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!

Autumn Math Walk

"Notice that autumn is more the season of the soul than of nature."

 Friedrich Nietzsche

What better time of year to head outside and enjoy the beauty of nature than in the fall!

We have been spending long amounts of time each day exploring the treasures in our yard. The children have been fascinated by how the world around us is changing - leaves are changing colours and falling from trees, Monarchs are gathering the last bit of nectar from the garden before heading South, and we are enjoying the last flowers in our gardens before they wilt and dry.

The children have had many questions about some of the interesting objects they have found in the yard - stumps, leaves, creatures and flowers.

  

   

Many of their wonderings have been mathematical in nature - Why is there a pattern on the sunflower's seedhead? What are those holes in the stump and where did it come from? Why is a Daddy Long Legs an arachnid and not a spider?  How do leaves change colours?

There is math everywhere. If one looks deeply enough, there is always a mathematical connection in nature. The sunflower seeds follow the Fibonacci Sequence - a numerical pattern meant to help maximize space and fit as many seeds into the head as possible. The perfect little circles in the stump might have been caused by a wood boring insect or bird looking deep into the bark for food. Daddy Long Legs have a different body than spiders even though they have eight legs. Leaves change colour because the amount of sunlight they need to create their own food lessens in cold weather (as the Earth's axis tilts us away from the sun), resulting in a chemical change in the leaves. 

I've been motivated to continue to look for rich mathematical wonderings and opportunities for inquiry each time I'm outside - even on the weekend with my own children. I find it fascinating to see math applied in an authentic, interesting, real world connection. The math in nature is beautiful! Consider going on your own autumn math walk and seeing what amazing questions and connections emerge with on your journey!

I'm excited to publish my first children's book Autumn Math Walk (Kindle edition) on amazon now. Stay tuned for a print version!

Math and Literacy Family Bags

Many families are eager to help their children practice literacy and numeracy work from school. Although traditional 'paper and pencil' homework is not developmentally appropriate in many circumstances, providing 'take home' games and activities in the form of literacy and math bags is welcomed and appreciated by many families. These interactive, hands-on, developmentally appropriate activities are easy to create and target many emergent skills and knowledge needed by young children. They are a good alternative when the school community expects work to be sent home from school. Take home bags help parents and guardians understand how literacy and numeracy can be nurtured and celebrated in the lives of young children.

You can access these, along with many free math printables, here:  https://www.teacherspayteachers.com/Store/Joyful-Learning-In-The-Early-Years

As always feedback and suggestions for future resources is always appreciated!

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. 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.

What does the Equal Sign Really Mean?

A few years ago I was presented with this question at a workshop and asked to consider how a group of students would respond. After some discussion our group thought that children might recognize the third as incorrect. I was surprised when the presenter shared that most children, regardless of grade or age, think that the third example is right and the rest are incorrect. Why is that?

Most children associate the equal sign (=) with the word 'answer', so they look for traditional algebraic representations. This is why despite the third statement being incorrect, it looks like something most children regularly see and use in math (addend plus addend equals sum) so they assume it is correct. Example one, two and four don't look typical for many children, so they aren't sure about them and assume they are incorrect.

Mathematical equations must have an equal sign indicating that two expressions have the same value.

10 is the same (or equal to) 10.
3 + 7 and 8 + 2 both equal 10.
10 is the same as 9 + 1.

Therefore providing children introductions to many different ways of writing equations, and tangible, hands-on experience with the idea of equality is very important. Despite their age young children are capable of using complex math in context, including the proper terminology for symbols like the equal sign. This can be done in many ways in kindergarten. Over the course of the last year we have been on a journey to help children understand the equal sign. This blog post outlines some of what we have done in order to achieve success.

Using Proper Terminology in Math Discussion and Discourse

In our classroom we start each morning with a number talk during our morning message. I was curious to see what my students knew about the equal sign, and how they would describe their thinking mathematically. I asked the following question:

The first few times we reviewed this prompt children replied by telling me that the equal sign meant 'answer'. They knew that four added to one was the same as five, but they could not articulate this clearly. I knew that much practice was needed to help children look at numbers in new ways, explore the idea of equal amounts and equality, and play with equations in different ways. After a few months exploring these throughout many whole and small group conversations and math invitations, I again asked children the same question. They responded by saying:

"Four plus one is the same as five. They are both five."
"Both sides are the same. They are equal. It's like if I gave you four and one cookies and I had five. We would both have the same. It would be fair."
"Each side is the same as the other."
"It's like this." (child holds up one hand and shows five fingers and then holds up the other hand with five fingers. "Each hand has five fingers. They are the same."

In our classroom we explored the following activities many times and in many different contexts to help build this algebraic understanding. Much of this work happened before we even looked at a written equation with numbers and symbols.

Building on Mirrors

We offered children mini wooden cubes on mirrors. As they built towers children realized that the reflections of their creations were doubling the total amount that they used. This was a rich opportunity to discuss the idea of equal (e.g., "The number of blocks used in your tower is equal to the blocks in its reflection.") and doubling (e.g., "We can double the number of blocks you used in your tower to calculate the total number of blocks used.").

       

Subitizing Match

Understanding that there are many different ways to represent the same, or equal amounts, is a foundational number sense strategy. Not only does this help children become more accurate and confident when identifying/calculating/comparing sets of objects, it provides an opportunity to show equal amounts (e.g., five tallies = five dots = the number 5).

We used subitizing cards and encouraged children to match them to random numbers written on a chart...

         

 ...and also played games where children were encouraged to find similarities between number representations. In this game children were asked to find at least three different dot arrangements to represent the same number.

      

Creating equal number strings is also helpful. Sometimes we will use the date as a number prompt and ask the children to explore representations in different ways. In the following picture we showed children three different ways of arranging 8 hearts and asked them to create equations based on what they saw. 

After exploring the arrangements the children shared the following:

4 = 4 

4 + 4 = 8

2 + 2 + 2 + 2 = 8
8 + 0 = 8
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8

Sharing at Centers

Play dough is one of the most popular centers in our classroom and despite making a double batch each week, sharing equally among the large number of friends tends to be problematic. Usually the first child to visit the center grabs the entire big ball of dough, and reluctantly tears off small amounts to the children who slowly make their way there. "That's not fair! You have more than me!" is frequently heard at the table. As educators we felt this would be an excellent, real life situation to help children think about equality and equal amounts in a meaningful context. In addition to supporting and scaffolding this directly at the center, we encouraged children to think about fair, equal amounts by adding plates and laminated photos of each child to the center.    

             

We also added tools like cutters and asked children how they could divide the play dough into equal amounts. "How do you know it's equal?" was an interesting conversation starter and the children's ideas for equality were interesting (e.g., "We could see if it fits in the same container.", "We could measure it with a scale to see if it weighs the same.")  

Real Life Math Problems

Inspired by the children's problem solving at the play dough center, we used our morning message to ask children deeper, more complex questions regarding equality and fair sharing. Because they love seeing themselves on the morning message, it was effective to ask how four children might share six cookies equally. 

 

The children saw the cookies as two groups of three, and then split the three cookies in three ways. We used arrows to represent what it was they were saying. After some conversation and use of real props they also recognized that three halves were equal to one whole and one half of a cookie, helping us delve in early fraction work.

1/2 + 1/2 + 1/2 = 1 + 1/2 

  Building Equals

The children love to create with pattern blocks and are especially skilled at designing intricate tessellations. Wanting to introduce the concept of rotational symmetry we created eight equal sections using tape on the carpet. After building the children recognized that the blocks used in each section were equal to, or the same, as the other seven. This activity was also made available during outdoor play by placing tape directly on the pavement and offering children a basket of pattern blocks.  

  Equation Clothesline

Another equality invitation offered to children for exploration was the equation clothesline. This consisted of a string hung between two posts, clothespins, and subitizing cards. Children were able to represent balanced equations by finding different representations of numbers and pinning them on the clothesline. Equations could be simple (as shown in the photo where the number 2 = 2 dots on a five frame) or complex by adding addition or subtraction signs on each side of the equation (1 + 1 = 3 - 1). This provided multiple entry points into the activity with a way of differentiating it for children's needs and interests. 

Visual Representation of an Equation

In order to help children move towards thinking in algebraic representations we provided a visual 'scale' along with numbers written on sticky notes. Children were invited to try and create a balanced equation by first placing numbers on the scale and then adding the equal sign (also written on a sticky note) to the visual. We did not write the equal sign directly on the paper because we also had 'greater than' and 'less than' signs offered on stickies in order to differentiate the activity for children who were working at that level. 

Equation Sort

Another activity to help children practise identifying correct equations is the 'equation sort'. In this activity we presented children with a number of equations and asked them to sort them as 'correct' or 'incorrect'. Children had to justify their choices by using math language to describe their thinking. A great extension is to offer children blank strips and encourage them to create their own correct and incorrect equations and place them under the corresponding categories.

Greater Than, Less Than

Now that children are comfortable with the concept of equality, we are exploring other relationships that numbers have with one another. Inequality is something that children have expressed an interest it. We are starting our explorations by using the language 'less than' and 'greater than' in contexts to describe sets of objects, and creating the  <  and  >  symbols to show these relationships. Cubes and craft sticks are an easy invitation to try out.

It will be interesting to see where this journey continues. Please feel free to share your explorations and activities with equality and inequality in the comments below, or tweet us your ideas and feedback at @McLennan1977.