mathematical problem posing framework of undergraduates in learning basic calculus

Problem posing is defined as the generation of new problems or reformulation of a given problem. contemporary educational practice not only place a heavy emphasis on problem solving but also on problem-posing. problem-posing tasks in learning basic calculus (calculus-1) have yet remained unexplored at the tertiary level. this study investigatesundergraduates’ problem posing abilities regarding task organization, knowledge base and preferred strategies. in this exploratory research, one hundred and twenty-four first year engineering students of four iranian universities responded to “mathematical problem posing test”. after analysing pen- paper data, in second phase, twelve of respondents werepurposefully selected for individual “retrospective task-based interview” to obtain more evidences for confirming students’ problem posing difficulties. the study employed purposive convenience sampling. research instruments included problem-posing tasks organized through reconstructing the textbook integral problems based on structured and semi-structuredproblem posing situations. the thematic analysis of students’ pen-paper data demonstrated two main categories of undergraduates’ problem posing abilities were including “ability in performing cosmetic changing” and “ability in performing significant changing”. meanwhile, they were more competent to apply “modifying given” heuristics in terms of cosmetic changes in a structured situation, compared to significant changes i.e. “what ..., if not?” heuristics insemi-structured situations. this means that participants were only able to follow the processes of original textbook problem in the imitation manner which indicated their weakness in representation basic theorems as a cognitive aid, and constructing a novel link between two existing mathematics concepts or with the real life situations by using precise mathematicslanguage. these findings elaborates that the students’ problem posing performances can be fostered by incorporating problem posing activities in teaching-learning materials.