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TOO MUCH MATH & SCIENCE is/are TAUGHT WITHOUT PHYSICAL, VISUAL MODELS OR EXPERIENCES THAT ALLOW STUDENTS TO VISUALIZE  Models engage the senses and the brain. Students FOCUS long enough for a teacher to insert a prompt or prod that will provoke responses.


Once students respond, they are engaged: talking, questioning, drawing, acting out the space for learning is open.

your brain

THINKERS ARE Hooks are meant to provoke a reaction. To capture students’ attention. The Human Brain loves a puzzle… nothing too hard, nothing too easy but something that makes it think




Here is a piece of rope. Make a knot or series of knots….IMG_0900


Now tease your knot apart and diagram it… I want a map/diagram/visual representation that I could give to someone else and without seeing your knot, they could try to tie it.


knot 2 I made



did I make the same knot as you busy



diagram and knot














Knot table

Here is the table of knots I used at NCTCA. Does your knot match any? This is how mathematicians diagram knots. Did you notice they use a closed loop for their knots. Knots are classified by the number of over and unders… As the number of over and unders increases so do the possibilities… So there is only one 3 but how many 7’s.  Is there a pattern? Which knots can you make?


The basics of thinking. Studying knots for a few minutes a day hones these key skills in a unique and different way. That is just one reason to study knots.

Knot Theory is a current on going study in the world of mathematics. It is focused on discovery… Who said there is no “new” math.

A headline just last year:

knotty protein



READ MORE: MIT Finds Most Complex Protein Knot Ever Seen — ScienceDaily