Teaching Mathematics
with Technology
Birgit Loch
Mathematics
Engineering and Science Education
Research Group
Swinburne University of
Technology
bloch@swin.edu.au
Overview
• Why use technologies?
• Electronic writing in class and for
recordings
• 2 ideas to change the way we teach
• Immediate feedback (Step 1 and Step 2)
• Roaming about
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Chalk and blackboard?
• It worked for us!
• It needs minimal
preparation and no
post-production
Teaching Mathematics with Technology
www.cosmosmagazine.com
3
What’s wrong with chalk and
blackboard?
• We are teaching
mostly nonmathematicians
• Your back to students
• It is focused on face
to face teaching
www.cosmosmagazine.com
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What’s wrong with PowerPoint?
PDF slideshows?
• An example from MathsCasts
(also investigated with Jordan, Lowe, Mestel & Wilkins (2011))
•
•
•
•
Handwriting gives you ‘a sense of “doing maths”’
‘Handwriting imparts methodology better’
Students need to see how handwriting is set out
But: typed is neater and easier to read!
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How did I get involved in
educational technologies?
• Teaching first year calculus and linear
algebra at UQ
Loch (2005)
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Electronic writing in class
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Student feedback
• “Perfect lecture set up. Perfect course for that matter,
I’ve really enjoyed this subject, each maths subject
should have this setup” (UQ student, 2004)
• “It brings the whole lecture virtually anywhere along with
you. Loved it. Great approach.” (Swinburne student,
2010)
• “I found the slides to be vital in my learning” (Swinburne
student, 2010)
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Lecturer feedback
• led to more engagement with technology in
general
• made lectures more dynamic
• have led to a change in teaching approaches
• “Students are now more involved in contributing”
• “In terms of how the use has invigorated my
teaching. […] For the first time in years I have
felt excited about my teaching and that is
reflected in how I interact with students. So then
they get excited”
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“Pen screens”
• This technology may already be available
in a lecture theatre near you!
• Would you recognize a pen screen?
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Lecture recording
• “You can’t do this. Students won’t come
to class any more”
• Well, actually …
> Study at USQ with on-campus students
> Students kept turning up!
> They quoted “interaction” and “being
able to ask questions” as reasons
Loch (2010) and Loch (2011)
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Short focused recordings
• “There’s an app for this”
ScreenChomp
Mathscasts.org
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Student feedback
• “Yes, I watched them all. They are fantastic,
much better than a typed response.”
• “Every time I get stuck on something, I’ll go back
to a MathsCast, and it makes it a bit easier to go
through questions out of a book” .
• This student also said that not only does he find
maths easier to grasp, but he has even started
enjoying it.
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Changing the way we teach
• What if your students watched a short
screencast demonstrating how to explain a
solution in an assignment?
BEFORE they attempt the assignment.
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The flipped classroom
http://www.knewton.com/flipped-classroom/
• You record the important points of your lecture
and expect your students to watch BEFORE
they come to class
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The flipped classroom
http://www.knewton.com/flipped-classroom/
• Class time is used to discuss misconceptions, to
get students to work through problems, to
provide immediate feedback
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Immediate feedback (step 1)
• Audience response systems (“clickers”)
• Revision
• Explaining where students often go
wrong
• Checking understanding
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Some student feedback
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Some student feedback
• “Changes the form of the lecture”
• “Can move on if everyone understands a question”
• “Can cover in more detail if misunderstanding”
• “Fun”
• “Helps gauge class/own understanding”
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Challenging misconceptions
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Encouraging deeper understanding
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A warning…
• The results from clickers questions can
be demoralising!
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The problem with clickers
A)
B)
C)
D)
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Immediate feedback (step 2)
• Advanced Concepts Teaching Space
(UQ, with Diane Donovan (submitted))
• 100 pen-enabled screens, SynchronEyes software
• Test revision sessions
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Selecting student work
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The sessions
• Students were given (incorrect) solutions to
potential test questions, and asked to mark.
• Students were asked to solve potential test
questions
• Student work was then selected, displayed and
discussed
• Interaction took time
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Student feedback
Themes from comments:
• ‘engaging’
• ‘involved’
• ‘interactive’
• ‘fun’
• ‘useful’
• ‘cool’
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2011: Did you learn more in the ACTS lab
session than you would have in a normal
classroom? (n=87)
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Lecturer feedback
“Was able to emphasise the principles of
problem solving strategies, analytical
thinking and logical presentation, and to
implement these strategies straight
away.”
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Is there a cheaper version?
• Tablet PCs for students
• Graphics tablets connected to lab
computers
• MeTL software (Monash Uni)
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Exam preparation sessions
• Offered by the Maths and Stats Help Centre
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Roaming about
In a large lecture theatre,
• what if you were no longer physically
separated from your students?
• what if you gave the stylus to your
students?
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Going wireless
• Various solutions
http://www.monash.edu.au
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Example
Solve:
𝑥 − 𝑦 + 2𝑧 = 7
2𝑥 + 3𝑦 − 𝑧 = 9
4𝑥 − 𝑦 − 2𝑧 = 11
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More research needed!
• Best practice in the use of technologies for
mathematics learning and teaching
• How to involve other lecturers in the
effective use of educational technologies?
• What PD is needed?
• How to convince ITS divisions?
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