Title: Tasks to Foster Mathematical Creativity in Calculus I
Fostering students’ mathematical creativity necessitates certain instructional actions - one of which is designing and implementing tasks that foster creativity. Drawing on the literature on mathematical creativity, we describe existing research-based features of tasks for eliciting student creativity, or creativity-based tasks, and provide suggestions for implementation of such tasks. Based on these features, we analyzed two instructors’ first experiences designing and implementing creativity-based tasks in Calculus I. Both instructors’ frequent use of the multiple- solutions feature suggests that this feature could be an entry-point for designing and implementing creativity-based tasks for other instructors seeking to foster creativity. more »« less
Satyam, V.R.
(, Proceedings of the 24rd Annual Conference on Research in Undergraduate Mathematics Education)
S. Karunakaran, Z. Reed
(Ed.)
Fostering mathematical creativity in the classroom requires intentional actions on the part of the instructor. We examine the teaching actions that students in a creativity-based Calculus I course report as contributing to their sense of creativity. Based on interview data, we found the four overall types of teaching actions: Task-Related, Teaching-Centered, Inquiry Teaching, and Holistic Teaching. We discuss subtypes as well as concrete actions, to provide actionable steps practitioners can take to foster students’ creativity.
Tang, G.; Savić, M.; El Turkey, H.; Cilli-Turner, E.; Karakok, G.; Regier, P.
(, Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education)
null; null; null
(Ed.)
Through participation in a research project on fostering creativity in calculus, two instructors showed shifts in their beliefs on teaching. Participation in the project entailed creating mathematical tasks designed to elicit creative responses from students. Support for task development included participation in weekly online professional development sessions. In this paper, we share one instructor’s shifts in beliefs as well as alignment of her pre-existing beliefs with pedagogical actions. Preliminary analysis of her entrance tickets to the professional development sessions and her exit interview indicates that this instructor a) shifted her previous beliefs about a perceived time pressure and b) manifested her existing beliefs into actions regarding multiple-approach tasks.
Gunay, E.E.; Chu, C-Y.; Delgado Tapia, L.; ElMenoufy, O.; Yam, A.; Raje, S.; Jonczyk, R.; Dickson, D.; van Hell, J.; Siddique, Z.; et al
(, ASEE North Midwest Section Annual Conference 2020 Publications)
null
(Ed.)
Background - One of the most critical challenges in engineering education is improving students’ divergent thinking skills. Usually, we observe students’ fixating on only one single solution for engineering problems. However, their ability to think outside the box and provide alternative solutions should be developed. Research shows that engagement may foster the development of thoughts and boost creativity. Purpose/Hypothesis – Our aim was to investigate students’ engagement with tasks that inspire different facets of creativity (verbal, numeric, and visual). Considering the role of demographics in student engagement, we explored the relationship between their engagement level and demographic traits such as gender, major, age, grades (GPA), and the languages they know besides their native tongue. Design/Method - We utilized electrodermal activity (EDA) sensors, a well-documented proxy of emotional engagement, to measure students’ engagement level while performing tasks that inspire different facets of creativity (verbal, numeric, and visual). Due to the non-normal distribution of the data, non-parametric statistical tests were conducted considering engagement as a dependent variable and demographic traits as independent variables. Results - Statistically significant differences in students’ engagement when exposed to creativity inspired tasks were observed. However, no association between demographics and engagement levels were detected. Conclusions - The results of the study may support educators in designing the instructional materials considering creativity-inspired activities so that students’ engagement level can be increased. Further, results from this study can inform experimental designs, specifically participant selection, in engagement focused studies.
Strubbe, Linda E.; Madsen, Adrian M.; McKagan, Sarah B.; Sayre, Eleanor C.
(, Physics Education Research Conference 2020)
null
(Ed.)
Instructor professional development in physics often focuses on a linear path towards using research-based teaching methods. However, this does not reflect how instructors frame their teaching. Instead, we propose a professional development focus on supporting physics instructors' creativity in teaching. Creativity is important as instructors teach in diverse contexts and hold diverse educational values. Creativity research indicates that having a well-structured space to explore many ideas can support creativity. We investigate this for the case of PhysPort, a website for physics professional development. We present results from interviews with PhysPort users, to show how they joyfully explore, feel trust in materials on the site because they are research-based, and use ideas from PhysPort creatively. We also discuss how better site organization could support users' creativity more. Through this case study, we encourage designers of instructor professional development to consider supporting instructors' teaching creativity as a key goal.
Tang, G.
(, Proceedings of the 24rd Annual Conference on Research in Undergraduate Mathematics Education Boston, MA.)
S. Karunakaran, Z. Reed
(Ed.)
In this paper, we describe the student-reported affective outcomes from teaching actions of professors involved in a professional development experience to explicitly value creativity in their Calculus 1 courses. Using the four main teaching themes that emerged (Task-Related, Inquiry Teaching, Teacher-Centered, and Holistic Teaching), we further explored the data for affective outcomes resulting from teaching actions that foster student creativity. We observed five distinct affective outcomes: Enjoyment, Confidence, Comfort, Negative then Positive Feelings, and Negative Feelings. Enjoyment and Confidence were the most reported affective outcomes from the creativity-fostering teaching actions. Particularly, Enjoyment was reported the most from Holistic Teaching and Task-Related teaching actions; Confidence was reported the most from Holistic Teaching actions among all the types. Finally, we offer concrete creativity-based teaching actions that have the capacity to build students’ mathematical enjoyment and confidence.
El Turkey, H., Karakok, G., Tang, G., Regier, P., Savić, M., and Cilli-Turner, E. Tasks to Foster Mathematical Creativity in Calculus I. Retrieved from https://par.nsf.gov/biblio/10297667. Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education .
El Turkey, H., Karakok, G., Tang, G., Regier, P., Savić, M., & Cilli-Turner, E. Tasks to Foster Mathematical Creativity in Calculus I. Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education, (). Retrieved from https://par.nsf.gov/biblio/10297667.
El Turkey, H., Karakok, G., Tang, G., Regier, P., Savić, M., and Cilli-Turner, E.
"Tasks to Foster Mathematical Creativity in Calculus I". Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education (). Country unknown/Code not available. https://par.nsf.gov/biblio/10297667.
@article{osti_10297667,
place = {Country unknown/Code not available},
title = {Tasks to Foster Mathematical Creativity in Calculus I},
url = {https://par.nsf.gov/biblio/10297667},
abstractNote = {Fostering students’ mathematical creativity necessitates certain instructional actions - one of which is designing and implementing tasks that foster creativity. Drawing on the literature on mathematical creativity, we describe existing research-based features of tasks for eliciting student creativity, or creativity-based tasks, and provide suggestions for implementation of such tasks. Based on these features, we analyzed two instructors’ first experiences designing and implementing creativity-based tasks in Calculus I. Both instructors’ frequent use of the multiple- solutions feature suggests that this feature could be an entry-point for designing and implementing creativity-based tasks for other instructors seeking to foster creativity.},
journal = {Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education},
author = {El Turkey, H. and Karakok, G. and Tang, G. and Regier, P. and Savić, M. and Cilli-Turner, E.},
editor = {null and Z. Reed, A. Higgins}
}
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