Karismath Sat 14th at 2pm: videos, computer-based math. Pre-event challenge: GRIDS!

[Maria Droujkova]

During the event, Shad Moarif, the founder of Karismath, will lead brainstorming about mathematical videos and dynamic mathematics in general.

The recording will be at http://mathfuture.wikispaces.com/Karismath
All events in the Math Future weekly series: http://mathfuture.wikispaces.com/events

Event challenge! Reply to this email with your thoughts!

What types of the Grid do you see from the pedagogical perspective?

Other discussion places:
Math Future wiki: discussion tab http://mathfuture.wikispaces.com/message/list/Karismath
LinkedIn: "Math, Math Education, Math Culture" group http://www.linkedin.com/groupItem?view=&gid=33207&type=member&item=88774229&qid=00e42ab4-4f69-453e-8a79-0a181ab07bc9
Facebook: http://www.facebook.com/karismath/posts/334691806549990

In a grid, there is an obvious connection between the product cell and the simultaneity of two bits of information coexisting within it. Shad is exploring ways of breaking this connection down into a sequence of transitional steps by distilling them visually. Shad has categorized the Grid into eleven types according to their uses for storing, sorting, and displaying numerical information (see below).

What pedagogical types of the Grid come to your mind?

How to join

• Follow this link at the time of the event: http://tinyurl.com/math20event
• Saturday, January 14th 2012 we will meet online at 11 am Pacific, 2 pm Eastern time. WorldClock for your time zone.
• Run the Java applet and follow instructions.
• If this is your first time, come a few minutes earlier to check out the technology. The room opens half an hour before the event.

The GRID as Pedagogical Tool

Shad explains in more detail:

The grid, composed as it is of horizontal and vertical “bands”, produce trapped spaces of specific sizes:
These spaces represent the congruency of a pair of simultaneously existing elements (a) and (b).
There is an obvious connection between the product cell (ab) and the simultaneity of two bits of information coexisting within it. The connections take multiple forms. The grid, therefore, is generically designed as a tool for creating mathematical content (the Math itself) as well as explaining it (pedagogy).
I am exploring ways of categorizing types of Grids from "an ordered pair" perspective i.e. (x) ascending levels of cognitive development (Elementary to High School), and (y) rising levels of mathematical complexity:

1. Grid for Analysing Visuo-Spatial Correspondence
2. Grid for Pairing People with Corresponding Activities
3. Grid for Pairing Abstract Values and their Quantity
4. Grid for Product Relationships
5. Grid for Displaying Identical and Similar
6. Grid for Intepreting Data
7. Grid for Representing Ordered Pairs
8. Grid for Displaying Transformations
9. Grid for Measuring Slopes
10. Grid for Measuring Length of Straight Lines
11. Grid for Visualising Functions

The idea is achieve as much accuracy as possible in pairing x and y. All the courseware that envelopes and integrates the use of the grid has to be created and explained simultaneously via animation, and accurate pairing is integral to designing the courseware.

This webinar is to invite ideas, insights and suggestions regarding my Grid Categorization, more specifically around the labels I have used. 

About Karismath

Karismath mediates visually between Math and the learner. It makes math concepts visible, accessible and useable. Learners delve deeper behind the numerical surface of mainstream Math to explore visual constructs of concepts. The use of visual scaffolding traces this natural path of learning. Initially using imagery but no numbers, the program gently moves learners to abstract concepts and mathematical operations. Designed for all whom the curriculum has failed.

Karismath YouTube channel offers free lessons http://www.youtube.com/user/Karismath such as this one on early algebraic thinking  http://www.youtube.com/watch?v=zKqEMcys8Uk

Event Host

Shad Moarif, Ed.M., President, CLSO Learning Systems Inc. is the developer of the Karismath program.
Shad is a Harvard graduate who was a student of Dr. Jeanne Chall (of the Harvard Literacy Lab) and also of Dr. David Rose, Professor of Neurosciences at Harvard Univerity, and the pioneer of Universal Design in Learning, or UDL. He has a background in Science, Psychology, Reading and Mathematics.
An ardent advocate of UDL himself, Shad’s work has been influenced by his 35 years of teaching Math and Language to children (and adults) with learning difficulties. He was Vice-President of the International Dyslexia Association (British Columbia), and also served as a member on IDA (BC) Advisory Board. 

Cheers,
Maria Droujkova
919-388-1721

Make math your own, to make your own math

 

[Alexander Bogomolny]

Maria,

this is in response to your early morning inquiry, viz., " Do you have content related to grids or tables?"

Tables:

1. Modulo arithmetic

http://www.cut-the-knot.org/Curriculum/Algebra/Modulo.shtml 

2. MinMax theorem

http://www.cut-the-knot.org/Curriculum/Algebra/MinMax.shtml

3. Calendar magic

http://www.cut-the-knot.org/SimpleGames/Calendar.shtml

4. Arithmetic magic matrix

http://www.cut-the-knot.org/Curriculum/Arithmetic/ArithmeticMagicMatrix.shtml

5. Gergonne magic trick

http://www.cut-the-knot.org/Curriculum/Magic/GergonneMagic.shtml

6. Magic in Square

http://www.cut-the-knot.org/Curriculum/Magic/MagicInSquare.shtml

7. Filling an array with 0s and 1s and counting

http://www.cut-the-knot.org/Curriculum/Algebra/Numbers01.shtml

Grids

1. Affirmative action

http://www.cut-the-knot.org/Curriculum/Combinatorics/AffirmativeAction.shtml

2. Pick's Theorem, Geoboard

http://www.cut-the-knot.org/Curriculum/Geometry/Geoboard.shtml

3. Ballot Lemma

http://www.cut-the-knot.org/Curriculum/Combinatorics/BallotLemma.shtml

4. Fill hexagonal grid

http://www.cut-the-knot.org/ctk/PlayHexDesign.shtml

5. Framer and Wife to catch Rooster and Hen

http://www.cut-the-knot.org/SimpleGames/RFWH.shtml

6. Getting a scout out of desert

http://www.cut-the-knot.org/Curriculum/Games/ReverseDesert.shtml

7. Sending scouts into a desert

http://www.cut-the-knot.org/Curriculum/Games/CheckerJumping.shtml

8. Skyscrapers puzzle

http://www.cut-the-knot.org/Curriculum/Games/Skyscrapers.shtml

9. Toads and Frogs in 2d

http://www.cut-the-knot.org/SimpleGames/FrogsAndToads2d.shtml

10. Wythoff's Nim

http://www.cut-the-knot.org/Curriculum/Algebra/Wythoff.shtml

11. The Game of Life

http://www.cut-the-knot.org/Curriculum/Combinatorics/Life.shtml

12. Four pegs that form a square

http://www.cut-the-knot.org/Curriculum/Algebra/FourPegs.shtml

13. The Rascal Triangle

http://www.cut-the-knot.org/arithmetic/algebra/RascalTriangle.shtml

14. Treasure hunt in a square grid

http://www.cut-the-knot.org/Curriculum/Arithmetic/CityBlockHunt.shtml

15. Moving chips in pairs down a checkerboard

http://www.cut-the-knot.org/Curriculum/Arithmetic/MovingInpairs.shtml

16. Plainim

http://www.cut-the-knot.org/Curriculum/Games/Plainim.shtml

17. Latin squares

http://www.cut-the-knot.org/Curriculum/Algebra/Latin.shtml

18. Equations of a straight line

http://www.cut-the-knot.org/Curriculum/Calculus/StraightLine.shtml

19. All Peano curves

http://www.cut-the-knot.org/Curriculum/Geometry/PeanoComplete.shtml

20. Rectangle on a chessboard

http://www.cut-the-knot.org/Curriculum/Algebra/IntegerRectangle.shtml

If need be, I can probably dig a few more.

Thank you,

Alex

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[Maria Droujkova]

Alexander, incredible resources as usual!!!

This illustrates the modest statement "Grid is a rich topic" - richly!

[Shad Moarif]

Absolutely brilliant!

Shad