Joyful Math Trailer!

In Deanna Pecaski McLennan’s kindergarten classroom, math isn’t limited to a specific block of time. It’s built into the environment and inseparable from everything her young students do. All of the math is infused with a sense of exploration, wonder, and joy.

Deanna’s book, Joyful Math, is about creating invitations for young children to engage with math ideas through art, literacy, and outdoor play. She focuses on building spaces in early childhood classrooms where children see themselves as mathematical thinkers with valuable ideas from the very start.

Joyful Math is filled with a range of tools and models, including:

• stories, vignettes, and photos illustrating how to develop a classroom environment that fosters curiosity and wonder for mathematics
• practical tips for inviting students to engage in mathematical play throughout the day
• examples of ways to document children’s experiences to make math learning visible to parents and the greater community

Supported by her experiences exploring math with young children, Deanna’s methods will inspire educators to be curious about math, take risks, try different approaches, observe carefully, and collaborate with children as co-learners.

Get a copy here!

Stenhouse Publishers (United States)

Barnes & Noble (United States)

Pembroke Publishers (Canada)

Amazon (United States and Canada)

Small World Play and Math

 "Old things are better than new things, because they've got stories in them."

Kami Garcia

What is hiding in your cupboards and closets? For 20 years now I have kept an old, beautiful china set from my grandmother high up on my shelves. I can honestly say that I haven't used it once; life with busy children doesn't lend itself to tea parties and fancy dinners. Each time I opened the particular cupboard in which these beautiful objects were stored, I'd feel a sense of guilt. They were treasured by my Nana and used for special gatherings. Now they collected dust.

As I look ahead to the next school year, I am eager to bring beautiful, inspiring materials back into our classroom. Covid has meant that many children have been home with their families, isolated from the world. I anticipate a higher than normal level of anxiety and stress as we return to school, even if we are eager and ready for this new chapter. Having beautiful, interesting materials in the classroom space can often welcome children and pique their curiosity, helping them transition into the space and overcome their feelings of anxiety.

Last week I cleaned the kitchen and as I handled the china, I wondered if it could be integrated into the classroom as play props. Not only would that give the bowls and cups a sense purpose, they would beautify our space. I liked the idea of being able to enjoy them on a regular basis; each time I look at them they remind me of my grandmother and I love feeling her presence in my life.

I had been eager to use a small teacup set (found at Value Village) in some way. I knew that the children loved small world play, and that imaginative mini playscapes held potential for rich math learning. I decided to turn my china into a tea garden. In each piece I placed small stones at the bottom for drainage. I planted succulents in the potting soil because of their hardiness and ease of care. 

     

I anticipate placing these materials on a low shelf in the classroom. They will be a semi-permanent fixture there. They will beautify our space when not in use, and be accessible enough that children can access them without needing to move them around the classroom. I have always felt comfortable integrating fragile materials into our space. My experience has been that when children feel empowered as learners, they care deeply for the materials and handle them gently. I'm also prepared for the possibility of accidents. The children are capable and careful when something breaks and I am willing to trade this risk with the reward of using these materials.

I am purposely not adding character props to this learning invitation. I would rather see how children integrate other materials we have into their play (e.g., mini animals, wooden clothespin dolls), or create their own fairies and other figures at the art center. I also see potential for creating a similar invitation outdoors in some way (e.g., fairy door in a stump). As I observe the children I will take note of their ideas and interests, and help to scaffold and support the math learning as it emerges. Some math ideas I think might present include:

• a discussion of proportional reasoning as children explore the size of the small world and create additional play props
• an observation of pattern as children see, think and wonder about what they find on the china
• practice with one to one correspondence as children set the table for a tea party and create additional props to support their storytelling (e.g., plates, forks, food)
• STEAM as children create their own figures to integrate in this play (e.g., dolls, fairies) or create their own mini worlds (e.g., dollhouses from boxes)
• observations of shape and size as teacups are compared to one another
• connections with capacity as children consider how much liquid might fit into the cups, or create their own tea parties while playing in the mud kitchen or water table

I'm sure as children explore the materials additional ideas will emerge. I can't wait to see what they discover! I'm eager to search my closets for other materials to upcycle and bring into our learning space!

A Playground for Mr. Big Legs - STEM in the Outdoor Classroom

"Look! Look at this spider! His legs are so long! Let's call him Mr. Big Legs!"

The children found an interesting spider in the garden one day. Curious, they gently picked it up and let it climb up and down their arms. It was so graceful in its movements that even reluctant children came for a closer look.

"He's so cute! Why was he in the garden?"

"Maybe that's where he lives."

"How do you know he's a boy?" 

"The garden is so boring for him - nothing is growing right now."

"I know! Let's build him a playground!"

Curious about the children's ideas and how I could use their interest in spiders to enrich our outdoor space, I took photos and mentally planned for how we might proceed next. I considered what curriculum expectations might be met, and anticipated the math that might emerge. Such a simple and quick interaction with nature sparked a rich mathematical inquiry in our outdoor classroom that lasted for several days.  

Our first step was to conduct some research. What did children already know about spiders? What did they wonder about Mr. Big Legs specifically? How might they design a playground that he would like? What could they use to help them acquire more information?

We read a number of texts together to gather information that might help enrich their understandings of what exactly a spider was and needed in order to survive. We organized our ideas on a large chart paper and referenced this over the course of our inquiry.

                 

While exploring our school yard for more spiders, we noticed a really interesting tunnelled web just outside our window. The location was the perfect place to set up a 'spider observation window' where children could safely check on the spider during play time and carefully watch it in its habitat. Not only did this give children an additional opportunity to research, it provided children who weren't comfortable holding a spider a safe way to observe one up close without needing to handle it. (We wondered if the spider had eaten two others, or if this particular one shed its skin.)

 

The more the children learned about spiders, the more determined they were in their quest to create a playground for Mr. Big Legs. They designed spaces for him - a garden, house, slide, swing, and bridge - by drawing blueprints on their clipboards. They considered the size, shape, and materials needed for each creation.

     

 

During the next outdoor play time, the children brought their drawings outside and referred to them as they worked in the garden. Some children enhanced their drawings and others started anew. They looked to the materials available outdoors, and planned for how to build using only natural materials found in our space. 

 

                           

Their work was stunning; the level of thought put into creating the tiny structures was incredible. Children considered measurement and proportional reasoning as they built to scale. Here are some of their creations:

A bed - notice how the sticks point upwards in a circular direction and there are leaves to cushion the center. "The leaves will be so comfortable for him! It will be a soft place to sleep, and the sticks will keep other bugs away."

 

A swing - notice how this child has balanced the top section of the swing onto two sticks. Later on he would add a long, slender leaf in the middle for Mr. Big Legs to swing on. "I hope that he can balance because this isn't very stable right now."

An obstacle course - notice how Mr. Big Legs will have to climb through the structure, along the stick, hop on top of each of the stones and land on the leaf. The child who build this sequenced the steps in her course and articulated exactly what the spider would need to accomplish along the way while playing here. "This would be so much fun to play on - do you think he will know where to start and where to finish?"

 

A bedroom - this child created a circular structure so that Mr. Big Legs could weave a web near his playground using the rocks as anchors. She knew that many spiders used webs as a home and place to catch prey, and wanted to be sure he had this in his new area. "Spider webs are circles, so I put the rocks in a circle."

A garden - this child dragged his fingers in the dirt to make rows for Mr. Big Legs to use when planting rows of vegetables. "They need to be evenly spaced, because they need room to grow. That's what my dad does in our garden."

A slide - this child placed two sticks together on a slope resting in the corner of the garden. "I wonder if he will know to lift his legs. If he doesn't then he won't go down as fast because they are long and will bump against the slide."

A bridge - this child broke twigs so that they were approximately the right fit to be placed in the narrow hole in the garden. "I couldn't find any sticks that fit, so I broke them. I think Mr. Big Legs needs a bridge in case this hole is too deep for him. If it rains maybe he can pretend it's his pool.

Towards the end of the week the children found another Mr. Big Legs climbing on the brick wall. They eagerly picked him up and placed him in the garden so he could explore everything they had created. Proud of their work, they pointed out each structure and explained to him how he could use the equipment.

"This is your slide and here's your swing. You can play on those!"

"I made you a garden in case you don't catch any bugs in your web."

"And when you get tired, here's a bed for you to sleep on!"

I couldn't help but smile at their enthusiasm. I was amazed that something as simple as finding a spider in our yard could inspire such authentic STEM learning.

Encouraging Computational Thinking In Kindergarten

Young children are capable of engaging in rich computational thinking activities in the classroom. In emergent programs, the questions and wonderings children have about the world around them can easily be embedded into unplugged coding activities. Activities that incorporate computational thinking are often misinterpreted as 'more screen time' for young children, when in fact, all of the activities I use in my classroom to encourage computational thinking are screen-free without the need for computers or tablets.

Computational thinking is a foundation of computer science, and intricately related to many of the big math ideas and practices found in early childhood curriculum. It involves many concepts and approaches.

There are many different elements of computational thinking including:

• using logic to predict and analyze when engaging in problem-solving
• making judgments when faced with problems in order to evaluate what is happening and consider how to move forward
• creating and following algorithms (or steps of action) in order to move through the problem solving process
• using patterns in his/her work to find and use similarities efficiently 
• deconstructing larger problems or actions into smaller, more manageable parts
• filtering out information that isn't directly related to the problem or an efficient way of solving it

The computational thinker:

•  tinkers with loose parts and other open-ended materials
• designs innovative projects and follows through on creating them in some capacity
• debugs by finding errors in his/her work and correcting them in order to move a project forward
• perseveres and continues with projects even when they are challenging
• collaborates with others as part of a team for the betterment of a project 

'Hour of Code' is December 9 to the 15 this year. Hour of Code originally started as a project to inspire people everywhere to spend one hour coding, in order to show that anyone, anywhere can code. It has become a world wide celebration of computational thinking and coding, and many global classrooms participate. 

Looking to engage children with computational thinking in your classroom? Here are some ideas to get you started. 

1. Use a read aloud to introduce the concept to children. Computational thinking can seem abstract, especially out of context. The book 'Think Like a Coder' introduces computational thinking to everyday activities that children experience including cooking, building, and even exploring the outdoors.

2. Look for everyday activities that naturally engage children in inquiry, problem solving, and computational thinking. Building with wooden blocks is a great start! Help children articulate the steps they took to build their structure, and ask them how they problem solved when difficulties arose with their creation (e.g., how they fixed a tower that kept falling over).

3. Provide STEM challenges to children. Ask them to use specific materials to achieve a certain goal, and encourage them to articulate the steps and criteria they used in order to be successful. In this photo a child turns a geoboard into a marble run maze. 

                                

4. Introduce the idea of coding using arrow coding cards and positional language. Children can easily explore pathways by creating them using different building materials (e.g., blocks, legos, magnetic tiles) and then exploring direction of movement.

                                  

 5. Transfer coding into algorithms by helping children create and follow specific sequences of actions. Here children create and follow an 'exercise code' where they must look at each line of code in the script, and follow the movements precisely.

                          

Computational thinking is a versatile, foundational approach to learning that helps engage children in rich mathematical activities. As Hour of Code approaches be sure to check out my twitter and instagram @McLennan1977 for more ideas on how to bring computational thinking and coding to your early years and primary classroom. 

Let's connect! Have a great idea to share? Leave it below in the comment section or tweet me and use the hashtags #kindercoding #joyfulmath #HourofCode and #MTBoS!

Printable Pentominoes

In our kindergarten classroom children enjoy spending time working with math manipulatives 
that encourage playful explorations with shape in a variety of ways. One of our favourite tools are 
versatile pentominoes.

Pentominoes are polygons made of five, equal-sized squares connected edge-to-edge. There are twelve 
different pentominoes in one set. You can purchase pentominoes from educational resource stores, or 
print paper copies on card stock and laminate for children’s use here:https://bit.ly/2wtFt0d

There are many reasons why pentominoes are an essential math tool for any early childhood classroom. 
Pentominoes:

1. are gamelike in nature and promote a positive attitude towards math

2. encourage cooperation and collaboration among children 

3. Promote math thinking in a variety of areas including spatial reasoning (logic when solving

 puzzles, symmetry, reflection, rotation, design), measurement (considering the area and perimeter 

of designs), and number sense (counting the number of tiles or squares in a design, calculating the 

total number of squares using the anchor of 5)

 We have used pentominoes in many classroom activities. To see what we've done and follow our math journey, follow us on twitter @McLennan1977. Share your favourite pentomino activities in the comment section below!

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!