TACTics Journal
A Publication for and by TOC for Education Practitioners
In this week’s issue:
Elementary/Secondary TACTics
(1) Using the Math Logic Tree, Sears Taylor
(2) Tom Sawyer—Interdisciplinary Instruction, Michael Round
Connections
(3) Please, Take Note,
Editors’ Notes
(4) Kay Buckner-Seal, Cheryl A. Edwards
ELEMENTARY/SECONDARY TACTICS
(1) Using the Math Logic Tree
Demonstrated by Michael
Round at the 7th International TOCFE Conference
From Sears
After Audrey showed me the Tom Sawyer Tree, which was developed by
Michael, I saw many possibilities. I teach Algebra I at an
alternative high
school. My students have wide
ranging abilities. Because I had short 25-
minute periods on Thursday, I
decided to experiment with the TOC tree. I
used the Tom Sawyer example. I
gave the class a written sheet with the
following information:
• It is
looking forward to leaving with his
old friend Huck on a riverboat for a
weekend cruise. Tom and Huck will
work for tips as bus boys in the Ship’s
Bar and Restaurant.
• Tom’s Aunt Polly tells Tom, “You’re not going anywhere until you
paint the
backyard fence.”
• Tom has plenty of white paint and brushes. The fence is 100 feet
long
and 5 feet high. An experienced
painter can only paint 60 square feet
per hour.
• Aunt Polly’s house is only 5 minutes away from the dock.
• Can Tom go with Huck on the boat?
• Present your argument and analysis of the problem in the form of
a
picture or in a diagram.
My observations from the first three 25-minute classes included
the
following:
1. Students, who in the past had exhibited little to no enthusiasm
for Math,
wrote the diagram down in logical
steps and either drew ovals for the
events or made lists of the events.
2. The top-level students had been bored at times in past classes
because
we have to keep the rest of the
students engaged. The TOC trees were
fascinating to them and they took up the
challenge of properly spacing
the event bubbles and refining
the names of the steps.
3. A student, who refused to write steps, drew in empty ovals
connected by
arrows. When I asked him to explain
what he had drawn, he said
emphatically, “I know exactly what goes
in each circle. But, I can’t fit my
writing in the circle.”
I said, “Well you can use numbers inside the circles and then make
a key
list showing what words match up
with the numbers you used on your
tree.”
He thought about it for a while and then said, “It will be easier
for me to
redraw the boxes bigger so I can
fit my writing inside.”
This student’s logic tree was perfect.
4. The arrows branching out from event bubbles caused the students
to
investigate other possibilities once
they realized Tom could never paint
the fence himself.
The students’ alternatives were:
a. Tom gets help to paint.
b. Tom gets a spray paint gun to increase his speed.
c. Tom disobeys Aunt Sally.
The students also showed the results of each action. For the
option of
disobeying Aunt Polly the negative
effects were discussed and it was
decided that it was in Tom’s best
long-term interest to obey Aunt Polly.
5. The TOC Tree helped math resistant students to clearly see how
each
key data element fit into the
problem solution.
I will not get to play with the kids at the pump. I want to play
with the kids at the pump.
I need to get someone to paint the fence. Jim is gullible.
I’ll get Jim to paint the fence.
(2) Tom Sawyer—Interdisciplinary
Instruction: Literature/
Math Lesson
By Michael Round
Mike was participating in the TOC Cloud Training at the
International
Conference in
problem:
I have to paint a fence that is 30 yards long and 9 feet high. If
the fence is
9 feet high and there are 3 feet in a yard; then, the fence is 3
yards high.
If I have to paint a fence that is 30
yards long and 3 yards high and 30
yards times 3 yards equals the
total yards of fence to be painted; then, I
have to paint 90 square yards of
fence.
If I have to paint 90 square yards of fence and I can paint 9
square yards
per hour; then, it will take me
10 hours to paint.
If it takes me 10 hours to paint and it is now
until
If I will not finish until
will not get to play with the
kids.
If I will not get to play with the kids and I want to play with
the kids; then,
I need to get someone to paint for me.
If I need to get someone to paint for me and Jim is gullible;
then, I’ll get
Jim to paint the fence for me.
have to paint a fence 30 yards
long.
The fence is 9 feet high.
3 feet = 1 yard
The fence is 3 yards high.
I have to paint 90 square yards of fence.
30 yards times 3 yards equals the total
yards of fence to be painted.
It will take me 10 hours to paint the fence. It is now
I will not finish until
I can paint 9 square yards per hour.
CONNECTIONS
(3) Please, Take Note
From
John has posted Michael Round’s Math PowerPoint presentation from
the
conference as a downloadable file on
our web page: www.tocforeducation.com.
It can be found on the opening page, after the introduction, as a
blue button
in the bottom right hand
corner: “New TOCFE Math Application”.
EDITORS’ NOTES
(4) Kay Buckner-Seal, Cheryl A. Edwards
This week’s TACTics includes graphics, which can only be seen in
the pdf
version of TACTics. Please note that
the pdf version is attached. However,
you must have Adobe Acrobat
Reader to open the file. It is freely available
for download from:
www.adobe.com/products/acrobat/readstep.html.
If you have the Reader installed but still can’t open the file,
drag it from
this e-mail to your desktop,
launch the Reader, and open from the FILE
menu.
You may also view TACTics in its intended formatting, by visiting
our web
site at www.tocforeducation.com.
Click on "What's New."
We welcome your responses, applications of the thinking processes,
lessons,
announcements, and etc. Send by mail to:
Cheryl A. Edwards, 2253 S. Hill
Island Rd.,