Math Mindset?

"Verifying number principles for ourselves is more important than just reading about them. No matter how conversant we are with the details of any map or restaurant menu, it's more informative to take the journey and more nourishing to eat the food. We can discover for ourselves the timelessness of nature's creating process by consciously participating in geometric activities." 

- Michael S. Schneider

This book has already influenced my math
mindset, and I wonder how it will influence
the math program for 2015-2016.

Do we foster math mindsets in our classrooms?

What questions do we ponder with children to help our young students become mathematical thinkers?

How do we create enthusiasm for mathematical thinking and learning?

During my summer exploration I was led to the book, A Beginner's Guide to Constructing the Universe, The Mathematical Archetypes of Nature, Art, and Science written by Michael S. Schneider. As I began reading, I thought, why didn't I learn this before? A thought like that always propels me to think differently about the work I do with children, and further makes me wonder if our paths to math learning and instruction are well routed?

I plan to couple the research in the book with the Examine Landmark Numbers curriculum I am currently writing since it is a direct match to the book's powerful intent and focus.

For starters, however, I wonder if you entertain the following questions, culled from the book's introduction, with your students or as you prepare your math lessons:

• When you look at an object, do you wonder what are the numbers within? (From the notion attributed to Pythagoras (c.580-500 B.C.), "Number is the within of all things." 
• What "fixed types" do you see in nature? For example what geometric shapes do we see repeated again and again in nature?
• Plato considered mathematical subjects including number itself, music, geometry, and astronomy to be most effective to preparing the mind for understanding--do students' study menus include those subjects?
• If geometry is the purest visible expression of number, how do you connect number with geometry as you teach?
• Have we reduced the scope of math in schools by trading, as Schneider suggests, a wide-ranging vision for narrow expertise? The word, mathematekoi, described advanced ancient Greek scholars, or "those who studied all," and the word, mathema, signified "learning in general," while Methuen meant "to be aware" and then Old German, munthen, "to awaken."
• Schneider demonstrates how in the ancient times a profound understanding of number was prevalent and wove mathematics, philosophy, art, religion, myth, nature, science, technology, and everyday life. Do we allow young students in math class to see, find, and discuss those connections? (or as Schneider suggests, do we train children to be "human pocket calculators.")
• Do we teach math as a "servant of commerce" or as a study that "makes us aware of the patterns with which the world and we are made?"
• Do we teach math imaginatively so that "mathematics can delight, inspire, and refine us?"
• Do we make the connection that "reading the book of nature" (understanding the world we live in) "requires familiarity with its alphabet of geometric glyphs?"
• Do children understand, that number, geometric shape and their patterns, like consonants and vowels, are the building blocks that "symbolize omnipresent principles, including wholeness, polarity, structure, balance, cycles, rhythm, and harmony"?
• Do we combine our naturalist studies with math, and allow students, similar to the ancients, to study nature, number, and shape to understand patterns and relationships?
• Do we allow students to verify number principles themselves rather than just reading about them?
• Do we prompt children to seek harmonious patterns? Do we ask what patterns do you see and how do those patterns fit together?

As I continue to read Schneider's book and create Examine Landmark Numbers curriculum, I will embody these quotes from the book:

• "It is a shame that children are exposed to numbers merely as quantities instead of qualities and characters with distinct personalities relating to each other in various patterns." 
• "If we had looked at numbers to see how they behave with each other in wonderful patterns I might have liked math. Had I been shown how numbers and shapes relate to the world of nature I would have been thrilled. Instead, I was dulled by math anxiety and pop quizzes."

Have you read Schneider's book? If so, how do you embed his work into your math curriculum? What difference has this made with regard to your students' enthusiasm and understanding for the subject?

In the days ahead I will continue to read and embed the research into my math plans for the 2015-2016 school year. In the meantime, I look forward to your questions and thoughts in this regard.