Pazuju – the great new puzzle you never heard of

I remember years ago reading about Sudoku. Already popular in Japan, the reviewer predicted that it would be featured in newspapers as regularly as crossword puzzles. Since then it indeed had, as predicted, a meteoric rise.

Math educators tend to be fans of Sudoku and similar puzzles (especially KenKen). Logic puzzles motivate the same sorts of thinking we use when we solve math problems: if I do this, then what’s the result? What can I learn if I assume the opposite of what I think is true?

Still, I’ve never been a huge fan of Sudoku. I find the puzzle a little dry, and don’t usually bother with it.

Cut to a few months back, when a publisher contacted me about a new puzzle called Pazuju. Pazuju is a kind of marriage of Sudoku and Tetris, including both logical and geometrical elements. It was hard for me to imagine.

Pazuju

The publisher sent me a sample of the book, and I tried one out. Then another. And suddenly, I was hooked. What I found was a puzzle that had the same logical appeal of Sudoku, but with more variety and interest. In my opinion, it’s quite simply a superior puzzle.

Will Pazuju be featured in newspapers everywhere, and eclipse Sudoku? I don’t know; it’s always hard to know what will rise to the top. But frankly, I think it deserves to be played everywhere Sudoku is. If you find yourself with a little time to spend on puzzles, I highly recommend this one. (I’m especially partial to the smaller 6 x 6 versions, which are generally quicker, though can still be quite subtle to solve.)

You can play Pazuju puzzles for free here. There’s also a book and an app available.

Math Circles for Teachers

Growing Squares.

We’ll thrilled to be offering math circles for elementary and middle school teachers in partnership with the Washington Experimental Math Lab at the UW. With their generous support, these unique professional development meetings are absolutely free. Clock hours will be available.

You can sign up by filling out this survey:

Elementary Math Teacher Circle

Middle School Math Teacher Circle

If you know teachers who would be interested in joining us, please spread the word!

More details:

Meeting place will be at UW main campus – specific location TBA
Meeting time 5:00 – 7:00, or possibly a little longer, to accommodate dinner
Participation is free!

Our dates are as follows, most of which are the third Tuesday of each school month:

Sep 20
Oct 25
Nov 29
Jan 24
Feb 28
March 28
April 25
May 23

Questions? Contact Kristine Hampton at kristine.l.hampton@gmail.com

Summer Staircase Retrospective Part 1

Summer Staircase 1

We recently wrapped up our most ambitious project ever, and as data on it starts to roll in, I thought I’d take a moment to share.

Summer Staircase stats:
—19 schools
—57 teachers
—2500 students (plus or minus)

This summer, we produced a math curriculum for Seattle Public Schools Summer Staircase, a six-week program in Seattle to prevent summer slide and, ambitiously, help kids like school.

Our job was to write a 6-week math curriculum for three grade bands: Kindergarten, 1st/2nd grade, and 3rd/4th grade (these are the grades the students completed in 2015-2016). We also trained the teachers in the spring, and provided support during the summer.

The curriculum was built on the idea that play is the engine of learning. We featured games, explorations, and story problems that were actually stories. Our goals were high engagement, differentiation, critical thinking, and productive disposition. This last one was maybe the most important goal. We wanted students to leave the program believing in the project of education, especially mathematical education.

I’ll share more about the details of the program soon, especially as we begin to parse the data. Browsing through the teacher feedback, I feel like we’re onto something incredibly exciting. The overwhelming response from teachers and site leaders—the summer “principals”— was that something great was happening in these classes.

Math for Love Summer Staircase Teacher Recommendation

Math for Love curriculum recommendation

For example, of the 30 out of 57 teachers who have so far filled out a survey:
100% would recommend teaching math in summer staircase to a colleague
97% would recommend our curriculum to other schools or districts

At first glance, the students seemed to improve on every measure—pre/post assessments, teacher observations of their math understanding, perseverance, sense-making, and argument skills, and even their enjoyment and engagement in math. I’m deeply excited about how using a play-based curriculum can engage an enormous range of students in an experience of mathematics that is both more fun and more rigorous. I’ll be sharing more about the details of the program, the types of lessons we wrote for the curriculum, and the outcomes as we crunch the numbers.

But for now, I wanted to share some of the less tangible growth that teachers reported seeing this summer:

“In their pre-tests students were only writing the answer to each question. I didn’t see any work or thought on their papers. In the post-tests, every students showed thinking and pictures or used counters. They were excited to show their strategies. That’s really exciting to see as a teacher!”
“I think they all (or most of them) learned that they could love school and learning could be fun. This was awesome.”
“For many of them, the enjoyment of math was the single best growth they could have had. They definitely deepened their math understanding of certain concepts. Learning how to win and lose games graciously was huge for them.”
“They all shared a valuable experience in learning with each other (and the teaching staff- we, too learned a great deal), and being a part of the collective and individual student growth!”
“They grew in confidence, grew in their ability to talk about math and share ideas, and growth was evident as they played games and treated one another with respect.”
“[This program] renewed my faith and love in learning and teaching.”

And this from a site leader:

“The kids were so happy and had fun, and LOVED telling me how they figured something out. So even if the scores didn’t move that much, I know that the kids will return to school with a greater acceptance of math, and without that, “I hate math,” attitude.”

Will the scores move? We’ll find out. But I’m very, very hopeful. I think we’re on the cusp of something big.

An Interview with Emily Grosvenor, author of Tessalation!

Tessalation Cover Tessalation! is a new children’s book about a little girl who discovers tessellations in the outdoor world. I backed the project when it was on Kickstarter earlier this year, and my book just arrived. Both the drawings and the writing is beautiful, and it is, to my knowledge, the only book for kids about tessellations.

Emily Grosvenor, the author of Tessalation!, and I have been interviewing each other about tessellations, the mathematical projects that stick with us from elementary school, and big words for little kids. A lightly edited version of this conversation is below.

The website for the book is here.
Tessalation! is also on Kindle here.

____________________________________________

Dan: Why did you choose to write a book about tessellations?

Emily: I’d say tessellations chose me. I’m a magazine writer and memoirist, but one day I got it in my head that I was going to write a children’s book and sat down to do it. I think most parents have this compulsion — when you’re reading a dozen every night you start to see the world in picture book ideas. From there, I thought about what I loved as a child and what I love now. I had discovered tessellations in a 4th grade gifted class and remembered having a blast making them. But I also love tessellated pattern as an adult. All I had to do was look around my home and its patterned curtains and pillows and floors to see I had an obsession. All that remained was the challenge of creating a book where tessellations were organic to the story. Patterns are soothing to look at.

D: Your description of the love of patterns cuts close to my own feelings. I used to imagine the imaginary ball that would ricochet around the room just right to hit some chosen spot, like a trick pool shot. Tessellations are similar—the shapes that align perfectly so foreground and background flip back and forth. There’s a visual beauty there that’s easy to fall in love with. For me, mathematical love is like that: the recognition that ideas fit together with the same sort of elegance and precision as shapes, so that everything meshes perfectly. There’s a deep satisfaction and also a sense of awe that can arise when all the pieces fit. Elation, you might say.

I’m curious about your original encounter with tessellations in fourth grade. Do you actually remember the lessons you did with tessellations? What about that experience grabbed you?

E: Yes, I do remember. Fourth grade was a seminal year for me. Nearly everything I’m passionate about had its seeds in fourth grade: tessellations, Germany (our country of study, I later majored in German and worked for the German Embassy in Washington, D.C.), poetry (our teacher made us memorize a poem a month and I still know three of them and write my own), novels (I specifically remember a book report I did on Mischievous Meg) and Oregon (I think Emily’s Runaway Imagination is the real reason I moved across the country as an adult). All I remember about the tessellation lesson was being shown how to make my own using a square. I made some seals leaping out of waves which, admittedly, was not a very compelling tessellation. But I think it stuck most because of the setting. I was shy and gifted class gave me a small group setting where we could do creative projects and where I felt comfortable enough to participate. It was also distinctly hands-on. Nearly every lesson I remember from elementary school had that quality. And it involved art. Dreamy, imaginative kids absolutely need to make art. I did not connect tessellations to math at all.

What do you think determines whether or not lessons “stick?”

D: That’s a great question, and one I’m often preoccupied with. I remember certain lessons and experiences from elementary school too, and I do think there are some hallmarks that distinguish the memorable ones from those we forget.

I think having control over the experience is critical to making an experience memorable. This is why art can be so compelling: we get to be the actor, the doer. We choose where the line goes, what the colors are, and even if we can’t always make it look like what we imagined, we’re still in charge. Mathematical experiences can involve the same kind of creative ownership, and when they do, they stand out.

Looping this back to tessellations, I taught a class for 2nd and 3rd graders on tessellations a little while ago. It eventually centered on the question of whether you can create a polygon with any number of sides that still tessellates. Can you make a 17-gon that tessellates? A 31-gon? A 99-gon? The problem is really fascinating. It starts with the more artistic project of just finding examples that do tessellate, and there’s a fair amount of coloring and decorating polygons to make cool looking designs. Eventually, we start discovering certain “moves” that change the number of sides of our polygon in a predictable way, and still produce something that tessellates: joining two polygons together, for example, or adding a bump to an existing tessellating shape. Suddenly we have families of tessellating polygons with 4, 8, 12, 16, 20, etc. sides, for example. And then there’s a very clear goal: how do we get those missing ones?

I don’t know for sure, but I suspect this problem, and problems like it, are memorable. There’s a clear answer, but constructing the argument (and all the tessellations) calls for a tremendous amount of choice and autonomy from the students. The fact that the products are so pretty is nice. And the arguments are just as beautiful, even though they’re harder to draw pictures of.

Reading Tessalation! with my nieces

But back to the book! Do you have a vision of how it will be used? A good book for bedtime reading, or for classroom use, or to launch a rainy Sunday craft project at home, or for a walk in the woods? Or is it for all of the above?

E: Tessalation! definitely works best in the classroom or as an introduction to an afternoon activity at home. I am already getting emails from teachers who are using the book as a jumping off point to a discussion of patterns, tessellations and pattern-making. One of my backers hasn’t got the book yet in her hands but printed out her digital PDF for just that.

I specifically designed the book to have entry points for several age groups. For younger kids, such as preschoolers, just finding Tessa within the tessellations is excitement enough. My three-year-old, Griffin, points out tessellations wherever we go.
Older kids will want to make their own and may respond to some of the other, more complicated ideas in the text. For example, on one page I write about bees dancing where to imbibe. What does imbibe mean? Why are they dancing?
Children 3-8 have a natural obsession with animal life and the outdoors and love learning about how nature works. Conventional wisdom in children’s books holds that you use the simplest words possible, but if I want my children to know that the back of a turtle is called a carapace, and it works with the rhyme, I’m going for it!
As for getting kids outside, I have a strong fondness for the international nonprofit Hike It Baby and have been developing a Tessa Hike to do at Hike It Baby meetups. Basically, you read the book, gather objects on your hike, and then make patterns with them in the parking lot. Fun!

D: One more question for you. Tessalation! include lots of long words. Why use advanced words in a children’s book? And are there implications for math learning here?

E: I’ve long bristled at the thought that young people can’t handle big words. The publishing market is designed within evermore defined reading age groups, and understandably so. A teacher or parent who goes looking for a story or book kids can connect with will inevitably search out one that has the themes, language and subject matter appropriate for that age.

I will always be a fan of the simple story well told in simple language — the Llama Llama books are still big in our house — but I also know that children will take ownership of words that they hear. So when my 3-year-old tells me he just found a tessellation on the bottom of his new shoe, it is because he has been exposed to the word and the visual of a tessellation.
Here’s another 4th grade story for you. I remember doing a book report on Mischievous Meg by Astrid Lindgren and using the word “fabricate” to describe the main character’s penchant for storytelling. The teacher marked it with a little note that said: “Your word?”
I was highly insulted — was she asking if my mom had helped or suggesting that that couldn’t be my word?
One of my all-time favorite children’s books is Bubble Trouble by Margaret Mahy. Here’s an example, from the climax of the book’s action:
“But Abel, though a treble, was a rascal and a rebel,
fond of getting into trouble when he didn’t have to sing.
Pushing quickly through the people, Abel clambered up the steeple,
With nefarious intentions and a pebble in his sling!”
When my older son was young, he simply basked in the rhythms of the language, but as he got older he started asking what the words meant. With language, exposure is important. How would you rather learn a word — spoken by your parents, in your favorite book, or on a worksheet in Middle School?
As for Tessalation!, the reason it sat in a drawer for a year and a half was because I got some early feedback that it was a book for highly literate children, and I might think about making it more accessible to all readers. I sat on that for a while. It’s valid criticism. But in the end, I plowed ahead with my original goal, which was to make the cleverest book I could. Kickstarter was a good way to connect with people who respond to that.
____________________________________________
Thanks, Emily Grosvenor, for a wonderful conversation, and best of luck with the book!
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QAMA – the calculator that won’t make you lazy

I got a call months ago from someone with what sounded like like a bizarre idea: he claimed he’d invented a special calculator to use as a pedagogical device in the classroom. I was about to dismiss the call as being a crank, when I realized that what he was describing, if it worked, was potentially a brilliant idea.

I bought myself a calculator, and began to check it out. It’s called QAMA, and it’s now available as an app, which is a much better deal, and you won’t accidentally kill the batteries if you leave the calculator on, as I did after the first time I used it. Nevertheless, I’m blown away by QAMA, since it elegantly solves one of the central problems of using calculators in the classroom: the problem of students handing all the thinking to the calculator.

Here’s how it works.

You plug in whatever equation you want to solve. For example, I entered “65.86 x 21.” IMG_0905

Then you hit the equals button. And the calculator doesn’t give you an answer. And therein lies its genius, its usefulness, and also, according to my conversation with the designer, the great technical difficulty in creating it in the first place.

IMG_0906 To get an answer, you have to enter an estimate. If it’s just an arbitrary number, the calculator won’t accept it. Your estimate must prove that you were thinking. And the calculator expects that you can work at a pretty decent level. It requires perfect answers for single digit multiplication for example—it is no help with memorizing your multiplication tables. IMG_0907For this particular problem, I figured that 1300 would be a decent estimate. I entered it, and the calculator showed me the real answer: 1383.06.

It can be fun to play around with how good the estimates need to be. I tried 13/21. First estimate: 1.6, and this turned out to be an excellent guess. Second estimate: 1.5. QAMA wouldn’t accept it. Third estimate: 1.55. That was acceptable. IMG_0908The promise of this innovation is no doubt obvious to middle and high school teachers. QAMA has reinforced in its architecture the process of thoughtful calculator use, by making the tool that much more difficult to use mindlessly. Here’s what students should do when they use a calculator:

  1. Decide if the problem actually requires a calculator.
  2. If it does, get a rough sense of what a reasonable answer might be, then enter the problem on the calculator.
  3. Pay attention to whether the answer the calculator gave you makes sense.

Here’s what students too often do once they have easy access to calculators:

  1. Grab a calculator whenever they have an arithmetic problem to do.
  2. Take whatever comes out as fact, and move on.

I’ve seen eighth graders reach for a calculator to solve 100 – 98. I’ve seen college students accept total gibberish from their calculator after mis-keying, without considering whether the answer makes sense on a gut level. (“The swimming pool costs… 53 billion dollars.”) Any teacher who gives their students access to calculators knows who pervasive these problems can become. “Does your answer make sense?” we ask, repeatedly, and often to no avail. But QAMA prevents students from having the option to be lazy. Their motto is: “The calculator that thinks only if you think too.” And that seems true.

Personally, I’ve come down against having students use calculators until middle school (except for occasional use in 4th-5th grade). But I think QAMA could take all the worst parts (mindlessness, laziness, etc.) of calculator use out of the middle and high school classroom. I think they’re on to something.

 

 

 

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Book Reviews

I read pop math books. Quite a few, in fact. Also, sometimes publishers send me advance copies and ask for reviews. I generally read these too. What makes me a bad reviewer is that I then wait for 6 – 20 months before I actually write anything down.

Time to remedy this situation! Here are a batch of quick reviews for books on or related to math that I’ve read in the past couple of years.

How Not to Be Wrong: The Power of Mathematical Thinking

Jordan Ellenberg has written one of the finest books on mathematics in decades. How Not to Be Wrong belongs in the pop-math canon, alongside Simon Singh’s best works (The Code Book; Fermat’s Enigma) and Robert Dantzig’s Number: The Language of Science.

There are two qualities that make How Not to Be Wrong exceptional. The first is how much news it contains. So many math books are rehashes of classic stories: Zeno, Archimedes, Pythagoras, Newton & Leibnitz, Euler, Gauss, and so on. Read a few accounts of the history of math and the stories, fun as they are, start to run into each other. Ellenberg begins with Abraham Wald studying bullet holes in airplane fuselages during WWII and goes off in all sorts of new directions from there. I was shocked at how much I had never seen before, and how seamlessly Ellenberg ties together statistics, mathematics, and common sense.

Fourth from the top is How Not to Be Wrong

The second quality that makes this book necessary reading is the sense of humor. The asides and footnotes are laugh-out-loud funny, and Ellenberg is a masterful and delightful writer to read. Bill Gates picked How Not to Be Wrong as one of his top five recommendations for reading this summer, and it’s at the top of my list too. Don’t miss it.

Love and Math: The Heart of Hidden Reality

How I wanted to like this book. It’s name is almost identical to this website’s, and Ed Frenkel had been on a tear, speaking on the Colbert Report and other TV and radio shows about the book, which promised to share what he loved about math. I started reading hopefully, and the first five or so chapters didn’t disappoint. Frenkel’s story of learning math despite anti-semitism in Soviet Russia is compelling and readable. Soon enough he’s invited to the West, and the story loses its dramatic tension: Frenkel’s career heads up, and the sailing is smooth. Frenkel tries to create dramatic tension around whether an important mathematician might show up at a conference or not, but the stakes just feel too low.

Wisely, with little narrative left to mine from his own story, Frenkel pivots in the second half of the book mainly to explaining the math and the story behind the Langlands Program, an ambitious and collaborative mathematical undertaking. While points of this project are interesting, the complexity of the mathematics exceeds Frenkel’s ability (and possibly anyone’s ability) to explain it to a lay audience. I’d estimate the necessary mathematical background for much of the second half of this book to be roughly graduate school level, and the layperson who tries to read it may find themselves scared off.

Meanwhile, there are two undermining details that become more glaring as the book goes on. First, Frenkel’s presentation of the mathematical world is deeply male. The female characters appear as charming wives who serve tea to their hardworking mathematician husbands, then disappear. Frenkel seems to have no problem with this, and his video project (looking for the equation for love) in the last chapter doesn’t do a lot to present a more positive space for women in mathematics. While professional math continues to be dominated by men, it feels more important than ever to celebrate female mathematicians and make clear that women belong in the field. Frenkel seems happy with his Mad-Men-esque vision of the field.

Second, Frenkel’s self regard unbalances the story. He’s a master of the humble-brag, and the longer you read, the more you have a sense that the story he’s really interested in telling is the one about how great Ed Frenkel is. Frenkel is taking on more and more of a place in the conversation around popular mathematics, and I think he has something important to share about the passion and beauty of mathematics. If he can make a little more room for underrepresented groups and a little less room for himself, I think his contributions will be that much more valuable.

The Math Olympian

This is a peculiar and kind of wonderful book. It reads like a soap opera, almost: a sort of Slum Dog Millionaire for a female Canadian Math Olympian, who, in the course of a 5-question test, flashes back through all her preparation and through important life moments.

There’s some solid math throughout this book, and, compared with Frenkel, a very clear place for women in math, along with a clear-eyed view of some of the specific difficulties they might face. What makes the book exceptional, though, is the diverse picture it paints of great math mentoring, and the emphasis on what really matters in mathematics—not the contests, it turns out, but the work of doing math itself. A wonderful book to read, especially for math teachers and mentors interested in improving their math-educational craft.

The New York Times Book of Mathematics

The Times sent me a review copy of their Book of Mathematics last year, and I’ve been slowly reading it since then. There’s a lot here: over 100 years of reporting on mathematics. Overall, it’s a pretty impressive collection. More than anything else, it’s amazing to see what they got right: in so many articles, they’re interviewing the pivotal players, and capturing the most important breakthroughs just as they’re happening. Reading through the book gives you a sense of what the news was in 20th century mathematics: chaos theory, cryptography, computers, mathematicians and their major breakthroughs (Wiles, Perelman, Erdos, Conway, Godel and others make appearances throughout the book). There are some whimsical sections too, like an interview with the real Monty Hall, who takes the writer to school.

If you want to get a sense of what the news in mathematics actually was this past century, this is a great place to start.

The Mathematics Devotional

Clifford Pickover has written a number of big, beautiful, coffee-table-grade books on mathematics and physics, and I’ve been a fan. But when his publisher sent me this one, I was skeptical. A Devotional? As in, read an inspirational quote and ponder a picture? Indeed, that’s exactly what this book is: one quote and one image per day of the calendar year. And yet, I’ve had it for over a year now, and find myself opening it up all the time, and using it exactly how it’s meant to be used. It’s exactly what it set out to be, and I continue to be a fan.

Here’s today’s quote: “The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was ‘out there’ all along I just couldn’t see it. And now I can! This is really what keeps me in the math game—the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.” —Paul Lockhart, A Mathematician’s Lament, 2009

 

So there’s some reading to check out this summer! I’ll return now to my stack of books and start reading. Next summer is coming fast.

 

Tiny Polka Dot has funded!

tiny polka dot (11b of 29)

We’re thrilled to announce that our Kickstarter campaign for Tiny Polka Dot has funded! This means we’ll be bringing this game into the world before the end of the year.

There are still 66 hours in the campaign, and you can still support the project, help us reach our stretch goals to make the game even better, and get your own copy locked down.

Here’s the link.

A friend of mine—a homeschooling mom and long-time K-2 teacher—said recently that:

Every time we sit and play I think how really with pattern blocks, some beans and a Tiny Polka Dot set…  you could cover math from k-2 and have lots of fun doing it.

While it is impossible to know how these things will go in the long run, I’m hopeful that Tiny Polka Dot has will be the kind of game that ushers mathematical play into classrooms and families that much more quickly.

Speaking of which, Emily Grosvenor, author of Tessalation, just interviewed me (and some fantastic colleagues) in a piece on mathematical play in Parent Map. Take a look!

Pyramid Puzzle

This Pyramid Puzzle was recently featured in a post in Forbes about our Tiny Polka Dot campaign.

Take two suits–that’s 22 cards, with 0 – 10 each occurring twice. The puzzle is to make a pyramid using 10 cards of those 22 cards, so that each number in the pyramid is the sum of the two below it. Here’s a near-solution: every card is the sum of the two dots below it; the only problem is that there’s no third 1 to go in the last space on the bottom. (Excess cards are on the right.)

TPD-Pyramid-Puzzle-1200x900

I just received this email from a friend who’s been play-testing Tiny Polka Dot with her kids.

“[my daughter] couldn’t make it work [with 10] with two sets then decided “OK let’s try 9.” Off to verify 10 really doesn’t work”

Here’s the photo she attached with the email (note: spoiler below!)

IMG_20160510_133341

I actually convinced myself that 10 couldn’t work at the top of the pyramid… for a while. Turns out, I was wrong! More ends up being possible with this puzzle than meets the eye.

But I love this puzzle for precisely the reason that it worked so well for my friend’s daughter: 10 doesn’t seem to work, so she takes a leap of faith and tries 9 at the top of the pyramid; the puzzle rewards the courageous step of trying an even harder puzzle!

Is it possible to put an even smaller number at the top of the Pyramid?

[Sidenote: you can now get Prime Climb and Tiny Polka Dot together at a big discount if you support our campaign. Pledge here!]
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What are the aims and goals of math education, K-2?

As part of the Math for Future Elementary School Teachers class we’re teaching at the UW, we regularly ask our students to reflect on what they’re learning in the class. This particular student reflection felt so dense and comprehensive that I thought it would be worth sharing here (with her permission, and her name removed).

The prompt: What do you think are the aims and goals of math education for grades K-2? Include topics, values, and outcomes.

Reflection on K-2 Math Ed

 

What do you think?

How to help your kids fall in love with math: a guide for grown-ups

So you want your kid to know math? Of course you do. Math is an important tool, used widely in many disciplines, and helps us make sense of our world. It’s also beautiful, fun, and interesting, especially for young children.

Kids are just entering the world of patterns and numbers, and their love of math is ready to bloom. They are ready and excited to count, classify, name, and look for patterns. But too often, parents unintentionally do damage, either by neglecting their kids’ mathematical development, or by pushing them too hard, too quickly. It’s important to find the right balance, but many parents aren’t sure how.

This is an issue now, as more attention is being paid to the development of a human intellect. Pre-Kindergarten education, Head Start, Common Core, and the achievement gap are all looming large in public discourse right now because we care so much about educating our children. Research has shown the best education begins at home, with a thoughtful approach to nurturing your child’s natural math instincts.

The following guide is adapted from our new math game deck for three to eight year olds, Tiny Polka Dot. These ideas are, essentially, the keys to nurturing the natural mathematical instinct that is growing in every child.

Guide for Grown-ups

1. Play! Play is the engine of learning for young children. Provide your kids with a rich environment to play in, and let them take the lead. What makes for a rich math environment?

  • Blocks – pattern blocks, legos, tangrams, and other blocks for building, sorting, and playing are the best.
  • Games – Classics like Uno, concentration, war, dots and boxes, and Tiny Polka Dot are great as soon as kids are ready for them. Winning is irrelevant at first, and many games can be played collaboratively. Keep it light, and have fun yourself!
  • A mathematical perspective – a walk in the woods, a pile of buttons, an old egg carton… these all hold rich mathematical structure if you look at them with the right eyes. Any pile of assorted object can become an opportunity to group by color, by number of holes, or by size. Walks become a chance for counting steps or physical challenges that involve gut estimations and intuitions.

EXAMPLE
You: How many steps do you think it will take to get to that tree?
Your Child: 100?
You: Let’s find out!
[You walk and count. The answer, it turns out, was 15.] You: How many steps to that next tree?
Your Child: Hmmm. 15?
You: Let’s find out!

Math teachers in elementary, middle and high school know how hard it is to get kids to intuitively understand whether their answers make sense. Connecting numbers up to the world with fun guess-and-check challenges pays off big time later.

As for egg cartons, check out the patterns emerging from kids playing with colored plastic eggs and egg cartons at Math-on-a-Stick at the Minnesota State fair. (These taken from Christopher Danielson’s aptly titled blog post, Let the Children Play.)
Kids at the FairYou might not recognize this as mathematical play, but sorting, symmetry, and grouping by equal numbers is precisely the foundation of the more abstract mathematics that will come later in school. And most importantly, it’s fun!

2. Learning takes time! The process of learning and mastering a new skill can be slow and complex. This is not a test. Do not to rush your child or expect them to know something after they have seen it once or twice. You may find a child makes the same mistake over and over again. As long as they are having fun, trust that your child is learning! It’s easy to over-help. Take a breath, and make sure you are letting your child take as active a role in the game as possible. It doesn’t matter if they get the answer right. Because it isn’t a test.

  • WRONG QUESTION: “Is my child smart?”
  • RIGHT QUESTION   “How is my child thinking?”

3. Think out loud. Your child is imitating everything you do, and the more you can narrate your thoughts, the better a model of thinking you can be. Slow down, find reasons to count slowly and clearly, and use mathematical language to describe what’s happening in your head. Never say, “Mommy (or Daddy) is terrible at math!” If you don’t have the ideal relationship to math, now’s your chance take a fresh look.

The happy truth about doing math with your kids is that it’s way more fun than you’re expecting it to be. It’s not about right answers, and it’s not about speed. It’s about playing, counting, building, sorting, and studying the wonderful, colorful world around us.

If you’re interested in more ways to explore math with your three- to eight-year-olds, our new math game, Tiny Polka Dot, is on Kickstarter now. It provides multitudes of ways to play with number and pattern in a colorful and fun family game.

Because really, we should all be having way more fun.

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