Targeted Discussion Example
Bridging Student Understanding
Conclusion
More on Targeted Discussions
Dr. Roger Fischer
EMAT Project Facilitator
Montana State University
October 21, 2015
References
Targeted Discussion Example
Bridging Student Understanding
O VERVIEW
Targeted Discussion Example
Bridging Student Understanding
Conclusion
Conclusion
References
Targeted Discussion Example
Bridging Student Understanding
Conclusion
References
M ARGARET ’ S E XAMPLE
Margaret sent in a really nice example of what a “Troubleshoot
and Revise” Targeted Discussion could look like. She has
graciously agreed to discuss it with us. Digital copies of her
template will be available on the project website. Take it away
Margaret!
Targeted Discussion Example
Bridging Student Understanding
Conclusion
M AKING C ONNECTIONS
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Consider the following description of analogous tasks:
Analogous mathematical tasks can be used to activate and
bridge relevant student knowledge.
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Margaret’s graphical approach to solving quadratic
inequalities was an analogous mathematical task which
was used to “activate and bridge relevant student
knowledge.”
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What relevant student knowledge was activated by
Margaret’s task?
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Please share your thoughts via the chat window as they
occur to you. If you want microphone control, just ask!
References
Targeted Discussion Example
Bridging Student Understanding
Conclusion
References
C OMING FULL CIRCLE
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Quadratic inequalities are typically treated in a precalculus
course, as was the case for Margaret.
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This suggests that solving quadratic inequalities is an
important skill for success in a calculus course.
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So here’s a question to make you think: Where in a
calculus course would students need to solve quadratic
inequalities?
Targeted Discussion Example
Bridging Student Understanding
Conclusion
C OMING F ULL C IRCLE
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Sketch the graphs of the following curves
y=
2x2
x2 − 1
y = ln(4 − x2 )
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Oh snap! I have to solve a quadratic inequality!
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Good thing I took Margaret’s precalculus class!
References
Targeted Discussion Example
Bridging Student Understanding
Conclusion
References
M AKING C ONNECTIONS A MONG R EPRESENTATIONS
Principles and Standards for School Mathematics (2000) gave
us process and content standards. One of the process standards
is representation. Specifically. . .
. . . instructional programs in mathematics should enable all
students to select, apply, and translate among mathematical
representations to solve problems.
Margaret’s analogous task lays the framework for making
connections between the very abstract algebraic representation
of the solution set for a quadratic inequality and the more
concrete graphical representation.
Targeted Discussion Example
Bridging Student Understanding
Conclusion
A N EXTENSION USING TECHNOLOGY
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http://www.desmos.com is a free, dynamic, online,
graphing calculator
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It is AH-MAZ-ING!
I made a Desmos graph that could be useful for anyone
who wants to replicate Margaret’s targeted discussion in
their precalculus classroom. The link is below:
I
I
https://www.desmos.com/calculator/
ze0zilbuns
References
Targeted Discussion Example
Bridging Student Understanding
A TASTE OF D ESMOS
Conclusion
References
Targeted Discussion Example
Bridging Student Understanding
Conclusion
References
A N INVITATION
For next week:
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Think about a partial understanding or point of confusion
your students have been working through recently.
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Find a particular wrong answer that could serve as a
catalyst for discussion
Prepare a targeted discussion, using the template from
Kazemi and Hintz (2014).
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I
Blank copies will be available on the project website.
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Send a copy to fluo@montana.edu by our next meeting
(October 21).
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We will look them over and give you feedback at that
meeting.
Targeted Discussion Example
Bridging Student Understanding
Conclusion
References
A R EMINDER
On November 13, we will meet in Brooke’s
classroom again. Please bring a videorecording
of a lesson that you taught to your class (about
20-40 min) to share with the group.
Targeted Discussion Example
Bridging Student Understanding
Conclusion
C ONCLUSION
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A targeted discussion “zooms in on a particular idea to
focus a conversation with a group of learners.”
References
Targeted Discussion Example
Bridging Student Understanding
Conclusion
C ONCLUSION
I
I
A targeted discussion “zooms in on a particular idea to
focus a conversation with a group of learners.”
ATTEND TO PRECISION!
References
Targeted Discussion Example
Bridging Student Understanding
Conclusion
References
C ONCLUSION
I
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A targeted discussion “zooms in on a particular idea to
focus a conversation with a group of learners.”
ATTEND TO PRECISION!
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Students can learn to use precise vocabulary. It begins with
you modeling it in the classroom!
A targeted discussion will most likely surprise you in what
it reveals. It is simple, takes little time, and is quite
insightful!
Targeted Discussion Example
Bridging Student Understanding
T HANKS FOR COMING !
Dr. Roger Fischer
Mathematics Instructor
Gallatin College – Montana State University
201 Hamilton Hall
Bozeman, MT 59717
roger.fischer@montana.edu
Conclusion
References
Targeted Discussion Example
Bridging Student Understanding
Conclusion
References
R EFERENCES I
National Council of Teachers of Mathematics. (2000). Principles
and standards for school mathematics. Reston, VA: National
Council of Teachers of Mathematics.
Kazemi, E., & Hintz, A. (2014). Intentional talk: How to structure
and lead productive mathematical discussions. Portland, ME:
Stenhouse Publishers.