Mathematical Discourse, Part 3: Planning for the Task (Monitoring and Connecting)
By Zack Hill, posted August 29, 2016
In the last post,
we discussed the importance of anticipating student solution strategies before
implementing a task with students. Also, we discussed the importance of
selecting and sequencing which strategies are shared and from which students.
In this post, we’ll discuss the implementation of the task and how to monitor
what students actually do with a task. Also, we’ll discuss how to support
students in making important connections, both to one another’s strategies and
to the important mathematics of the lesson.
Stein (2011) stress the importance of students making connections during a
mathematical discussion. Students need to draw connections between one another’s
representations and strategies they use to complete the task. A question stem
that I use often is, “Where do you see ______ in ______?” For instance, I might
ask, “Where do you see the equation 24 ÷ 6 = 4 in Michael’s drawing?” This can
also take the form of accountable talk, such as asking a student to explain
another student’s work. Also, students need to connect the discussion and
sharing of student strategies to the important mathematical ideas of the
lesson. Otherwise, students can walk away without any real clarity about what
big mathematical ideas they should be taking away from the discussion. I often
come back to a carefully crafted “I can . . .” statement as the discussion is
wrapping up, to ensure that I connect the discussion to the mathematical goal
of the lesson. Ensuring that these types of connections are made is not
happenstance; I plan for it deliberately, keeping in mind potential student
approaches to the task and the mathematical goal of the lesson.
After a task
has been planned, it’s imperative that you circulate and monitor what students
actually do as they work on a task. When monitoring, there’s a lot to notice.
First, it’s important to keep an eye out for the anticipated strategies and make
decisions on which strategies you’ll share as well as from which students.
Second, you’re looking for where differentiation needs to occur. I may need to
support struggling students in finding an entry point for the task. Typically,
I’ll suggest a representation or start them with a line of reasoning as a
scaffold. For students who are making progress, I’ll ask clarifying questions
to ensure they are making sense of the task and the strategy they are using to
complete the task. For the student who has quickly finished the task, this is
an opportunity to deepen understanding of the mathematics. I like to encourage
the use of an alternative representation or to extend the task itself. This
ensures that all students are engaged with the task and working toward the
mathematical goal of the lesson.
To the right
is an example of a modified version
of Smith and Stein’s (2011) monitoring chart that I have used to capture what
students do with a task. Notice the following:
approaches to the task have been anticipated in the left column.
plan has been laid out for the order of sharing student work, progressing from
a drawing to more abstract representations.
the bottom of the sheet are questions that could be used to support students in
making important connections to one another's’ work and the important
mathematical ideas of the lesson.
Monitor/Select column has been left open to jot students’ names as well as notes
about how students actually approach the task as they work.
How do you
monitor students as they work on a task? How do you differentiate for students
as they work on a task? In what ways do you support students in making
connections to one another’s ideas and the important mathematical ideas of the
lesson? Please share in the comments section or reach out on twitter
Hill has worked in education for fourteen years and is currently an elementary
school mathematics staff developer for Pinellas County Schools in Florida. He
is currently serving on the board of the Florida Council of Teachers of
Mathematics (FCTM) and is a member of NCTM. He earned his Master’s in Education
from the University of Florida and is interested in how mathematical discourse
supports understanding of mathematical concepts