Out of the corner of my eye, I notice three-year-old Saaliha, who is patiently working her way through a rainbow puzzle. Her friends are busy in other parts of the classroom, but Saaliha is problem-solving her way to puzzle mastery. I sit down next to her to observe her learning style, and she is so engrossed in her learning that my presence goes unnoticed.

Open-ended materials such as Saaliha’s rainbow puzzle often lead to long periods of deep concentration and learning. Today is no different.  Although this rainbow puzzle often lands in the block area in the shape of a snake, a tunnel or a flowing river, Saaliha is trying to assemble the pieces so that the puzzle will fit back into its round wooden tray for storage.

Puzzle play is a great time to build cognitive and fine-motor skills. In addition to finding the correct sequence of sizes, Saaliha must determine how each block must be placed to complete the puzzle. I watch as Saaliha flips, turns and rotates the pieces to figure out where they go and in what order.

I love observing Saaliha’s learning style and seeing how it corresponds to her developmental level. I see her set aside pieces that are not needed at the moment. Saaliha’s spatial awareness is growing with each try.

As Saaliha plays with the puzzle, I note how her choices and strategies change. She begins to recognize and understand how the pieces fit together to complete the puzzle. I watch her sorting and testing pieces of different sizes and moving them in different directions until each piece fits properly.

As she builds her spatial awareness, Saaliha is also strengthening the small muscles in her hands while improving her manual dexterity and building foundational problem-solving and critical-thinking skills. This is a learning adventure that requires the eyes, hands and brain to work together!

Saaliha is soon joined by her two-year-old buddy, Eleanor. These two best friends are 11 months apart in age—with different learning styles and different levels of brain development.

As they work together to fit the yellow arch into the puzzle, they discuss and test out different strategies. The collaboration continues as Eleanor tries to solve a problem her older friend could not.

Saaliha never reaches over to remove the piece from her younger friend’s hand. She is observing and reasoning as deeply as she had been moments earlier when the puzzle piece was in her own hand. Eleanor quickly loses interest, but Saaliha perseveres.

Saaliha tries new pieces and new directions. I can practically see the wheels turning in her brain. She is coming up with new ideas and testing out different theories.

She is not rushed or agitated, and she doesn’t ask for assistance. She simply keeps trying new patterns and new pieces. In short, she is riveted to this learning opportunity.

Suddenly it all clicks into place. Saaliha has an “Aha” moment, and I can see her confidence surge as she fits the pieces together more quickly. She has solved the puzzle!

There is no celebration, just a smile of satisfaction. She studies the finished project. Before I can capture her expression of satisfaction with my camera, she disassembles the puzzle to do it over again.

As Saaliha starts over, I continue to observe her strategies and methods. Her perseverance continues to reward her with stronger puzzle-solving skills.

What better way to build an early math foundation?

Today is one of those magical winter mornings when snow blankets the ground and clings to the trees around our center.  The sun is shining and the world looks so sparkly and irresistible that we head outside in spite of the freezing temperatures.

“Hey! Who has the smiling boot?” Jacoby calls out to the group. He scans the play space, which looks like a snowy white canvas dotted with boot prints.

“Do you have the smiling boot?” he asks Maria.  

Maria looks confused as she glances down at her boots. “No, my boots are pink.” 

“No, no…on the bottom!” Jacob points to her boots. “Does your boot have a smiling face on the bottom?” 

Even I am confused by Jacoby’s question—until he points to the clue in the snow. 

“Look!” he declares. “Somebody has a smiley face on the bottom of their boot.”

Ah-hah! Indeed, we do have a smiley face boot print staring up at us from the snow-covered ground. Well, this will warm us all up!  Let the STEM investigation begin!

After a fresh snowfall, it’s so much fun to find and follow animal tracks. But we’ve never really paid attention to the patterns on the soles of our boots until now.

One by one, Maria and Jacoby begin to check the bottom of each friend’s boot. This simple moment of exploring patterns leads us to measurement, reasoning and comparing attributes.

Young children instinctively seem to notice attributes. It may be the shape, size, color, length or some other characteristics of an object, such as today’s smiling boot face.

Children develop their understanding of matching and patterns through experience. Because it’s difficult to consider a lot of attributes at once, children often begin creating sets by finding exact matches.

When children create pairs of boots or find an exact match to the smiling boot face, they are creating sets of items that are exactly alike. Maria and Jacoby are using rudimentary math, science and engineering skills as they observe and ask questions—all while solving the smiling boot print mystery!

Suddenly, everyone is stomping their boots and comparing and analyzing the shapes and patterns that their boots are leaving in the snow.

“I have zigzags!” announces Liam.

Sure enough, as we all run over to look at Liam’s boot print in the snow, we see row after row of zigzags.

“They look like mountains!” laughs Rokia. “That’s so cool!”

 “I have rectangles!” announces Rachel. “If I turn around, it looks like a house with a roof. Look!  See, at the bottom of my boot print?”  

Our focus is now very intentional and the mood has shifted from playful curiosity to deep observation and concentration. 

This is what child-led learning looks like. For those of you who believe that “child-led learning” can only lead to chaos, I urge you to put on your winter wear, head outside and see how effective and wondrous it can truly be.

“I have diamonds!” shouts Julio, “Oh and triangles at the top and bottom. Wow! Look at my boot print, it has really cool patterns.”

We are working on spatial reasoning, direction and positional vocabulary. This is the deep learning that takes place when children have ample time to explore and investigate.

Every day, children learn something new.  Every day, they deepen their understanding of STEM principles and share their insights and theories with their fellow STEM explorers.

Time is the key to deep learning!

“I have snakes!”  Josie shouts.

“Snakes?” 

Everyone comes running to see the newly discovered boot-print pattern. And, yes indeed, Josie’s boot print really does look like snakes.

But Isaac sees it differently. “I think it looks like waves,” he counters. “You know, like when you throw a rock in the river and it makes those lines?”

Then five-year-old Maya reorients the group to the smiley-face boot prints that started the morning’s STEM investigation.

“Where did that smiley face boot come from?” she asks, putting an end to the snake-shape and wave-shape discussion.

“I don’t know!” retorts a frustrated Jacoby. “That’s what I am trying to figure out!” 

“No, I mean, where did the smiley face boot print start?” Maya clarifies, assuming the role of lead investigator. “Where did you find it? Did you follow it, like we followed the cat paw prints last winter?” 

Jacoby pauses and I can see the wheels turning as he considers Maya’s questions. This is a lightbulb moment when the children suddenly recall a forgotten game from winters past. We have plenty of wandering cats in our neighborhood. For years, we have engaged in follow-the-cat-print expeditions on snowy days, following the tracks and trying to figure out the exact route that the cat took and why. Today has ushered in a new season of snow—and now we are rediscovering the game all over again.

Five-year-old Maya has had a few more years of brain development and a few more years of winter play, so she has retained more memories of those snowy-day games than the younger children who started the smiling boot print investigation.

Suddenly we are tracking movement, direction and the changes in how the boot print is left. We don’t have paper and pencils to collect data outside today, but our friends are forming hypotheses and making deductions as they piece the clues together and abandon the ideas that don’t pan out.

Maya continues as the lead investigator. “Look at the size of this boot track. It’s much bigger than our boots. See? I think it’s an adult boot print. Look how far it is between the foot prints. It takes me three steps to their two steps.”

“Maybe it’s the mail carrier,” suggests Lois.  “She brought a package to the door yesterday.”

“It can’t be the mail carrier,” reasons Maya. “She doesn’t walk on this side of the center.”

“It must be a parent!” shouts Jacoby. “Who has a parent with a smiling boot?”

The question is met with dead silence. No one knows the answer.

Suddenly, Maya turns to me and asks, “Do you have a smiling boot? You are an adult.”

Much to my disappointment and the chagrin of my young friends, I am not the owner of the smiling boot. We are getting cold and our investigation has hit a dead end. We decide to go indoors and warm up with some hot cocoa and banana muffins.

At pickup time, the children check the boots of every parent for a smiling face, but no one has the matching boot. Many weeks later, we discover that the smiling boot belongs to a grandparent of one of the children at our center. By then the thrill of the hunt is over. But the learning has not been lost. A great morning of STEM investigation is tucked away safely in the developing brains of our early math explorers.

Ready to start your own Snowy Day STEM Investigation? Check out Show Me Your Shoe, an Early Math Counts lesson plan that can be adapted for your own boot-matching investigation!

Our moment of silent concentration and focus is interrupted by Parker ecstatically showing off her geoboard.

“You made a house?” asks Linnea, looking a little wide-eyed and confused. “How did you do that?”

“I just added shapes and it worked!” Parker answers, equally amazed by her own creation.

“I want to try that!” shouts Rowen.

“Me too!” echoes a chorus of four-year-old voices. “Show us how you did that!”

Geometry has entered our world today—and what better way to learn about early math and science concepts than through play?

I have come to believe that geoboards are one of the ultimate learning tools for peer mentoring. I watch as the four-year-olds follow Parker’s example and create their own versions of her rubber-band house.

I am a huge fan of these little powerhouses known as geoboards. Hands-on activities with these simple learning tools get children’s brain synapses firing like crazy and stimulate the development of new neural connections.

The boards, with their colorful rubber bands and infinite possibilities, also make math and engineering fun!

Our geoboard play tends to occur in cycles. Today, the geoboards have resurfaced after long hiatus.

Because the children haven’t used the geoboards in a while, I notice how much their brains have developed since the last time the boards were in play. Seeing these leaps of brain development is one of the great joys of teaching.

Geoboards are always developmentally appropriate in the hands of the creator. Some children simply work on stretching the rubber bands onto the nails. My “artsy” early learners—who are happy designing anything and everything—can play with these boards for hours. And there’s a child in every class who insists on attaching every single rubber band in the bag to the geoboard, persisting long after the other children have moved on to new activities.

Geoboards enable even young children—and those who may have difficulty drawing shapes—to construct and investigate the properties of early geometry without a pencil in their hands.

I see geoboards as a chance to level the playing field for those who struggle with grasp, fine-motor or visual-motor skills.

Children begin to notice shapes before they have the language to name those shapes. Geoboard play acquaints children with simple shapes—as well as more advanced concepts such as symmetry, angles and fractions—as they engage in activities such as measuring, counting or investigating 2D shapes like Parker’s rubber-band house.

Look at those little fingers and hands going to work! With just one geoboard and a bagful of rubber bands, children can create and learn about shapes while developing their hand muscles, fine-motor skills, spatial skills and math skills. This is why geoboards have been a part of our classroom curriculum for more than 30 years.

Children can use their rubber bands to create squares, rectangles, triangles and other “sided” shapes. They can also explore number concepts as they try to stretch a single rubber band around a certain number of pegs. They may try to stretch it around three or four pegs—or maybe even all of the pegs. This early math exploration evolves quite naturally as the children engage in geoboard play with their friends. 

When I introduce geoboards to new students, I leave the lesson plans and benchmark checklists for later and let the children simply play with their boards. I want them to engage in geoboard play at their own level of development.

It’s important to give the children ample time to engage in this process. It can’t be rushed. For my young learners who love to make shapes, letters and designs, a longer play period gives them time to get their creative juices flowing. As their brain development continues, you will see their shapes and designs become more intentional.

Young children develop ideas and concepts about science, technology, engineering, art and mathematics (STEAM) naturally. They think about size, shape, quantity, order and speed throughout the day as they play and explore. As teachers of young children, we need to tap into their natural curiosity with intentional STEAM learning opportunities such as geoboard play.

Intentionality is acting with knowledge and purpose. It is the opposite of chance because it is planned and thoughtful. In order to become intentional about math teaching, we need to think about math the way we think about literacy.

By making shapes on their geoboards, the children are actually developing important pre-reading and pre-writing skills too.

Here’s how it works: When Linnea sees a shape on the geoboard and names it, she is preparing herself to identify letters and numbers and then naming and eventually writing them.

Simply by placing a basket full of geoboards near a table, we can encourage children to experiment with shapes, sizes and direction through hands-on play.

We can call this math, science, engineering, art or literacy because it’s laying the groundwork for the STEAM disciplines, as well as language development.

But in our hearts—as early childhood educators—we simply call it play.

“Will the children be kindergarten ready if they spend their days playing outside?”

As educators, we are often asked about kindergarten readiness by nervous parents who want to give their children the best possible start in life.

It’s important for parents—and educators—to understand that there are endless opportunities for deep learning when children are connected to nature. Young children learn primarily through their senses. The natural world—with its stimulating and constantly changing elements—provides the ultimate sensory learning environment.

When children explore the world through sensory play, they are actively building new neural pathways, which is crucial for brain development. When we slow down enough to observe this process, it’s easy to see the learning that takes place, and the social skills that are being developed, as the children collaborate on projects in the great outdoors.

On an unusually warm day in May, the boys in our program are busy building a large castle in the sandbox. This may look like nothing more than sandbox play, but there’s some deep learning going on here as our castle architects lay the foundation for future academic success.

“We should build a moat!” declares Joshua.

“Yeah, a moat!” agrees the gang. “We definitely need a moat!”

With these words, the digging begins. Before long, the castle builders decide that it’s time to add water to the moat. We have plenty of buckets at our center, but today most of the buckets are already in use.

Looking around for a way to transport the water from the pump to the sandbox, the boys settle on a nearby piece of fabric from one of their forts.

We’re all hot, tired and likely a little dehydrated at this point. A glance at the clock tells me that it’s almost closing time. But who am I to redirect the boys by pointing out the empty bucket next to the fence?

I watch as the boys carefully stretch the material out and center it beneath the pump spigot to catch as much water as they can. Asa begins pumping and, to my astonishment, the fabric holds the water without any leakage.

WHAT in the world?  I’m marveling at this unexpected development when it occurs to me that the cloth I’d purchased from the resale shop is actually a waterproof fabric used in hospital settings.

When I ask the boys if they were aware that the fabric was waterproof when they grabbed it, they respond with a question of their own: “What does waterproof mean?”

I try to explain that waterproof means that the water will not flow through the fabric. But there are times for discussion and times for action—and the boys are already focused on the next step in their plan.

First, they gather the corners of the cloth, taking care to keep the water from gushing out the sides. Then they make their way gingerly across the yard to the sandbox and carefully place the fabric in the moat.

I realize at this point that the boys had deliberately ruled out the use of buckets because they needed a flexible, waterproof liner for their castle moat.

They had assumed that the fabric they chose would hold water and, at the same time, conform to the shape of the moat. Wow! They were way ahead of me!

The boys did eventually make multiple trips to the pump to fill some buckets and add more water to the moat. But they knew that the bucket wasn’t the best tool for the initial phase of moat construction. Silly me!

This is just another example of the importance of giving young children sufficient time to engage in deep play and problem-solving (without any interference from those of us who think we have all of the answers), as well as the importance of loose parts in creative play.

Look at the delight on their faces! Okay, so the castle architect on the far right in the photo below seems to be grimacing at the weight of the load, but the other two look pretty thrilled with the success of their mission!

When we look at children playing in sand, what are WE missing? They are busy designing, creating, collaborating and communicating. They are adding and subtracting, working with shapes and molds and inclines and declines. They are adding water to change the nature of their building material. They are using spatial awareness and math and science vocabulary. They are theorizing, hypothesizing and collecting data. They are engineering and deepening their knowledge—all while playing in a box of sand!

This is the ultimate in STEM learning. Give them as much time as they need. Let them play. Add fabric to your play centers. You never know where their outdoor play will lead them—and what YOU may learn in the process!

“AUGGGHHHH!” I hear screams, a crash and giggles galore.

The joy of Magna-Tiles® has returned to our ever-popular window-stacking play. When these colorful magnetic tile mosaics come crashing down from the window frame, the children respond with laughter and joy. By contrast, the collapse of three-dimensional block formations often elicits groans and tears.

Something about the suspense of the build (and the challenge of stacking the magnetic tiles higher and higher without triggering a collapse) keeps the children coming back to this activity time and time again.

For anyone unfamiliar with Magna-Tiles, they are magnetized tiles of different shapes that can be used to build the most amazing creations. We have purchased other magnetic block sets, but the children had difficulty figuring out the polarization or were frustrated by the lack of versatility. Ultimately, those more expensive sets were abandoned to collect dust in a corner while the children spent endless hours playing and learning with the Magna-Tiles.

Is there a more perfect block than a Magna-Tile? If I were stranded on an island with a group of preschoolers, this would be on my top-ten list of must-have learning tools. Heck, it would be on my top-three list. These are, without a doubt, the favorite block in our program. What’s not to love? Magna-Tiles build confidence and fuel hours of creative play. Our only problem with Magna-Tiles is that we never seem to have enough!

I read somewhere that you know you have enough blocks when there are still blocks on the shelves. I’m still not sure I have enough Magna-Tiles on any given day, and I always find myself purchasing more. (Full disclosure: I often purchase PicassoTiles, which are less expensive, equally rugged and nearly identical to my original Magna-Tile set. So, if your program is on a budget, don’t hesitate to buy this less expensive set.)

Magnetic tiles are a STEM classroom delight. We have math opportunities with shapes and colors, counting, blending colors, angles and geometry galore! We have science and engineering as we explore different designs and building techniques. The magnetic feature opens doors to design and construction options that regular wooden blocks cannot provide.

“What color is your tree?” Harrison asks his best friend, Jack, as they use their magnetic tiles to change the colors of the scene outside our window.

The collaboration continues as the two boys follow their creative impulses and develop their ideas.

Then Jack proposes a new challenge. “What if we try a triangle this time?”

The boys determine that the results will be the same regardless of the shape. I am convinced that the children’s understanding of different shapes has been greatly enhanced by the use of these magnetic tiles. Magnetic tiles are the perfect educational tool for teaching all things geometric!

I also love to observe the children as they engage in problem-solving when they are confronted with a shortage of large square magnetic tiles. They quickly determine that they can create the same shape with four smaller magnetic tile squares.

Magnetic tiles also lay the foundation for an understanding of sets and quantities, as well as concepts such as location and ordinal positioning as the children expand their STEM knowledge and vocabulary.

“Jack, do you think we can add this square and it won’t fall down?” asks Jack’s twin sister, Eve, who is working through her predictions and collecting data on what works and what doesn’t.

I watch as Eve gingerly pries the corner of the bottom tile away from the window and triggers a structural collapse that brings all of the magnetic tiles tumbling down.

This investigation of “What happens if…?” is met with delight and infectious laughter from Eve’s peers as the building collaboration starts all over again.

“If we add this triangle to the top, the trees will turn green and look different from the red trees down here.”

Jack and Eve continue to pursue different avenues of learning with the tiles. One minute they are investigating colors and the next they are observing patterns or determining which shape should be added to the mosaic.

I’ve noticed yet another benefit of our window-frame magnetic-tile mosaics: The activity often brings children together who don’t naturally play side-by-side.

In other words, this group endeavor builds community. I am not sure if it’s a team effort of US versus the WINDOW BLOCKS or if it’s simply the contagious joy of the activity that makes everyone want to join in the fun.

When the temperatures drop below zero for days on end, I know that I can count on our magnetic tiles to lighten the mood and enrich our learning through play.

One more note: I have been known to remove the magnetic tiles from our play on occasion.

Why? Because I believe that magnetic tiles are so easy to use that they create “lazy builders.” This is just a personal theory of mine, but I’ve seen it play out over and over again. Sometimes the children in my program need to be pushed out of their comfort zone.

I do this by pulling out my wooden unit blocks, which require the children to perfect the balance and symmetry skills needed to build a stable block tower.

When those wood towers fall, I remind my wee ones that they are great builders and then I help them start building again from the foundation up.

When I rotate the magnetic tiles back into our play after a period of going “back to basics” with the wooden blocks, I nearly always notice that the children’s building skills have improved.

Try it and let me know your results. Happy building!

Out of the corner of my eye, I am drawn to the persistence of three-year-old Saaliha. She is calmly and patiently working her way through a rainbow puzzle.  Her friends are busy in other parts of the classroom, but Saaliha is problem-solving her way to mastery. I sit down next to her to observe her skills. She is so deep in her learning that she doesn’t notice.

Open-ended materials such as these often create learning scenarios that allow long periods of deep concentration, and today is no different. Although this puzzle often lands in the block area as a snake, a tunnel or a flowing river, today Saaliha is trying to fit it back together the way it is stored in the tray.

Puzzle play is a great time to build cognitive and fine-motor skills. Besides finding the correct sequence of sizes, Saaliha needs to evaluate which directions the blocks sit so that she can complete the puzzle. I watch as Saaliha flips, turns and rotates the pieces to figure out where they go and in what order. This is spatial transformation. I love watching her learning style and seeing how it corresponds to her developmental level. I see her set aside pieces that are not needed at the moment. Saaliha’s spatial awareness is growing with each try.  

Watching Saaliha play with the puzzle, I can see her choices and strategy change. She begins to recognize and understand how the pieces fit together to complete the puzzle. I watch her sorting and testing pieces of different sizes and moving them in different directions until one piece fits properly. Through this task, Saaliha is developing small-muscle movements and dexterity in her hands and fingers, along with critical-thinking and problem-solving skills. This creates a learning adventure in which the eyes, hands and brain are working together to make the puzzle pieces fit. 

Saaliha is soon joined by her two-year-old buddy, Eleanor. These two best friends are 11 months apart in age—with different learning styles and levels of brain development. They work together to fit the yellow arch into the puzzle. There is discussion as they describe their strategies to one another. The collaboration is delightful as Saaliha patiently watches her younger friend try to master the same issue that she is having. Saaliha never reaches over to remove the piece from Eleanor’s hand. She is observing and reasoning as deeply as she had been moments earlier when the puzzle piece was in her own hand. Eleanor quickly loses interest, but Saaliha perseveres!

Saaliha tries new pieces and new directions. I can see the wheels turning in her head. She is collecting ideas and working out theories. She is not rushed or agitated.  She is riveted to this learning opportunity. She doesn’t ask for assistance. She just keeps trying new patterns and new pieces. 

Suddenly it all clicks into place. The lightbulb of understanding goes on in Saaliha’s mind and I can see her confidence surge as she fits the pieces together more quickly. She’s got it! She’s figured it out! There is no celebration, just a smile of satisfaction. She studies the finished project. Before I can capture her expression of satisfaction, she disassembles the puzzle to do it over again.

Saaliha continues to struggle and I continue to observe her strategies and methods of choice. Her perseverance continues to reward her with success and a better understanding of the puzzle in front of her. She is a finely tuned machine, working on all cylinders as she masters the task at hand with patience and confidence. 

Puzzles offer a wide variety of developmental benefits and enable children to learn important skills as they play. From critical thinking and problem solving to concentration and attention span to spatial awareness, playing with puzzles adds layer upon layer to our strong math foundation! 

As teachers, we constantly remind students about the importance of mathematics if you want to be an engineer, chemist, architect, archaeologist, astronaut, astrologist, biologist, and many more. What people don’t realize is that spatial skills are key in transforming mathematics into three-dimensional objects with limitless uses. Spatial reasoning is essentially the ability to think about, visualize, and mentally organize objects in 3 dimensions.

Here is an example of a standard spatial reasoning test question:

Which of the following cubes represents the unfolded picture on the left?

Question and photo from http://dudye.com/challenge-your-creativity-77-problem-solving-exercises

The correct answer to the above question is the cube shown in choice C. These visualization exercises involve the same thought processes that allow surgeons to visualize the next steps in surgery, architects to convert floor plans into real life buildings, engineers to use formulas and programs to form electrical circuits, and so on.

Most people think spatial reasoning is specific to geometry class, but spatial reasoning is involved in all mathematics and science classes. I teach high school students, but spatial reasoning skills can be built and expanded from a very early age. We all use our spatial intelligence on a daily basis. When you look at a map to figure out relative location, rearrange your living room, try to figure out if your stroller will fit down the aisle in the grocery store, or decide whether or not that last pan will fit in the dishwasher; you are using your spatial intelligence skill set. Even something as simple as involving your children in these types of questions, decisions, and activities can help strengthen spatial reasoning skills.

Playing with toys and games that allow imaginative building can help improve spatial skills. Some things that probably come to mind immediately are toys like Legos and building blocks, but there are many more options for individual play or group play and board games available. A great list of construction toys is available here: http://astore.amazon.com/parenscien-20?_encoding=UTF8&node=35

There are also countless puzzles and games that involve spatial reasoning skills. A list of board games that involve spatial reasoning is here: http://astore.amazon.com/parenscien-20?_encoding=UTF8&node=35

(Blokus is one of my all-time favorite games! I think playing this game has made me much better at visualizing when teaching geometry.)

If the test question above was interesting for you to think about, there are a number of spatial reasoning challenges and tests you can find online. I did a quick Google search for online spatial reasoning tests and I found one similar to the question above at https://www.123test.com/spatial-reasoning-test/

(This is not a test you’d give young children, but I found it to be a fun mental challenge).

One of the best things about working with construction toys or board games that involve spatial reasoning skills is that they truly are games that allow children to come up with their own plans, outlines, or strategies without one correct answer. This is always the goal of inquiry based mathematics, so introducing games and play objects that allow for this type of thinking early on will go a long way in students’ future success in mathematics.

Sometimes I dread meetings.  Honestly, I dread most meetings but this past week I attended the annual Board Meeting for the Chicago Children’s Museum (since I am on the Advisory Board of the Tinkering Lab and we were invited to the BIG meeting) and it was exceptionally fun and entertaining.

Once the voting was over and introductions had concluded, a puzzle maker by the name of Sandor Weisz took over the meeting, broke us into groups and together we worked out an interactive and engaging puzzle.  His business, The Mystery League, is all about creating puzzle hunts for groups of people (meetings, parties, etc.).  We worked in teams, hunted for clues, uncovered the hidden meanings and solved the puzzle.

When Jennifer Farrington, the President and CEO of the museum introduced the activity, she reminded us that young children unravel the mysteries of the world much like we approach puzzles.  They examine the pieces and consider how they fit.  They twist and turn them until they make sense. The pieces are complicated and seemingly disconnected yet they try and err and try again. This is the beginning of the lifelong process of assembling understandings and making meaning of their lives, the people around them, and the world they live in.

I love this analogy.  It is accurate and uncomplicated.

PS. In each area of the museum, staff members were there to answer questions and to ask provocative questions in order to scaffold our understandings.  Brilliant.

Howard Gardner of Harvard University argues that we all have various intelligences that manifest themselves in varying amounts and degrees and reveal themselves over time.  He calls these the Multiple Intelligences (MI).

The 9 Multiple Intelligences are as follows:

Visual-Spatial
Think in terms of physical space, as do architects and sailors. Very aware of their environments. They like to draw, do jigsaw puzzles, read maps, daydream. They can be taught through drawings, verbal and physical imagery. Tools include models, graphics, charts, photographs, drawings, 3-D modeling, video, videoconferencing, television, multimedia, texts with pictures/charts/graphs.
Bodily-kinesthetic
Use the body effectively, like a dancer or a surgeon. Keen sense of body awareness. They like movement, making things, touching. They communicate well through body language and be taught through physical activity, hands-on learning, acting out, role playing. Tools include equipment and real objects.
Musical
Show sensitivity to rhythm and sound. They love music, but they are also sensitive to sounds in their environments. They may study better with music in the background. They can be taught by turning lessons into lyrics, speaking rhythmically, tapping out time. Tools include musical instruments, music, radio, stereo, CD-ROM, multimedia.
Interpersonal
Understanding, interacting with others. These students learn through interaction. They have many friends, empathy for others, street smarts. They can be taught through group activities, seminars, dialogues. Tools include the telephone, audio conferencing, time and attention from the instructor, video conferencing, writing, computer conferencing, E-mail.
Intrapersonal
Understanding one’s own interests, goals. These learners tend to shy away from others. They’re in tune with their inner feelings; they have wisdom, intuition and motivation, as well as a strong will, confidence and opinions. They can be taught through independent study and introspection. Tools include books, creative materials, diaries, privacy and time. They are the most independent of the learners.
Verbal/Linguistic
Using words effectively. These learners have highly developed auditory skills and often think in words. They like reading, playing word games, making up poetry or stories. They can be taught by encouraging them to say and see words, read books together. Tools include computers, games, multimedia, books, tape recorders, and lecture.
Logical -Mathematical
Reasoning, calculating. Think conceptually, abstractly and are able to see and explore patterns and relationships. They like to experiment, solve puzzles, ask cosmic questions. They can be taught through logic games, investigations, mysteries. They need to learn and form concepts before they can deal with details.
Naturalist Intelligence (“Nature Smart”)
Designates the human ability to discriminate among living things (plants, animals) as well as sensitivity to other features of the natural world (clouds, rock configurations). This ability was clearly of value in our evolutionary past as hunters, gatherers, and farmers; it continues to be central in such roles as botanist or chef. It is also speculated that much of our consumer society exploits the naturalist intelligences, which can be mobilized in the discrimination among cars, sneakers, kinds of makeup, and the like.
Existential Intelligence
Sensitivity and capacity to tackle deep questions about human existence, such as the meaning of life, why do we die, and how did we get here.

So, people who have Visual/Spatial Intelligence or Logical/Mathematical Intelligence are probably more drawn to puzzles- and may be better at solving them.  Have you ever met a child who could complete a puzzle that was clearly far too advanced for his age?  Chances are, that child has a strong leaning toward one or both of those Intelligences.

As adults or more competent peers support a child’s learning, the child moves from one level in which he can complete tasks independently to the next.  This process is called, “scaffolding.”

Take a look at this video of a teacher and another boy supporting a child as he attempts to complete a puzzle.

Did you see the friend show him how to move the pieces around so they fit?  Listen as the teacher reminds him that the piece he is holding is a corner piece.  Both of these are examples of how an adult or a more sophisticated peer can provide just enough information to a child so that the learning is scaffolded.

Now watch the child complete the puzzle completely in his own.  Notice the spatial knowledge required to do so.