Showing posts with label mathematical mindset. Show all posts
Showing posts with label mathematical mindset. Show all posts

Wednesday, August 23, 2023

ETFO PLEY Chat - A Classroom that Fosters Mathematical Thinking

As an educator helping children develop a love of and appreciation for math is one of my greatest professional interests. I strive each day to engage children in authentic math learning through play and inquiry. I was super honoured and excited this past spring to welcome ETFO into our kindergarten classroom and record a number of chats regarding how children explore math in our classroom. 

All videos are now available here: A Classroom that Fosters Mathematical Thinking

The Beliefs that Drive Practice

Moving the Learning Forward

 Math is Relevant and All Around Us

Understanding how Children Develop Mathematical Understanding

Math Happens Everywhere

 Thinking Through a Mathematical Lens

Documenting and Communicating the Learning


Thursday, January 5, 2023

Daily Math Talks with Young Children

 

  “Mathematics is a very broad and multidimensional subject that requires reasoning, creativity, connection making, and interpretation of methods; it is a set of ideas that helps illuminate the world; and it is constantly changing.”
Jo Boaler

Math talks are a great way to engage children in open-ended explorations that invite them to think critically and creatively about a concept. An effective math prompt to facilitate a rich math discussion will be layered; it should be open-ended with multiple entry points for engagement. Even children as young as kindergarten are capable of participating in complex math conversations. In our classroom I aim to invite children into a math talk at least once a day; I sometimes use the numerical date on our morning message as the spark for exploration. Other times an interesting photo or collection of loose parts will be engaging and incite children into further exploration. I try to vary the invitations I provide in order to diversify the math we discuss and to reach as many learning interests as possible.

Recently I posted two Instagram Reels regarding our daily math talks that has generated many questions regarding how we engage young children in robust discussions about math each morning. There was much interest in these math prompts and many educators reached out with questions regarding how I create these prompts.

 
 
In our program we have a morning circle time. This circle is our first whole group gathering time for the day and helps set a positive atmosphere in our classroom. It is also a time to celebrate being together, and share news from our homes. We often use it as an opportunity to read a story and discuss any new and exciting activities or additions to our classroom space about which the children should know in order to be successful for the day. 
 
When I first started teaching kindergarten many years ago it was expected that the morning circle would begin with 'calendar time' where children would put a sticky number on a large grid to depict the day and there would be an extensive discussion about the calendar (e.g., day of the week, month, year). However over the years I realized that this was a very teacher-directed task and not as meaningful a use of our time. After reading Sherry Parrish's work on number talks I was inspired to use our morning message as an anchor for math talks. Wanting to still introduce the date to students, the numerical representation of the date became the foundation for our number talks most days. Sometimes I would use other prompts depending on the events and interests emerging in our classroom. If you would like to read more about number talks in kindergarten, you can access an article I wrote for the Journal of Teaching and Learning here: Joyful Number Talks in Kindergarten
 
I enjoy participating in a professional learning community with educators on social media and often tweet or Instagram my number talk prompts. Many educators have reached out to me how I create these open ended math talks, and to ask if I would consider sharing some ideas to try. Here are some examples of number talks we have used in the classroom. Feel free to share your own ideas in the comment section or tweet/instagram me @McLennan1977. 
 

To help support educators who are interested in starting daily math talks with children, I have published a book called Calendar Math: Daily Prompts for Math Explorations with Children

To help give an idea of what this book is about, and to help educators create their own math prompts, here are the first few pages of the book!

              


Friday, August 27, 2021

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)


Saturday, September 14, 2019

Exploring the Outdoors Mathematically with the Five Senses

Stop! Listen!”

We were outside lining up next to the school ready to head in and start our morning when Carleigh held up her hand indicating that she wanted her peers to halt their conversations and pay attention.

“Do you hear that?”

In the distance I heard what had caught Carleigh’s attention. It was the joyful ‘chick-a-dee-dee-dee’ of a Black Capped Chickadee, a friendly native bird that enjoyed foraging in the yard adjacent to our playground.

“It’s a pattern!” Emme observed. “I hear it too! I hear the dee-dee-dee part over and over.”

The chickadee continued its happy song and we stood as still as we could and listened.

“I hear it too!”

“Chick a dee, dee, dee! Chick a dee, dee, dee!” Carleigh sang-song and within a few minutes the rest of her peers joined in, repeating the cadence of the neighboring bird’s early morning song. 

The natural world is waiting to be discovered and often the math that children first uncover is through mindful observation with their senses - sight, touch, taste, smell, and hearing. Children who emotionally connect with and nurture their surroundings will grow to be environmentally conscious and mindful of their impact on the earth. We spend at least an hour outside each day - this includes guided, teacher provided invitations and activities for learning, and also free exploration by children in the yard. This year we are also hoping to start 'Forest Fridays' where we walk the local nature trails in the community around our school on a weekly basis. The outside holds amazing learning for children. Helping children notice and name their mathematical findings by incorporating the senses increases their understanding and connection with the world. There are also many wonderful children’s books about the human body that can be used to introduce each sense and help children focus on paying attention to a particular sense when outside. ImageImage One of our favorite math activities is going on nature walks mindfully focused on one sense at a time. Children walk together and use technology to capture their findings (when going on a ‘hearing walk’ the children listened for different sounds in nature and we used the microphone feature of our iPads to capture what they discovered). Sometimes the math may begin to blend and blur with science topics. This is an important connection for children as they see the relevance and authenticity of math in their everyday life. It is also another way for educators to justify the time spent outside; integrating subjects such as math and science helps to fulfill more standards while making learning more meaningful and relevant to children's lives. So many children (and adults!) consider math (and science) to be 'textbook subjects' - ideas that are taught in a classroom in isolation from the rest of the world - when tangible and concrete exploration of these concepts is developmentally appropriate and helps children see the relationship between school subjects and their own lives.
Some suggestions of starting places include:
Sight *Ask children to observe the world around them. Using your eyes/sense of sight, what do you notice? What do you wonder?” These open-ended prompts help children to think deeply about their surroundings and notice and name small details. It also empowers them to ask the math questions about the world around them instead of following the teacher's lead.
*What patterns can you see and identify in our space?
*What shapes do you notice in your surroundings?
*Can you locate different numbers or groupings of objects? A pair? A group of three, four, five, etc. *How many different shades of one color do you see?
*Can you group objects based on a sorting rule?
*What’s a reasonable estimate for something large - how many leaves are on the tree? How many ants might be in the garden?
*Can you search the yard and locate/match similar objects based on how they look?
*Play a game of “I Spy” using math language and encourage children to make predictions on what object you are referring to (“I spy with my little eye something larger than my hand…. Something taller than our fence…) 
Touch *How do different objects feel? Can you describe them? What do you notice? What's the same? Different? After children have shared their observations you can also highlight the size, shape and texture of the various objects.
*Can you describe the object in a mystery bag by how it feels? Can you guess what it is?
*Run your hand along a patterned object and describe what it feels like.
*Can you sort objects based on how they feel (hard, soft, squishy)? 
*Encourage children to create a collage using natural objects they find in the yard. Identifying the object’s characteristics and then classifying and sorting helps children build data management skills. Children can discuss the inspiration behind their choices or their placement on the collage.
*Bring sculpting materials outside including play dough or clay and encourage children to sculpt it using natural loose parts. What prints can they make in the dough using different objects including pinecones, leaves or sticks? Can they see or feel patterns pressed in the dough? How do they describe these patterns to others? Can they continue a pattern? 
*Give children touch challenges - who can find the heaviest item in the yard? How many children does it take to lift this object? Is it even possible to lift it? How do children problem solve when they find an object that cannot be moved? Can they find the lightest? Can children order a collection of rocks by weight (lightest to heaviest) or flowers by shades of the same color (lightest to darkest)? 
*Ask children to feel different objects and describe their temperature. Are items hot? Cold? Can their properties change if heat or cold are added?  
Taste *Eat snack or lunch together picnic style - as children eat ask them to classify their food. What kinds of food do they have? Can they describe what they are eating using mathematical terms? (“This jam sandwich is so sticky I need to chew it ten times before I swallow!" "My celery stick takes five crunches to eat." "I lined up my crackers in a pattern!").  
*Harvest seeds, fruit or veggies from a garden and ask the children to count how many of each item they have grown. Can children measure to see how long their fruit or veggies are? Provide samples of each food and have children vote on whether or not they enjoyed the taste. Children can write their own recipes using these harvested foods and experiment with preparing or cooking them in different ways. 
*Offer children foods grown from the local area. After tasting samples of each ask the children to classify the foods using a common characteristic (crunchy, sweet, tangy, mushy, sour). Photos can represent each food and be placed in the appropriate place on a sorting ring or on a chart. 
Smell *Ask children to identify and describe the different smells they notice in various areas of the classroom, yard or school. What connections to the smells can they make?
*Encourage children to go on a ‘smell hunt’ around the yard and find natural items with different kinds of smells (sweet, strong, unpleasant). Children can place the object on a chart placed in a central location. After the hunt children can calculate how many of each item were found.
*Play a game of mystery smell. Place an object in a bag and have children close their eyes and smell. They can use language to describe the smell and then indicate whether or not they liked it by voting on a class chart. 
*Children love to create their own ‘potions’ outside. Often when objects are crushed they release a stronger smell. Encourage children to create their own recipes or smell equations by gathering different objects outside and mixing them together. Children can also use large rocks to crush and mix the objects together. Provide clipboards and pencils so children can write down their ‘equations’ (10 rose petals plus a handful of grass equals a sweet and strong smell). 
Hearing *Ask children to mindfully sit on a blanket in the middle of the outdoor space and close their eyes and observe what they hear. Can they identify what the sounds might be? How many different types of sound can they count? Can they guess the direction and distance of each sound? What patterns can they identify (bird calls, insect chirps). 
*Ask children to use their bodies to make different sound patterns. They can clap, stomp their feet, tap their knees, and snap their fingers in different rhythms. Play follow the leader where one child plays a pattern and the others have to repeat it. Children can articulate the pattern rules they hear (one clap, two stomps, one clap, two stomps).
*Study different animal calls - many have a repeating pattern in their sound. Play recorded animal calls on the iPad and ask children to describe what they hear. Challenge children to sit quietly in an area and try to get a bird’s attention by echoing its call. Record the noises you hear in the outside world and play these during quiet mindful time later on in the classroom.
*Create a musical wall by hanging recycled materials on a fence for children to explore - pots, pans, muffin tins, bells, metal pieces - and encourage children to create their own songs. These can be recorded as musical notations and ‘played’ by others. Encourage children to read other children’s music and play it using the materials provided.
*Provide a portable music source (wireless speaker, iPad) and encourage children to listen to and identify the different rhythms they hear. Add colourful scarves and other fun props to encourage big body creative movement incorporating patterning. Encouraging children to internalize and make emotional connections to the world around them using the five senses cultivates strong eco-stewardship and math learning. In addition to guiding children through the teacher-initiated games and activities listed above, there are many more ways to cultivate a mathematically rich and responsive learning environment in any outdoor space.

Friday, April 13, 2018

Coding Stories and Games

We are pleased to have presented our workshop  Creating Coding Stories and Games at the 2018 ETFO Kindergarten Conference!





 


 


 


 



Here is our presentation for those interested in what we shared.


                   
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