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Abstract
Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that are deemed appropriate for undergraduate students and which foster mathematical habits of mind. These are: generating examples; analyzing reasoning; evaluating mathematical statements; conjecturing and/or generalizing; visualizing; and using definitions. We give rationales for our choices and examples of each type of task suitable for use in an introductory calculus course.
ACKNOWLEDGEMENTS
The authors would like to acknowledge the support of a National Academy for Integration of Research, Teaching and Learning grant for the Task Design Network project.
Additional information
Notes on contributors
Sinéad Breen
Sinéad Breen holds a Ph.D. in mathematics from Dublin City University and has recently returned there as a mathematics lecturer. She conducts research in mathematics education, her main interest being in the teaching and learning of mathematics at undergraduate level.
Ann O’Shea
Ann O’Shea received a Ph.D. in mathematics from the University of Notre Dame. Since 1992, she has been a mathematics lecturer at Maynooth University and was Director of its Mathematics Support Centre there from its inception to 2016. She conducts research in mathematics education at the undergraduate level.