TACTics Journal

A Publication for and by TOC for Education Practitioners

June 13, 2003

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, Kathy Suerken

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 Taylor, Washington, USA

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 8 AM Saturday morning in St. Louis, Missouri. Tom Sawyer 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 USA

Mike was participating in the TOC Cloud Training at the International

Conference in Florida this spring when he developed this math story

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 8 AM; then, I will not finish

until 6:00 PM.

If I will not finish until 6 PM and the kids at the pump leave at 5 PM; then, I

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 8 AM.

I will not finish until 6 PM. The kids at the pump leave at 5 PM.

I can paint 9 square yards per hour.

CONNECTIONS

(3) Please, Take Note

From Kathy Suerken <suerken@cox.net>

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., Cedarville, Michigan 49719, USA. Or, send hyperlink to

cedwards@cedarville.net or bucknek@earthlink.net.