Friday, October 13, 2017

Playful Symmetry

"Mathematics is one of the essential emanations of the human spirit - a thing to be valued in and for itself - like art or poetry."  
(Oswald Veblen)

Math has become one of the most engaging and aesthetic experiences in our inquiry-based classroom. The more I experience math pedagogy in practice, the clearer it seems to me that math and the arts are intertwined. I have been inspired to look at all actions in our classroom through a mathematical lens, regardless of which learning domain they appear to belong. Many of our recent endeavors have been inspired by a wonderfully rich book I have been exploring regarding geometric and spatial thinking. In Taking Shape the reader is taken on a journey of understanding regarding the importance of engaging young children in rich spatial reasoning activities and inspired to replicate and evolve many of the activities in the classroom. Many of these also celebrate aesthetics in shape and design, something the arts encourage as well.

The authors advocate for the inclusion of more spatial reasoning in the classroom for many reasons: spatial reasoning and mathematical thinking are intimately linked, spatial reasoning can always be improved regardless of the age or experience level of the students, spatial thinking is an important predictor of achievement in STEM careers, spatial reasoning is currently an under served area of math instruction, and spatial reasoning provides multiple entry points and equitable access to mathematics.

One section in particular, symmetry, stood out to me.  Recently I had noticed symmetry appearing in many of the children's wooden structures made from large and small blocks. I wondered if they had previous experiences with symmetry and felt that it would be an excellent place to begin some intensive spatial reasoning work.

 "In simple terms, two shapes are symmetrical if you can slide, flip, or turn one of them to have it match the other exactly...Symmetry provides an engaging context in which to explore mathematical structures and patterns. Symmetry - in particular, reflection symmetry - is a rich area of spatial reasoning that we can tap into as educators of young children. Symmetry is also important for later mathematics when making efficient mathematical arguments and working with graphs."
(Taking Shape, p. 20)

I have collected 12 of our most engaging activities exploring symmetry and described them below in the hopes it will inspire you to continue to explore symmetry together with children in your classroom or home!

Pattern Blocks on Sticky Paper

For this experience we have added clear, sticky mack tack to an extra easel in the classroom. Engaging math manipulatives like wooden pattern blocks can be non-permanently affixed in different patterns and designs to the mack tack. A line of symmetry can be added to help guide children in their work. When finished, a child simply removes the pieces and the easel is ready for another.

Hole Punchers

Hole punchers are excellent tools for encouraging fine motor work - they are difficult to squeeze and require patience and perseverance on the part of the user. A paper that is folded in different ways and has holes punched in various designs will open to reveal one, or many, lines of symmetry.

Building with Unifix Cubes

Many classrooms have linking cubes or unifix cubes. Our children have been drawn to using them to create small robots and airplanes. Because of their versatile nature, these cubes can be linked on all sides, and children can easily incorporate symmetrical design into their creations.

Working with Sticky Loose Parts

Loose parts offer endless opportunities for exploration of spatial reasoning and design. A recent trip to the Scrap Box in Ann Arbor, Michigan (a recycling centre for art materials) provided us with many foam pieces that had one sticky side. We drew various lines of symmetry on paper (horizontal, vertical, diagonal) and encouraged the children to place the foam pieces symmetrically on the paper. It was interesting to see their designs being built in 2D across the paper, and in 3D upwards off the paper. 

Recycled Game Boards

Recycled wooden game boards are excellent grids to use when encouraging children to consider spatial reasoning and symmetry in their design. The grid design helps children 'picture and place' geometric shapes symmetrically. In this experience we've offered recycled carpet samples to entice children who enjoy tactile experiences into creating interesting mathematical designs.

'Follow the Leader' Game with Foam Pieces 

Taking math outdoors is always fun! In this game, a line of symmetry is created with masking tape on the ground. Large foam shapes (easily cut from Dollar Store art foam) are used as game pieces. One child is the leader and the other the follower. The leader places a shape on his/her side and the follower has to create a symmetrical design by placing the same shape in reflection on the opposite side of the line. The result is an intricate symmetrical design. 

Paper Cutting

Similar to using hole punches, encouraging children to cut shapes onto folded paper results in the creation of interesting symmetrical designs. This is also a fun activity to bring outdoors. 

Paint Droppers

Children love to drop paint onto paper and fold it in half to create interesting colours and designs. In this activity the paper is folded first, indicating the line of symmetry. Children are encouraged to carefully use droppers/pipettes to drip paint onto one side of the paper only. 

The paper is folded on the line of symmetry...

...and is opened to reveal a symmetrical picture! When the primary colours of paint are used the creation of secondary colours is an added bonus!

Finding Lines of Symmetry

Helping children find symmetry in the world around them is an important discovery to instill the idea that math is everywhere. We offered books about symmetry for the children to explore, along with laminated photos of real objects from nature. The children were encouraged to look at the different pictures and then use dry erase markers and rulers to draw the lines of symmetry they saw.  

Pentominoes on Trays

Pentominoes are complex math manipulatives that fit together in interesting ways. In order to challenge children we added a line of symmetry to a tray and encouraged the children to see if they could create a symmetrical design with the pentominoes, while trying to fill the tray at the same time!

Pattern Blocks on Mirrors

Building on mirrors is an interesting way for children to explore symmetry. Whatever is constructed on the mirror will naturally reflect symmetrically with the mirror as the line of symmetry. Children are often amazed to see their creations reflected, which sometimes results in an interesting discussion of 'doubling' in addition to symmetry.   

Symmetrical Letter Guess

Many letters are symmetrical in nature (e.g., A, B, C, D, E, H, I, M, O). In this game children are shown a letter that is folded in half and asked to guess what the letter might be. 

We like to use plastic plates and dry erase markers to make games more interactive and also encourage letter writing. After children observe the folded letter they can write their guess on the plate...

..and then look to see the letter revealed! The line of symmetry is evident as the fold line on the letter.

We will continue to explore symmetry this upcoming week! Stay tuned for more ideas! Feel free to add comments and additional ideas for exploring symmetry in the comments below!

Sunday, September 17, 2017

New Beginnings...

“Come to the edge," he said.
"We can't, we're afraid!" they responded.
"Come to the edge," he said.
"We can't, We will fall!" they responded.
"Come to the edge," he said.
And so they came.
And he pushed them.
And they flew.” 

Guillaume Apollinaire

I am a creature of habit; I love routine and predictability. So when I was offered a chance to move to a school much closer to my home, during this past 'reorganization week', I hesitated to take the chance to move because I was fearful of change and the unknown.
However after being at my current school for many years and burdening my young children with early mornings, hours at latchkey and long commutes, I took a breath and accepted a kindergarten position at a school thirteen minutes from home.

On Friday, after saying goodbye to the families I have cherished working with for many years, I packed up my belongings (yes in a 27 foot UHaul!) and moved to my new classroom.

Being in a new space was interesting. I was nervous and excited at the same time. I'm sure that as I get to know my new children and surroundings we will work together to evolve our space. But for now I have the 'footprint' of the room established for our new start this week.  

Here's a sneak peek:

I look forward to seeing what new learning awaits me! Change is often the catalyst we need to expand our own thoughts and actions as we have the opportunity to collaborate with new people who have diverse interests, experiences and ideas. I am excited for the opportunity!

Saturday, September 9, 2017

Printable Activities to Support Open-Ended Mathematics

I continue to be inspired by the rich math learning I have been offered in my recent professional development. Research shows that early math experiences are key to a child's future math success - both in their confidence and math abilities. We know that having a strong partnership between home and school can enhance this mathematical mindset in the early years.

This year I will be pleased to continue to send home math 'take home bags' to our children, beginning towards the end of September. Each of these bags is numbered. On Fridays your child will bring a new math bag home to explore with you. In each bag are activities that are designed to refine math concepts from the Ontario Kindergarten Curriculum, with a special emphasis on number sense and numeration, specifically subitizing and composing/decomposing numbers. Please send the bag back to school by the following Wednesday so that we can send a new bag home with your child.

Inside each bag will be an instruction card and any applicable materials you will need to play the game together.

I am excited to see how the children's math mindset and abilities are influenced by these activities. We will continue to focus on math rich tasks at school as well. Any feedback regarding these bags is greatly appreciated.

If you would like a sneak peek at some of the activities, or are a fellow educator interested in printing a set of these activities for use in your classroom, please click this link: Family Math Bags

Saturday, June 3, 2017

Treasures in the Classroom

"To a young child, the world is full of materials to touch, discover, and explore. To find, collect, sort, and use materials is to embark on a special kind of adventure. For adults, gathering materials means rediscovering the richness and beauty in natural, unexpected, and recyclable objects that are all around us, but not often noticed." 
(Weisman Topal & Gandini, 1999)


There is something so magical about being in a thrift store - one of my favourite things to do is grab a hot coffee and spend an hour wandering the aisles and appreciating the beauty that lies within. There are so many interesting things to see and appreciate and it's fun to image the stories that the objects might tell if they could. Sometimes objects will transport me back into my childhood and remind me of things I haven't thought of in years (seeing a basket similar to the one my Nana used to use when hanging laundry too little to help but eager to stand beside her on those warm, sunny days). Those are the absolute best finds.

In our program we value found, recycled and natural loose parts. They are incorporated into all learning areas in the classroom and children are free to use them however they wish as they become play props to support their imaginative stories. Because we don't typically use commercial toys in our program, many of the loose parts and materials to support activities come from interesting places like yard sales and thrift stores. I want our classroom to be as unique and diverse as possible... not some image plastered in any glossy educational resource catalogue but one true to the heart and spirit of our children and community itself.

Last time I visited Value Village I came across a delightful bag of decorative spoons. As my daughter and I explored them we realized that someone had carefully curated these over time. Spoons from far away - the coasts of Canada, the Southern United States and even Europe - were included in the collection. It was clear that this was once a special collection for someone. Had this person traveled extensively and acquired each one? Did love ones travel abroad and always remember to bring a spoon home for this person? Cadence was enamored with the spoons. 

"'s so sad that these were so special to someone and now they ended up here!" She clutched them in her hand and enunciated her point by waving around the store. 

I smiled. That was exactly the point! Who better than to continue to appreciate the rich intricacies of the spoons - the carefully carved pictures, dangling charms, and interesting handles - than my vivacious group of kindergarteners. They find beauty and wonder in the most ordinary of objects and I knew the spoons would continue to be meticulously valued and appreciated in their care.

A few days later I introduced the spoons to the children. I offered them the opportunity to first explore them on a table and then use them around the room. At first most children were so excited to explore each one, often noticing things that had evaded me - the gentle way the handle twisted, the funny flamingo on the Florida spoon, and how one even appeared to have a diamond encased within. And as I carefully observed the children I noticed that including these treasures offered so much rich literacy and numeracy potential. As I listened I heard the complex vocabulary they were using to describe what they noticed. I heard them read the locations listed on each. I saw many who were inspired to sketch the spoons in their journals or ask for books about plants and birds so they could correctly identify which were on the spoons. They were engaging in rich conversations with one another and suggesting different children in the class who might appreciate specific spoons (e.g., "Emma would like the Texas one...she loves horses and this one has a little horsey on the end!").

Over the next few days the children incorporated the spoons into other centres and I observed math emerging in their work. Some children sorted the spoons based on characteristics like those with and without animals on them. Other children lined up the spoons by length or created simple patterns using them. As they used them at the sensory tables I overheard children counting as they measured sand into bowls or reciting recipes being stirred in the big pot. It was amazing to see just how diverse and rich the experiences that incorporated the spoons were.

After a few weeks I watched the children slowly find interest in other materials in our classroom. The spoons are displayed in a decorative basket on the shelf and are still explored by the children when they are needed to support their dramatic play. I know that many groups of children will continue to enjoy and appreciate the beauty of these spoons for many years to come. And I reflect back to what Cadence said many weeks ago when first discovering the spoons and think of whoever might have owned them before we did. Who was she or he? Where did they live? What were their life experiences? How long did it take to collect the spoons? What story accompanied each one? I wish I knew the answers so that I could thank them and assure them that our children will continue to treasure the spoons just as much as they did, one treasure at a time.

Monday, May 15, 2017

Communicating in Algorithms: Connecting coding to literacy

"We should think about what we mean by literacy. If you say, "He's a very literate person," what you really mean is that he knows a lot, thinks a lot, has a certain frame of mind that comes through reading and knowing about various subjects. The major route open to literacy has been through reading and writing text. But we're seeing new media offer richer ways to explore knowledge and communicate, through sound and pictures."

Seymour Papert, 1997

Mother's Day was filled with sunshine, laughter and the usual mess of having the kids home for two days in a row; roaming indoors and out and savouring the freedom that unstructured time provides. However what was interesting for me was that this weekend Caleb expressed an interest in learning how to use the Rainbow Loom. Not one to spend much time on crafty business, he had passed up opportunities using the extra loom I had picked up for him a few weeks ago. But early Saturday morning I noticed him watching Cadence work from afar. He eventually made his way to her side and spent several minutes observing her. Was it hard? Could he borrow her stuff? Did she have extra elastics for him too? Would she help him if he got stuck? He peppered her with questions. She timed her answers to the crescendo of video clips as she worked on her Ninja Turtle design. And then something caught his eye in the corner of her screen. He was sold. There, in bright red and yellow, was the most comical looking elastic-y hotdog. And with that he was off to gather his loom and iPad, and set to work on the kitchen table.

After an hour or so I heard him set his hook down with a clatter. I approached him to see how it was going.

"Terrible!" he responded. "The girl is this video doesn't give good directions. I have no clue what to do. She's not making any sense."

Caleb's frustration trying to following someone's inadequate directions reminded me of how powerful and precise oral language has to be in many of life's situations. Not only do we need clear and direct explanations, we also must be ready and able to carry out the directions in the manner they were given in order to experience success. He was unable to make a Rainbow Loon hotdog because the directions did not make sense to him. I immediately thought of coding. In the past I have spent much time linking coding to math due to the rich, integrated opportunities for number sense and geometry it provides. But what about literacy? Many educators are continuously looking at ways to embed and improve meaningful language-based activities in their emergent programs. Can coding help with this? How does coding encourage users to become more proficient communicators? Can coding strengthen kindergarten literacy programs in the same ways it does math?

I believe that kindergarten children who utilize complex, integrated coding activities in their daily lives will have opportunities to strengthen their literacy skills. Here are some of the ways:

Coding requires accurate language in order to be successful. Computers follow the code outlined in their programs. There is no room for interpretation, and as a result, a programmer must be incredibly clear and detailed in their algorithms. When children use coding as a language of communication in the classroom they practise this succinct way of articulating directions to others on a regular basis. Over time they will improve in their abilities to be precise when crafting these programs and directing others in activities.

Coding reinforces concepts of print.  In our classroom children are encouraged to write their code in different ways. They can order our class set of coding cards on the floor or in a pocket chart, or they can write their directions using a series of predetermined symbols (e.g., arrow, stop sign). When writing or reading these directions they are encouraged to move from top to bottom, left to right replicating the way we read and write in the English language. I always ask them to use their 'reading finger' and point to each card as they work. This reinforces the same concepts of print we are working on in our whole and small group literacy activities.

Coding uses symbolic language that children will be able to read and write even if they are not yet fluent using letter and sound relationships. Because kindergarten coding uses pictures, many children can easily create messages for one another by sequencing coding cards, or drawing established symbols digitally or on paper. A class can determine their own set of symbols before coding work begins so that everyone understands what they represent. Over time and with experience children will become proficient communicators using these. Just as early mark-making is a foundational part of establishing positive literacy behaviors, coding helps children easily communicate their ideas to others showing that oral language can be translated and preserved in multiple ways.

Coding builds confidence and fluency in early readers and writers. With practice children will improve in their abilities to communicate using symbolic language. In our classroom coding activities are always very popular and as a result even the most reluctant children in more traditional literacy activities want to participate. This grows their mindset and confidence because the more they practice, the better they become.

Coding encourages active listening. Regardless of how well constructed an algorithm is, it can only be successfully implemented if a child is listening intently and following through successfully on the given directions. Coding work requires concentration and full engagement. This helps children practise being attentive and responsive listeners.

Coding is a universal language that helps people speak to one another all over the world. In our classroom children blog and tweet extensively about their daily experiences. A very important part of the inquiry process is sharing one's understanding beyond the metaphorical 'walls of the classroom'. Because coding is used all around the world (and such a hot topic in education right now) children can participate in a global event, communicating with children in different countries, even where English is not the common language. One of my daughter's favourite things to do online is look inside the many creations posted on the Scratch website so she can see the code that was used.

Coding sequences a story from beginning to end which requires users to group events together and retell them in the proper order. In our classroom children often use favourite texts as the foundation of their coding games (e.g., retelling the events in the Gingerbread Man; helping the Gingerbread Man escape the fox at the end of the story). This means that children need to be able to accurately sequence a story in the correct order so that it makes sense. They need to consider the beginning, middle and end events and retell these in their coding directions so that the game makes sense. This strengthens their comprehension of literature and encourages them to demonstrate their knowledge in hands-on ways as they play with stories. 

Coding often tells a story that requires users to imagine setting, characters, and plot. This reinforces comprehension of texts, especially when favourite read alouds are used as the inspiration behind activities. When creating their own stories using the coding board, children need to establish their own engaging characters and plots in order for the activities to be fun to play.

Coding is found in our daily routines as we compose instructions to one another in our classrooms and beyond. Thinking and communicating in algorithms extends beyond coding activities. There are multiple opportunities each day for adults and children to give and receive directions to others. When we think as coders, we realize that we are more effective and efficient when our communication is clear and easy to follow. Children can be reminded of this in their work outside of programming. Educator Brian Aspinall (@mraspinall) emphasized at a recent PD event that I attended that he asks his students to "speak to each other in algorithms" in daily activities, even those unrelated to coding, in order to emphasize clear and direction language.

Coding can become an expressive language, much like the arts, helping children to articulate their ideas and show their comprehension to others. Emergent programs influenced by Reggio Emilia encourage children to explore and share their learning using 'hundreds of languages' including the arts, physical expression, and building. Coding can become another language children use to communicate in inquiry-based classrooms, especially once they are proficient using it on a regular basis. For example, why not encourage a child to demonstrate their understanding by creating a code to show and share their new knowledge with others (e.g., coding the lifecycle of a butterfly).

How else does coding encourage literacy in the classroom? Share your ideas in the comment section below or tweet me @McLennan1977 and tag it #codingandliteracy. 

Saturday, May 6, 2017

Thinking in Algorithms: Why kids need to code in kindergarten

Kids already have too much screen time.
Isn't coding just another buzz word in education right now?
I don't have time to learn something new.
My kids play too many video games.
I don't believe in using technology in the kindergarten classroom.

This weekend I had the great pleasure of attending the 2017 ETFO Innovate Conference in rainy Niagara Falls. Each year ETFO AQ instructors meet for two days of rich collaboration, inspiration and networking. We are online instructors and as a result, embrace technology in our personal and professional practices. I will state upfront that I write this post as a biased educator and mother; teaching children for lives in an unknown future, I believe that we have an obligation to consider what 21st century competencies are and how we can immerse our children in robust and authentic educational experiences that infuse their lives with motivation and passion.

I have been speaking a lot lately about the importance of coding in the kindergarten classroom. This past year I had a vivacious group of children who ventured on a journey with me to explore how we could use coding in our math and storytelling activities. Over the last 8 months these children have become proficient using unplugged coding manipulatives (e.g., grids, props, directional cards) in order to engage in complex math games and retell/innovate favourite texts. This has sparked much interest in how we can use coding to enrich one’s existing math and literacy program by outsiders to our program.

My love of math and coding was heightened this weekend after listening to the inspirational Brian Aspinall (@mraspinall) speak about his experiences using coding and technology in the classroom. He challenged us to consider how we might use “technology as a language of learning” to motivate children.

“Coding is the new literacy helping students communicate their ideas to others.” 

He pressed upon the importance of encouraging our children to communicate using complex ways in a digital age and to “think in algorithms” in all aspects of their day.

Brian instilled a sense of urgency in me. I believe that coding is an important foundational skill that all children have a right to learn. If we introduce unplugged coding games in kindergarten then children will learn to speak and use that language fluently in their daily lives. Just as emergent spaces encourage children to personalize their learning through multifaceted sensory experiences, technology gives children one more of the ‘hundreds of languages’ through which to explore, experiment and communicate their ideas to others.

Although however essential coding might be, in my travels I have found that there is still some reluctance for infusing our early childhood spaces with technology. Confusing coding as passive, entertainment-style gaming, many worry that it will be a harmful distraction in the kindergarten classroom. That fear, coupled with an inspiring few days spent with tech-minded educators, inspired this blog post explaining what I feel are the many reasons why children in kindergarten need to learn to code.

Why code in kindergarten?

Coding is everywhere. Most appliances and everyday household items require code in order to work - your fridge, car, and even washing machine use code. When children learn coding in school they acquire a sense of how the world around them functions. In inquiry-based spaces educators hope that children will look deeply at their surroundings through a lens of curiosity. Coding helps them explore something more deeply and consider how it works, and how it might be modified to work in a different way.

Coding is easy. An educator does not need to know computer programming in order to use coding activities. Starting slowly and exploring together with the children will model curiosity and a willingness to take risks while helping teacher-learners build community and knowledge in a safe and supportive space.

Coding is cost-effective.
In a time of reduced budgets and tech-constraints, unplugged coding in kindergarten requires no computers in order to be successful. All one needs is a grid, arrow cards, and small props (e.g., blocks, animal figures). These materials can be easily made or found around the classroom and are transportable to other areas of the school (e.g., hallway, outdoors).

Coding activities naturally incorporate 21st century skills like collaboration, creativity, teamwork, critical thinking and problem solving. Children who code learn to speak a new language. They quickly realize that their directions need to be clear and precise in order to have fun and be successful in the coding play. Children learn to strategize as coding play becomes more complex and obstacles and challenges are added to their games. Algorithms that don’t work out build resiliency and persistence as children try new sequences and use mistakes as learning opportunities.

Coding integrates learning opportunities from multiple domains of development. In our world of dense curriculum and overwhelming assessment demands, it's essential that educators weave together expectations from different subjects and strands. Not only does this make the classroom a richer place to be, integrating subjects often engages children and make learning deeper and more authentic. Coding has the potential to use expectations from math, science, literacy, the arts, and physical education depending on the context.

Coding is a social activity that builds communication and relationships. Each person in the activity has a special role to play and these roles must work together in order to be successful. The directions given by the programmer must be clear and succinct and followed precisely by all players involved. Children work together to create more complex coding paths and play from one day can be continued into the next. Coding strengthens children's oral language as they describe movement while giving and receiving directions.

Coding provides opportunities for children to engage in meaningful, problem-based math that is highly engaging and of relevance to their lives. These activities integrate spatial awareness, reasoning and number sense into a highly motivating opportunity for applying math in a realistic situation that can then be transferred to a coding application (e.g., Scratch Jr., Scratch) when children are ready. The math is often complex and layered.

Coding is empowering. Learning how to program a game or animation is a very entertaining and enjoyable activity for children. Today’s kindergarten classrooms are maker spaces filled with opportunities for children to engage in the problem-solving process by manipulating loose parts in order to create. Coding is no different but in place of tangible objects that can be tinkered with, children who code are digital makers.

Coding is versatile and can be easily adapted to activities in the gym and outside learning spaces, captivating kinesthetic learners and adding another dimension to physical activities. It is an easy to adapt activity that is fun to play outside or on a very large grid. Children can code one another to move around a space or use the change in scenery to inspire a new programming narrative.

Coding can be extended with technology such as easy to use apps, websites, and robots for those who want to delve more deeply into the concepts (or for those subsequent teachers who have these children in grade 1 and beyond). Many of these are available as free apps or websites and can be suggested to families who want activities that promote home-school connections.

Coding is a global phenomenon and connects your students to their community and beyond! Educators can create their own personal learning networks by connecting with others on Twitter (#coding, #code, #program, #kindercoding). Classes can participate in the Hour of Code or learn new skills by visiting Children can tweet what they are doing to others. There is worldwide support and encouragement for educators who are embracing new and exciting ways of learning including using coding as a language of communication with young children!

Ready to get started? Learn how here: Creating Coding Stories and Games TYC Volume 10 (3)

Let's connect! If you code with kids, tweet me @McLennan1977 and tag it #kindercoding. Let's create an amazing network of kindercoders out there and support each other on this journey!

"When you learn to read and write, it opens up opportunities for you to learn so many other things. When you learn to read, you can then read to learn. It's the same thing with coding. If you learn to code, you can code to learn." 
Mitch Resnick

Saturday, April 29, 2017

The Power of a Puddle

Our children are drawn to water. This past week we had a lot of rain and it created a giant puddle in the playground. The children were curious about how to cross the puddle. It was too big and deep to skip or jump over and they needed to cross it in order to get to the other side where their stumps and other favoured areas were.

One child decided to try using some of our loose building parts. He gathered many pieces of wood and laid them starting from one edge of the puddle. As he placed them side by side he observed the edges of the wood to see if the puddle was deep enough for the wood to sink into.

"I don't know if the wood is high enough. If the puddle is deeper than the wood, then this won't work."

I observed him as he placed the wood and then stepped on each piece, watching to see if the water rose higher then the wood. I noted the complex math and problem solving that had emerged in his work. He was considering the depth of the water and whether it was deeper than the wood was tall.  After a few minutes some friends joined him.


As each piece was added the children continued to test their design to see if their feet stayed dry.

"We're making a bridge so we can cross!" 

The children continued to lay the wood side by side. When it ran out, they were perplexed.

"We don't have enough to finish the bridge!"

They stood around for many minutes, stepping on their bridge, counting the pieces that were side by side, and then looking around the yard for any loose pieces of wood they might have missed.

"I know! Let's take half of the pieces and move them so that we can make the bridge longer! We'll just have to walk one at a time instead!"

The children realized that if they narrowed their bridge they could double the length by moving the pieces in different positions. The amount of wood they used hadn't changed but their problem solving allowed them to complete a workable way of crossing the water.

 Success! The children children spent the majority of their outdoor time racing one by one across the big puddle. They even tried driving the tricycles across it - the process of experimentation in doing so led to some amazing conversations about the weight of the bike and if the wood would hold it, the position of the wood pieces and if they would stay in place while being driven on, and how fast the bike could be driven across without the pieces shifting and becoming ineffective.

The outdoors is full of possibilities for children to mathematize their play; this authentic experience of crossing the puddle motivated the children to engage in robust math that incorporated measurement and problem solving!

Saturday, April 8, 2017

Math Learning - and a Touch of Science - in the Outdoor World

With spring in full bloom many kindergarten children are spending time exploring the outdoors! There is so much opportunity for rich math learning hidden among the natural treasures in any play space! If you'd like to learn about the potential for math in the outdoor world, check out my newest article:

Math Learning - and a Touch of Science - in the Outdoor World

Thursday, March 30, 2017

Creating Coding Stories and Games

We are pleased to be presenting Creating Coding Stories and Games at the 2017 ETFO Kindergarten Conference! You can access our powerpoint here: Coding Stories and Games

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