Source: Journal of Mathematics Teacher Education, Vol. 16, Iss. 1, (February, 2013) p. 7–31.
(Reviewed by the Portal Team)
In this article, the author argues for the importance of enhancing teachers’ knowledge of the cognitive demands of mathematical tasks.
Therefore, this article explores changes in teachers’ knowledge of the cognitive demands of mathematical tasks following their participation in the ESP ‘‘Improving Practice’’ workshop throughout the 2004–2005 school year.
The article also examines how those changes connect back to teachers’ experiences in the workshop.
Specifically, the workshop focused on the selection and implementation of cognitively challenging mathematical tasks.
Hence, this investigation examines the following questions:
1. In what ways did teachers’ knowledge of the cognitive demands of mathematical tasks change following their participation in the ESP professional development workshop?
2. What is the relationship between changes in teachers’ knowledge of the cognitive demands of mathematical tasks and their learning experiences in the ESP professional development workshop?
The participants were nineteen secondary mathematics teachers, which their teaching experience ranging from three to 30 years.
At the time of their participation in the study, ten teachers were teaching middle school mathematics (grades 6–8) and nine were teaching high school mathematics (grades 9–12).
A group consisting of ten teachers was selected to compare whether the knowledge and instructional practices of ESP teachers following their participation in the workshop would differ from the knowledge and instructional practices of teachers who did not participate in the ESP project (and were not provided with professional development experiences).
Data consist of a pre/post-assessment of teachers’ knowledge of the cognitive demands of mathematical tasks and videotaped discussions and written artifacts from the professional development sessions.
A mixed methods approach was used to identify connections between teachers’ learning and their experiences in the ESP workshop.
The findings reveal that at the end of the ‘‘Improving Practice’’ workshop, ESP teachers significantly increased their knowledge of the cognitive demands of mathematical tasks and had significantly higher knowledge than teachers in the contrast group.
Increase in teachers’ knowledge of cognitive demands
The improvements occurred in teachers’ criteria and rationales for describing high- and low-level tasks.
The responses from novices and pre-workshop teachers consisted of surface-level features, while responses from post-workshop teachers identified aspects of the tasks that provided opportunities for understanding, sense-making, and students’ thinking and actions required to solve the tasks.
Similarly, ESP teachers’ post-workshop task-sort responses reflected an enhanced knowledge of the characteristics of mathematical tasks that influence students’ opportunities for high-level thinking and reasoning (i.e., generalizations, representations, connections).
Furthermore, ESP teachers used language for describing the cognitive demands of mathematical tasks different from language they had used prior to the workshop and different from language used by teachers who had not participated in the workshop.
The differences between ESP teachers’ pre- and post-workshop task-sort responses and between ESP and contrast teachers’ responses indicate that ESP teachers learned to characterize tasks with high- and low-level cognitive demands using ideas in the Task Analysis Guide and other ideas made salient in the workshop.
Connecting teachers’ learning to changes in their instructional practices
ESP teachers improved their ability to identify aspects of tasks that provide opportunities for different levels and types of student thinking (i.e., cognitive demands).
ESP teachers increased their knowledge of the cognitive demands of mathematical tasks and their awareness of how high-level tasks support students’ learning, which together changed teachers’ orientation toward their curricula in ways that supported the selection of high-level instructional tasks in their own classrooms.
Improvements to the ESP ‘‘Improving Practice’’ workshop
Though effective in transforming teachers’ knowledge and instructional practices, the ESP ‘‘Improving Practice’’ workshop could be improved in ways that would further enhance teachers’ knowledge of the cognitive demands of instructional tasks.
The author concludes that the strong connections between changes in teachers’ knowledge and their experiences in the ‘‘Improving Practice’’ workshop provide indications that learning occurred during the workshop, and this learning may have influenced subsequent changes in teachers’ classroom practices.
In addition, many of the findings have broad implications beyond the specifics of this project.
First, teachers’ experiences in solving mathematical tasks appear to have greatly influenced their learning.
Second, the use of a mixed methods approach facilitated connections between teachers’ experiences in the ESP workshop and gains in their knowledge of cognitive demands.