Describing cognitive orientation of Calculus I tasks across different types of coursework

Abstract

We discuss the findings of an analysis of cognitive orientation of 4,953 mathematical tasks (representing all bookwork, worksheets, and exams) used by five instructors teaching Calculus I in a two-year college in the United States over a one-semester period. This study uses data from one of 18 cases from the Characteristics of Successful Programs in College Calculus (CSPCC) and characterizes the tasks using and adaptation of an analytical framework developed by Tallman & Carlson (2012). We found differences in the cognitive orientation by type of course work assigned (graded vs. ungraded) and differences by the instructors who assigned the course work. We discuss implications for practice and propose some areas for further exploration

Research on Teaching and Learning Mathematics at the Tertiary Level: State-of-the-Art and Looking Ahead

“…In contrast to these studies that point to the limitations of textbook problems and final examinations, White and Mesa (2014) found that the assigned homework problems at a particular community college were more cognitively demanding than one might expect in light of previous research. Using a similar task analysis framework to that used by Tallman et al (in press), White and Mesa found that nearly half of the assigned tasks were classified as complex procedures or rich tasks.…”

Integral Students’ Experiences: Measuring Instructional Quality and Instructors’ Challenges in Calculus 1 Lessons

“…White and Mesa (2014) analyzed 4,953 tasks that instructors gave to students. They underlined the potential cognitive demand of a task which indicates "the hypothetical operations used to produce the answer" (p. 676) in their definition of tasks.…”

“…When they categorized the tasks into three groups (Simple Procedures, Complex Procedures, and Rich Tasks) across the instructors, 53% of tasks in all types of coursework were in Simple Procedures while 29% were Rich Tasks. In addition, White and Mesa (2014) suggested that instructors" enactment of learning goals could vary even though they used a common textbook.…”

“…In particular, the findings in White and Mesa (2014) showed that more tasks with high cognitive demand appeared when fewer resources were available for a task, or tasks (namely exams) had greater weight in a course grade (49%). In contrast, Tallman and Carlson (2012) showed that 14.8% of test items in 150 Calculus I final exams required students to demonstrate their understanding.…”

“…In contrast, Tallman and Carlson (2012) showed that 14.8% of test items in 150 Calculus I final exams required students to demonstrate their understanding. Using the task categories of White and Mesa (2014), at most, 15% of tasks in the final exams were classified as Rich Tasks. These findings reveal the necessity for more empirical evidence about tasks from low to high cognitive demand.…”