Introducing direction fields to students learning ordinary differential equations (ODEs) through guided inquiry

Abstract

This paper reports on an intervention as part of which direction fields were introduced to students learning ordinary differential equations (ODEs). The intervention was designed and implemented to address issues with students’ conceptions of the solutions of ODEs. These were identified by a diagnostic survey and through a review of the literature. The intervention comprised fifteen guided inquiry tutorials, one of which introduced students to direction fields in the context of first order ODEs. A combination of interviews and immediate and delayed post-testing was used to measure the impact of the tutorial. The design of the tutorial and the results of the interviews and post-test data are reported. A large majority of the students who completed the tutorial were able to successfully complete tasks linking direction fields to their study of ODEs. A significant improvement was also observed in relation to students’ conceptions of solutions to an ODE.

KEYWORDS:

• Differential equations
• direction fields
• solutions to differential equations
• guided inquiry

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Forum for the Enhancement of Teaching and Learning in Ireland [grant number GOIPG/2014/1529].