6 X 6 Cube Model--Even Numbers Squared

  Michael Punzak: Story and Pattern

The Patterner's Tale Consulting Availability Bio and Contact Math model examples and explanations

The Kindle edition of my new book, The Moths of Math is now available at Amazon


If kids have trouble learning math and science it is largely the fault of we educators.

Under the pressure to prepare kids to "do math and science" we must not forget their attraction to play and playful materials...


nor should we ignore the fascination all people have for a good story and the power of narrative to engage the imagination and fix a concept in the mind.

On the STORYTELLING page you can read one of my shorter tales about Pattern... or you may stream or download an audio clip of the story.

Hello and Welcome --

This site has been created to express my convictions that:

•  for many, even most people, math is best learned not as a set of procedures and calculations, but through an exploration of pattern and relationship.

•  if kids have trouble learning math and science it is largely the fault of we educators.

In these pages, I hope to share some of the techniques and physical models that I have found useful over the past few years, and to make it easier for folks who have shown interest and curiosity to access images of these models along with their associated concepts.

Of course, I hope this site will also be a useful adjunct to my storytelling and consultancy business by providing some hint of the potential of adding narrative, music, humor, and beauty to math and science teaching.


A constructed three-dimensional model grabs attention. The proportions, symmetry, and patterns inherent in our number system become visual and compelling. I hope educators will see the potential of using riveted attention to further a deeper understanding of mathematics.

When we look at math as an interconnected field of simple and beautiful ideas we want to explore further. But math viewed as a jungle of procedures that must be memorized can lead to shut-down behaviors that inhibit progress.

The 3-D visualization of the multiplication table proceeds from very simple concepts, and is beautiful. Using the riveted attention of students, the model becomes a launching pad for exploration. Measurement, volume, surface area, symmetry, pattern, pre-algebra, computation, fractions--whatever area the educator wishes to emphasize, there is a connection to be made.

On the MODELS page you'll find photos and explanations of some of these models.

Copyright 2011, Michael Punzak

Web Production and Photo Credits