Dear GCPS Families,
Earlier this past week we had the opportunity to work with our OCDSB Instructional Coaches, Claire and Rebecca, and Sonja Karsh, retired Principal and former Ministry of Education Student Achievement Officer. Staff members spent the day learning together and exploring how to increase student persistence with challenging math problems. Guiding their work was the article, “Orchestrating Discussions” in which 5 practices are offered for using student responses effectively in the consolidation component of a mathematics lesson.
The 5 practices outlined in the article are:
- Anticipating student responses to challenging mathematical tasks
- Monitoring students’ work on and engagement with the tasks
- Selecting particular students to present their mathematical work
- Sequencing the student responses that will be displayed in a specific order
- Connecting different students’ responses and connecting the responses to key mathematical ideas
All of these practices require careful planning on the behalf of the teaching team, but they are designed to ensure that the following two outcomes occur:
- teachers use students’ responses to advance the mathematical understanding of the class as a whole
- teachers gain time to make instructional decisions during the lesson and greater control over what happens in the discussion (consolidation) component of the lesson
During the planning of the lesson, teachers anticipate the variety of solutions students might generate as they work through the problem. They also think through how the strategies used in the different solutions are related to the targeted mathematical concepts being addressed.
Anticipating solutions requires that the teacher do the problem as many ways as he or she can. However it is often helpful to expand on what one might be able to do individually by working on the task with other teachers and reviewing responses to the task that might be available (Smith et al, 2009)
This is where the work with our Instructional Coaches began on Tuesday. Opportunities for staff to work together bolster individual teacher’s capacity. On Tuesday, staff generated a list of possible solutions and prepared observation sheets to use when they went into the classroom. For our work with the Grade 5/6 class, two problems were presented. The first was:
Four friends have 7 brownies to share. How many brownies does each friend get if they are shared equally?
The second problem was:
Six friends have 11 brownies to share. How many brownies does each friend get if they are shared equally?
The anticipation / observation tool shown here was prepared after staff generated possible solutions to the problems in their planning together. They then went into the classroom to present the problems and then observe the students working on the problems.
As students work through the problems, the teaching team moves through the classroom, stopping to observe and listen to students, quickly recording observations in the chart above, ensuring that all students are participating and asking questions where necessary to help students clarify their thinking.
Questioning a student or group of students while they are exploring the task gives them the opportunity to refine or revise their strategy before launching a whole-group discussion (Smith et al, 2009)
Monitoring students as they work and asking clarifying questions are activities that I try to engage in whenever I visit classrooms. I am always interested to know how students are approaching tasks and what skills and strategies they are calling upon and developing. The samples below show student work from the session on Tuesday:
Selecting and Sequencing
Deciding which students share their work and in what order is based upon the learning goals set out while planning the lesson. In this sense, the teacher uses student responses to weave the narrative of the desired learning goals.
As students share their solutions, the teacher asks questions and helps students to connect their work to the different solutions presented by their peers and to the mathematical goals of the lesson.
Effective discussions can help students evaluate accuracy and efficiency in solving such problems, and the kinds of mathematical patterns that can be most easily discerned. Rather than having mathematical discussions consist of separate presentations of different ways to solve a problem, the goal is to have student presentations build on each other to develop powerful mathematical ideas. (Smith et al., 2009)
Do Try This At Home!
You may be wondering how this information will apply when you are working to support your child in their mathematical thinking and communicating at home. From my observations of students working through problems, a key support you can provide is to ask questions. Students struggle to explain their thinking to me and to their peers and need as many opportunities as possible to develop this skill. The Partnership for 21st Century Skills identifies communication as a crucial skill for our students to succeed. While it may be tempting to direct your child in his or her approach, especially if you feel that they are off course, focus instead on asking questions to help make their thinking more visible and to have them reflect on their thinking. A simple, “tell me what you are thinking as you solve this.” can provide insight into the skills your child is using and those still in the development stage. Furthermore, additional practice in talking through their solutions prepares students for sharing their thinking in class. If your child does not have math homework to work on, don’t forget that we have a weekly “Minds on Math” challenge that students can work at on their own time.
I hope you all enjoyed a restful long weekend!