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Tools

As the activities take place outside the classroom or even outside the school premises, the tools for such activities have to be easily portable: for example measuring tools and cameras are very useful. Tablets or smartphones can offer a wide range of apps. Here are some examples.

Android apps: sketching and annotation tools (such as Sketch Box or Skitch), Geogebra, mindmapping tools (such as Mindomo), QR readers (such as ScanLife), photo editors (such as Pixlr or PicsArt), sound recording and sharing (such as Soundcloud), screenshot tools (such as Screenshot), doodling tools (such as You Doodle or Sketch for Keep), or even astronomy tools (such as SkyView). A very simple tool for creating QR codes treasure hunts is here or you can find ready-made treasure hunts on this website.

And a few useful iPad apps: 30hands for creating a narrated slideshow using photos from your camera roll or drawing images or these tools for recording audio notes . A good tool can also be Educreations, for creating a lesson and sharing it. You can draw on a whiteboard or on photos while narrating what you are doing. The lesson can also be published on the Educreations website. I am not an iPad user, so if you need more STE(A)M apps, you can find them here https://ictevangelist.com/periodic-table-steam-ipad-apps/

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Module 3- Activities involving movement and constructions

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Module 3- Activities involving movement and constructions

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Tools

Building activities are often used in the flipped classroom - a very popular teaching strategy nowadays. In this blog post you have a list of 12 tools that can be used in such an activity. Many of them have tutorials or suggestions for educational use.

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During the lesson, students first work individually to review their initial work. They then work in pairs to compare their approaches to the task, choosing a strategy that will produce an improved model and together implement that strategy. Students next review some sample work before discussing as a class the strengths and weaknesses of different approaches to the modeling task.

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This webpage illustrates some of the patterns I have made with LEGO. If you define mathematics as "the science of patterns" then LEGO are a tactile/visual computer to explore mathematics. Most of these experiments are in 2 dimensions, which seems quite enough space to get started!

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To Little's surprise, the students dove in. They put themselves in their own groups based on personal interest, and worked together to grapple with these mysterious tools. Little herself was unaware of the MaKey MaKey instrument. "I'm afraid of maker-type technology," she told me. But she imagined that she and the students could figure out together how to use the alien circuit board to interesting effect.

"I didn't know how to do it, but I could teach them how to learn," she said.

Inspired by an online investigation, one group of students decided to build a banana piano. This meant they needed to program the computer -- Little's laptop -- to the MaKey MaKey circuit board, which the students were able to do. Then, by trial and error, the 12-year-olds learned how to build a full circuit: They attached one set of wires from the circuit board to six bananas (borrowed from lunch), and another connector to the laptop.

Little gets fuzzy explaining exactly how the banana piano worked. "I could not build one," she said. But the students understood, and one day they brought the unorthodox instrument to the entire regular math class.

"They played a song for everyone, and everyone went wild," Little said. "'We want to come to math support!'" she recalled the students saying.

Little then invited all her math students to attend the twice-weekly optional remediation classes where she'd first introduced the practical tools. "They all opted for extra math," Little said.

Intrigued by the bananas, one group worked with lemons, this time completing the circuit by holding hands. The electricity ran through every kid in the class to the last one, who could then "play" the lemon bongos. Kids with a more literary bent wrote a book and set music to it; they rigged the MaKey MaKey device to play exciting music during adventurous passages and dirge music during sad ones. Other students flocked to the sewing, 3-D pen and marble maker, including one child who cross-stitched the emblem of the San Francisco Giants as a gift for his grandmother.
Student Empowerment
The learning didn't stop when supplies finally dwindled. Rather than solicit parents for money, Little turned the need for materials into an immersion in marketing and sales. They would sell pencils, the children decided, but at what price? They debated strategies: If we sell 60 pencils at $2 per pencil we'll reach our goal. But who will spend that much on a pencil? Maybe 50 cents per pencil this week, and 75 cents every day thereafter.

"The kids were totally in control of how the price would vary and how it would affect profit," Little said. In the end, the children earned $120, enough to resupply the 3Doodler, buy more circuits and restock the sewing basket.

Little is astonished by the changes she saw among her students. By making the classroom hands-on, she upended the traditional social hierarchies: Kids who might have been ostracized for being deficient in math were suddenly valuable when their strengths -- like problem-solving or brainstorming -- became visible and needed.

Likewise, the stigma attached to remediation classes, and even to math itself, disappeared. Everyone wanted to join in. In addition, kids abandoned their usual roles: Some who traditionally sat quietly and waited for direction began to take charge, and others who claimed to hate reading devoured turgid manuals. And Little herself became more of a facilitator than an instructor, helping kids find what they needed but not spoon-feeding them information.

"Teachers are no longer the holders of all knowledge," she said. Rather, the students themselves, having discovered on their own how to program fruit to play a tune, developed unexpected confidence.

"They became bold and self-directed when they realized I did not have the answers," Little wrote about the experience. "I became a curious and excited partner in their discoveries." She shared her findings at the FabLearn conference at Stanford and wrote a report about the results.
Meeting Standards
When school began in September, Little brought back the MaKey MaKey contraption and other tools to her classroom, this time introducing them to all her students from the start. She remains ebullient about the possibilities, and encourages her math-teaching peers to give it a try.

At a minimum, teaching this way satisfies the Common Core requirements for students to solve problems and understand concepts, she said.

"Math teachers who have only paper and pencil at their disposal, find some of these important standards very difficult to illuminate," according to Little. "When students must work in groups to complete a real project, all of these mathematical standards come into play. Instead of being told, 'Your calculations are wrong,' students experience a real setback in their creation and must problem solve to get it working."

She discovered that this approach stimulates children to learn, helping them to understand and use math in ways they've never considered. For example, Little uses cross-stitch to develop understanding of math.

"Cross-stitch is like creating art with pixels," according to Little. "You cannot actually make a curve but can approximate one by using a stair step method. Distance from the piece creates the illusion of a smooth curve." She said students were excited by this discovery and were giving feedback on one another's projects.

Little had hesitation over these new maker tools, but she saw in them the same qualities that made sewing and wood shop classes a practical way of learning math, back when they were available. Both require planning, visualization and precise measurements. Educators may not feel fully prepared to start these hands-on projects, but Little says not to worry about lesson plans or about not fully understanding how it all works. "Just start," she said. "Get some supplies and go. Don't be afraid!"

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How Turning Math Into a Maker Workshop Can Bring Calculations to Life

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To Little's surprise, the students dove in. They put themselves in their own groups based on personal interest, and worked together to grapple with these mysterious tools. Little herself was unaware of the MaKey MaKey instrument. "I'm afraid of maker-type technology," she told me.

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The Spacecraft Race_2014_7C - Free download as PDF File (.pdf), Text File (.txt) or view presentation slides online.

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Module 3- Activities involving movement and constructions

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Module 3- Activities involving movement and constructions

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Teacher Uses LEGOs To Explain Math To Schoolchildren

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As if LEGOs weren’t enough of an awesome childhood toy, one teacher has found another awesome educational/developmental use for this super-toy – as a math education aid! Alycia Zimmerman, a 3rd-grade teacher in New York, uses them to explain fractions, squares and other mathematical concepts.

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Module 2- Activities using paper or string

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Module 2- Activities using paper or string

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Tools

Thinglink is a tool for creating interactive images by annotating. You can add links to a wide variety of content areas. You can look at this example.

Tess is a tool for creating interactive lessons by combining online content, media and files. It's reliable and easy to use. You already had the A4 Math examples above.

Artsteps is a tool for creating virtual exhibitions. You can create a gallery with your students' works. Here is an example.

Sliceform Studio is a free tool for creating Mathematical art. You can create your own tiling design online, customize it, download it and assembly it in reality. There are tutorials and a gallery for inspiration.

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Math art projects are a unique way to combine right and left brain learning. Both my boys enjoy math, but they often balk when I suggest, "let's do an art project!" It's sort of depressing for me, since I'd much rather get out the paints than perform calculations. My solution has been to make math learning creative with math art projects and activities.

I need to get better about taking photos of our math art sessions. Perhaps now that I have a new camera I can get some decent pictures. But I digress. Anyway... I thought it would be fun to round up some math art ideas that we've tried, plus a few I've found on the internet that are in my virtual "to try" pile.

The best thing about all of these math art projects is that they will get math kids thinking about art and art kids thinking about math!

Math Art Projects and Ideas

Tessellations.We've done this several times, and somehow it never gets boring.

Explore Symmetry.

Turn number sequences into art.

Use math tools to create art. This is one of my favorite ideas!

Explore math art with shapes.

What do your kids prefer, math or art? Do you ever do math art projects with the kids? Need more ideas?

25 Playful and Creative Math Ideas.
Math art activity and picture books
Make sure you don't miss any of our upcoming math art projects! Subscribe to our weekly-ish newsletter.

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Math art projects are a unique way to combine right and left brain learning. Both my boys enjoy math, but they often balk when I suggest, "let's do an art project!" It's sort of depressing for me, since I'd much rather get out the paints than perform calculations.

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Creating Fractal Christma(th)s Trees For the Visual Intelligence

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Learning about graphs, formulas with movement

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Module 2- Activities using paper or string

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Module 2- Activities using paper or string

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I've been playing with paper folding recently, and exploring the mathematics involved. I'm simply amazed by the number of mathematical ideas that can be represented by paper folding, so I thought I would share a few of my discoveries here.
Sequences
As you can see above, you can generate the sequence of numbers 1, 2, 4, 8, 16, 32 and so on, just by folding the paper in half again each time. This means that there is an exponential relationship between the number of folds you have made and the number of areas created on the paper.

Notice that if I instead fold the paper into thirds each time, the sequence changes into 1, 3, 9, 27, etc... which suggests that folding a piece of paper is a little bit like multiplication.
Fractions
First, form the fraction by folding the paper into quarters and shading three of them in.

Now fold the paper in the other direction into thirds, and shade , ideally in the other direction. Where your two shadings have overlapped is the product of your two fractions, in this case .
Symmetry
Here is an example of folding the paper around the centre to produce rotational symmetry. I worked with a student to produce snowflakes with 9 points, 12 points, and other points, after watching this interesting video by Vi Hart.

Tessellations

If you fold a paper in half a bunch of times, you can create a tesselation by cutting portions of the paper out. The number of folds and the size of the repeated portion of the tessellation have an interesting relationship.
Circle geometry
If you very carefully cut a circle out of a piece of paper (which will finally give you a use for all of those CDs you have laying around you aren't using anymore), you can prove quite a large number of the theorems from circle geometry by folding the paper in certain ways.

For example, if you fold the paper in half twice in two different directions, the intersection of the folds has a useful property.

For further resources on paper folding and mathematics, see this TED talk by Robert Lang, this book on the mathematics of paper-folding, and this useful PDF describing some geometry theorems that can be demonstrated through paper folding. See also this very interesting article on fraction flags (via @DwyerTeacher).

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I've been playing with paper folding recently, and exploring the mathematics involved. I'm simply amazed by the number of mathematical ideas that can be represented by paper folding, so I thought I would share a few of my discoveries here.

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Module 2- Activities using paper or string

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Module 2- Activities using paper or string

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Origami Proof of the Pythagorean Theorem

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Tes provides a range of primary and secondary school teaching resources including lesson plans, worksheets and student activities for all curriculum subjects.

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Naturally Connected Curriculum - Outdoor maths

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Six lesson plans full of ideas for teaching maths skills in the school grounds.

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Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

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eTwinning project called GOAL - Go Outside and Learn

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Publishing platform for digital magazines, interactive publications and online catalogs. Convert documents to beautiful publications and share them worldwide. Title: Orienteering For Erasmus, Author: Alessandra Basso, Length: 50 pages, Published: 2016-09-13

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The  Manifesto opens with the statement, “We believe that every young person should experience the world beyond the classroom as an essential part of learning and personal development, whatever their age, ability or circumstances.” Such experiences “help us to make sense of the world around us by making links between feelings and learning. They stay with us into adulthood and affect our behaviour, lifestyle and work. They influence our values and the decisions we make. They allow us to transfer learning experienced outside to the classroom and vice versa”. The document offers an insight on the benefits, strategies, aims and supporting actions connected to outdoor learning.

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Learning mathematics outside the classroom is not enrichment, it is at the core of empowering an individual’s understanding of the subject. If you haven’t experienced ‘real’ Maths in the environment yet, you – and your students – are missing out on some wonderful, powerful learning experiences. Take some Maths activities outside and feel the learning become richer and more meaningful – better yet, don’t take Maths activities outside – find the Maths that’s already there!

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It's one of the hottest days of the year and the last week of term - and which teacher doesn't want to fling open the doors and take their class on to the field, the playground or even just to sit in the courtyard?

Now, education guru Sir Ken Robinson has shared his thoughts on why learning outside is a good idea, leading to many benefits for learning, in this exclusive video for TES.

"What really drives education is curiosity, trying to fill gaps in our understanding," Sir Ken says, author of Finding Your Element and other books on creativity in education. "And the world around us is a tremendous resource to stimulate that curiosity."

He lists five reasons why taking learning outdoors is a good idea:

1. Nature is a powerful resource.

2. Children can learn through practical hands-on activities.

3. You can tap into children's curiosity.

4. It is a social experience and children learn from working together.

5. Learning outdoors is fun.

"Education takes up a great deal of children's time," Sir Ken adds. "This is their childhood, the only one they get and learning outdoors, working together, playing together is fun. It's about the quality of our lives and experiences."

Sir Ken Robinson supports Empty Classroom Day, an initiative to inspire learning and play outside the classroom, backed by Persil's Dirt is Good campaign.
Want to keep up with the latest education news and opinion? Follow TES on Twitter and like TES on Facebook

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Watch: Sir Ken Robinson shares five reasons you should take your class outside

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It's one of the hottest days of the year and the last week of term - and which teacher doesn't want to fling open the doors and take their class on to the field, the playground or even just to sit in the courtyard?

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An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself.

Here is a chart detailing the all Primes from 1 - 100

We know via the proof-by-contradiction by Euclid that there are an infinite number of prime numbers, yet, this doesn't reveal them. Unlike a standard integer (whereupon whatever number you can come up with, for example n, i can surpass this number with the simple exercise of n+1), large prime numbers are incredible difficult to find. There is no formula for churning out prime numbers, they must be found :)

In 2008, a mathematician won $100,000 for finding the next highest prime number (the largest known to date)

Most likely you students won't be able to grasp how big this number really is, but, for intents and purposes, if you were to sum up all the atoms in the entire universe you would get a number roughly 10^80 (vastly smaller than the one shown here)

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four hundred seventy quattuormilliamilliatrecensexviginmilliasexagintillion,
two hundred sixty nine quattuormilliamilliatrecensexviginmillianovemquinquagintillion,
three hundred thirty quattuormilliamilliatrecensexviginmilliaoctoquinquagintillion,
two hundred fifty five quattuormilliamilliatrecensexviginmilliaseptenquinquagintillion,
nine hundred twenty three quattuormilliamilliatrecensexviginmilliasexquinquagintillion,
one hundred forty three quattuormilliamilliatrecensexviginmilliaquinquinquagintillion,
four hundred fifty three quattuormilliamilliatrecensexviginmilliaquattuorquinquagintillion,
seven hundred twenty three quattuormilliamilliatrecensexviginmilliatrequinquagintillion,
nine hundred forty nine quattuormilliamilliatrecensexviginmilliadoquinquagintillion,
three hundred thirty seven quattuormilliamilliatrecensexviginmilliaunquinquagintillion,
five hundred sixteen quattuormilliamilliatrecensexviginmilliaquinquagintillion,
fifty four quattuormilliamilliatrecensexviginmillianovemquadragintillion,
one hundred six quattuormilliamilliatrecensexviginmilliaoctoquadragintillion,
one hundred eighty eight quattuormilliamilliatrecensexviginmilliaseptenquadragintillion,
four hundred seventy five quattuormilliamilliatrecensexviginmilliasexquadragintillion,
two hundred sixty four quattuormilliamilliatrecensexviginmilliaquinquadragintillion,
six hundred forty four quattuormilliamilliatrecensexviginmilliaquattuorquadragintillion,
one hundred forty quattuormilliamilliatrecensexviginmilliatrequadragintillion,
three hundred four quattuormilliamilliatrecensexviginmilliadoquadragintillion,
one hundred seventy six quattuormilliamilliatrecensexviginmilliaunquadragintillion,
seven hundred thirty two quattuormilliamilliatrecensexviginmilliaquadragintillion,
eight hundred eleven quattuormilliamilliatrecensexviginmillianovemtrigintillion,
two hundred forty seven quattuormilliamilliatrecensexviginmilliaoctotrigintillion,
four hundred ninety three quattuormilliamilliatrecensexviginmilliaseptentrigintillion,
sixty nine quattuormilliamilliatrecensexviginmilliasextrigintillion,
three hundred sixty eight quattuormilliamilliatrecensexviginmilliaquintrigintillion,
six hundred ninety two quattuormilliamilliatrecensexviginmilliaquattuortrigintillion,
forty three quattuormilliamilliatrecensexviginmilliatretrigintillion,
one hundred eighty five quattuormilliamilliatrecensexviginmilliadotrigintillion,
one hundred twenty one quattuormilliamilliatrecensexviginmilliauntrigintillion,
six hundred eleven quattuormilliamilliatrecensexviginmilliatrigintillion,
eight hundred thirty seven quattuormilliamilliatrecensexviginmillianovemvigintillion,
eight hundred fifty six quattuormilliamilliatrecensexviginmilliaoctovigintillion,
seven hundred twenty six quattuormilliamilliatrecensexviginmilliaseptenvigintillion,
eight hundred sixteen quattuormilliamilliatrecensexviginmilliasexvigintillion,
five hundred thirty nine quattuormilliamilliatrecensexviginmilliaquinvigintillion,
nine hundred eighty five quattuormilliamilliatrecensexviginmilliaquattuorvigintillion,
four hundred sixty five quattuormilliamilliatrecensexviginmilliatrevigintillion,
ninety seven quattuormilliamilliatrecensexviginmilliadovigintillion,
three hundred fifty six quattuormilliamilliatrecensexviginmilliaunvigintillion,
one hundred twenty three quattuormilliamilliatrecensexviginmilliavigintillion,
four hundred thirty two quattuormilliamilliatrecensexviginmillianovemdecillion,
six hundred forty five quattuormilliamilliatrecensexviginmilliaoctodecillion,
one hundred seventy nine quattuormilliamilliatrecensexviginmilliaseptendecillion,
six hundred seventy three quattuormilliamilliatrecensexviginmilliasexdecillion,
eight hundred fifty three quattuormilliamilliatrecensexviginmilliaquindecillion,
five hundred ninety quattuormilliamilliatrecensexviginmilliaquattuordecillion,
five hundred seventy seven quattuormilliamilliatrecensexviginmilliatredecillion,
two hundred thirty eight quattuormilliamilliatrecensexviginmilliadodecillion,
one hundred seventy nine quattuormilliamilliatrecensexviginmilliaundecillion,
three hundred fifty seven quattuormilliamilliatrecensexviginmilliadecillion,
nine hundred quattuormilliamilliatrecensexviginmillianovemtillion,
eight hundred seventy six quattuormilliamilliatrecensexviginmilliaoctotillion,
four hundred twenty six quattuormilliamilliatrecensexviginmilliaseptentillion,
one hundred three quattuormilliamilliatrecensexviginmilliasextillion,
nine hundred forty three quattuormilliamilliatrecensexviginmilliaquintillion,
seven hundred eighty two quattuormilliamilliatrecensexviginmilliaquattuortillion,
three hundred seventy six quattuormilliamilliatrecensexviginmilliatretillion,
four hundred ninety four quattuormilliamilliatrecensexviginmilliadotillion,
five hundred ninety one quattuormilliamilliatrecensexviginmilliauntillion,
seven hundred forty two quattuormilliamilliatrecensexviginmilliatillion,
nine hundred thirty four quattuormilliamilliatrecenquinviginmillianongennovemnonagintillion,
five hundred eighty eight quattuormilliamilliatrecenquinviginmillianongenoctononagintillion,
four hundred ninety seven quattuormilliamilliatrecenquinviginmillianongenseptennonagintillion,
one hundred seventeen quattuormilliamilliatrecenquinviginmillianongensexnonagintillion,
five hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenquinnonagintillion,
one hundred forty six quattuormilliamilliatrecenquinviginmillianongenquattuornonagintillion,
nine hundred sixteen quattuormilliamilliatrecenquinviginmillianongentrenonagintillion,
nine hundred seventy two quattuormilliamilliatrecenquinviginmillianongendononagintillion,
nine hundred eighty four quattuormilliamilliatrecenquinviginmillianongenunnonagintillion,
seven hundred sixty one quattuormilliamilliatrecenquinviginmillianongennonagintillion,
one hundred fifty nine quattuormilliamilliatrecenquinviginmillianongennovemoctogintillion,
sixty quattuormilliamilliatrecenquinviginmillianongenoctooctogintillion,
eight hundred seventy three quattuormilliamilliatrecenquinviginmillianongenseptenoctogintillion,
two hundred fifty quattuormilliamilliatrecenquinviginmillianongensexoctogintillion,
nine hundred thirty nine quattuormilliamilliatrecenquinviginmillianongenquinoctogintillion,
four hundred sixty two quattuormilliamilliatrecenquinviginmillianongenquattuoroctogintillion,
eighty five quattuormilliamilliatrecenquinviginmillianongentreoctogintillion,
five hundred seventy five quattuormilliamilliatrecenquinviginmillianongendooctogintillion,
seven hundred forty quattuormilliamilliatrecenquinviginmillianongenunoctogintillion,
seven hundred fifty four quattuormilliamilliatrecenquinviginmillianongenoctogintillion,
five hundred seventy seven quattuormilliamilliatrecenquinviginmillianongennovemseptuagintillion,
ninety eight quattuormilliamilliatrecenquinviginmillianongenoctoseptuagintillion,
six hundred twenty quattuormilliamilliatrecenquinviginmillianongenseptenseptuagintillion,
five hundred fifty eight quattuormilliamilliatrecenquinviginmillianongensexseptuagintillion,
eleven quattuormilliamilliatrecenquinviginmillianongenquinseptuagintillion,
seven hundred seventy nine quattuormilliamilliatrecenquinviginmillianongenquattuorseptuagintillion,
five hundred twenty nine quattuormilliamilliatrecenquinviginmillianongentreseptuagintillion,
eight hundred eighty four quattuormilliamilliatrecenquinviginmillianongendoseptuagintillion,
forty two quattuormilliamilliatrecenquinviginmillianongenunseptuagintillion,
one hundred ninety eight quattuormilliamilliatrecenquinviginmillianongenseptuagintillion,
two hundred eighty seven quattuormilliamilliatrecenquinviginmillianongennovemsexagintillion,
six hundred forty three quattuormilliamilliatrecenquinviginmillianongenoctosexagintillion,
three hundred nineteen quattuormilliamilliatrecenquinviginmillianongenseptensexagintillion,
three hundred thirty quattuormilliamilliatrecenquinviginmillianongensexsexagintillion,
four hundred sixty five quattuormilliamilliatrecenquinviginmillianongenquinsexagintillion,
sixty four quattuormilliamilliatrecenquinviginmillianongenquattuorsexagintillion,
four hundred fifty five quattuormilliamilliatrecenquinviginmillianongentresexagintillion,
two hundred thirty four quattuormilliamilliatrecenquinviginmillianongendosexagintillion,
nine hundred eighty eight quattuormilliamilliatrecenquinviginmillianongenunsexagintillion,
one hundred forty two quattuormilliamilliatrecenquinviginmillianongensexagintillion,
one hundred thirty nine quattuormilliamilliatrecenquinviginmillianongennovemquinquagintillion,
five hundred sixty five quattuormilliamilliatrecenquinviginmillianongenoctoquinquagintillion,
seven hundred eighty five quattuormilliamilliatrecenquinviginmillianongenseptenquinquagintillion,
four hundred forty seven quattuormilliamilliatrecenquinviginmillianongensexquinquagintillion,
four hundred seventy four quattuormilliamilliatrecenquinviginmillianongenquinquinquagintillion,
twenty three quattuormilliamilliatrecenquinviginmillianongenquattuorquinquagintillion,
five hundred forty six quattuormilliamilliatrecenquinviginmillianongentrequinquagintillion,
three hundred fifty three quattuormilliamilliatrecenquinviginmillianongendoquinquagintillion,
seven hundred fifty eight quattuormilliamilliatrecenquinviginmillianongenunquinquagintillion,
five hundred thirty seven quattuormilliamilliatrecenquinviginmillianongenquinquagintillion,
three hundred twenty four quattuormilliamilliatrecenquinviginmillianongennovemquadragintillion,
eight hundred one quattuormilliamilliatrecenquinviginmillianongenoctoquadragintillion,
eight hundred thirty eight quattuormilliamilliatrecenquinviginmillianongenseptenquadragintillion,
one hundred twenty quattuormilliamilliatrecenquinviginmillianongensexquadragintillion,
three hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenquinquadragintillion,
six hundred quattuormilliamilliatrecenquinviginmillianongenquattuorquadragintillion,
eight hundred sixty eight quattuormilliamilliatrecenquinviginmillianongentrequadragintillion,
four hundred sixteen quattuormilliamilliatrecenquinviginmillianongendoquadragintillion,
five hundred twenty five quattuormilliamilliatrecenquinviginmillianongenunquadragintillion,
four hundred quattuormilliamilliatrecenquinviginmillianongenquadragintillion,
seven hundred ninety quattuormilliamilliatrecenquinviginmillianongennovemtrigintillion,
three hundred eighty one quattuormilliamilliatrecenquinviginmillianongenoctotrigintillion,
two hundred eighty five quattuormilliamilliatrecenquinviginmillianongenseptentrigintillion,
eight hundred eighty eight quattuormilliamilliatrecenquinviginmillianongensextrigintillion,
two hundred fifty six quattuormilliamilliatrecenquinviginmillianongenquintrigintillion,
six hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenquattuortrigintillion,
eighty five quattuormilliamilliatrecenquinviginmillianongentretrigintillion,
eight hundred fifty five quattuormilliamilliatrecenquinviginmillianongendotrigintillion,
four hundred fifty six quattuormilliamilliatrecenquinviginmillianongenuntrigintillion,
two hundred thirty one quattuormilliamilliatrecenquinviginmillianongentrigintillion,
five hundred seventy seven quattuormilliamilliatrecenquinviginmillianongennovemvigintillion,
five hundred twenty seven quattuormilliamilliatrecenquinviginmillianongenoctovigintillion,
nine hundred thirty nine quattuormilliamilliatrecenquinviginmillianongenseptenvigintillion,
three hundred five quattuormilliamilliatrecenquinviginmillianongensexvigintillion,
nine hundred twenty quattuormilliamilliatrecenquinviginmillianongenquinvigintillion,
eight hundred eleven quattuormilliamilliatrecenquinviginmillianongenquattuorvigintillion,
seven hundred sixty six quattuormilliamilliatrecenquinviginmillianongentrevigintillion,
five hundred eighty five quattuormilliamilliatrecenquinviginmillianongendovigintillion,
three hundred eight quattuormilliamilliatrecenquinviginmillianongenunvigintillion,
six hundred seventy quattuormilliamilliatrecenquinviginmillianongenvigintillion,
one hundred thirty two quattuormilliamilliatrecenquinviginmillianongennovemdecillion,
one hundred twenty nine quattuormilliamilliatrecenquinviginmillianongenoctodecillion,
one hundred fifty five quattuormilliamilliatrecenquinviginmillianongenseptendecillion,
two hundred twenty one quattuormilliamilliatrecenquinviginmillianongensexdecillion,
eight hundred four quattuormilliamilliatrecenquinviginmillianongenquindecillion,
three hundred eighty one quattuormilliamilliatrecenquinviginmillianongenquattuordecillion,
five hundred forty eight quattuormilliamilliatrecenquinviginmillianongentredecillion,
six hundred twenty five quattuormilliamilliatrecenquinviginmillianongendodecillion,
seven hundred eighty seven quattuormilliamilliatrecenquinviginmillianongenundecillion,
nine hundred forty three quattuormilliamilliatrecenquinviginmillianongendecillion,
twenty quattuormilliamilliatrecenquinviginmillianongennovemtillion,
six hundred ninety four quattuormilliamilliatrecenquinviginmillianongenoctotillion,
five hundred twenty eight quattuormilliamilliatrecenquinviginmillianongenseptentillion,
fifteen quattuormilliamilliatrecenquinviginmillianongensextillion,
nine hundred ninety nine quattuormilliamilliatrecenquinviginmillianongenquintillion,
two hundred twenty one quattuormilliamilliatrecenquinviginmillianongenquattuortillion,
seven hundred eighteen quattuormilliamilliatrecenquinviginmillianongentretillion,
one hundred ninety one quattuormilliamilliatrecenquinviginmillianongendotillion,
five hundred fifty seven quattuormilliamilliatrecenquinviginmillianongenuntillion,
seven hundred sixty one quattuormilliamilliatrecenquinviginmillianongentillion,
seven hundred eighty nine quattuormilliamilliatrecenquinviginmilliaoctingennovemnonagintillion,
thirty eight quattuormilliamilliatrecenquinviginmilliaoctingenoctononagintillion,
five hundred thirty nine quattuormilliamilliatrecenquinviginmilliaoctingenseptennonagintillion,
five hundred twenty two quattuormilliamilliatrecenquinviginmilliaoctingensexnonagintillion,
three hundred forty nine quattuormilliamilliatrecenquinviginmilliaoctingenquinnonagintillion,
seven hundred forty six quattuormilliamilliatrecenquinviginmilliaoctingenquattuornonagintillion,
eight hundred eight quattuormilliamilliatrecenquinviginmilliaoctingentrenonagintillion,
seven hundred ninety seven quattuormilliamilliatrecenquinviginmilliaoctingendononagintillion,
four hundred seventy six quattuormilliamilliatrecenquinviginmilliaoctingenunnonagintillion,
nine hundred seven quattuormilliamilliatrecenquinviginmilliaoctingennonagintillion,
six hundred sixty four quattuormilliamilliatrecenquinviginmilliaoctingennovemoctogintillion,
fifty quattuormilliamilliatrecenquinviginmilliaoctingenoctooctogintillion,
six hundred one quattuormilliamilliatrecenquinviginmilliaoctingenseptenoctogintillion,
two hundred forty eight quattuormilliamilliatrecenquinviginmilliaoctingensexoctogintillion,
four hundred seventy three quattuormilliamilliatrecenquinviginmilliaoctingenquinoctogintillion,
two hundred six quattuormilliamilliatrecenquinviginmilliaoctingenquattuoroctogintillion,
eight hundred seventy four quattuormilliamilliatrecenquinviginmilliaoctingentreoctogintillion,
one hundred thirty three quattuormilliamilliatrecenquinviginmilliaoctingendooctogintillion,
one hundred ninety four quattuormilliamilliatrecenquinviginmilliaoctingenunoctogintillion,
six hundred sixty three quattuormilliamilliatrecenquinviginmilliaoctingenoctogintillion,
five hundred eighty five quattuormilliamilliatrecenquinviginmilliaoctingennovemseptuagintillion,
three hundred thirty four quattuormilliamilliatrecenquinviginmilliaoctingenoctoseptuagintillion,
nine hundred eighty three quattuormilliamilliatrecenquinviginmilliaoctingenseptenseptuagintillion,
eight hundred five quattuormilliamilliatrecenquinviginmilliaoctingensexseptuagintillion,
seven hundred thirty four quattuormilliamilliatrecenquinviginmilliaoctingenquinseptuagintillion,
eight hundred three quattuormilliamilliatrecenquinviginmilliaoctingenquattuorseptuagintillion,
six hundred twenty quattuormilliamilliatrecenquinviginmilliaoctingentreseptuagintillion,
seven hundred five quattuormilliamilliatrecenquinviginmilliaoctingendoseptuagintillion,
seven hundred seventy eight quattuormilliamilliatrecenquinviginmilliaoctingenunseptuagintillion,
two hundred seventy quattuormilliamilliatrecenquinviginmilliaoctingenseptuagintillion,
nine hundred ten quattuormilliamilliatrecenquinviginmilliaoctingennovemsexagintillion,
five hundred sixty one quattuormilliamilliatrecenquinviginmilliaoctingenoctosexagintillion,
seven hundred sixteen quattuormilliamilliatrecenquinviginmilliaoctingenseptensexagintillion,
seven hundred sixty seven quattuormilliamilliatrecenquinviginmilliaoctingensexsexagintillion,
six hundred eighty quattuormilliamilliatrecenquinviginmilliaoctingenquinsexagintillion,
nine hundred fifty four quattuormilliamilliatrecenquinviginmilliaoctingenquattuorsexagintillion,
eight hundred fourteen quattuormilliamilliatrecenquinviginmilliaoctingentresexagintillion,
four hundred fifteen quattuormilliamilliatrecenquinviginmilliaoctingendosexagintillion,

What a mouth full!!!!

So, here is the goal. Using a large fake check made out for $100,000 and a small bag of candy, pose the challenge to see who can come up with the largest prime number using only paper, pencil and calculator (don't let them cheat on their cell phones by Googling)

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An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself. Here is a chart detailing the all Primes from 1 - 100 We know via the proof-by-contradiction by Euclid that there are an infinite number of prime numbers, yet, this doesn't reveal them.

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TOUCH this image to discover its story. Image tagging powered by ThingLink

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Moreover, the types of activities we will be focusing on benefit and empower an important and often neglected skill: the spatial creativity. There are many students who have high spatial talent but relatively lower math and verbal talent who are likely missed by modern talent searches and therefore fail to have their talent developed to the extent it could. Hereyou have an article on the importance of spatial skills for future STEM careers and ways to develop it. Putting new skills to use will help students acquire a growth mindset, focused on progress, instead of a fixed one, focused on immediate results. (We will learn more on the mindset theory advocated by Carole Dweck later in the course!)

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Einstein imagined with his mind. Tesla imagined with his mind and built with his hands. Edison imagined with both. They all had extraordinary spatial talent -"the ability to generate, retain, retrieve, and transform well-structured visual images."

Spatial thinking "finds meaning in the shape, size, orientation, location, direction or trajectory, of objects," and their relative positions, and "uses the properties of space as a vehicle for structuring problems, for finding answers, and for expressing solutions." Spatial skill can be measured through reliable and valid paper-and-pencil tests-primarily ones that assess three dimensional mental visualization and rotation. Read more about examples of items that measure spatial skill here.

But despite the value of these kinds of skills, spatially talented students are, by and large, neglected. Nearly a century ago, a talent search conducted by Lewis Terman used the highly verbal Stanford-Binet in an attempt to discover the brightest kids in California. Perhaps due to the fact that the Stanford-Binet did not include a spatial test, William Shockley and Luis Alvarez, who would go on to become famous physicists and win the Nobel Prize, missed the cut.*

[RELATED: Can Playing Video Games Give Girls an Edge in Math?]

Today talent searches often use the SAT and ACT which include math, verbal, and writing sections, but do not include a spatial measure. All of the physicists described above (and Tesla who could do integral calculus in his head) would likely qualify today at least on the math section, and Edison would likely have qualified on the verbal section due to his early love of reading. However, there are many students who have high spatial talent but relatively lower math and verbal talent who are likely missed by modern talent searches and therefore fail to have their talent developed to the extent it could. Also, because colleges use the SAT and ACT for selecting students, many high spatial students likely do not make it onto college campuses.

Nearly every standardized test given to students today is heavily verbal and mathematical. Students who have the high spatial and lower math/verbal profile are therefore missed in nearly every school test and their talent likely goes missed, and thus under-developed. What's more, spatially talented people are often less verbally fluent, and unlikely to be very vocal. Finally, teachers are unlikely to have a high spatial profile themselves (and typically have the inverted profile of high verbal and lower math/spatial), and although they probably do not intend to, they're more likely to miss seeing talent in students who are not very much like themselves.

So what does the research tell us? In a study published in the Journal of Educational Psychology, my colleagues and I used longitudinal data from multiple data sets across 50 years to show that spatial talent (in addition to math and verbal talent) is important for success in STEM domains. The data came from the Study of Mathematically Precocious Youth (SMPY), Project Talent, and the GRE. Of those students in the top 1 percent of spatial talent, roughly 70 percent were not in the top 1 percent in either math or verbal talent-showing a large fraction of students having the high spatial but lower math/verbal profile.

Now a new study by Harrison Kell, David Lubinski, Camilla Benbow, and James Steiger published in Psychological Science has made the connection between early spatial talent and creativity in adult life even stronger. The study, based on SMPY data, showed that spatial skill had an increment of prediction over and above math and verbal skills (assessed at age 13) when looking at scholarly publications and patents-even those in STEM.
Can We Enhance Spatial Skill?
So, can enhancing spatial thinking improve outcomes in STEM? A new study by David Uttal, David Miller, and Nora Newcombe published in Current Directions in Psychological Science notes that "a recent quantitative synthesis of 206 spatial training studies found an average training improvement of 0.47 standard deviations." The authors suggest that including spatial thinking in STEM curricula would "enhance the number of Americans with the requisite cognitive skills to enter STEM careers."

The research is clear that spatial skill is important for STEM careers, and perhaps we can even enhance spatial skill to help more people join the STEM fields. What we need is research directed at understanding the best ways to develop the talent of students who are high spatial, but relatively lower math/verbal. Perhaps spatial video games and online learning coupled with hands on interventions might help these students.

[RELATED: How Thinking in 3D Can Improve Math and Science Skills]

This is what's so great about the Maker Movement and "Why Kids Need to Tinker to Learn": It will help encourage all students to tinker, invent, and to use their hands to make things again. Certainly the skills encouraged by the makers might be helpful to students who go on to pursue STEM careers. But the movement probably will be most effective for spatially talented students who have been neglected in our school systems.

One student who felt neglected in the school system was researcher Matthew Peterson. As a child, Peterson felt that he was drowning in words and numbers. And in many ways he was, as he was identified as dyslexic-similar to Einstein and Edison. This bothered him so much that today he has developed a way to teach math in an entirely visual manner called ST Math.

Ultimately we need to have the individual skill profile of each student matched to individualized instruction tailored to them. We need to experiment in the laboratory and classroom and conduct rigorous evaluations to find out what actually works.
Redefining and Valuing a Different Kind of Creativity
Today we idolize creative actors, dancers, artists, musicians, and writers. But when was the last time someone raved to you about a creative engineer or mathematician? Why isn't STEM considered creative or cool? Longitudinal research has made a solid link between early spatial talent and later creativity. Yet for whatever reason, we don't appreciate the highly creative nature of science, technology, engineering, and mathematics.

It would seem impossible to argue that the theory of relativity, alternating current, or the light bulb were not creative innovations. And yet it is easy to forget that these advances fall squarely in the STEM disciplines. Consider the device you are reading this article from right now. Spatially talented people imagined it in their minds eye and then they built it. Not everyone is going to be an Einstein, Tesla, or Edison, but if we identify the many spatially talented students who have been neglected in our school systems we might discover many brilliant kids who are just waiting to develop their creative potential. We need to help them. After all, we will ultimately depend on their visions to help create our future.
Jonathan Wai is a researcher at the Duke University Talent Identification Program and Case Western Reserve University and writes "Finding the Next Einstein: Why Smart is Relative" for Psychology Today. *An earlier version of this post stated that former President Richard Nixon was identified as part of the Terman talent search. We regret this error.

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Why We Need To Value Students' Spatial Creativity

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Einstein imagined with his mind. Tesla imagined with his mind and built with his hands. Edison imagined with both. They all had extraordinary spatial talent -"the ability to generate, retain, retrieve, and transform well-structured visual images."

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The power of yet | Carol S Dweck | TEDxNorrköping

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A few weeks ago I (Jo Boaler) was working in my Stanford office when the silence of the room was interrupted by a phone call. A mother called me to report that her 5-year-old daughter had come home from school crying because her teacher had not allowed her to count on her fingers. This is not an isolated event-schools across the country regularly ban finger use in classrooms or communicate to students that they are babyish. This is despite a compelling and rather surprising branch of neuroscience that shows the importance of an area of our brain that "sees" fingers, well beyond the time and age that people use their fingers to count.

In a study published last year, the researchers Ilaria Berteletti and James R. Booth analyzed a specific region of our brain that is dedicated to the perception and representation of fingers known as the somatosensory finger area. Remarkably, brain researchers know that we "see" a representation of our fingers in our brains, even when we do not use fingers in a calculation. The researchers found that when 8-to-13-year-olds were given complex subtraction problems, the somatosensory finger area lit up, even though the students did not use their fingers. This finger-representation area was, according to their study, also engaged to a greater extent with more complex problems that involved higher numbers and more manipulation. Other researchers have found that the better students' knowledge of their fingers was in the first grade, the higher they scored on number comparison and estimation in the second grade. Even university students' finger perception predicted their calculation scores. (Researchers assess whether children have a good awareness of their fingers by touching the finger of a student-without the student seeing which finger is touched-and asking them to identify which finger it is.)

Evidence from both behavioral and neuroscience studies shows that when people receive training on ways to perceive and represent their own fingers, they get better at doing so, which leads to higher mathematics achievement. The tasks we have developed for use in schools and homes (see below) are based on the training programs researchers use to improve finger-perception quality. Researchers found that when 6-year-olds improved the quality of their finger representation, they improved in arithmetic knowledge, particularly skills such as counting and number ordering. In fact, the quality of the 6-year-old's finger representation was a better predictor of future performance on math tests than their scores on tests of cognitive processing.
Many teachers have been led to believe that finger use is useless and something to be abandoned as quickly as possible.
Neuroscientists often debate why finger knowledge predicts math achievement, but they clearly agree on one thing: That knowledge is critical. As Brian Butterworth, a leading researcher in this area, has written, if students aren't learning about numbers through thinking about their fingers, numbers "will never have a normal representation in the brain."

One of the recommendations of the neuroscientists conducting these important studies is that schools focus on finger discrimination -not only on number counting via their fingers but also on helping students distinguish between those fingers. Still, schools typically pay little if any attention to finger discrimination, and to our knowledge, no published curriculum encourages this kind of mathematical work. Instead, thanks largely to school districts and the media, many teachers have been led to believe that finger use is useless and something to be abandoned as quickly as possible. Kumon, for example, an after-school tutoring program used by thousands of families in dozens of countries, tells parents that finger-counting is a "no no" and that those who see their children doing so should report them to the instructor.

Stopping students from using their fingers when they count could, according to the new brain research, be akin to halting their mathematical development. Fingers are probably one of our most useful visual aids, and the finger area of our brain is used well into adulthood. The need for and importance of finger perception could even be the reason that pianists, and other musicians, often display higher mathematical understanding than people who don't learn a musical instrument.

Teachers should celebrate and encourage finger use among younger learners and enable learners of any age to strengthen this brain capacity through finger counting and use. They can do so by engaging students in a range of classroom and home activities, such as:

Give the students colored dots on their fingers and ask them to touch the corresponding piano keys:

Give the students colored dots on their fingers and ask them to follow the lines on increasingly difficult mazes:

(The full set of activities is given here.)

The finger research is part of a larger group of studies on cognition and the brain showing the importance of visual engagement with math. Our brains are made up of "distributed networks," and when we handle knowledge, different areas of the brain communicate with each other. When we work on math, in particular, brain activity is distributed among many different networks, which include areas within the ventral and dorsal pathways, both of which are visual. Neuroimaging has shown that even when people work on a number calculation, such as 12 x 25, with symbolic digits (12 and 25) our mathematical thinking is grounded in visual processing.

A striking example of the importance of visual mathematics comes from a study showing that after four 15-minute sessions of playing a game with a number line, differences in knowledge between students from low-income backgrounds and those from middle-income backgrounds were eliminated.

Number-line representation of number quantity has been shown to be particularly important for the development of numerical knowledge, and students' learning of number lines is believed to be a precursor of children's academic success.

Visual math is powerful for all learners. A few years ago Howard Gardner proposed a theory of multiple intelligences, suggesting that people have different approaches to learning, such as those that are visual, kinesthetic, or logical. This idea helpfully expanded people's thinking about intelligence and competence, but was often used in unfortunate ways in schools, leading to the labeling of students as particular type of learners who were then taught in different ways. But people who are not strong visual thinkers probably need visual thinking more than anyone. Everyone uses visual pathways when we work on math. The problem is it has been presented, for decades, as a subject of numbers and symbols, ignoring the potential of visual math for transforming students' math experiences and developing important brain pathways.

It is hardly surprising that students so often feel that math is inaccessible and uninteresting when they are plunged into a world of abstraction and numbers in classrooms. Students are made to memorize math facts, and plough through worksheets of numbers, with few visual or creative representations of math, often because of policy directives and faulty curriculum guides. The Common Core standards for kindergarten through eighth grade pay more attention to visual work than many previous sets of learning benchmarks, but their high-school content commits teachers to numerical and abstract thinking. And where the Common Core does encourage visual work, it's usually encouraged as a prelude to the development of abstract ideas rather than a tool for seeing and extending mathematical ideas and strengthening important brain networks.

To engage students in productive visual thinking, they should be asked, at regular intervals, how they see mathematical ideas, and to draw what they see. They can be given activities with visual questions and they can be asked to provide visual solutions to questions. When the youcubed team (a center at Stanford) created a free set of visual and open mathematics lessons for grades three through nine last summer, which invited students to appreciate the beauty in mathematics, they were downloaded 250,000 times by teachers and used in every state across the U.S. Ninety-eight percent of teachers said they would like more of the activities, and 89 percent of students reported that the visual activities enhanced their learning of mathematics. Meanwhile, 94 percent of students said they had learned to "keep going even when work is hard and I make mistakes." Such activities not only offer deep engagement, new understandings, and visual-brain activity, but they show students that mathematics can be an open and beautiful subject, rather than a fixed, closed, and impenetrable subject.

Some scholars note that it will be those who have developed visual thinking who will be "at the top of the class" in the world's new high-tech workplace that increasingly draws upon visualization technologies and techniques, in business, technology, art, and science. Work on mathematics draws from different areas of the brain and students need to be strong with visuals, numbers, symbols and words-but schools are not encouraging this broad development in mathematics now. This is not because of a lack of research knowledge on the best ways to teach and learn mathematics, it is because that knowledge has not been communicated in accessible forms to teachers. Research on the brain is often among the most impenetrable for a lay audience but the knowledge that is being produced by neuroscientists, if communicated well, may be the spark that finally ignites productive change in mathematics classrooms and homes across the country.

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Using Fingers to Count in Math Class Is Not 'Babyish'

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A few weeks ago I (Jo Boaler) was working in my Stanford office when the silence of the room was interrupted by a phone call. A mother called me to report that her 5-year-old daughter had come home from school crying because her teacher had not allowed her to count on her fingers.

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We all know how important it is that children experience mathematical activities across a range of contexts and locations and by using direct sensory experience – and that outdoor learning is just as important as ‘desk work’. Connecting Maths to every-day life and to our real environment gives Maths topics a purpose and a meaning. Remember that question that students ask: “Why do we have to study this?”? In order to avoid it, we can try to show them how Maths can be applied to other sciences, such as Biology studies, but also how one can use it in every-day tasks such as cooking, cost-effective packaging, gardening, in order to make difficult situations simpler and above all getting to know more about each other. Task such as treasure hunts, origami, paper folding, construction projects can combine modeling, object manipulation, problem solving, performing, movement and collaboration into a rich learning experience.

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The answer:

"Kids who acted out the story did better on this problem," Beilock said. The kids who read the problem often got "eleven" as a solution. They had missed the word "each" in the problem. But because the acting kids had physically mimed giving each hippo seven fish before moving on, the difference was ingrained.

"What was important was matching the words with specific action; that led to enhanced learning," Beilock said. "And after they'd acted it out they could actually do it in their head and get some of the same benefits."
THE BODY AND THE BRAIN
Scholarly study goes back a long time in history, but in terms of human evolution, many of the academic skills now required for successful functioning in the world are fairly new to the human brain. As neuroscientists investigate how humans learn, they often find that newer skills and aptitudes are mapped onto areas of the brain that also control basic body functions. Increasingly, this work is helping to illuminate neurological connections between the human body, its environment and the process of learning.

"In order to really engage our students and help them perform at their best we have to move beyond what's happening in the head," said Beilock at a Learning and the Brain conference. "We have to go beyond that."

This area of study, called "embodied learning," is not new to many educators. Maria Montessori highlighted the connection between minds and bodies in her 1936 book The Secret of Childhood: "Movement, or physical activity, is thus an essential factor in intellectual growth, which depends upon the impressions received from outside. Through movement we come in contact with external reality, and it is through these contacts that we eventually acquire even abstract ideas."

Increasingly scientists are proving Montessori right. Researchers are studying the body movements of children as young as four-to-six months old and have found earlier and more frequent movement correlates with academic learning down the road. Kids who could sit up, sustain "tummy time" longer and walk were all correlated with future academic success, even when researchers controlled for socioeconomics, family education and type of future education, among other mitigating factors.

"A very strong predictor of academic achievement was how early kids were moving, exploring their world," Beilock said. "When kids can explore their surroundings, all of a sudden, things change." Once kids are on the move the adults in their lives use directives and other more complicated language forms. As kids are coached by their parents, they begin to understand the directions and change behaviors. And once a child can do something on her own, she's more likely to internalize what's happening with others. "There is evidence that our ability to use our hands affects the structure and functioning of the brain," Beilock said.

"Encouraging kids to use their hands brings out unsaid, and often correct ideas, which then makes them more open to instruction and more likely to learn."

As young children move and explore their worlds, they are learning through touch. Early bimanual training correlates with the robustness of the corpus callosum, a part of the brain that facilitates quick communication between the left and right brain hemispheres, Beilock said. This connection between using ones hands and swift communication in the brain may be part of the reason learning to play music is often correlated with math ability.

"Math is a very recent cultural invention," Beilock said. The part of the brain responsible for numerical representation also controls finger motion. Many children first learn to count on their fingers, a physical manifestation of the connection. The studies of very young learners have solidified Beilock's conviction that academic learning is inherently connected to the body.
GESTURING TO LEARN
A colleague of Beilock's at the University of Chicago, Susan Goldin-Meadow has done extensive research into how student gestures can indicate a more nuanced understanding of math than students are often able to articulate verbally. Goldin-Meadow did a lot of work around problems of equivalence, which children often struggle to understand. She found that often students gesture in ways that indicate they understand how to solve the problem even if they are simultaneously describing an incorrect solution.

"It's particularly helpful for teachers because it may give you insight into things students may not be able to express," said Goldin-Meadow at the same conference. Not only could gestures be a good clue for teachers, but when students produce what Goldin-Meadow calls "mismatches," meaning they are saying one thing and gesturing a different understanding, it indicates they are primed to learn. And, when teachers produce "mismatches" in their own speech and gestures, it helps students already in that primed state to learn by offering several strategies.

"Encouraging kids to use their hands brings out unsaid, and often correct ideas, which then makes them more open to instruction and more likely to learn," Goldin-Meadow said. She also found that showing two ways of doing a problem with speech had very little effect on learning, but showing two methods when one was in gesture helped learners.

And the connection between bodies and learning doesn't stop with the younger grades. Beilock studies how well students comprehend abstract concepts in high school physics. Many classes focus on listening to lecture, reading a textbook and doing physics problems. Beilock hypothesized that if students could feel an abstract concept like angular momentum on their bodies, they would both understand and remember it better.

She and her colleagues used a rod with two bicycle wheels attached to test their ideas. Students spun the wheels and then tilted the rod in different directions. As they changed the angle, the force they felt changed dramatically. In her experiment, one set of students got to hold and experience the wheel. Another group just watched the first group and observed the effects they were feeling. They were all quizzed on the material a week later.

"Those students who had more motor activation did better on the test," Beilock said. "And those students were the ones who got the experience." But what if one set of students was just better at physics? Researchers at DePaul University have replicated this experiment, strengthening the scientific link between hands-on experimentation and powerful learning.
ENVIRONMENT MATTERS
Just as body movement and involvement can have a huge impact on learning, so too can the spaces where we learn. While neuroscientists are starting to be able to prove this link with their experiments, this concept is nothing new. Philosophers, writers and practitioners of Eastern religions have long made the same connection between the power of nature to relax the mind and readiness to take on the world.

"When we are in nature, our directed attention has time to rest and replenish," Beilock said. That's important because focus is like a muscle that gets tired. One researcher asked students to take a walk through the downtown of a college town. They weren't asked to do anything in particular, but they naturally encountered a lot of stimuli. The other group took a walk in a natural setting. The nature walkers were better able to focus when they returned.

Visual distractions apply to the classroom as well. Carnegie Mellon researchers recently found that when students learn in highly decorated classrooms, their gazes tend to wander, they get off task and their test scores suffer. Limiting visual stimulus is particularly important for very young learners who are still learning how to focus, and yet kindergarten classrooms are often the most brightly and densely decorated in an effort to make institutional buildings feel more cheerful.
THE BODY AND ANXIETY
One way to help students reduce test anxiety is to let them work it out through their bodies beforehand. Beilock did an experiment with freshmen high school students before their first final. She asked them to write down concerns about the test and connect to other times when they felt similar. They were told to be as open as they wanted and that their writing would be confidential. A control group of kids were told to think about what wouldn't be on the test.

This activity had little effect on kids who didn't experience much test anxiety. But students experiencing high levels of anxiety saw a six percentage point gain on their test scores. And, when Beilock analyzed those students' writing, she found the strategy was particularly effective for students whose writing revealed an eventual acceptance that the test was a minor hurdle, not the big scary all-consuming event they'd been worried about.

"We can start leveraging the power of our bodies to help us learn, think and perform at our best," Beilock said. Too often students are cooped up inside for six or more hours, sometimes without an adequate recess ,and more likely than not, with little attention paid to how their bodies could be powerful learning tools in the classroom.
Note: An earlier version of this story misstated the publication date of "The Secret of Childhood" as 1966. We regret this error.

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Why Kids Need to Move, Touch and Experience to Learn

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The answer: "Kids who acted out the story did better on this problem," Beilock said. The kids who read the problem often got "eleven" as a solution. They had missed the word "each" in the problem. But because the acting kids had physically mimed giving each hippo seven fish before moving on, the difference was ingrained.

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I teach Mathematics in School no. 195 Bucharest, Romania, at the lower secondary level. My students are between 11 and 15 years old. The school is very big (about 2000 students) with pupils between 6 and 15 years old. In every classroom we have access to video projectors and Internet (but not in the same time). We also have a computer room.

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I am a Maths teacher in Bucharest, Romania. I am always interested in improving my teaching methods, and in making my classes more interesting, motivating and engaging.

My hobbies are: reading, watching movies, travelling, trekking and sports.