Using a Journal Article as a Professional Development Experience
Title: Thinking Through a Lesson: Successfully Implementing High-Level Tasks
Author: Margaret S. Smith, Victoria Bill, and Elizabeth K. Hughes
Journal: Mathematics Teaching in the Middle School
Issue: October 2008, Volume 14, Issue 3, pp. 132-138
Rational for Use
High level mathematical tasks are often challenging for teachers to implement. The authors of this article suggest that one way to both control teaching with high-level tasks and promote student success with them is through detailed planning prior to the lesson. This article presents such a plan, named TLLP: the Thinking Through a Lesson Protocol, a process designed to support teachers in the use of cognitively challenging tasks. It is a framework for lesson planning that uses students’ mathematical thinking as the critical ingredient in developing student’s understanding of mathematical ideas.
This article reinforces the statement made in the Teaching Principle (NCTM 2000). “In effective teaching, worthwhile mathematical tasks are used to introduce important mathematical ideas and to engage and challenge students intellectually.” p.18.
- The article begins by noting that teachers are often challenged by implementing high level tasks. Have participants discuss the challenges they experience in implementing cognitively challenging tasks that promote thinking, reasoning, and problem solving. At the end of the discussion, suggest that this article presents a framework for lesson planning that may help with these challenges.
- Make a copy of the problem, Bag of Marbles, in Fig 1, page 133 and give to participants. It will be used in this session as a ground to evaluate the use of the TTLP model.
Note that participants in their real situation would have decided on the learning goals as outlined in their curriculum and then chosen a suitable task to meet these goals. For this session, the Bag of Marbles is used as the ground for the lesson planning.
- Ask participants, working in small groups, to solve the problem.
- Share solutions and record strategies used on chart paper.
- Brainstorm some other ways students may solve the problem (other than the ways shared).
- Ask: Why do you think this task is classified by the authors as high level (see Getting Started, page 135 for authors’ ideas on the matter)?
Participants, working in small groups, use the TLLP to prepare a lesson.
- Before participants read the framework for TTLP, figure 2, page 134, the facilitator can give a short overview of the three main parts of the framework in a PowerPoint presentation.
Part 1: Selecting and Setting Up a Mathematical Task
Part 2: Supporting Students’ Exploration of the task
Part 3: Sharing and Discussing the Task
- Participants working in small groups read and discuss the TTLP framework described in Figure 2, page 134. A short discussion could follow on their first reaction to the TTLP. There will be more in-depth discussion as participants use the framework.
Ask participants to use the TLLP framework to develop a lesson, using the Bag of Marbles Task completed above.
Groups share and discuss experiences in developing the plan and especially the implications for everyday use in their lesson planning.
Ask participants to consider student solutions to Bag of Marbles, Figure 3, page 136. Assign two or three solutions per group.
- You could display on chart paper the critical parts for the lesson as a quick reminder of the main points in TLLP:
- What are your mathematical goals for the lesson (what you want your students to learn)?
- What are all the ways the problem can be solved (participants have already discussed this above)?
- What questions might you ask students as they work on the task?
- How will you orchestrate the class discussion, with special attention to accomplishing the mathematical goals determined in Part 1?
- How will you know the students have accomplished the mathematical goals?
- What are the next steps to build on the learning from this lesson?
If you were able to interview the students who wrote each solution, what questions would you ask to:
- gain better insight into his or her thinking?
- advance his or her thinking?
- better communicate his or her thinking based on the work represented?
Share and discuss the group’s suggestions for selected solutions.
- Ask participants to design a TTLP for a lesson they are about to teach. If participants are preparing to teach similar goals in their curriculum they could plan together, using electronic communications. In a follow-up session, participants share experiences they had developing and using the plan and what they learned about their teaching practice.
- The Teaching Principle (PSSM, 2000) states, “Worthwhile tasks alone are not sufficient for effective teaching. Teachers must also decide what aspects of a task to highlight, how to organize and orchestrate the work of students, what questions to ask to challenge those with varied levels of expertise, and how to support students without taking over the process of thin king for them and thus eliminate the challenge” p.19. Ask participants to discuss considering their own classroom teaching experiences or the lesson developed by the authors of the article discussed above.
Connections to Other NCTM Publications
- Brucker, E. L. (2008, December). Journey into a standards-based mathematics classroom. Mathematics Teaching in the Middle School, 14, 300-303.
- Cleaves, W. P. (2008, April). Promoting mathematics accessibility through multiple representations jigsaws. Mathematics Teaching in the Middle School, 13, 446-452.
- Fello, S. E., & Paquette, K. R. (2009, March). Talking and writing in the classroom. Mathematics Teaching in the Middle School, 14, 410-415.
- Hackbarth, A. J., & Wilsman, M. J. (2008, September). 1P + 4R = 5D: An equation for deepening mathematical understanding. Mathematics Teaching in the Middle School, 14, 122-126.
- Hoffman, L. R., & Brahier, D. J. (2008, March). Improving the planning and teaching of mathematics by reflecting on research. Mathematics Teaching in the Middle School, 13, 412-417.
- Knuth, E. J., Alibali, M. W., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2008, May). The importance of equal sign understanding in the middle grades. Mathematics Teaching in the Middle School, 13, 514-519.
- Koellner, K., Pittman, M., & Frykholm, J. (2008, December). Talking generally or generally talking in an algebra classroom. Mathematics Teaching in the Middle School, 14, 304-312.
- Murrey, D. L. (2008, October). Differentiating instruction in mathematics for the English language learner. Mathematics Teaching in the Middle School, 14, 146-153.
- Sharp, B. (2008, October). Mathematical explorations: getting a “bee” in math class. Mathematics Teaching in the Middle School, 14, 182-189.
- Smith, M. S., Hughes, E. K., Engle, R. A., & Stein, M. K. (2009, May). Orchestrating discussions. Mathematics Teaching in the Middle School, 14, 548-556.