TACTics Journal
A Publication for and by TOC for Education Practitioners
May 14, 2004


In this week’s issue:
Elementary/Secondary TACTics
(1) Applying TOCFE, the Mother of All Graphic Organizers to Improve Students’ Problem-solving Strategies, Sears Taylor
Editors’ Notes
(2) Kay Buckner-Seal, Cheryl A. Edwards


ELEMENTARY/SECONDARY TACTICS
(1) Applying TOCFE, the Mother of All Graphic Organizers, to Improve Students’ Problem-solving Strategies
From Sears Taylor, USA

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

Learning Objectives:
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.

An example from Sears’ presentation:
TOCFE- Inside the Box/Outside the Box Problem Solving
Graphic Organizing Your Attack Plan for Solving Problems.

Contextual Knowledge: “Aunt Polly’s Old Fence” from Tom Sawyer, by Mark Twain—It is 8:00 AM, Saturday morning in St. Louis, Missouri. Tom Sawyer lives in a nice home with his dear Aunt Polly. It’s a two story white colonial with green shutters. Tom has to paint his Aunt Polly’s fence before he can do anything else today. She often has Tom do chores for her as a way to build character and to earn extra money. It’s a bright sunny day with little wind and no chance of rain. Tom really wants to go on a riverboat cruise with his friend, Huck. It’s not really a cruise, it’s a chance for them each to make over $150 in tips working as bus boys in the restaurant on a Mississippi river boat. The boat leaves the dock at 10:10 AM. Tom lives 5 minutes from the dock.

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.

Will Tom be able to go to the riverboat on time?
- Show what decisions go into your argument and write them out in a logical order.
- What other things could Tom do so that he could get to the riverboat on time?
- Diagram your logic so it is clearly understandable.
- List the key items that are constraints in Tom getting this job done.
- How could you modify the TOCFE graphic to include other solutions?
- 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.


TOCFE Thinking Process Template
(Remember to start at the bottom and work up.)
7. Use numeric answers to answer questions.

6. Calculate numeric answer.

5. Put data in formula.

4. Is there any missing information not given?

3. What information can I ignore as unneeded? What is non-essential contextual background?

2. What information do I need to solve problem? More data, formulas, etc.

1. What is the problem from reading the story?


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.

Example of how ovals could be filled in:
7. There is not enough time if only Tom.
There is enough paint.

6. A = 120 x 5 = 600ft2
T = 600/60 = 10 hours
Paint = 20 x 32 = 640ft2

5. Area = L(120’) x H(5’)
Time = Area/Rate(60ft2)
Paint Coverage = Cans x 32

4. Is Tom the only worker? Is there a hi-tech solution?

3. Description of house, Tom’s friend Huck, job on boat, cost of paint.

2. Area to be painted, Time available for painting, How much paint do we have?

1. Can fence be painted in 2 hours?


How could you modify the TOCFE graphic to include other solutions?
- 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.


TOC Logic Diagram for Problem Analysis and Step by Step Solution:
- State problem: Paint the fence by 10:00 AM

- Determine amount of paint: 120 X 5 = 600 square feet

- Apply efficiency factor: 600/60 = 10 hours

- Get time to do total job: 10 hours

- Determine how much time is available to game: 2 hours

- 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.

- Evaluate alternatives:
A 1. Do not do job
2 Deal with angry aunt and very negative consequences

B 1. Determine how much help you need and how many friends
2. Recruit a minimum of 4 friends for 2 hours

- Complete fence in 2 hours
- Go to ship with Huck by 10:05AM


What did we learn today?
- 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.


EDITORS’ NOTES
(2) Kay Buckner-Seal, Cheryl A. Edwards

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.

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.

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., Cedarville, Michigan 49719, USA. Or, send hyperlink to cedwards@cedarville.net or bucknek@comcast.net.