Insights from Academic Research

MƒA knows that many teachers have an interest in learning about current and foundational education research in their content area – and who better to provide this insight than a practicing Master Teacher.

New to the MƒA Teacher Voices blog is this focus on important and practical academic research articles in mathematics.

Doug Shuman, two-time MƒA Master Teacher and mathematics teacher at Brooklyn Technical High School, will summarize key mathematics pedagogy research articles over the school year. We hope, over time, this will grow to serve as a valuable resource for both our teacher community and the greater education community.

Article of Focus:

Kara Jackson, Anne Garrison, Jonee Wilson, Lynsey Gibbons and Emily Shahan, Exploring Relationships Between Setting Up Complex Tasks and Opportunities to Learn in Concluding Whole-Class Discussions in Middle-Grades Mathematics Instruction, Journal for Research in Mathematics Education, Vol. 44, No. 4 (July 2013), pp. 646-682, National Council of Teachers of Mathematics

Summary:

You spent hours developing today’s lesson, a unique and interesting problem steeped in great mathematics and brought to life by an interesting and funny context. You handed it out with a short introduction and set the kids to work, some in earnest, some not so much, and some with apparent confusion. With a few minutes left, and after seeing most groups come to some sort of conclusion, you brought the group back together to close the lesson in a crescendo of brilliant discourse. You asked your first question, a question that deftly balances procedural fluency with conceptual understanding. You waited for the hands to fly up and… crickets. Students looked blankly at you as though what you just asked had nothing whatsoever to do with the number crunching they just completed. Has this ever happened to you?

Debriefing after an activity is often the most difficult and least successful part of a lesson. Especially lessons that are demanding in nature, built in context, and require more than procedural fluency. Following Mary Kay Stein’s groundbreaking research on implementing cognitively demanding tasks in the middle school math classroom, the authors Kara Jackson, Anne Garrison, Jonee Wilson, Lynsey Gibbons and Emily Shahan have taken a close look at the whole class discussion phase in their article Exploring Relationships Between Setting Up Complex Tasks and Opportunities to Learn in Concluding Whole-Class Discussions in Middle-Grades Mathematics Instruction, published in the Journal for Research in Mathematics Education in 2013.

This often-cited article rigorously investigates the links between the setting up of a task before students are set free to work and the quality of the ensuing whole-class discussion.  In particular, the authors seek to identify high-leverage practices that teachers can develop that lead to increased student engagement in the task as well as increased learning from the concluding discussion. The authors adopt Stein’s four aspects of high quality task set up:

1. Key contextual features of the task scenario are explicitly discussed.
2. Key mathematical ideas and relationships are explicitly discussed.
3. Common language is developed to describe contextual features, mathematical ideas and relationships.
4. The cognitive demand of the task is maintained over the course of the setup.

By meticulously coding components of videos from 460 lessons implemented by 165 different teachers over two years from 2009-2011, the authors sought to establish a correlational link between the quality of the different aspects of task set up with the quality of the ensuing whole class discussion. The measures of the whole class discussion were grouped into three categories: its academic rigor as maintained by both the teacher and the students, the degree to which students’ responses linked and built upon one another, and the degree to which students supported their contribution with conceptual evidence.

The authors found a positive relationship between the quality of the introduction of mathematical relationships in the set-up and the quality of the whole class discussion. In particular, they found the strength of the relationship increased when the initial discussion was formally orchestrated rather than ad-hoc. They also found that students made more connections to each other’s ideas and provided more conceptual evidence in support of their ideas when the contextual features of the scenario were clearly established and discussed during set up. Finally, they found that teachers paid more and better attention to setting up the mathematical rather than the contextual features of the problem. When they paid quality attention to both, discussions after the task were of higher quality. A common feature running through all of these results was the influence of having broad and active student participation in the set-up, to gauge student understanding but more importantly so students could develop a common language to discuss the mathematical and contextual features of the task.

How can you use task set-up to have a better closing discussion?

1. Make the time for task set-up. Don’t assume that reading the instructions will be sufficient.
2. Always carefully plan how you will introduce a task. Think through both the mathematical and contextual features.
3. Orchestrate discussion about the mathematical and contextual features during set up. Let students come to mutual understanding about what math they are about to use and in what context.
4. Pose some big, open-ended questions during the set up and leave them up during the task. Let students know that these are the big ideas you’ll be circling back to in the closing.
5. Let students discuss big ideas at their tables before bringing the group together as a whole so they can voice their ideas in a small group before sharing them with the whole class.