# data[].attributes.headline
                                                    About this event

# data[].attributes.subject
                                                    About this event

# data[].attributes.body
EXPERT: Irina Vasilescu, Lower Secondary School Maths teacher with a 29 years teaching experience from Bucharest, Romania
EVENT DATE: 29 November – 9 December
TARGET GROUP: The target group consists of Math teachers in Primary and Secondary schools

# data[].attributes.body
Even if the outdoors and hands-on activities are so involving and enjoyable, they should include opportunities for reflective thinking. In order to support this, teachers can offer reflection prompts as a way to encourage students to think about what happened, to discuss and think deeply about the purpose and implications of the activity, reinforcing what was learned. Students can be encouraged to analyze the new approaches and compare them to their prefered method, finding new ways to study mathematics.
The reflection activities could offer the educator  valuable information to help him/her adapt the class to the students’ needs, have a more dynamic approach to teaching in order to align better with students’ individual and collective needs, rather than adopt a “one size fits most” approach. The reflection prompts can ask students to take about 15 minutes to discuss in their groups and then respond in writing (on the worksheet) to  a few simple questions such as:
1. Describe several things that you learned from this activity?
2. How could you apply what you learned in your current class work?

# data[].attributes.body
Motto: "The biggest room in the world is the room for improvement"

# data[].attributes.headline
9 strategies you can use to motivate your students

# data[].attributes.subject
9 strategies you can use to motivate your students

# data[].attributes.attachment_link.title
9 Strategies for Motivating Students in Mathematics

# data[].attributes.attachment_link.description
Keep your high school math students engaged with these techniques.

# data[].attributes.body
Grit in psychology is a positive, non-cognitive trait based on an individual's passion for a particular long-term goal or end state, coupled with a powerful motivation to achieve their respective objective. This perseverance of effort promotes the overcoming of obstacles or challenges that lie within a gritty individual’s path to accomplishment, and serves as a driving force in achievement realization.

# data[].attributes.attachment_link.title
Grit: The power of passion and perseverance

# data[].attributes.attachment_link.description
Leaving a high-flying job in consulting, Angela Lee Duckworth took a job teaching math to seventh graders in a New York public school. She quickly realized that IQ wasn’t the only thing separating the successful students from those who struggled. Here, she explains her theory of “grit” as a predictor of success.

# data[].attributes.attachment_link.description
TOUCH this image to discover its story. Image tagging powered by ThingLink

# data[].attributes.attachment_link.readable_text
Not only fun to roll, stack, throw, and catch, these Polyhedral ('many-faced') Balls are very special: they are crocheted versions of the five Platonic solids; the only five geometric solid shapes possible where every face is identical and the same number of faces meet at each vertex (corner). Fun and educational!

Not ready to make it yet? Add it to your Ravelry queue!

Or, buy the Polyhedral Balls crochet pattern right now and download it instantly from the PlanetJune shop 🙂

I carefully designed the component shapes so that (within the limits of 1 round of crochet) the finished balls are all the same size. And my construction and edging methods mean that they don't turn into spheres when you stuff them - the sides stay relatively flat without any hidden reinforcements, which not only makes them simpler to crochet together, but with no rigid plastic inside the balls, these are totally child-safe toys, made from only yarn and stuffing.

As well as being great as toys for kids to play with, they make good stress toys for adults! Plus I've discovered an excellent concentration/relaxation game: try balancing them all, one on top of the other - it is possible (provided the tetrahedron is always on the top), but surprisingly difficult to get all 5 to balance. You'll see I managed it for my cover pictures - there's no photo trickery there 🙂

The 5 Platonic solids, L-R: Cube (6 sides), Octahedron (8 sides), Icosahedron (20 sides), Dodecahedron (12 sides), Tetrahedron (4 sides)

If you're not tempted yet by the fun or math-geeky aspects of these balls, here's one more fact that might persuade you: these are no-sew patterns. 100% crocheted, you only need a yarn needle to weave in a few ends and you're finished! And most of the ends are cunningly hidden on the inside, so even the end-weaving is very minimal too.

This pattern includes:

Crochet instructions for the 5 component shapes

A step-by-step photo tutorial for how to crochet the special edging

Right- and left-handed step-by-step assembly diagrams, if you'd like to assemble your balls in the same order I did (leaving the minimum number of ends to weave in)

Tips for speedier assembly and less yarn ends

A special technique to improve the look of the finished corners

This is also a modular pattern: although it includes all the detailed instructions you need to be able to recreate these balls perfectly - 16 pages total - if you'd like to save on paper and ink, you can choose to print only the pages with the pieces you need: a) the crochet patterns, b) the general assembly photo tutorial and tips, c) the right-handed assembly order diagrams and/or d) the left-handed assembly order diagrams. If all you want to do is print the crochet patterns for the 5 component shapes, that's all included on one page! I'm doing my bit for the environment 🙂

Gamers take note!
Now, I don't know how much of a geek/RPG audience I have, but there's an obvious application to these balls that is just missing one little piece: with this set, we have a d4, d6, d8, d12, and d20... We're just missing a d10 to have a complete set of gaming dice! The construction and ridged edging of these balls mean that, as well as being a cute decorative set, they can actually even be used like real dice: they'll always land on one face. (To actually use one as a die it's best to throw it up in the air, spinning, and let it land - as it's large but lightweight, unless you have a large area to roll it across, you'll get a more random result if you throw it in the air first.)

The only problem is that a d10 is not a platonic solid - its shape is a little more complicated, as each of the 10 sides are slightly truncated kite shapes. I can do it, of course, but it would take a little more time, and trial and error, to figure out a) the right shape for a d10, and b) the right size so that the finished ball would match the rest of the set. So, the question is, would there be a demand for a 10-sided dice ball to complete this set?

If so, I'll design an add-on to this pattern that would include:

A truncated pentagonal trapezohedron (better known as a d10 to gamers) ball

Instructions for how to properly label the sides of all 6 balls to turn them into a set of functional gaming dice (embroidered numbers would look great for this, or fabric painted numbers would be a far easier option if you're not confident in your embroidery skills!)

So please do let me know in the comments if you'd be interested in buying the add-on pattern. I mentioned it on Facebook yesterday and I've already had a small positive response, so I need to know if there are more interested gamers/geeks (or people with gamers in the family - what better Christmas present than a set of giant crocheted gaming dice?!) before I design the d10. I'd do it with my commissions process, but of course I'm not going to charge anyone $6 for an add-on pattern!

But, for now, if you'd like to, you can pick up the Polyhedral Balls pattern in my shop 🙂

Hope you like it!

# data[].attributes.attachment_link.description
Not only fun to roll, stack, throw, and catch, these Polyhedral ('many-faced') Balls are very special: they are crocheted versions of the five Platonic solids; the only five geometric solid shapes possible where every face is identical and the same number of faces meet at each vertex (corner). Fun and educational!

# data[].attributes.attachment_link.readable_text
When you slice a cone the surface produced is either a circle, an ellipse, a parabola or a hyperbola.

When you slice a cone the surface produced is either a circle, an ellipse, a parabola or a hyperbola.

These curves are known as the conic sections.

And when you slice a scone in the shape of a cone, you get a sconic section - the latest craze in edible mathematics, a vibrant new culinary field.

On their fabulous website, the folk at Evil Mad Scientist provide a step-by-step guide to baking the sconic sections.

In fact, the raspberry jam parabola and the nutella ellipse join a pantry of geometrical foodstuffs guaranteed to liven up afternoon tea.

Bread is the perfect medium for creating tangrams - a puzzle in which a square is divided into seven pieces and rearranged to make a variety of shapes, such as a polar bear:

These images are taken from Dashing Bean, which has several more excellent suggestions, with beautiful pictures, including fish, foxes, birds, pigs and chickens.
For some background, here's a video from Maths on Toast that shows you how to make tangrams from, well, toast.

Perhaps the most famous dough-based mathematical mouthful, however, is the Möbius bagel, in which a bagel is sliced in such a way as to turn it into two linked parts:

The Möbius bagel was thought up by George Hart, and his site provides a full explanation of the steps required.

This video explains it too:

It all makes a change from pi.
Topics

# data[].attributes.attachment_link.title
Geometry bake-off: sconic sections, toast tangrams and the Möbius bagel | Alex Bellos

# data[].attributes.attachment_link.description
When you slice a cone the surface produced is either a circle, an ellipse, a parabola or a hyperbola. When you slice a cone the surface produced is either a circle, an ellipse, a parabola or a hyperbola. These curves are known as the conic sections.

# data[].attributes.attachment_link.description
Make your own tangram puzzle out of toast, and then make giraffes, cats or whatever you want. It's playing with your food, but it's also definitely mathematical. (Acknowledging here also the influence of Vi Hart)

# data[].attributes.headline
A formative assessement lesson on motion laws called Rolling Cups

# data[].attributes.subject
A formative assessement lesson on motion laws called Rolling Cups

# data[].attributes.attachment_link.description
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.

# data[].attributes.attachment_link.readable_text
Symmetry is one of those tricky concepts that is good to practice frequently. I love that nature produces lots of fun examples of symmetry -- one of my favorite is the butterfly. S and I spoke a little about this when we made her DIY Butterfly Wings last year, so I think my mind naturally settled on that example yet again.

LEGOs have such fun bright shapes and colors that I thought they would be perfect for having fun with symmetry. I set S up with a giant butterfly with sticky wings (to prevent frustration with bumping blocks) and two piles of various sized LEGO blocks on either side of her.

We talked about how to make the wings symmetric - to put the same colored and shaped LEGO in the same spot on each side of the butterfly's body. I made sure that each pile S was grabbing from had the same colors/sizes of LEGOs to make the process faster for her.

She had so much fun designing her butterfly. I only got to place two blocks myself - she had a lot of investment and a total plan for how this butterfly was going to look.

When it was nearly done, we found that it was easier to rotate the butterfly so that S could reach the blank spots on its wings more easily.

And voila! The finished masterpiece!

This post contains affiliate links for your convenience.

To make your own sticky butterfly, take a piece of posterboard (or cardboard) and fold it in half. Trace a wing on one side and cut out the butterfly. Add a body to the center, and if you'd like, some pipecleaner antennae. :) Then, using the back of some contact paper, trace the outline of each wing. Peel the paper off of the contact paper and place it sticky side up. Use some tape around the edges of the contact paper wing to hold it in place. The contact paper is not quite strong enough to hold the LEGOs if you hang the butterfly vertically on a wall, but it is strong enough to prevent the LEGOs from scattering as you work.

Here are the other fun ideas shared today:

Check back all this week for more fun ideas for playing and learning with LEGOs!

All activities here are activities I feel are safe for my own children. As your child's parents/guardians, you will need to decide what you feel is safe for your family. I always encourage contacting your child's pediatrician for guidance if you are not sure about the safety/age appropriateness of an activity. All activities on this blog are intended to be performed with adult supervision. Appropriate and reasonable caution should be used when activities call for the use of materials that could potentially be harmful, such as scissors, or items that could present a choking risk (small items), or a drowning risk (water activities), and with introducing a new food/ingredient to a child (allergies). Observe caution and safety at all times. The author and blog disclaim liability for any damage, mishap, or injury that may occur from engaging in any of these activities on this blog.

# data[].attributes.attachment_link.title
Learning Symmetry with LEGOs and Butterflies

# data[].attributes.attachment_link.description
Symmetry is one of those tricky concepts that is good to practice frequently. I love that nature produces lots of fun examples of symmetry -- one of my favorite is the butterfly. S and I spoke a little about this when we made her DIY Butterfly Wings last year, so I think my mind naturally settled on that example yet again.

# data[].attributes.headline
Engineering for Kids: Straw Geodesic Dome & Sphere

# data[].attributes.subject
Engineering for Kids: Straw Geodesic Dome & Sphere

# data[].attributes.attachment_link.readable_text
For our third and final straw project (for now....) I'm completely geeking out with this straw geodesic dome & sphere. I have pretty much lived and breathed architecture my entire life (my father is an architect as well) so I have been familiar with geodesic domes practically since I learned to walk...okay maybe not quite that long but you get the picture.....so I'm really curious if everyone else out there is as fascinated by them as me. If you are please leave a comment below telling us your favorite example of a Geodesic Dome!
For those of you that are just tuning into domes scroll down to the "Looks Like" section of the post for a quick primer on domes and their master, the one and only Bucky Fuller, as architects and designers go he considered a legend.
We have a fabulous Geodesic Climbing Dome in our backyard that has provided a lot of fun for my kids over the past few years. My son and I tried to replicate it when building straw structures out of triangles, you can see our version here, but it wasn't a true geodesic dome. Building a true geodesic dome out of straws involves some math. But don't be scared by that! I promise it's only one simple equation that I you can do with a calculator! I also wanted to create a tutorial that makes it about as easy to make a geodesic dome out of straws as humanly possible. I think I got pretty close.
This post contains affiliate links to products I love and recommend to my readers, plus it keeps this little blog o'mine afloat! Thank you!
Materials

Straight Straws like these For a dome you will need 33 straws (18 of one color and 15 of a second color). For a full sphere you will need 60 Straws (30 of each color)

Chenille Stems AKA Pipe Cleaners

Scissors

Ruler

Instructions
To visualize this project ahead of time here's the basic plan:

1. Cut straws into two different lengths (Strut A & B)

2. Make 6 pentagon sections

3. Join them together in the shape of a dome

Yes, it's that easy.
Note: We will be cutting two sizes of straws. For ease of understanding it's best to cut the different sizes from different colors. That way it's easy to keep track of which are the longer struts and which are the shorter.
Basic Pentagon

Step One Select one color to be Strut A and one to be Strut B. Strut A will be longer than Strut B. For Strut A simply cut each straw in half. Make a total of 35 Strut A's.

Step Two Strut B should be smaller than Strut A by a factor of 0.885. To determine what length to cut Strut B measure Strut A then multiply that number by 0.885. Now you have the size of Strut B. Here's an example:

For an 8" long straw Strut A will be 4" and strut B will be 4" x 0.885 = 3.54". Round up to 3.5" here people, you don't have to be that accurate! Just get close to the ratio. Hint- Cut one strut B length and use it as a guide to cut the rest of the straws to that size.

Step Three Cut a total of 30 Strut Bs.

Step Four Make some pentagons! Strut A will be the outside of each pentagon and Strut B will be the middle sections. Take (1) Strut A and feed a pipe cleaner through it. Bend back the end to secure it in place around the straw. Join additional pipe cleaners on as necessary to make one continuous length of pipe cleaner by twisting the ends of pipe cleaners together tightly.

Step Five Thread 4 more straws onto the pipe cleaners for a total of 5 straws) then bend into the shape of a pentagon and secure the ends together.

Step Six Thread (2) Strut B's onto the long end of the pipe cleaner (adding more pipe cleaners as necessary) then thread the pipe cleaner into an adjacent straw and out the other side.

Step Seven Thread (2) more Strut B's through the pipe cleaner and an adjacent straw.

Step Eight Thread 1 final Strut B onto the pipe cleaner and then secure all Strut B's at the center of the pentagon. It helps to wrap the pipe cleaner around the joint of one pair of strut B's and then wrap it around the second pair. Thread the end of the pipe clearer back into one of the straw struts to conceal it.

Step Nine Make 5 more pentagons as described above. For a full sphere grab a glass of lemonade and make 11 more pentagons!

Make the Dome

Now that you have the basic shape that will form the dome all you need to do is connect them together. For a dome you will need 5 Strut B's to form the base. If you are making a full sphere you can eliminate the extra struts as the pentagons from one side will join the second side of the sphere.

Dome- For ease of reference I have shaded in the center pentagon in this visual tutorial. Trust me, it look more complicated than it is.

Step One Take one pentagon and thread a pipe cleaner through one side, secure at the end. This will be your center pentagon.

Step Two Thread the long end of the pipe cleaner through one Strut B of a second pentagon. Make sure the pointed sides of the shapes are facing OUT. Pull them together.

Step Three Repeat Steps one and two to connect a third, fourth, and fifth pentagon at the joints of the center pentagon. Pull tightly.

Step Four Take the (5) single Strut B's and feed them through the base of the row of pentagon at the bottom, alternating pentagons and struts. Pull tightly.

Sphere

Step One Take one pentagon and thread a pipe cleaner through one side, secure at the end. This will be your center pentagon.

Step Two Thread the long end of the pipe cleaner through one Strut B of a second pentagon. Make sure the pointed sides of the shapes are facing OUT. Pull them together.

Step Three Repeat Steps one and two to connect a third, fourth, and fifth pentagon at the joints of the center pentagon. Pull tightly.

Step Four Repeat Steps one through three to make a second half of a sphere.

Step Five Join the two side together! Thread a pipe cleaner through Strut B of one pentagon on one sphere. Secure at the end.

Step Six Instead of threading single Strut B's around the base as we did to make a dome, you will use the Strut B's of the second sphere as the connectors. Thread the pipe cleaner through one Strut B on the second sphere half. The second sphere half should be positioned facing the opposite direction of first half. Continue threading pipe cleaners through the bottom loop of both halves to form a complete sphere. Secure the starting and ending points together.

Why are geodesic dome so fascinating to designers?
You may think it looks complicated and but it's actually really easy to make both the dome and sphere once you see the pattern. In all fairness I built this dome and sphere. My kids are just a wee bit young to tackle this project, although my baby had fun trying to thread pipe cleaners through straws... I know it takes some time but breaking this project down to basic shapes made it very easy to build and understand. Here's my son with the dome so you can see how big it actually is.
The Math Behind the Dome
About Geodesic Domes
*Theoretically a 1-frequency dome is possible but it makes the shape of an icosahedron, which doesn't quite have a spherical shape. More on Domes
Geodesic domes are very efficient structures. Triangles are inherently stable shapes, so creating structures out of interlocking triangles makes very strong, yet incredibly lightweight structures that can be adapted on a small level, like our project here, to a massive level as in the Montreal Biosphere constructed for the 1967 World's Fair.

The first step in designing a geodesic dome is to determine the frequency of the dome, denoted by the letter V. At a minimum you need a frequency of 2*. In simplified terms it means you need 2 different strut or chord lengths. The more struts/chords you have the more rounded the final shape will be. The straw geodesic dome/sphere here is 2V. 3V and 4V domes are also very popular t make. If you want to build one or even a more complex dome check out this geodesic dome calculator.

If you can't get enough Geodesic domes here are a few more places you should check out:

Looks Like

Buckminster Fuller. Of.course. In the architecture world Bucky Fuller is a legend. He ranks up there with Frank Lloyd Wright and Le Corbusier. Are you familiar with him? Well you are now. He didn't invent the Geodesic Dome, it was actually invented by Walther Bauersfeld, but Bucky Fuller made it a household word. His love of geodesic domes has spread to generations of young architecture students in the past half-century. He saw the potential in geodesic triangulated structures to build strong yet lightweight super structures was awarded patents for a number of his designs. Bucky Fuller is also renowned in design circles for his forward thinking philosophies. He designed the Dymaxion House in the 1940s to be a mass produced type of housing. Imagine if houses were made like cars in factories. In my opinion this makes him the predecessor to the pre-fab home movement. He also developed theories about the world's limited amount of natural resources and was a environmental visionary. For these reasons and more he is a hero of mine and many, many other designers.
P.S. This would make a fantastic STEM project for older kids! If you enjoyed this engineering project for kids check out Tensile Bubbles and Paper Building Blocks for a more structural fun.
Conclusion
Don't miss out on more STEM projects here on Babble Dabble Do! Your child's inner Buckminster Fuller thanks you! Subscribe below, like us on FB, or follow along on Pinterest! Visit Babble Dabble Do's profile on Pinterest.
My father the architect was visiting us this week and helped us make our geodesic straw dome. His verdict on this project? "Incredible!" He was impressed at how we broke down the construction into a few simple repeatable steps using very basic materials. You can do it too! Maybe you want to make one to explore geometry with kids or engineering ideas or maybe just for decorative purposes, I mean who wouldn't want to hang a geodesic sphere from the ceiling? Ha! In any case I hope you are inspired to try making one and join the ranks of Bucky Fuller fans worldwide!

Now that you are pumped about geometry here are three amazing toys you might want to consider adding to your collection, they might just turn your kids into the next Bucky Fuller:

# data[].attributes.attachment_link.title
Engineering for Kids: Straw Geodesic Dome & Sphere - Babble Dabble Do

# data[].attributes.attachment_link.description
For our third and final straw project (for now....) I'm completely geeking out with this straw geodesic dome & sphere. I have pretty much lived and breathed architecture my entire life (my father is an architect as well) so I have been familiar with geodesic domes practically since I learned to walk...okay maybe not quite that long but you get the picture.....so I'm really curious if everyone else out there is as fascinated by them as me.

# data[].attributes.attachment_link.readable_text
Kassia Wedekind tweeted:

@Simon_Gregg Group of Ts and Ss new to Cuisenaire rods want to explore, investigate. Besides open exploration, what else would u start w?

- Kassia Wedekind (@kassiaowedekind) October 14, 2016

Knowing Kassia as a writer and blogger with a lot of understanding about young children's explorations of mathematics, I'm a little daunted trying to answer. But I'll have a go anyway.

First of all I'm impressed with just open exploration. My K3 class show no sign of losing enthusiasm for it. At first, when I asked them, they had no idea that the rods were linked with numbers or measurements, but there is so much implicit maths in what they do, and just doing it extends their understanding of it. It's an aesthetic enterprise as much or more than a mathematical one, but that seems right. After all, mature mathematicians often describe their motivation as a kind of aesthetic pleasure they find in it.

I document a lot by taking photos. This makes it easier to break up our creations at the end of a session, because they are not "lost", but more importantly we look again at what we've made, and I refer back to particular ones as starting points for new departures.

Students need a lot of rods. This is true for any material you use where students like either a large scale or want to continue a pattern. The little sets that people usually buy are not enough.

One of the things the teacher can then do is to say, did you see the way Ana made that wall? Do you think you could all make a wall of some kind?

And they have been so creative, there's enough for many sessions of this kind of return. You can see it right from our first meeting.

For instance, there's been lots of rectangles and surrounded rectangles:

I've used Cuisenaire trays in sessions after this:

Other things that have appeared are plans, maps really, of roads and carparks, models of houses with walls and chairs of different sizes. All of which could be followed up. Helen Williams suggested using different-sized rods to represent the three bears as the story is told, with students choosing their three sizes of rods, and holding the right one up at the right time. There could be three different chairs made, beds...

Using narrative seems is a great way in. We've been reading and writing stories about rockets, aliens and going to the moon, and T created several beautiful rocket images, which also showed one of the first examples of a staircase. So it got returned to twice. Once for a, "let's all try to make that kind of pattern in some way" session, and once for a " show a way to get to the moon" session!

We've just been making some faces within squares with sides as long as the orange rod - which was challenging but also delightful.

Alongside this, we play games. Rods behind backs, can you take out the red rod? Together and with partners. Or, here's the sandwich with something missing, what needs to go in to finish it off.

And we're just beginning writing.

- Simon Gregg (@Simon_Gregg) October 6, 2016

As you can imagine, there's been some great opportunities for sitting with students and listening to them talk about what they're doing. But here I think I've go a lot more to learn form Kassia and her colleagues and their students...

# data[].attributes.attachment_link.description
Kassia Wedekind tweeted: @Simon_Gregg Group of Ts and Ss new to Cuisenaire rods want to explore, investigate. Besides open exploration, what else would u start w? - Kassia Wedekind (@kassiaowedekind) October 14, 2016 Knowing Kassia as a writer and blogger with a lot of understanding about young children's explorations of mathematics, I'm a little daunted trying to answer.

# data[].attributes.attachment_link.description
Uploaded by Maria Petrescu on 2014-10-25.

# data[].attributes.headline
How I Teach Math & Dance at the Same Time 

# data[].attributes.subject
How I Teach Math & Dance at the Same Time 

# data[].attributes.attachment_link.readable_text
0:00 / 2:52•Watch full video

# data[].attributes.attachment_link.title
How I Teach Math & Dance at the Same Time

# data[].attributes.headline
Movement and Math Activity - Bilateral Math 

# data[].attributes.subject
Movement and Math Activity - Bilateral Math 

# data[].attributes.attachment_link.title
Movement and Math Activity - Bilateral Math

# data[].attributes.attachment_link.readable_text
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!"

# data[].attributes.attachment_link.title
How Turning Math Into a Maker Workshop Can Bring Calculations to Life

# data[].attributes.attachment_link.description
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.

# data[].attributes.body
Math teachers who have only paper and pencil at their disposal, find some of the curriculum contents very difficult to illustrate. A lot more objects and materials can be used for modeling mathematical knowledge! Activities such as object manipulation, dancing, movement, measuring, mime, crochet can be turned into an opportunity to learn Math.  Students can prove theorems and properties in a practical way, based on object manipulation, self-made models, experiments and observations, using different materials and auxiliary tools.

# data[].attributes.attachment_link.description
TeachersPayTeachers.com -- 2,500,000+ free and priced teaching resources created by teachers for instant download including lesson plans, interactive notebooks, unit plans, novel studies, worksheets, printables, PowerPoint Presentations, quizzes, exams, task cards, workbooks, projects and more. Join over 8 million teachers on the web's most vibrant collaborative exchange.

# data[].attributes.headline
List of six tips for nurturing a growth mindset

# data[].attributes.subject
List of six tips for nurturing a growth mindset

# data[].attributes.attachment_link.readable_text
Washington
Stanford researcher Carol Dweck clearly tapped into a powerful and compelling idea when she linked the concept of growth mindsets to academic success.

As fans of Dweck's research can quickly explain, people with fixed mindsets see strengths and skills as inate traits, like eye color. You're either born with them, or you're not. But people with growth mindsets recognize that the brain can grow and change through effort, and they embrace failures as opportunities for developing new strategies and approaches to learning content and concepts they find challenging.

Enthusiasm for Dweck's work has spread rapidly, and her name is a buzzword in many schools as teachers buy into the idea that helping students shift their mindsets can lead to academic gains.

But, in recent years, Dweck has worked to balance that enthusiasm by busting some misconceptions about her research and its applications in schools. That includes a wildly popular Education Week commentary and, on Friday, a keynote address at EdWeek's Leaders to Learn From event in Washington.

"I fear that my work, which grew up to counter the failed self-esteem movement, will be used for the same purpose, trying to make kids feel good but not actually changing the process of learning," Dweck said, explaining her concerns.

As people have embraced the growth mindset idea, they haven't always fully understood every dimension of the research. Among the biggest misconceptions? That boosting students' mindsets is simply a matter of praising effort rather than results or helping students develop new strategies for approaching content they struggle with, Dweck said.

"Sheer effort is highly important, but it is not the ultimate value; learning and improvement are," Dweck said. "Effort is one route to learning and improvement."

Here are six tips pulled from Dweck's talk:

1. Acknowledge the nuance in the research.

Growth mindsets are not a magic trick that will solve every challenge in the classroom, Dweck said. The enthusiasm for the research sometimes leads to an expectation of unrealistic results, researchers have said. And that same enthusiasm can lead skeptics to dismiss them all together. Fellow mindset researcher David Yeager has even published a paper called "Social-Psychological Interventions in Education: They're Not Magic," which he just calls "The Magic Paper."

"A growth mindset is not a panacea, but it does empower [students] and help them learn," she said.

2. Everyone has a fixed mindset sometimes.

There's a misconception that every student and teacher can be put into one of two categories: those with growth mindsets and those with fixed mindsets, Dweck said, but in reality, everyone "has a little bit of both." The either/or mentality causes some people to ignore chances they have to address the fixed mindsets they do have about some areas.

"Let's legitimize that fixed mindset, because we all have it somewhere; we are all a mixture," Dweck said. "And watch for those fixed-mindset triggers."

What sparks students' fixed mindsets? It's whatever makes them retreat to that place where avoiding "looking dumb" is more important than being vulnerable and learning a new idea, she said. Those triggers are different for different people. They could be struggles, setbacks, criticism from others, or even meeting someone who is smarter or more talented, Dweck said.

"Do you hate them just a little bit? Or do you say, 'wow how did they develop those skills?' Maybe I can learn from them."

3. N ame your fixed mindset.

Dweck told of a consultant in Australia who encouraged business executives to name their "fixed-mindset persona" so they could have a fun, comfortable way of discussing it with peers.

In schools, the name gives a quick identifier to the triggers students and teachers identify, and it helps them recognize their responses that might not be productive, she said.

"Name it, claim it, and talk about it," she said. "And over time, recruit it to work with you on your growth mindset goals."

For students, that might mean calling their mindset by their middle name or a goofy nickname.

"When we're in a crunch, when we're on deadline and I'm not sure we're gonna make it, Duane shows up," one Australian man told his coworkers, according to Dweck. His organization's morale and productivity shot up as they adopted those strategies, she said.

4. Move beyond effort.

If teachers and parents want to nurture growth mindset in children, they should move beyond just pushing them toward effort. They should also help them identify new strategies and approaches so that effort can be productive, Dweck said. I discuss that a bit in this story about how math teachers can strengthen growth mindsets by changing their approach to the content.

Children can then move beyond just asking for answers when they don't understand and instead ask "What can I do to help myself?" she said.

5. Put mindsets into a greater school-culture context.

The larger culture of a school can influence their mindset formation, Dweck said. Students are less likely to avoid "looking dumb" and more likely to try new approaches if they believe that their school is interested in their success, she said. Similarly, in workplaces, employees are more likely to display growth mindsets when they believe that the organization believes in developing abilities.

Social-emotional learning efforts and school climate initiatives that encourage students to build supportive relationships may help build this attitude in a school, Dweck said.

"What is the larger culture that allows teachers and students to feel safe? That we're out for your development? We're not here to sort you into who can succeed and who can't."

6. D on't use mindsets to label students (or yourself).

Dweck said she's been disappointed to hear that some teachers have used a student's mindset as an excuse, saying things like "that child can't learn; he has a fixed mindset."

"We used to say kids don't have the ability. Now we're saying they don't have the mindset? I think it's protective. It's our way of saying 'It's not my fault that child isn't learning.'"

You can watch the whole address here.

Photo: Stanford Professor Carol Dweck speaks at Education Week's Leaders to Learn From event. --Charlie Borst/Education Week
Follow @evieblad on Twitter or subscribe to Rules for Engagement to get blog posts delivered directly to your inbox.

# data[].attributes.attachment_link.title
Nurturing Growth Mindsets: Six Tips From Carol Dweck

# data[].attributes.attachment_link.description
Washington Stanford researcher Carol Dweck clearly tapped into a powerful and compelling idea when she linked the concept of growth mindsets to academic success. As fans of Dweck's research can quickly explain, people with fixed mindsets see strengths and skills as inate traits, like eye color. You're either born with them, or you're not.

# data[].attributes.headline
The Journey to a Growth Mindset: Carol Dweck's Live Keynote Presentation 

# data[].attributes.subject
The Journey to a Growth Mindset: Carol Dweck's Live Keynote Presentation 

# data[].attributes.attachment_link.title
The Journey to a Growth Mindset: Carol Dweck's Live Keynote Presentation

# data[].attributes.body
Students’ mindset - important aspect
A growth mindset, that is the understanding that the abilities and intelligence can be developped.
Student with a learning goal will pursue interesting and challenging tasks in order to learn more. In subsequent studies,
growth mindset shows how cognitive, affective, and behavioral features are linked to one’s beliefs about the malleability of their intelligence.

# data[].attributes.headline
         Why Origami Improves Students' Skills

# data[].attributes.subject
         Why Origami Improves Students' Skills

# data[].attributes.body
https://www.edutopia.org/blog/why-origami-improves-students-skills-ainissa-ramirez

# data[].attributes.headline
Card Games to Boost Second Grade Math Skills

# data[].attributes.subject
Card Games to Boost Second Grade Math Skills

# data[].attributes.body
http://www.education.com/slideshow/card-games-second-grade-math/let-it-slide/

# data[].attributes.body
http://mathcraft.wonderhowto.com/how-to/create-concentric-circles-ellipses-cardioids-more-using-straight-lines-and-circle-0131356/

# data[].attributes.headline
Tools and resources forpaper/string activities

# data[].attributes.subject
Tools and resources forpaper/string activities

# data[].attributes.body
Puzzlemaker: http://puzzlemaker.discoveryeducation.com/CrissCrossSetupForm.asp
Snowflake tutorials   http://www.itsalwaysautumn.com/2016/11/23/cut-snowflake-video-tutorial-free-templates.html, http://krokotak.com/2015/12/paper-snowflake-decorations/
String art with GeoGebra
https://www.thinglink.com/scene/862059431964180480

https://scratch.mit.edu/projects/50076/

# data[].attributes.body
- Folding activities from NRICH
- The Math in a simple A4 paper! . Here you have the second part of the activity.

- Take a look at the fold and cut activity in the video. Some templates for such activities, they can be found at http://howtofoldit.org/
http://www.kizoa.com/embed-18278791-5697473o1l1
- Creating interactive notebooks

- More Math art project ideas here, if you need more inspiration

# data[].attributes.body
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.

# data[].attributes.attachment_link.title
Origami Proof of the Pythagorean Theorem

# data[].attributes.body
Here is a comic explaining the MI theory in a visual manner…so using its own tools!

Article and video interview with Howard Gardner on Multiple Intelligences

Description of each MI type, including characteristics, class activities, useful tech tools etc.

Explanations from the psychological point of view

Scientific paper by John Munro on Multiple Intelligences in Mathematics Teach

# data[].attributes.headline
Optional Reading- Gardner's Multiple Intelligence Theory

# data[].attributes.subject
Optional Reading- Gardner's Multiple Intelligence Theory

# data[].attributes.body
The Multiple Intelligences  theory states that pupils will benefit more from a broader vision of education, that would drive teachers to use different methodologies, exercises and activities to reach all students, not just those who excel at linguistic and logical intelligence and challenege them to discover "ways that will work for this student learning this topic" According to Gardner’s theory, students have different types of dominant intelligence and they can be reached more effectively by using a wider array of approaches. “Pupil engagement is a multi-faceted construct that includes affective, behavioral and cognitive dimensions” (Fredricks, Blumenfeld and Paris , 2004)

# data[].attributes.headline
              Tools and resources for outdoors activities

# data[].attributes.subject
              Tools and resources for outdoors activities

# data[].attributes.body
1.  GeoGebra
2. My Story book creating app
3. Google Map
4. Free phones apps on Google Play

# data[].attributes.headline
Some examples and ideas of outdoors Math activities

# data[].attributes.subject
Some examples and ideas of outdoors Math activities

# data[].attributes.body
1. http://photopeach.com/album/iprehf

# data[].attributes.body
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”

http://webarchive.nationalarchives.gov.uk/20130401151715/http:/education.gov.uk/publications/eorderingdownload/lotc.pdf

# data[].attributes.body
https://docs.google.com/document/d/19F3oQqYGVlo1LivgVBY4Ztv7GvArRAQRP50JLP9mBe4/edit

# data[].attributes.body
Paper and string are cheap and easy to use anywhere, which makes them valuable materials in any class. Students can be encouraged to use their kinesthetic intelligence to play with tangram, create tessellations, make geometrical paper objects, such as platonic solids and carry out simple proofs of their geometrical properties through paper folding or origami, create drawing techniques etc.

# data[].attributes.attachment_link.title
Make Your Own Impossible Cylinder--Mathematical Association of America's Math Horizons

# data[].attributes.attachment_link.title
MathLapse: Constructions by pin-and-string: conics | Construções de fio esticado: cónicas

# data[].attributes.attachment_link.description
Ellipse: There is a string attached to two nails. The string is stretched using chalk; when the chalk slides along the string, an ellipse is drawn. Parabola: There is a string attached to a nail and to the top of a set-square that is resting on a ruler (not touching the nail).

# data[].attributes.body
Teachers taking part in this project cooperated, planed and shared ideas of lessons outside the classroom, which are a part of ordinary school timetable. During lessons pupils solved concrete problems situated in typical context and environment.

# data[].attributes.attachment_link.authors[].name
ΦΩΤΙΟΣ ΧΑΤΖΗΒΑΣΙΛΕΙΟΥ

# data[].attributes.body
Getting out of the classroom facilitates authentic or experiential learning (the engagement of learners with the world as they actually experience it) and gives better access to the main pathways to learning (Visual, Auditory and Kinaesthetic). Pupils not only experience mathematics in concrete and novel settings, but can be liberated from the sometimes restrictive expectations of the classroom. We can expect:
1) higher levels of motivation
2) almost limitless resourcesan opportunity to see maths as cross-curricular
3) greater curiosity leading to more effective exploration
4) creative ideas driving investigations
5) meaningful application of problem solving strategies and thinking skills
a heightened sense of purpose and relevance
6) the all important bridge between theory and reality
7) greater independence and an improved attitude to learning
greater enjoyment and achievement
8) a realisation that our environment offers opportunities for learning and enjoyment

# data[].attributes.body
,,What really drives education is curiosity, trying to fill gaps in our understanding. And the world around us is a tremendous resource to stimulate that curiosity"
Sir Ken Robinson

# data[].attributes.body
Technical School ,,15th May" Prokuplje, Serbia

# data[].attributes.attachment_link.title
Техничка школа "15. мај" Прокупље

# data[].attributes.body
My name is Sladjana Trajkovic, math teacher in Technical School, Prokuplje, Serbia. I really love teacher's job and I try to teach my students the essence of mathematics learning...

# data[].attributes.body
,,Experimentation is better understanding. Mathematics operates with symbols, these symbols build her language, but the symbols are not what Math really means. Math is about seeing the patterns of life. It only needs our "Touch"."

by Gabriela Chirca

# data[].attributes.body
"If you present math the way it really is, this fantastic expression of human creativity and ingenuity, people do want to read that!" -Steven Strogatz, professor

# data[].attributes.attachment_link.title
Mathematician Shares 'Secret Universe' of Patterns, Beauty, Interconnectedness

# data[].attributes.attachment_link.description
Playing mathematically with fruits by the foot. Mobius Story, Wind and Mr. Ug: http://www.youtube.com/watch?v=4mdEsouIXGM Mobius Candy buttons: http://www.youtube.com/watch?v=OOLIB3cjFqw Mobius Music box: http://www.youtube.com/watch?v=3iMI_uOM_fY Doodling Snakes + Graphs (Useful for drawing Borromean rings): http://youtu.be/heKK95DAKms My personal website, which you might like: http://vihart.com

# data[].attributes.body
"Hands-on activities give the students more freedom to move and get physically involved in solving Math problems..."

by Tania Formosa

# data[].attributes.body
,,Hands-on activities provide students with a rich environment in which they can explore, create, and justify answers"

by Doina Andrei