Challenges of maintaining cognitive demand during the limit lessons: understanding one mathematician’s class practices

ABSTRACT

In this study, we examined five limit lessons using Mathematical Tasks Framework to understand students’ opportunities to learn cognitively challenging tasks and maintain cognitive demand during limit lessons. Our analysis of Dr A’s five lessons shows that students rarely had opportunities to maintain or increase cognitive demand. There are two main factors that shaped her instructional practices, students and time. These two factors greatly influenced how she selects and implements limit tasks in her classes. To serve her students’ needs of knowing more rules, formulas and procedures, she selected and discussed those simple tasks a lot. Although Dr A thinks challenging tasks and asking demanding questions can be potentially good instructional practices, she thinks these instructional practices would not serve her students well. With these factors, we made possible recommendations to have more student-centred teaching.

KEYWORDS:

• Calculus
• cognitive demand
• instructional practices

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Dae S. Hong http://orcid.org/0000-0003-0529-6448

Notes

1 We did not videotape classes when they were taught by another person when the instructor was away or when the students had an exam in class.

2 Only questions with mathematical content were considered. Non–mathematical questions such as ‘how are you?’ and ‘how is everything?’ were not considered in our analysis.