The Art of Mathematical Thinking

"The Pure Mathematician,

 like the Musician, 

is a free Creator 

of his world of ordered

 Beauty."

Bertrand Russell

Young children are naturally inquisitive and it is this curiosity about the world around them that drives their initial engagement with materials in the learning environment. Keeping this in mind, the materials for our first mathematical offering this school year were carefully curated not only for their aesthetic properties but also their sensory capabilities. When a child's senses are activated learning takes place on a multi-facated level. The softness of the wool-felt balls, the smoothness of the glass gems and square tiles along with the sharp edges of the wooden cubes all inform the sense of touch and communicate to the child information about the properties and attributes of these materials. This beautiful 100 board from Mirus Toys had been on my wish list for quite some time. I purchased it this summer and I am delighted with the quality and beauty of this board. I will definitely be ordering again from Mirus Toys. It was packaged beautifully and I couldn't be happier with this product. This past week I offered the 100 board and the two loose part trays pictured in the photos to the children for exploration. 

I am sharing some of the children's explorations and  thinking while they engaged with the materials with a small group of peers. Through the documentation of their play the children's own ideas and mathematical thinking became visible. They were able to communicate through their words, the manipulation of materials and their interactions with peers their own thinking and mathematical theories. Their learning was built and shared through the children's interactions with each other. As ideas emerged some were challenged by peers and others were guided and pushed to new understandings in response to the materials. Here's a peek at the depth of the children's explorations and creativity within the art of mathematical thinking. I hope that you find it as fascinating as I did.

"I made a robot that is flying in the air that has lots of jets and can shoot fireworks. It is eating 16 dices at once. That's the number of the robot. There are billions of robots with different numbers. This one is 2, 66, 57."

"Is this a 6?" This child rolled the die counted the dots on top of the die and then located the wooden numeral six in the tray before asking her question. A peer verified that indeed it was a six. Next she found another smaller six and placed it beside the die. She continued exploring the tray this time it was to find the tile with the number six on it. The tile was placed beneath the row of square tiles."

This photo documents two children's exploration of the materials. It began with the one-to-one correspondence of the wooden cubes and the square tiles placed all in a row. Next they worked together using the 100 board. They placed one of the materials after selecting it from the tray in each of the spots on the board. Initially they began to count from 1 to 10 but then continued with the filling the board without counting. Below the row of wooden numbers a puppy is designed by one of the children. She shared, "So two eyes, two feet, two hands. Oh this can be a puppy. How about, we might need these, pom poms, cubes and little small decorations." This exploration was rich in math talk which was communicated as this child created with the materials; naming three-dimensional figures, labeling size, and counting were shared.

Many children rolled the die and then counted out objects. Adding the wooden numbers after counting how many; communicated the total amount of objects used by this child.

After placing each die on the table and counting the dots on top the corresponding number tile was placed by each die. This child shared, "I put them all together and the number." She concluded her exploration by placing the square tiles on top of the dice and number tiles creating identical sets of objects. 

Several of the children counted out the gems in a line. After counting to 12 this child said to his peer, "I have one more than you." He continued to add one gem and recount his row stating the amount counted at the end. This continued until he reached 15. Then he shared, "Oh my I have 15!" The long row of number tiles was created and then the child asked, "What number is this?" 

"Miss it's equal." She placed two rows of five filled with gems going down the 100 board. This child pointed to each gem and counted to five. Then she added more gems to one of the rows. "Now it's not equal. This one has 8 and that one has 5. They are not the same amount. If I add one more it's six." She continued and added two more gems and shared, "There are 8 and now and it's equal." The exploration continued until there were two rows of 10 filled with gems on the 100 board. She concluded and shared the following, "If you put them all in one row it's 10."

After asking for a piece of paper and a pencil the numerals 1 to 10 were recorded before exploring the loose parts and the 100 board together. She selected the glass gems from the tray and placed them in the perimeter of the board. Then she continued to fill in the interior row with gems beside the outside row creating two squares one inside of the other. Next this child shared as she pointed to each of the rows of gems she created, "Miss 2 rows 2 on each side. Twenty." Her design continued and the square tiles were chosen to indicate the square shape of the interior space of the board. 

Certainly the relationship between the materials, the children and their mathematical thinking were alive and visible. We will be reflecting on the documentation captured during this exploration with the children. As they share with each other the photos and their thinking the mathematical processes, language skills and artistic designs they engaged in will serve to teach, inspire and develop new ideas moving forward. 

Looking forward to extending this learning!

Wishing you many creative explorations!

Languages of Learning the newest hashtag!

#Languages of Learning

Sharing a love of learning!

Welcome to the newest hashtag
#Languages of Learning 

We are deeply rooted in the Reggio Emilia philosophy of education which celebrates the capabilities of children through their many languages. I would like to share with you a bit about how we began the Languages of Learning Journey. We began when Susan Wright from Nurtured Inspirations and I met several years ago. Susan shares her philosophical foundations on guiding and nurturing children in life and learning with practical ways on how to bring this into your everyday experiences with children. Since then there have been many hours of pedagogical dialogue and sharing of ideas and dreams. 

Our dream is to share our passion for nurturing children in the early years. We will help you and your child's everyday life so that the moments you share with your children are filled with creativity, wonder and joy. 

Visit the #languagesoflearning on Instagram to connect with like-minded people raising children in ways that honour their whole-being. Bring your insights, experiences and share your passion for creating a childhood filled with beautiful memories that will enhance children's lives. We welcome you to join this creative and inspiring community. 

With the launch of the Languages of Learning Facebook Page we couldn't be more thrilled with all the connections we've made with other amazing educators through social media. We would like to personally thank each and every one of you that has joined us in educational dialogue and thinking. 

"The artistic languages and poetic 

languages allow the other subject matters 

and disciplines to develop in a terrain

that's very fertile for development

of a more human kind of knowledge

where rationality, expressiveness, 

and emotion are all linked."

Vea Vecchi

Here is a peek into Susan's beautiful atelier which supports her student's creativity and inquiry.

We cannot wait to journey with you 

in supporting creative thinking 
through play with your child or classroom. 

If you would like to contact us

we would love to hear from you at: 

Languages of Learning Facebook Page

#languagesoflearning

Let's connect!

  

 Creatively Yours, 

  

Engaging the Senses ~ Creative Expression

"The senses, being explorers 
of the world, open the way to knowledge. 
Our apparatus for educating 
the senses offers the child a key to guide 
his explorations of the world..."

Dr. Maria Montessori

Many of the children within our learning space engage in imaginative play in the kitchen area on a daily basis. As they re-enact familiar experiences, roles and construct dramatic play with their peers the children build meaning about everyday life. As an observer of this play, one can gather a multitude of information about the children's thinking. We ponder the following: In what ways do the children communicate their ideas? How do they show their previous experiences? What connections through relationships with each other and materials are formed during this play? 

In response to the children's play they were offered the sensory play proposal in the photo above. To engage their senses dried chocolate mint was placed on the wooden scoops. Each material was carefully and thoughtfully chosen to enrich the children's experience. The children were already experienced with scooping and filling using many of the materials from previous experiences within the learning environment. Offering children these types of materials develops not only fine motor skills but leads to the development of their ability to problem solve, make decisions, and connect to the everyday experiences they may see in the kitchens in their homes. What the children within our learning space had not been offered before was the mortar and pestle. They curiously asked about this tool and eagerly added the mint to the mortar and began to pound with the pestle. It will be a tool that we will definitely include more in our provoking of the children's thinking. 

Relationships of Learning

"A child's play is not simply a 

reproduction of what he has experienced,

but a creative reworking of the 

impressions he has acquired."

Vygotsky

 The learning environment is rich in possibilities and has been curated carefully to engage the children creatively as they make meaning about the world around them. Often the children in our class bring toys from home to school. We have observed the children use these treasured toys in creative ways during play. 

Today a toy dirt bike inspired exploration and learning within the classroom. One of our year one children began this exploration by creating texture in the play dough using the dirt bike's wheels. First he flattened the dough with his hand and then he carefully observed the effects of the wheels as he zoomed the dirt bike back and forth over the dough. A few children gathered around and were drawn into his exploration. A friend asked if he could draw the dirt bike. After gathering the necessary materials from the atelier they sat at the table and discussed the dirt bike. Noticing many of it's details and sharing their own personal experiences with dirt bikes the friend began to draw the toy dirt bike. 

Collaborative Canvas ~ Exploring Creative Relationships

The atelier is a space that lives within each of us. As we go about our daily life, this space has the potential to communicate ideas, thoughts and dreams that otherwise might not be expressed. Supporting creative thinking and expression is key to unlocking the full potential that lives inside each one of us. 

Within the learning environment many opportunities are given to guide the creative spirit through materials, time and building of relationships. As children make meaning of the world around them the atelier supports their curiosity and wonder. As educators we engage the children to slow down, take notice and observe. This allows for deeper meaning to be made as we question and dialogue about what we notice. The creative cycle of notice, wonder, observe, dialogue and create is repeated over and over again until new connections and meaning emerge. Throughout the creative process in the atelier we share our journey visually with others and thus engaging them in the learning and building relationship with not only others but the creative materials held within this wondrous space. 

The Beauty of a Rose

"Everything has beauty,

but not everyone sees it."

Confucius

As we document children within our Kindergarten program I am always amazed at the depth of their ability to see the beauty around them. Their wonder and awe at the world which invites them to engage in a dialogue of creating understanding. As the children enter into relationship with the materials in their environment they begin a process of observing, exploring, discovering, and then rethinking and reimagining ideas. Children often repeat, rework, reconsider, and then make new connections to previous ideas to represent their thinking in a multitude of ways. This was evident throughout this inquiry into the beauty of a rose. Allowing the children time to move through this process at their own pace was paramount to authentically moving their thinking forward. The children were offered support and guidance in response to their daily explorations. Through artistic creation, their image of the rose became visible to those who could see its beauty. Below is the documentation collected to preserve the children's thinking for reflection and celebration of their learning.