Dawn Teuscher recently had a paper titled “Influence on Curriculum on College Students’ Understanding and Reasoning about Limits” published in the conference proceedings for the Research in Undergraduate Mathematics Education (RUME) conference. Dawn has answered a few questions about this article below:
Who were your co-authors on this paper?
Navy Dixon and Erin Carroll were my co-authors. They were undergraduates when we wrote the paper and are now graduate students in our department.
Who would you say is the target audience for this paper?
Undergraduate mathematics instructors.
What is the big problem you hoped to address with this paper?
The importance of curriculum AND teachers in helping students make sense of mathematics and connecting new knowledge with students’ current knowledge.
What are some of the key ideas in the article?
Students who took the Pathways college algebra course and reasoned with high covariational reasoning prior to learning limits in calculus continued to reason with high covariational reasoning regardless of their calculus instructor.
Some students tended to reason more about the limit as a procedure and this was typically related to what was emphasized by their calculus instructor in their class.
Students who had high covariational reasoning at the beginning of the study, which tended to be Pathways students, tended to have a more sophisticated understanding of limits at the end of the unit.
The Pathways curriculum helped students make sense of limits, even though limits was not a topic that was discussed during their College Algebra course. These students were aware of connections to the limit concept that they were taught during College Algebra.
What are some of the main ideas you hope your audience will take from the article?
Students need to learn to reason covariationally. This type of reasoning will help them in their mathematics courses, but more important it will help them make sense of the mathematics that is around them. Instructors need to also be focused on the covariational reasoning that their students are using or not using.
The abstract for the article follows:
The Pathways to College Algebra curriculum aims to build concepts that cohere with the big ideas in Calculus, and initial results suggest improved readiness for Calculus by students who use the curriculum. Our study examines similarities and differences of Pathways and non-Pathways students understanding and reasoning about the calculus concept of the limit. We compare students’ understanding of limits at the beginning and at the end of the unit. Our findings suggest that (1) students reliance on procedures, combined, or quantitative reasoning was dependent on the calculus instructors’ emphasis in the class; (2) students who begin their Calculus class with high covariational reasoning gain a more sophisticated understanding of limits; and (3) when curriculum is coherent students will identify mathematical connections.