Coaching Notes
Encouraging Math Talk
Context:
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A grade 10 academic lesson was co-planned by three teachers, the board and provincial math
coach, to introduce factoring quadratic expressions
The teachers were working on questioning techniques (open, parallel and scaffolding questions)
as well as math talk learning communities in their classrooms
The co-planning team examined two TIPS lessons on quadratics; TIPS4RM grade 10 Applied
7.4 and a grade 10 academic lesson developed during a lesson study in the Trillium Lakelands
DSB
Using suitable activities from both lessons, open and parallel questions were developed and
placed into the PPQ template with possible questions to scaffold learning when needed
Timing, classroom set-up, materials, and student groupings were all planned
The lesson was to be taught by one teacher period one and another teacher from the same
school period 2
All members in the co-planning team were able observe both classes with the intent of making
adjustments between the two classes if needed
Instructional Decisions- Lesson Adjustments to TIPS Lesson:
Minds On- The card match activity was used to promote students making connections through various
representations and encourage students reasoning with each other. To address the lessons goals the
table of values cards were deleted and the graph and algetile models were switched. Open questions
were developed to elicit and expose student thinking.
Action- BLM 2 contains the chart and first two questions from BLM 7.4.2. Two open questions replaced
a traditional practice question.
Consolidate/Debrief- Parallel questions were developed to allow students to work with less complex
numbers where needed. They provided the teacher assessment data to determine how well students
met the learning goals of the lesson. An open question was developed for homework to provide scaffold
and challenge for the range of learners as well as practice the next day.
What actually happened:
The teacher in the first lesson was pleased with the card match activity. The graph match exposed
some students’ difficulty in making connections to the graph. The whole class debrief was helpful for
those students particularly because of the questions asked and the rich vocabulary used by some
students. The teacher made a mental note to revisit those concepts with the students and probe further
to determine their issues. In the Action portion many students worked independently even though they
were sitting in groups. Some students finished early and others were still working on the problems.
Most students worked independently in the Consolidation portion as well. The teacher used a document
camera for the first time. She stood at the projector with the student’s work and asked questions of the
student. Some of the students continued to do their own work and listen to the discussion. During the
observation and in between the two classes the team discussed what changes could be made when
the lesson is taught again in the next period.
Coaching Notes
Suggested adjustments –
collaboration with: teachers
and coaches
Result of adjustment in
second class
Situation #1:
Although students were seated in
groups of three they were working
independently.
Instruct students to take turns with
the algetiles while the other two
members of the group ‘coach’ how
the tiles should be arranged. Switch
roles.
Students enjoyed taking turns acting
as coaches which prompted more
math talk and sharing of learning
during the investigation.
Situation #2:
Some the students were finished
A quick examination of the question
#3 prompted an instructional change
“ Find as many values and factors
as you can.”
This opened up the question even
more. The team was excited to see
some students used negatives even
though their experience with the
concrete materials was limited to
positives.
The team thought that beginning
independently is a good thing, but
wanted students to discuss their
work after some personal time with
the tasks. It was suggested that after
5 minutes of working independently
the students find someone who
worked on the same task set &
discuss solutions.
Discussing work around ‘like’ tasks
once again invited students to
engage in math talk as well.
Have the students present the work
at the projector while the teacher
stands at the back of the room and
asks some questions. Invite students
to ask questions.
Students enjoyed opportunities to
present their work. All students paid
attention as the teacher asked
questions from the back. At first
students asked silly questions, but
as the teacher modelled good
questions, they became better.
Instructional situations in first
class
while others were still investigating
the Action questions.
Situation #3:
Once again students worked
independently during the
consolidation.
Situation #4:
The teacher was the one presenting
the work at the document camera.
Some students continued to work on
their task.
Debrief after the adjusted lesson:
The teachers were pleased with the open questions and parallel tasks. They found thinking about scaffolding
questions ahead of time to be very beneficial. They were impressed with the impact the simple quick changes
made- having students act like coaches and having student present at the projector while the teacher asks
questions from the other side of the room. Both dramatically changed the classroom dynamics and promoted the
math talk learning community they were striving for.
Student work also brought out the importance of the numbers selected. The team realized they needed to include
some distracter graphs (same y-intercept, but different x-intercepts) next time. Teachers were pleasantly surprised
that students thought to use negatives and zero in open Q.3 BLM2.
This was the teachers and board coach first experience with a coaching cycle of co-planning, lesson observation
and co-debrief. The principal attended some of the planning time. She was present at both classroom observations.
She also attended the debrief portion after both lessons had been taught. The school team found this to be a
Coaching Notes
powerful professional learning opportunity. The principal has made a commitment to sponsor these opportunities
next year, thinking about 1 cycle/unit for the grade 9 and grade 10 teams.