TACTics Journal
/bigger>/bigger>/bigger>/bigger>/bigger>A Publication for and by TOC
for Education Practitioners
May 14, 2004
/fontfamily>
/fontfamily>In this week’s issue:
/smaller>/fontfamily>Elementary/Secondary
TACTics
/fontfamily>(1) Applying TOCFE, the
Mother of All Graphic Organizers to Improve Students’ Problem-solving
Strategies, /fontfamily>Sears Taylor
/fontfamily>Editors’ Notes
/fontfamily>(2) /fontfamily>Kay
Buckner-Seal, Cheryl A. Edwards
/fontfamily>
ELEMENTARY/SECONDARY TACTICS
/bigger>/fontfamily>(1) Applying TOCFE, the
Mother of All Graphic Organizers, to Improve Students’ Problem-solving
Strategies
/fontfamily>/flushboth>From Sears Taylor,
USA
/fontfamily>/fontfamily>/flushboth>Yakima,
Washington Mathematics Conference
April 29, April 30, & May 1, 2004
Presented on Friday, April 30 at 2:30 pm
By Mr. Sears Taylor & Sequoia H S
/fontfamily>/fontfamily>Learning
Objectives:
/fontfamily>Students will be able to:
- Define bottom-up and top-down problem solving & the importance of
connections.
- Explain why learning must begin with a connection to the learner’s
experience.
- Apply a TOCFE graphic organizer to a math problem.
- Discuss how the TOCFE provides problem solution step documentation for WASL(Washington Academic Standards of Learning.
/fontfamily>/fontfamily>An
example from Sears’ presentation:
/fontfamily>TOCFE- Inside the Box/Outside the
Box Problem Solving
Graphic Organizing Your Attack Plan for Solving Problems.
/fontfamily>/smaller>/smaller>/fontfamily>Contextual
Knowledge: “Aunt Polly’s Old Fence” from Tom Sawyer, by Mark Twain—/fontfamily>It is
/fontfamily>The fence is 120
feet long and 5 feet high. It only has to be painted on one side. An average
inexperienced painter can paint 60 square feet per hour. Paint is $10.00 per
gallon and Aunt Polly has 20 gallons of paint in the basement. One gallon of
paint covers 32 square feet.
/fontfamily>/flushboth>/smaller>/smaller>/fontfamily>Will
Tom be able to go to the riverboat on time?
/fontfamily>-/fontfamily>
/fontfamily>Show what decisions go into
your argument and write them out in a logical order.
/fontfamily>-/fontfamily>
/fontfamily>What other things could Tom do
so that he could get to the riverboat on time?
/fontfamily>-/fontfamily>
/fontfamily>Diagram your logic so it is
clearly understandable.
/fontfamily>-/fontfamily>
/fontfamily>List the key items that are constraints
in Tom getting this job done.
/fontfamily>-/fontfamily>
/fontfamily>How could you modify the TOCFE
graphic to include other solutions?
/fontfamily>-/fontfamily>
/fontfamily>What other solutions does Tom
have?
/fontfamily>-/fontfamily>
/fontfamily>How could we include them in
our graphic organizer?
/fontfamily>-/fontfamily>
/fontfamily>Make a graphic organizer with
multiple solutions. This is more related to real life.
/fontfamily>TOCFE Thinking Process Template
/fontfamily>(Remember to start at the
bottom and work up.)
7. Use numeric answers to answer questions.
/smaller>/smaller>6. Calculate numeric answer.
/smaller>/smaller>5. Put data in formula.
/smaller>/smaller>4. Is there any missing information
not given?
/smaller>/smaller>3. What information can I ignore as
unneeded? What is non-essential contextual background?
/smaller>/smaller>2. What information do I need to
solve problem? More data, formulas, etc.
/fontfamily>/smaller>/smaller>/fontfamily>/flushboth>1.
What is the problem from reading the story?
/fontfamily>Write the answer
to each question in an oval starting at the bottom of the page. Connect each
oval with an arrow going from the lowest number to the higher number.
/smaller>/smaller>/fontfamily>Example
of how ovals could be filled in:
/fontfamily>/flushboth>7. There is
not enough time if only Tom.
There is enough paint.
/smaller>/smaller>6. A = 120 x 5 = 600ft2
T = 600/60 = 10 hours
Paint = 20 x 32 = 640ft2
/smaller>/smaller>5. Area = L(120’)
x H(5’)
Time = Area/Rate(60ft2)
Paint Coverage = Cans x 32
/smaller>/smaller>4. Is Tom the only worker? Is there a
hi-tech solution?
/smaller>/smaller>3. Description of house, Tom’s friend
Huck, job on boat, cost of paint.
/smaller>/smaller>2. Area to be painted, Time available
for painting, How much paint do we have?
/smaller>/smaller>1. Can fence be painted in 2 hours?
/fontfamily>
/fontfamily>/flushboth>/fontfamily>How
could you modify the TOCFE graphic to include other solutions?
/fontfamily>- What other solutions does
Tom have?
- How could we include them in our graphic organizer?
- Make a graphic organizer with multiple solutions. This is more related to
real life.
/fontfamily>TOC Logic Diagram for Problem
Analysis and Step by Step Solution:
/fontfamily>- State problem: Paint the
fence by 10:00 AM
/smaller>/smaller>- Determine amount of paint: 120 X 5
= 600 square feet
/smaller>/smaller>- Apply efficiency factor: 600/60 =
10 hours
/smaller>/smaller>- Get time to do total job: 10 hours
/smaller>/smaller>- Determine how much time is
available to game: 2 hours
/smaller>/smaller>- Look at other technology or ways to
do it:
Use spray gun that makes up for lack of time and man hours
Get spray gun that covers 300 sqft/hr.
/smaller>/smaller>- Evaluate alternatives:
A 1. Do not do job
2 Deal with angry aunt and very negative consequences
/smaller>/smaller>B 1. Determine how much help you need
and how many friends
2. Recruit a minimum of 4 friends for 2 hours
/smaller>/smaller>- Complete fence in 2 hours
- Go to ship with Huck by
/fontfamily>
/bigger>/fontfamily>/flushboth>/fontfamily>What
did we learn today?
/fontfamily>/flushboth>- Students use
top-down & bottom-up thinking strategies switching back & forth.
- Our brains process information more effectively when graphics are used.
- TOCFE guides students in identifying constraints needed to solve problems.
- TOCFE graphic organizers serve as clear documentation of a students’ thinking
process. This helps prepare for WASL.
/fontfamily>
/fontfamily>/flushboth>/fontfamily>EDITORS’
NOTES
/bigger>/fontfamily>(2)/fontfamily>
Kay Buckner-Seal, Cheryl A. Edwards
/fontfamily>To gain optimum benefit of
Sears Taylor’s presentation (exceptional graphics and humorous transitions),
you must open the PowerPoint version of his presentation, which is attached. We
thank Sears for sharing his work with us this week.
/smaller>/smaller>/fontfamily>/flushboth>The
pdf version of TACTics is
also attached. You must have Acrobat Reader to open the file. It is freely
available for download from:
http://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.
/fontfamily>/smaller>/smaller>/fontfamily>/flushboth>You
may also view TACTics in its intended formatting, by
visiting our web site at www.tocforeducation.com. Click
on "What's New."
/fontfamily>/smaller>/smaller>/fontfamily>/flushboth>We
welcome your responses, applications of the thinking processes, lessons,
announcements, and etc. Send by mail to: Cheryl A. Edwards,
/fontfamily>