Using Photography and Video to
Support Math Learning
Andrew Shauver
high school math and science
Pennfield High School, Battle Creek, MI
thegeometryteacher.wordpress.com
@hs_math_phys
#MTBoS (Twitter-based international math PLN)
A quick word about #MTBoS (mitt-boss)
#MTBoS = MathTwitterBlogosphere
International PLC of math teachers who blog, tweet, or simply
read blogs and tweets.
Diverse, effective, and excellent sharers.
How many jars will
you need to frost that
wedding cake?
What information do
you need to know to
solve this problem?
What will you do
with the info when
you get it?
5 inches tall
4-inch radius
r = radius of cylinder
h = height of cylinder
frosts about
200 in2
5 inches tall
5 ½-inch radius
5 inches tall
7-inch radius
Solution I got
 Top frosted surface (only 1 base): ~176 in2
 Middle frosted surface (1 base minus on top base): ~218 in2
 Bottom frosted surface (1 base minus middle base): ~ 279 in2
 For a grand total of :~ 673 in2
 Which means you’ll need four containers of frosting.
What teacher moves did you see?
 Lesson design loosely modeled after the #3Act Instructional
Model (described and introduced by Dan Meyer, embraced
by many in #MTBoS)
Student Decision-Making…
 How does the math model the task?
 Cylinder
 Surface area (bases included?)
 Once I decide how to model the task, which measurements
do I need? Which do I not need?
 I have an answer. Is it reasonable?
The value of modeling with mathematics
“The tradition of formal mathematics… leaves many able
students both innumerate and undereducated.
However, when the traditional symbol-intensive curriculum is
anchored in authentic applications and modeling by students,
many will reveal aptitude for mathematics that was previously
undeveloped.”
Burkhardt, H., Muller, E.R. et al (2007)
Find the volume and surface area of…
Taken from Geometry, Holt © 2007, Pg 684
What teacher moves did you see?
 Also, I was snapping pictures the whole time.
 Part classroom-management (“manage-by-
walking-around”)
 But, pictures of student work can be used later…
Four students from a different hour
tried to reflect the trapezoid on the
right over the line.
Rank them in order from “closest -toperfect” to “most improvement
needed.”
All of them need some improvement
Questions for students:
1. What does it mean for a reflection
to be “better” than another?
2. What data can we pull from the
pictures to check?
Then…
 Using GSP or GeoGebra or paper/pencil/protractor/ruler,
have the students pull the measurements
 Or…
PROBLEM: Textbooks have to simplify the
complicated world, but simplify the wrong part.
You don’t simplify the thought process. That part
needs to stay thick and rich.
You simplify by using an accessible context and
asking a simple question.
How many jars will
you need to frost that
wedding cake?
What I’m NOT suggesting…
 I am not suggesting that peppering students with
pictures and videos is the magic bullet…
 The key is to allow the pictures and videos to
support an authentic experience of the content…
 This isn’t about increasing “real world problems”.
Pam and Tommy collect geodes. Pam’s
parents gave her 2 geodes to start her
collection and she buys 4 every year. Tommy
has two geodes that were given to him for his
birthday. He buys 4 every year. If Pam and
Tommy continue to buy the same amount of
geodes per year, when will Tommy have as
many geodes as Pam? Explain your answer.
Postage Stamps
Postage stamps are popular
collectors items. Many
cultures use them to
commemorate famous events
or people who are historically
significant for any of a number
of different reasons!
Pam and Tommy collect postage stamps.
Pam’s parents gave her 2 postage stamps to
start her collection and she buys 4 every year.
Tommy has two postage stamps that were
given to him for his birthday. He buys 4 every
year. If Pam and Tommy continue to buy the
same amount of postage stamps per year,
when will Tommy have as many postage
stamps as Pam? Explain your answer.
Stamp photo credit courtesy of Flickr user “matsuyuki” – used under Creative Commons
Bottle Caps
Bottle Caps are popular
collectors items. People like to
drink the drinks that are
bottled in the capped bottles.
Some of the drinks don’t exist
anymore making their caps
interesting to collect.
Pam and Tommy collect bottle caps. Pam’s
parents gave her 2 bottle caps to start her
collection and she buys 4 every year. Tommy
has two bottle caps that were given to him
for his birthday. He buys 4 every year. If Pam
and Tommy continue to buy the same amount
of bottle caps per year, when will Tommy
have as many bottle caps as Pam? Explain
your answer.
Bottle Caps photo credit courtesy of Ashley McKinnon – used under Creative Commons
Chewbacca Pez Dispensers
Chewbacca Pez Dispensers are
popular collectors items.
Chewbacca is a wookie from
Star Wars who became the
trusted companion of expert
bounty hunter Han Solo.
Pam and Tommy collect Chewbacca Pez
dispensers. Pam’s parents gave her 2
Chewbacca Pez dispensers to start her
collection and she buys 4 every year. Tommy
has two Chewbacca Pez dispensers that
were given to him for his birthday. He buys 4
every year. If Pam and Tommy continue to
buy the same amount of Chewbacca Pez
dispensers per year, when will Tommy have
as many Chewbacca Pez dispensers as
Pam? Explain your answer.
Chewbacca Pez Dispenser photo credit courtesy of Peter Taylor – used under Creative Commons
Effective use should…
 Create an intellectual need for the targeted
content
 Allow intuition to play a role in the
problem-solving process
 Reduce the literacy demand
 Make the context accessible to all students
(Meyer, 2013)
Hershey Bar
Pencil Sharpener Problem
https://www.youtube.com/watch?v=OEbgxRcePF4
https://www.youtube.com/watch?v=gQnHXbWRDVk
https://www.youtube.com/watch?v=13QnV9YMYf0
Speedometer
 https://www.youtube.com/watch?v=5AXYImzuV4c
Time – A common concern
Time – A common concern
 Don’t worry if you are intimidated by the
process.
 Dozens of these types of activities are made
available right now
 Research and steal
Open Q & A
For extended discussion - @hs_math_phys
http://thegeometryteacher.wordpress.com
For more info or extended discussion
Using Photography and Video to
support math class
Andrew Shauver
high school math and science
Pennfield High School, Battle Creek, MI
thegeometryteacher.wordpress.com
@hs_math_phys
#MTBoS (Twitter-based international math PLC)
The Process – Gather photos
 Make your camera your constant tag-along. Photos and
videos are cheap and disposable.
 I use an iPad and a cell phone.
 Lots in class. My students shave stopped being bothered by a
camera on their work.
Transfer photos to workspace…
 I use dropbox to transfer photos onto my laptop.
 “Snipping Tool” has become my best friend
 Also, Windows Movie Maker…