Entry #7

Smith, M. S., Bill, V., & Hughes, E. K. (2008). Successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14 (3), 132-138.

The authors address an issue resulting from previous research which has shown that cognitively challenging tasks that promote thinking, reasoning and problem solving often decline during implementation. The question becomes why such tasks are so difficult to implement in ways that maintain the rigor of the activity. One reason is that high-level tasks tend to be less intellectually controllable from the teacher's perspective, since a worthwhile task often has more than one specific solution path. Thus the authors proceed to present a plan to control teaching with high-level tasks which they call the TTLP (Thinking Through a Lesson Protocol). The TTLP is divided into 3 parts: Part 1: Selecting and Setting Up a Mathematical Task, Part 2: Supporting Students' Exploration of the Task, and Part 3: Sharing and Discussing the Task. The authors provide the framework of the TTLP (which is an outline of specific questions for teachers to consider) as a figure within the article. In general, Part 1 asks the teacher to identify mathematical goals and expectations of the task. Part 2 focuses on monitoring students as they explore the task and Part 3 focuses on orchestrating whole-group discussion of the task that uses different solution strategies to highlight mathematical ideas. The goal of the TTLP is to prompt teachers to think deeply about a specific lesson that they will be teaching through strategies such as anticipating student responses and creating good questions that will further students' thinking. The TTLP is meant as a reminder and a guide for teachers to gradually mold their teaching around, and not as a daily checklist of questions.

Just as the authors have stated, I too feel as though it is important for teachers to anticipate student responses and develop questions that promote critical thinking. Even with a task that is designed to be thought provoking, much of the value of the task can be lost if teachers do not know how to guide their students through the critical thinking process. I also believe that this is a necessary approach for any task, whether it be considered high-level or not. Even when a set solution path seems like the only approach, there are often many students who reason about things differently. Regardless of how hard the task might appear, I think it is valuable for the teacher to have attempted and thought about the problems for themselves beforehand. I have been in math classes where the teacher admitted they hadn't gone through the problems that they were using as examples because they seemed easy to solve, but in reality the problems had many solution strategies and interesting points that could have been expanded upon if the teacher was better prepared. When teachers are themselves involved in the task they can better guide their students and can build upon alternate strategies that may arise in order to promote deep thinking from the students.