Snaps shots from a computer program that helps kids learn math in a fun way. The program are short and the students are motivated to play with them and create their own art

1. Math Mentoring with a Heart
Making difference through mentoring Math

2. Introduction
I am now 67 years old. For 33 I worked as a Math teacher at Ithaca College, trying to bring the beauty of Math and Life to young
students and help alleviate the fears from Math that many students have. One of the tools I used in my teaching was a computer
program where the students could create “mathematical art”
Link to program: http://www.familymath.org/dogo/dogo.html
You can copy and paste the codes into the program and test it
Link to code: x=13 repeat(x/2) {star(150, x, index) with stroke = hue(index*720/x)}

3. Some Dogo Examples
polygon(80, 5) with fill=hue(50)
c/4 circle(50) with fill=red rect(100,60) with fill = blue
<<
{ c/4 g e g c g e g c g e g }
{c/1*3 layers(100) rot(0=>90)
{stargon(100,5,1=>2)} }
>>
x = 12
repeat (x) {
star(50, 12, index) with stroke =
hue((index*720)/x)
}

4. Teaching Principle: starts small and progress
Explore by changing numbers
Each time a picture is followed by a note
1. c/4 circle(10)
2. e/8 circle(20) with fill = Red
3. g/4 layers(10) circle(60=>20)
4. r/4 circle(60) at(-40,0) circle(20)
5. r/8 layers(5) at(10=>100,0) circle(15)
Each picture can be seen as a question
Or a puzzle and lead to other good questions

5. Numbers and Stars
1. c/8 star(80,7,3 )
2. e/16 star(60,7,3 )
3. g/8 star(80,7,2 )
4. r/8 star(70,9,3 ) circle(70)
5. r/4 layers(5) star(100,11,frame)

6. More shapes
The simplicity of the program is the key
1. r/4 rect(100,60) with fill=green
2. r/4 polygon(60,6) with stroke = red
3. r/4 stargon(30,5,2.5) with fill = purple
4. r/1 layers(10) stargon(80,5,0.5=>1.5)

7. Composing pictures and Music in Parallel
<<
{c/4 e g c}
{r/1 animate moveto(-100=>100,50) circle(20) with fill = red}
{r/1 animate moveto(100=>-100,-50) circle(20) with fill = blue}
>>

8. Dogo Puzzles
Change the lines of code to produce the shapes
polygon(40, 3) with fill=blue
star(50,5,3 ) circle(40)
circle(30) circle(40)
r/4 rect(10,100) rect(100,30)

9. Grid Puzzle
Change the line of code to produce this (animated) shape
r/1 animate grid(3,3,100,100){circle(0=>50 )}

10. In 2008 I discovered another
wonderful tool to teach
“School Math” that is called
GeoGebra
https://www.geogebra.org/
and
https://www.geogebra.org/graphing

11. Before the invention of Factory teaching there was
mentoring with a heart

14. True Story: Donuts on the Road
Teaching can be very difficult sometime. Imagine that you are sailing for days and nights in a small sailboat and there is no sun and no
stars. Only heavy clouds. Grey. Hopeless. This is how we felt every morning in our small Math Fundamental class that was meeting in
the basement classroom without windows in Dillingham Center three times a week; Monday, Wednesday, and Friday at 8:00 in the
morning.

15. There were 8 of us. Seven students and a teacher. No one really wanted to be there. There was no purpose, there was no meaning
and we did not perceive any light. It was late Fall and the days started getting shorter. Half a semester passed. Then one morning,
when I could not stand the isolation and despair any longer I asked one of the students to sit on a chair and held her hands. I looked
into her eyes and opened my heart. I shared how lonely I felt. How difficult it is for me to come to this class and how difficult my night
was.

16. Then it was her turn. She looked into my eyes and shared how difficult it was to wake up in the morning. How someone had activated
the alarm at 2:00 and everyone was evacuated from the East Towers and only an hour later was allowed to return. The mutual sharing
took only 20 minutes and when it ended something changed in the class. There was an air of optimism. A feeling of new life.

17. A few days later I decided to give all the students in the class a version the placement test again. The test that they had
failed when they first came to the college. The only change was that I allowed them to use a calculator. They all passed
the test!

18. I was so happy and they were so happy. It felt that now we can devote more time to explore deeper questions than just technical
ways to solve math problems. A few days after they passed the test I had to go to a conference in Oregon. I also learned that one of
the students is going to have her Birthday when I return. What an opportunity to celebrate. I decided in my heart to buy donuts when I
come back from Oregon and bring them to class on Monday and have a surprize party to celebrate that all passed the test and have a
birthday party at the same time. When I returned from Oregon on Sunday night, I was very tired and forgot my decision. The next
morning I went for a walk with my dog Dubie on Warren Rd. It was very cold. From the distance I saw something white on the road.
Snow?

19. But it was not snowing. Coming closer I saw a box of fresh donuts. They probably fell from a delivery truck to one of the local motels.
I took the donuts and brought it home and my small family enjoyed the feast with warm tea. Only then I remembered my decision.
There were enough donuts for the whole class and we had our party. Only at the end of the term I told the students the story.