*What is math readiness? Is it really possible to teach math readiness to very young children – toddlers and preschoolers? What does it look like? For several years Carolyn Galbraith ran a play and learning center, focusing on math readiness for preschool children. In this post, Carolyn describes some of her experiences and the outcomes she observed.*

We are lying on our backs looking up at the ceiling, searching for shapes. We see squares, rectangles. The smoke detector is a circle. One of the kids points out that the joins between the ceiling panels make crosses, and excitedly: “Parallel lines!”

When my kids were small, I ran a play & learning center in a small town outside Sydney, Australia. It held mostly building blocks and was a place where parents and kids could come and build whatever they liked. Inspired by Papert’s constructionism, it was a space where people could learn by constructing items meaningful to them, and sharing them with others. That’s why I called it **Kids Build Together.**

On Monday mornings I ran a math readiness group. It had mostly 2 to 4 year-olds. There were three main areas of focus – enjoying patterns, enjoying problems, and enjoying the process. We read a lot of math-themed picture books, tussle with simple problems. I tried to always end with a math-themed poem. Here’s a sample of one of our sessions:

“Today we’ve sung “Round about the circle” and passed a bag around with different shapes. Now the kids are going to try to fit them together. There’s no right answer, and it’s fun to see the different ways that the kids turn and feel and explore the properties of their shapes.

Next we read a gorgeously illustrated book about spirals in nature called “Swirl by Swirl” by Joyce Sidman. Afterwards, the kids use different colored stones to make their own spirals. They’re beautiful.

We’ve been reading “Measuring Penny” by Loreen Leedy and using different ways to measure things. Today the kids use big blocks to build towers as tall as themselves. They’re predicting how many blocks they’ll need, and I write it down on the board. They’re surprised to discover it only needs 15 blocks, rather than 100, to reach their height! I give them a measuring tape as another way to check their height, and 100 cm is close – so their predictions weren’t far off, after all.

To finish off I read a poem about time “Twenty-Four Hours” by Charles Causley. The kids love listening to poetry, the rhythm captures them instantly.

When I think back to learning math when I was at school, music, stories and games were the things I wished we used (I remember trying to design my own curriculum back in high school!) Finding the incredible mathematical patterns in nature, from fractals to Fibonacci spirals, has been a wonderful discovery of adulthood, as well as learning the stories of the mathematicians themselves. I hoped to share the pleasures of discoveries like these with the kids and their parents, and let them in on a secret – that math is more than memorizing numbers, and that readiness for math can be readiness for enjoying life.

Now my two kids are at school, and my center is no more. I help run a math class for the little ones at the local school, and include some Math in Your Feet dance activities there. I also tutor some children with literacy and numeracy challenges. It’s been fun sharing some of the resources with the older ones, such as the book about Fibonacci and the ideas of fractals.

It’s now I realize why all the work on symmetry in the younger years is essential – so much of mathematics is symmetry and balance! There’s not much time to cover it in school, a lesson or so. The ones who’ve spent years building with blocks are immediately advantaged. I encourage the parents of the older ones to bring the Lego back out, and build together; to walk in nature and observe the wonderful math in flower petals and tree branches. The secret hasn’t changed with their ages; math is still more than memory, and is still an important part for enjoying life.

*Enjoyed this story and feel inspired to try these math activities with your preschoolers? Let us know how it goes. Do you have a math story to share? We can’t wait to hear from you!*

Posted in A Math Circle Journey

Math Punday is Monday: the day to share math jokes on social media. I love Zeno’s paradoxes, and hope this recent post makes you and your children smile:

Math pun by JoeGP.com

All activities in Natural Math books are play-tested many times, not only by the authors, but also by our *beta readers*. These adventurous and caring early reviewers help authors make books better. Beta readers are parents, teachers, and math circle leaders who want their math materials to be beautiful, useful, enjoyable, and human-readable. As a beta reader, what do you get?

- You influence math materials, making them
**fit your needs**. The book is customized by and for you, and your children. - You and your children are the earliest users of the newest books even before they are off the press. It’s like
**test-driving**concept cars before they are even announced to the market. - You spend
**quality time with interesting people**. In the context of the book, you talk with authors about your children and your ideas on learning. Imagine the possibilities! - In the book, the authors will
**thank you**by your name or an alias of your choice.

Read on for two upcoming beta reader opportunities, one by email and one live.

Photo: Bard Math Circle

Meet new Natural Math authors Sam Coskey, Paul Ellis, and Japheth Wood. The working title of their book is *The Fantastic Five*. The book is for teachers, parents, and math circle leaders with students ages 10 and up as well as younger friends. It offers rich and original problem-solving activities in the contexts such as a trip to Mars or traditional Sona storytelling from Angola/Congo area. The authors write:

We are collaborating on a book of five math circle activities that we plan to publish with Natural Math. We would love it if you would agree to be a “beta-reader” of one chapter (or more, if you have time). If you have an appropriate forum in which to try the activity (such as a math circle or family math at home) that would be wonderful. If not, we would be happy if you would just read the chapter and provide feedback by email.

You are welcome to provide feedback in any form that you like. However, if you wish to have some guidance, we’ll suggest questions that we brainstormed together.

Sam Coskey, Boise Math Circle

Paul Ellis, Westchester Area Math Circle

Japheth Wood, Bard Math Circle

Alfreda Poteat is a Natural Math author who is passionate about the roots of modern mathematics in the world history, multiple cultures, and people’s stories. On **January 23 at 7 – 8:30 PM Eastern** (New York) time, Alfreda will lead a **live online workshop**. She invites parents and teachers of middle school children to join the workshop and play-test activities from her upcoming book with the working title *Math Talk: Math Roots*.

Alfreda’s thoughtful, playful, and kind book is especially suitable for a struggling learner. Children who’ve had some math grief or math anxieties are welcome to try accessible math activities. The book invites children to meet and pretend-play with the friendly geeks from the cave-people to modern-day scientists.

In the workshop, participants will improve on Euclid’s work, go on a math scavenger hunt in a cute board game, and explore mathematics of clay pottery.

*See you online!*

*Dr. Maria Droujkova, and the Natural Math crew*

Questions? Ideas? Email reach.out@naturalmath.com

Posted in Newsletter

Make Valentine’s Day crafts to celebrate loving one another… in the context of mathematics!

Grow your math eyes on these little field trips inspired by topology, dynamical systems, and algebraic geometry for the young, the very young, and the young at heart.

Know another romantic math craft? Tell us in the comments!

**Make math:** Fold paper in two. Sketch a teardrop in such a way that the fold forms one side of its triangular top part. Cut it out, open, and decorate the heart-shaped greeting card. My teen and I decorated with a cardioid (see below).

**Grow your math eyes:** What interesting shapes can you fold or unfold into other interesting shapes? What if you fold more than once? Choose shapes to experiment, on paper or in your imagination.

**Topic:** Mirror Symmetry. **Inspired by Big Math:** #14 Algebraic Geometry, #53 Differential Geometry.

**Bonus:**

**Make math:** Cut out two strips of paper and glue them together to form the + sign. Attach the opposite ends, with a twist, as if making Mobius strips. Cut the strips through the middle, and Mobius Hearts will happen! Video instructions:

**Grow your math eyes:** Try twisting two or more times. Try cutting 2/3 of the way rather than through the middle. What other surfaces can you make by connecting, twisting, and cutting paper strips?

**Topic:** Surfaces. **Inspired by Big Math:** #54 General Topology, #57 Manifolds.

**Bonus:**

*Roses are red. Violets are approximately blue.*

* A paracompact manifold with a Lorentzian metric,*

* can be a spacetime, if it has dimension greater than or equal to two.*

By Sarah Kavassalis

From participants in the Multiplication Explorers course

**Make math: **Draw a heart. Mark two or more points around it, for example, up top. Draw smaller hearts there. Mark the same points on them, and draw even smaller hearts. Keep going. Decorate your heart fractal, put it on a wall, or use as a greeting card.

**Grow your math eyes: **How tiny can your hearts become? Will you run out of space on paper if you keep going and going and going? How many hearts do you add to your fractal at each step of the process? For more versions, choose how many hearts to add at each step, how much to shrink at each step, how to turn the hearts around – then observe what happens.

**Topics:** Fractals and exponential growth. **Inspired by Big Math:** #11 Number Theory, #37 Dynamical Systems.

**Bonus:**

**Make math:** Trace a plate on scratch paper and cut out the circle. Fold it in half a few times, as if for making a snowflake. Unfold; your circle is now split into equal parts.

Trace the same plate on cardboard. Then use your folded circle as a guide to mark your new circle. You may need to insert more dots by hand.

Image by Cory Poole/WonderHowTo

You can also print out a marked circle, or use a protractor to mark it. Then follow instructions from MathCraft for drawing, or Almost Unschooling for string art. The craft involves skipping the dots by one and two, again and again. The repetition feels meditative, and there is a beautiful surprise at the end. The heart-shaped curve emerges as if by magic! Decorate it and put it on the wall or use as a greeting card.

**Grow your math eyes:** What other curves can you make out of straight lines? Choose your own “recipe” for skipping dots around a circle, and see what happens. What if you used a triangle or a square instead?

**Topic:** Curves. **Inspired by Big Math:** #14 Algebraic Geometry, #52 Discrete Geometry.

**Bonus:**

**Make math: **Customize variables and make your own greeting cards out of pretty graphs. Go to **Desmos Math-o-Gram site** to play and share the love.

**Grow your math eyes:** Peek behind the scenes to experiment with the equations. Replace numbers or functions in them and see what happens. Young children can start experimenting without knowing much (or anything) about the functions.

**Topic:** Functions and graphs. **Inspired by Big Math:** #14 Algebraic Geometry, #33 Special Functions.

**Bonus:**

Posted in Make & Grow

Doing math with your children’s friends or a small math circle? Chances are your students are of mixed ages and levels. How can you have good dynamics?

- Don’t focus on activities that are likely to invite competition, such as problem-solving.
**Use open, collaborative activities**: hands-on maker activities, scavenger hunts for math, games, or puzzles. **Invite parents or adult helpers to be students too**, to participate, and to do activities for themselves. Now the oldest child you have is not the oldest group member anymore – the adults are! Guide adults to share their discoveries with one another, rather than overwhelming the children, unless the kids ask.**Try Notice-Wonder activities**: show a fractal, a math sculpture, a mandala, or any curious object to the group, and invite everyone to ask questions. Younger children ask weird and wonderful questions. Adults and older children can research the wonder.**Have tables children can choose**, as if you are doing a mini-festival. Check out examples from Julia Robinson math fest, Reggio Emilia provocations, or Montessori centers.

Posted in A Math Circle Journey