Professors Doug Corey and Steve Williams recently published an article titled “Teachers’ Knowledge of Student Mathematical Thinking in Written Instructional Products” in the Journal of Mathematics Teacher Education. Doug has answered a few questions about this article below:
Who were your co-authors on this article?
Steve Williams, Eula Monroe, and Michelle Wagner.
Who would you say is the target audience for this article?
It is for teacher educators and for those interested in effectively sharing instructional knowledge among teachers via written lesson plans and similar products.
What is the big problem you hoped to address with this article?
We were trying to understand the nature of student mathematical thinking captured in high-quality written instructional products (think lesson plans or NCTM magazine articles). We looked at artifacts from the US and from Japan.
What are the some of the key ideas in the article?
From the abstract: One key find is that the knowledge of student mathematical thinking shared in the top written instructional products is specific to a task or mathematical topic, varied with descriptions of multiple solutions or ways of reasoning, and sufficiently detailed to make the knowledge usable for teachers.
Student thinking was salient throughout the lesson and took on a variety of roles. For example, student thinking and understanding of ideas related to the lesson were used to set up the lesson (and the thinking students brought into the lesson could be helpful or unhelpful in achieving certain new understandings). The student thinking related to the in-class activity was documented, and specific type of thinking that was the goal of the lesson was also carefully described.
The key instructional decisions were all tied to student thinking in some way. They were justified by the way students thought about related ideas coming into the lesson, how students responded to the task(s) (or sometimes how the teacher anticipated how the students would respond to the task), and the kind of student thinking the lesson was designed to develop. The student thinking in these lesson-plan-type documents included thinking that might be incorrect or unhelpful. All of this points us to the idea that we should be doing a better job of documenting actual student thinking connected to specifics tasks and lesson topics because it enables the teacher to make better instructional decisions to enhance learning.
What are some of the main ideas you hope your audience will take from this article?
We have tended to focus on what teachers should do in a lesson, but not focusing on why those instructional decisions are reasonable. Understanding student mathematical thinking in the way that we described in this article reveals insights about which instructional decisions are reasonable and which are not and really get a why certain instructional moves should be made. However, the student mathematical thinking and the instructional decisions based on that thinking is absent in so many instructional materials (especially commonly used US textbooks). These lesson plans or lesson-plan like documents had a CGI feel to them, but instead of the scope of understanding all addition and subtraction thinking, it was just thinking related to one specific topic and activity.
Abstract:
The successful use of lesson plans as the primary vehicle for storing and sharing teachers’ instructional knowledge in Japan has given impetus to calls by US researchers for the development of a system for sharing teachers’ knowledge through instructional products to improve teachers’ capacity to implement high-quality instruction and to build a knowledge base for instruction. These products would be created by, and for, teachers to use in guiding instruction, thus building and sharing teachers’ instructional knowledge. In this study, we try to characterize one aspect of teacher knowledge that is central in building a knowledge base for instruction, knowledge of student mathematical thinking. We analyze ten written instructional products from the USA and Japan to better understand what knowledge of student mathematical thinking can be shared in such products. We also look at how knowledge of student mathematical thinking is used to guide and justify instructional decisions. One key finding is that the knowledge of student mathematical thinking shared in the top written instructional products is specific to a task or mathematical topic, varied with descriptions of multiple solutions or ways of reasoning, and sufficiently detailed to make the knowledge usable for teachers.