 attained an A grade 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 of them 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 graduates can deconstruct their mathematical knowledge and reconnect it with the underpinnings and linkages of college mathematics requirements.

Mathematical Thinking; School Mathematics; Higher-order Thinking, Heuristics, Non-routine; Problem Solving.