Abstract

 
 
 We describe an approach to develop higher-order thinking skills (HOTS) among first-year calculus students. The ideas formulated by Brookhart to develop HOTS were used to identify from the literature three core abilities that should be targeted. Then eight expected learning outcomes for the development of HOTS were documented, in the context of the study of first-year university calculus. Those expected outcomes were used to formulate sample tasks that were designed to target the development of the eight abilities. A pilot study was done to determine whether the tasks had the high mathematical demand envisaged. It was found that about 37% of the participants did not give any response to the tasks. Further it was found that about 31% of the participants were able to critically evaluate a given possible solution to a problem and make a value judgement. It is recommended that to promote HOTS among students, the formulation of tasks should focus on developing the following abilities: interpreting a general definition or statement in the context of a given model; translating a worded or graphically represented situation to relevant mathematical formalisms; identifying possible applications of mathematics in their surroundings; identifying linkages between groups of concepts and interpreting these linkages in the context of a model; working systematically through cases in an exhaustive way; critically evaluating one’s and others’ presented solutions to a problem; interpreting and extending solutions of problems; and using with reasonable skill available tools for mathematical exploration.
 
 
 
 
 Significance: 
 
 
 
 A large proportion of the student intake at university level is unable to answer mathematics questions that focus on HOTS. There is therefore a need to deliberately focus on and promote HOTS amongst the average students in the context of calculus.
 
 
 
Highlights
Introduction and motivationDuring the past few years we have had informal discussions with colleagues who lecture first-year university calculus
Our formulation of expected learning outcomes is that students should be able to: interpret a general definition or statement in the context of a given model; work systematically through cases in an exhaustive way; identify linkages between groups of concepts and interpret these linkages in the context of a model; translate a worded situation to relevant mathematical formalisms; translate a graphically represented situation to relevant mathematical formalisms; identify possible applications of mathematics in their surroundings; critically evaluate one’s and others’ presented solutions to a problem/question by identifying errors, redundancies, alternative solutions and how a solution could be improved; interpret and extend solutions of problems; and use with reasonable skill available tools for mathematical exploration
The questions that we formulated to target the development of higher-order thinking skills (HOTS) abilities indicated in the above outcomes are documented in the following sample tasks
Summary
During the past few years we have had informal discussions with colleagues who lecture first-year university calculus Those discussions gave the impression that much of their energy was and still is consumed in getting students to become comfortable with the prerequisites for calculus and the basics (skills and concepts) of calculus. The former is a result of an increasing number of students gaining entry to study university calculus. The University of KwaZulu-Natal is one such institution This situation has resulted in a lack of focus on higher-order thinking skills (HOTS) in the context of the study of calculus. It is for these reasons that we decided to do a study on the formulation of tasks to develop among our students HOTS in the context of first-year calculus
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