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Children show their number sense in many everyday problem-solving situations. ©Shutterstock/kilukilu

In the second in a series of papers discussing neuroscience, psychology and research Dr Kate Reid explores preschool children's early numeracy development and how to help foster it.
Children think mathematically long before they start school, and there is substantial growth in numeracy skills during preschool. Such informal knowledge about numbers is often referred to as 'number sense'. Children show their number sense in many everyday problem-solving situations involving numbers and measurement. They may reason about who has more or less, devise strategies for creating equal shares of countable objects or amounts, or use counting in a range of situations to reason about a single group of objects or to compare two groups. Children informally build these skills in their everyday interactions with carers and with other children, and they can be encouraged to develop their understanding in play situations.
What does the research say?
Investigations in developmental and cognitive psychology have found that infants can detect changes in small numbers of up to about five (Wynn, 1995). They can also detect differences between large numbers. For example, six-month-old infants differentiated between displays of eight and 16 objects (Xu & Spelke, 2000). Other studies have shown that these abilities are not limited to visual displays, with infants discriminating differences between small (vanMarle & Wynn, 2009) and large numbers of sounds (Lipton & Spelke, 2003), and different numbers of actions (Wynn, 1996).

Research suggests that infants' number sense extends from simple number discrimination to more complex awareness of ordinal relationships (numbers ordered by size) and even the results of simple calculations. Infants seem to recognise when results of simple number transformations are correct (for example, 1 + 1 = 2 and 2 - 1 = 1) or incorrect (for example, 1 + 1 = 1 and 2 - 1 = 2).

Research from developmental and cognitive psychology has yielded significant evidence that infants have a basic capacity to respond to numerical information. Neuroscience has provided complementary evidence of structural location and changes in brain activity when infants detect changes in number. This evidence shows that infants have a basic capacity to process numbers, not as a fixed capacity for developing mathematical understanding, but as an early foundation that may provide some direction for children as they grow and develop their numerical skills.
How early learning affects later learning
Children enter school with a wide range of early numeracy skills but they vary greatly in how they acquire, and how quickly they acquire, different concepts (Klibanoff, Levine, Huttenlocher, Vasilyeva, & Hedges, 2006; Kroesbergen, Van Luit, Van Lieshout, Van Loosbroek, & Van de Rijt, 2009). Children's informal number sense when they enter school provides a foundation for their school mathematics achievement and strongly predicts their maths competence later in school (Geary, 2015).

Several recent longitudinal studies have investigated mathematical development in the transition from preschool to the early years of primary school. For instance, in one study, counting skills and understanding of quantities and the relationships between them in the year before starting primary school predicted children's maths achievement and teacher ratings of competence in maths one year later (Aunio, & Niemivirta, 2010). Other studies have demonstrated that, on entry to school, number sense and numeracy knowledge predict maths achievement in later school years (Aubrey, Godfrey, & Dahl, 2006).

Research illustrating the link between maths skills in infancy and preschool does not suggest that maths development is fixed, as a range of additional factors can promote and enhance maths achievement. For example, self-regulatory behaviour has been shown to be a significant predictor of the acquisition of academic skills, including early numeracy. Other research has suggested that working memory may contribute to maths achievement.
How to support early numeracy development
Given that early numeracy skills predict achievement in maths as children progress through school, interest has developed in identifying predictors of variation in numeracy growth, particularly as preschoolers already show wide variation in numeracy skills. This implies that school teachers will encounter children with a wide range of early numeracy skills even at school entry.

Already in preschool learning environments, teachers can vary significantly in the amount of mathematical information they convey while interacting with children. Such variation is related to the growth in numeracy skills over a year, with greater growth in numeracy skills related to greater maths-specific talk by teachers (Klibanoff, et al., 2006).

Fostering understanding of early numeracy development among early childhood educators is an important step in helping children in the early years to develop their mathematical thinking. Early childhood educators could be trained in the explicit use of 'maths talk' in their everyday interactions with children to enhance opportunities for children to develop their early numeracy skills.

Research strongly suggests that early numeracy development can be supported by interactions between young children, and family members and early childhood educators. Parents positively influence their preschool child's maths achievement when they engage with their child at home in direct numeracy practices like teaching their children the number words and counting, and indirect numeracy practices like integrating numeracy into everyday tasks such as cooking (LeFevre et al., 2009).

Understanding more about preschoolers' early numeracy development is important in informing educational practices, understanding the variation in early numeracy skills among preschoolers, fostering early numeracy among children whose skills are less developed, and understanding why some children with well-developed early numeracy have difficulties learning mathematics at school.

This is a summary of Counting on it: Early numeracy development and the preschool child by Dr Kate Reid, the second in a series of papers, Changing minds: Discussions in neuroscience, psychology and research, published by ACER. Read the full paper at www.research.acer.edu.au/learning_processes/19
References
Aubrey, C., Godfrey, R., & Dahl, S. (2006). Early mathematics development and later achievement: Further evidence. Mathematics Education Research Journal, 18(1), 27-46.

Aunio, P., & Niemivirta, M. (2010). Predicting children's mathematical performance in grade one by early numeracy. Learning and Individual Differences, 20(5), 427-435.

Geary, D. C. (2015). Development and Measurement of Preschoolers' Quantitative Knowledge. [doi: 10.1080/10986065.2015.1016823]. Mathematical Thinking and Learning, 17(2-3), 237-243.

Klibanoff, R. S., Levine, S. C., Huttenlocher, J., Vasilyeva, M., & Hedges, L. V. (2006). Preschool children's mathematical knowledge: The effect of teacher" math talk.". Developmental Psychology, 42(1), 59.

Kroesbergen, E., Van Luit, J., Van Lieshout, E., Van Loosbroek, E., & Van de Rijt, B. (2009). Individual Differences in Early Numeracy The Role of Executive Functions and Subitizing. Journal of Psychoeducational Assessment, 27(3), 226-236.

LeFevre, J.-A., Skwarchuk, S.-L., Smith-Chant, B. L., Fast, L., Kamawar, D., & Bisanz, J. (2009). Home numeracy experiences and children's math performance in the early school years. Canadian Journal of Behavioural Science/Revue canadienne des sciences du comportement, 41(2), 55.

Lipton, J. S., & Spelke, E. S. (2003). Origins of number sense large-number discrimination in human infants. Psychological Science, 14(5), 396-401.

vanMarle, K., & Wynn, K. (2009). Infants' auditory enumeration: Evidence for analog magnitudes in the small number range. Cognition, 111(3), 302-316.

Wynn, K. (1995). Origins of numerical knowledge. Mathematical Cognition, 1(1), 35-60.

Wynn, K. (1996). Infants' individuation and enumeration of actions. Psychological Science, 7(3), 164-169.

Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74(1), B1-B11.

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In the second in a series of papers discussing neuroscience, psychology and research Dr Kate Reid explores preschool children's early numeracy development and how to help foster it. Children think mathematically long before they start school, and there is substantial growth in numeracy skills during preschool.

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Hands-On Math Activities for Preschoolers

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Math is so fun to teach to preschoolers because there are a lot of daily activities that incorporate math. Preschoolers don't need worksheets for math...they should learn through play and hands-on activities.
1. Patterns with Bears
I created some pattern cards to help with this. The first page is an AB pattern, meaning two colors alternate in the pattern. The second page is an ABC pattern, meaning three are three colors in the pattern. For this activity, your preschooler will set the colored bear on top of the matching color to create a pattern. On the ABC pattern cards, the last circle is left empty. That is for your child to tell you what color it should be.
You can get the color patterns printable at the bottom of this post. Math Skill: Patterns and Relationships
You can find more pattern activities here.
2. Sorting Colors with Bears
Sorting is a skill preschoolers should work on a lot. One way to sort is by color. We do this with our counting bears and a sorting mat.
You can get the sorting mat printable at the bottom of this post.
You can even use colored tape and pom poms to practice sorting! Add in some tweezers for some extra fine motor practice.

We also love counting mats! These are great for learning to count and working on one-to-one correspondence.
Math Skill: Patterns and Relationships 3. Money Muncher
A fun way to work on sorting is with the Money Muncher! It's also a great activity for fine motor skills. To see all the fun details, click here.
Math Skill: Patterns and Relationships 4. Sorting Jelly Beans
Anytime we work with candy, my kids love it! You can sort M&Ms or jelly beans or whatever! To see how we did this with jelly beans, click here.
You can get the jelly bean sorting printable at the bottom of this post.
One more idea for sorting is by using toy animals. Have them sort by different characteristics, such as land animals and sea animals.
Math Skill: Patterns and Relationships 5. Graphing
Graphing is always good to introduce to preschoolers. It doesn't have to be complex, but you can do a simple activity like graphing the types of transportation on a bar graph and use small pictures or toys (or I used erasers from The Dollar Tree).

Make graphing hands-on using apples! Even young preschoolers can begin learning about graphing with this activity.

Check out this free gumball graphing activity right here.
Math Skill: Patterns and Relationships
This is a fun activity for learning shapes! Just print this shape wheel and draw the same colored shapes onto clothespins. Have your child match the clothespin to the shape on the wheel. This is great for working on fine motor skills!
6. Shape Wheel You can get the shape wheel printable at the bottom of this post. Math Skill: Geometry
An easy way to practice shapes is with a Shape Sorter! I bought these shapes at Michaels Craft Store many years ago, but these 3D geometric shapes would be a good option if you're interested in creating a Shape Sorter. Check out this post for details on how to make this easy math activity.
7. Shape Sorter Math Skill: Geometry
A neat sensory activity and a fun way to learn shapes are with noodles! See the post here to download the free shape cards.
8. Noodle Shape Cards Math Skill: Geometry
Learn shapes in the tub with these foam sticks! You can see how we did this here.
9. Foam Sticks
Another fun way to practice shapes is with the cookie shapes matching activity!

And my favorite way to teach about shapes is with my shape rhymes!

10. Dice Game
This is a really fun game! I took this Melissa & Doug wooden toy

and put white circle stickers on the top of the pegs. I wrote numbers 1-6 and had 2 stars. I had my son roll the dice and whatever number it landed on, he would pound with a toy hammer. If the number he rolled was already down, he hit the star. Not only was this fun for him, but he was able to "subitize", which simply means to recognize numbers instantly without counting the dots.

Practice counting and recognizing numbers with star number cards. This one is great for working on one-to-one correspondence and fine motor skills.
Math Skill: Number Concepts 11. Star Number Cards You can get the star number printable cards at the bottom of this post.
We made these adorable ladybugs and they were a hit! Not only were they fun to play with, but we did a lot of counting and sorting with them. Read all about it here.
Math Skill: Number Concepts 12. Ladybug Math
Learn the order of numbers with this really fun game involving balloons! Check out the details here.
Math Skill: Number Concepts
Math Skill: Number Concepts
13. Balloons
We learned about estimation with a dropper with some fun, hands-on water activities.
14. Estimating with Water
We practiced pouring skills with rice into these beakers. Then I had my son line them up from biggest to smallest. Using comparative words like big/small or empty/full help teach preschoolers about simple concepts of measurement. This is simple and you could elaborate on this activity.
Math Skill: Measurement
One more easy way to practice measurement is with Unifix cubes. Place different lengths of tape on the floor or poster board. Then have your child use Unifix cubes to measure the lines. This is a simple way to practice counting, measuring, and comparing lengths.
15. Pouring and Comparing
Lastly, check out this really easy and fun way to practice counting!

Math Skill: Measurement
If you're looking for digital math activities, make sure to check out my counting activities using Google Slides.

If you'd like to download the 5 free printables I shared in this blog post, just click on the button below!

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Hands-On Math Activities for Preschoolers

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15 Hands-On learning activities for preschoolers, including lots of free printables.

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Help Your Child Develop Early Math Skills

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Children are using early math skills throughout their daily routines and activities. This is good news as these skills are important for being ready for school. But early math doesn't mean taking out the calculator during playtime. Even before they start school, most children develop an understanding of addition and subtraction through everyday interactions. For example, Thomas has two cars; Joseph wants one. After Thomas shares one, he sees that he has one car left (Bowman, Donovan, & Burns, 2001, p. 201). Other math skills are introduced through daily routines you share with your child-counting steps as you go up or down, for example. Informal activities like this one give children a jumpstart on the formal math instruction that starts in school.

What math knowledge will your child need later on in elementary school? Early mathematical concepts and skills that first-grade mathematics curriculum builds on include: (Bowman et al., 2001, p. 76).

Understanding size, shape, and patterns

Ability to count verbally (first forward, then backward)

Recognizing numerals

Identifying more and less of a quantity

Understanding one-to-one correspondence (i.e., matching sets, or knowing which group has four and which has five)

Key Math Skills for School

More advanced mathematical skills are based on an early math "foundation"-just like a house is built on a strong foundation. In the toddler years, you can help your child begin to develop early math skills by introducing ideas like: (From Diezmann & Yelland, 2000, and Fromboluti & Rinck, 1999.)

Number Sense

This is the ability to count accurately-first forward. Then, later in school, children will learn to count backwards. A more complex skill related to number sense is the ability to see relationships between numbers-like adding and subtracting. Ben (age 2) saw the cupcakes on the plate. He counted with his dad: "One, two, three, four, five, six..."

Representation

Making mathematical ideas "real" by using words, pictures, symbols, and objects (like blocks). Casey (aged 3) was setting out a pretend picnic. He carefully laid out four plastic plates and four plastic cups: "So our whole family can come to the picnic!" There were four members in his family; he was able to apply this information to the number of plates and cups he chose.

Spatial sense

Later in school, children will call this "geometry." But for toddlers it is introducing the ideas of shape, size, space, position, direction and movement. Aziz (28 months) was giggling at the bottom of the slide. "What's so funny?" his Auntie wondered. "I comed up," said Aziz, "Then I comed down!"

Measurement

Technically, this is finding the length, height, and weight of an object using units like inches, feet or pounds. Measurement of time (in minutes, for example) also falls under this skill area. Gabriella (36 months) asked her Abuela again and again: "Make cookies? Me do it!" Her Abuela showed her how to fill the measuring cup with sugar. "We need two cups, Gabi. Fill it up once and put it in the bowl, then fill it up again."

Estimation

This is the ability to make a good guess about the amount or size of something. This is very difficult for young children to do. You can help them by showing them the meaning of words like more, less, bigger, smaller, more than, less than. Nolan (30 months) looked at the two bagels: one was a regular bagel, one was a mini-bagel. His dad asked: "Which one would you like?" Nolan pointed to the regular bagel. His dad said, "You must be hungry! That bagel is bigger. That bagel is smaller. Okay, I'll give you the bigger one. Breakfast is coming up!"

Patterns

Patterns are things-numbers, shapes, images-that repeat in a logical way. Patterns help children learn to make predictions, to understand what comes next, to make logical connections, and to use reasoning skills. Ava (27 months) pointed to the moon: "Moon. Sun go night-night." Her grandfather picked her up, "Yes, little Ava. In the morning, the sun comes out and the moon goes away. At night, the sun goes to sleep and the moon comes out to play. But it's time for Ava to go to sleep now, just like the sun."

Problem-solving

The ability to think through a problem, to recognize there is more than one path to the answer. It means using past knowledge and logical thinking skills to find an answer. Carl (15 months old) looked at the shape-sorter-a plastic drum with 3 holes in the top. The holes were in the shape of a triangle, a circle and a square. Carl looked at the chunky shapes on the floor. He picked up a triangle. He put it in his month, then banged it on the floor. He touched the edges with his fingers. Then he tried to stuff it in each of the holes of the new toy. Surprise! It fell inside the triangle hole! Carl reached for another block, a circular one this time...

Math: One Part of the Whole

Math skills are just one part of a larger web of skills that children are developing in the early years-including language skills, physical skills, and social skills. Each of these skill areas is dependent on and influences the others.
Trina (18 months old) was stacking blocks. She had put two square blocks on top of one another, then a triangle block on top of that. She discovered that no more blocks would balance on top of the triangle-shaped block. She looked up at her dad and showed him the block she couldn't get to stay on top, essentially telling him with her gesture, "Dad, I need help figuring this out." Her father showed her that if she took the triangle block off and used a square one instead, she could stack more on top. She then added two more blocks to her tower before proudly showing her creation to her dad: "Dada, Ook! Ook!"
You can see in this ordinary interaction how all areas of Trina's development are working together. Her physical ability allows her to manipulate the blocks and use her thinking skills to execute her plan to make a tower. She uses her language and social skills as she asks her father for help. Her effective communication allows Dad to respond and provide the helps she needs (further enhancing her social skills as she sees herself as important and a good communicator). This then further builds her thinking skills as she learns how to solve the problem of making the tower taller.

What You Can Do

The tips below highlight ways that you can help your child learn early math skills by building on their natural curiosity and having fun together. (Note: Most of these tips are designed for older children-ages 2-3. Younger children can be exposed to stories and songs using repetition, rhymes and numbers.)

Shape up.

Play with shape-sorters. Talk with your child about each shape-count the sides, describe the colors. Make your own shapes by cutting large shapes out of colored construction paper. Ask your child to "hop on the circle" or "jump on the red shape."

Count and sort.

Gather together a basket of small toys, shells, pebbles or buttons. Count them with your child. Sort them based on size, color, or what they do (i.e., all the cars in one pile, all the animals in another).

Place the call.

With your 3-year-old, begin teaching her the address and phone number of your home. Talk with your child about how each house has a number, and how their house or apartment is one of a series, each with its own number.

What size is it?

Notice the sizes of objects in the world around you: That pink pocketbook is the biggest. The blue pocketbook is the smallest. Ask your child to think about his own size relative to other objects ("Do you fit under the table? Under the chair?").

You're cookin' now!

Even young children can help fill, stir, and pour. Through these activities, children learn, quite naturally, to count, measure, add, and estimate.

Walk it off.

Taking a walk gives children many opportunities to compare (which stone is bigger?), assess (how many acorns did we find?), note similarities and differences (does the duck have fur like the bunny does?) and categorize (see if you can find some red leaves). You can also talk about size (by taking big and little steps), estimate distance (is the park close to our house or far away?), and practice counting (let's count how many steps until we get to the corner).

Picture time.

Use an hourglass, stopwatch, or timer to time short (1-3 minute) activities. This helps children develop a sense of time and to understand that some things take longer than others.

Shape up.

Point out the different shapes and colors you see during the day. On a walk, you may see a triangle-shaped sign that's yellow. Inside a store you may see a rectangle-shaped sign that's red.

Read and sing your numbers.

Sing songs that rhyme, repeat, or have numbers in them. Songs reinforce patterns (which is a math skill as well). They also are fun ways to practice language and foster social skills like cooperation.

Start today.

Use a calendar to talk about the date, the day of the week, and the weather. Calendars reinforce counting, sequences, and patterns. Build logical thinking skills by talking about cold weather and asking your child: What do we wear when it's cold? This encourages your child to make the link between cold weather and warm clothing.

Pass it around.

Ask for your child's help in distributing items like snacks or in laying napkins out on the dinner table. Help him give one cracker to each child. This helps children understand one-to-one correspondence. When you are distributing items, emphasize the number concept: "One for you, one for me, one for Daddy." Or, "We are putting on our shoes: One, two."

Big on blocks.

Give your child the chance to play with wooden blocks, plastic interlocking blocks, empty boxes, milk cartons, etc. Stacking and manipulating these toys help children learn about shapes and the relationships between shapes (e.g., two triangles make a square). Nesting boxes and cups for younger children help them understand the relationship between different sized objects.

Tunnel time.

Open a large cardboard box at each end to turn it into a tunnel. This helps children understand where their body is in space and in relation to other objects.

The long and the short of it.

Cut a few (3-5) pieces of ribbon, yarn or paper in different lengths. Talk about ideas like long and short. With your child, put in order of longest to shortest.

Learn through touch.

Cut shapes-circle, square, triangle-out of sturdy cardboard. Let your child touch the shape with her eyes open and then closed.

Pattern play.

Have fun with patterns by letting children arrange dry macaroni, chunky beads, different types of dry cereal, or pieces of paper in different patterns or designs. Supervise your child carefully during this activity to prevent choking, and put away all items when you are done.

Laundry learning.

Make household jobs fun. As you sort the laundry, ask your child to make a pile of shirts and a pile of socks. Ask him which pile is the bigger (estimation). Together, count how many shirts. See if he can make pairs of socks: Can you take two socks out and put them in their own pile? (Don't worry if they don't match! This activity is more about counting than matching.)

Playground math.

As your child plays, make comparisons based on height (high/low), position (over/under), or size (big/little).

Dress for math success.

Ask your child to pick out a shirt for the day. Ask: What color is your shirt? Yes, yellow. Can you find something in your room that is also yellow? As your child nears three and beyond, notice patterns in his clothing-like stripes, colors, shapes, or pictures: I see a pattern on your shirt. There are stripes that go red, blue, red, blue. Or, Your shirt is covered with ponies-a big pony next to a little pony, all over your shirt!

Graphing games.

As your child nears three and beyond, make a chart where your child can put a sticker each time it rains or each time it is sunny. At the end of a week, you can estimate together which column has more or less stickers, and count how many to be sure.

References

Bowman, B.T., Donovan, M.S., & Burns, M.S., (Eds.). (2001). Eager to learn: Educating our preschoolers. Washington, DC: National Academy of Sciences.

Diezmann, C., & Yelland, N. J. (2000). Developing mathematical literacy in the early childhood years. In Yelland, N.J. (Ed.), Promoting meaningful learning: Innovations in educating early childhood professionals. (pp.47-58). Washington, DC: National Association for the Education of Young Children.

Fromboluti, C. S., & Rinck, N. (1999 June). Early childhood: Where learning begins. U.S. Department of Education, Office of Educational Research and Improvement, National Institute on Early Childhood Development and Education. Retrieved on May 11, 2018 from https://www2.ed.gov/pubs/EarlyMath/title.html

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Help Your Child Develop Early Math Skills

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Most children develop an understanding of math through everyday interactions and informal activities. Help your child develop math skills.

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Math: Number Recognition and Subitizing 

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Math: Number Recognition and Subitizing 

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Narrator: Welcome to this presentation of the 15-minute in-service suite on number recognition and subitizing. This 15-minute suite highlights the development of this important math competency that is the foundation of math learning later in a child's life. This suite provides strategies that support number recognition and subitizing for children birth to age 5.

Math is a part of what you do every day as you work with young children and their families.

Woman: You don't even have to count it. My goodness. You really can count well.

Narrator: Children's success with mathematics depends on their developing number sense development. This includes interest, understanding, and, yes, even love of numbers. It begins when teachers and families support children's ability to recognize and eventually subitize numbers.

The Framework for Effective Practice or House Framework helps us think about the elements needed to support children's preparation and readiness for school. The elements are the foundation, the pillars, and the roof. When connected to one another, they form a single structure that surrounds the family in the center, because as we implement each component of the house, in partnership with parents and families, we foster children's learning and development.

Research-based curricula and effective teaching practices include supports for number recognition and subitizing. And just as the house needs a solid foundation, so does mathematics. Number recognition and subitizing provides that foundation.

This presentation on number recognition and subitizing is one in a series of modules designed to help adults support young children as they learn positive behaviors, develop skills in STEAM, math, and writing, and engage in dramatic play.

So, what do we know about how children develop skills in number recognition and subitizing? First, infants and toddlers begin showing number recognition and subitizing by paying attention to how many things there are...

Woman: One. Sophia, can I have one cracker, please? Thank you.

Narrator: ...like picking up one small toy in one hand and then picking up another toy in the other hand. They also begin to use a few basic words related to quantity, like "more," "all done," and the numbers 1, 2, and 3.

Research shows that very young children are sensitive to numbers and naturally compare small and large sets of objects during the first years of life. Preschoolers develop math skills that allow them to recognize the number of objects without counting. And when they can do that fluently, that is, when a child can look at dots and quickly say how many there are, this skill is referred to as subitizing.

The word "subitizing" comes from the Latin word for "sudden." Many teachers and parents have not learned about number recognition and subitizing, despite how important they are to mathematics development. These skills influence mathematics learning throughout the lifetime, especially within the years from birth to 5.

For example, the learning trajectory of children from birth to 5 shows us that infants and toddlers can first quickly see and name the number of objects in small groups. As children approach the preschool years, they can do the same thing for objects in a group with larger numbers. It's important for teachers and parents to help children by noticing and naming small numbers throughout the day. Adults can incorporate numbers and subitizing into their daily interactions during routine tasks, such as mealtime...

Woman: How many scoops are you gonna get? Two. Very good.

Narrator: ...or engaging in children's free play.

Woman: Okay. 1...2...3...4...5. Go!

Girl: Go!

Woman: Yay! 1...

Narrator: Teachers and parents can provide children with opportunities to learn numbers and subitize. Examples of this practice include labeling the number of Cheerios an infant has on his plate or by asking each toddler to pick up two blocks from the carpet or by naming how many puzzle pieces a preschooler is playing with.

Once you begin to notice and take advantage of these opportunities, you can build children's number sense with little or no extra effort. Naming numbers is just part of the way we talk to children everywhere, all day, and all year.

We hope you have new ideas about how you can support children's interest, engagement, and mathematics development. For more information and more ideas, see the complete 15-minute suite on number recognition and subitizing. And take a look at our tips and tools and helpful resources.

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Math: Number Recognition and Subitizing | ECLKC

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Narrator: Welcome to this presentation of the 15-minute in-service suite on number recognition and subitizing. This 15-minute suite highlights the development of this important math competency that is the foundation of math learning later in a child's life. This suite provides strategies that support number recognition and subitizing for children birth to age 5.

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Early numeracy skills: how to develop them

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Children develop maths and numeracy skills from birth. Build early numeracy skills by counting, sorting, looking at shapes, singing number songs and more.

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Email coach to schedule: mramos@child360.org | Manny Ramos

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Email coach to schedule: mramos@child360.org | Manny Ramos

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The teaching team will support children with challenging behaviors by using at least two, effective re-directing strategies that will engage children to follow-through with daily routines.

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To promote student autonomy and engagement during free play, the teachers will remind them of center expectations and ask at least one open-ended question.

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The teaching team will use at least one modeling strategy to encourage children to use their creative and critical thinking skills during group time.

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In the CLASS® dimension Regard for Student Perspectives, there is an indicator called Support for Autonomy. This means the ability to self-govern or make your own decisions about what, how, and why you do what you do. I recently have had a life lesson in autonomy.

My oldest daughter just turned 7. Since then, she has been asking me a lot lately: "Why do you make all of the decisions?"

Why do you decide what is in my lunch?

Why do you tell me when I can and can't watch TV?

Why do you tell me to clean my room? I'm okay with it being messy.

After some validation of her questions and emotions ("Yeah, that stinks that you can't always do what you want when you want"), we had a discussion about adults needing to set boundaries for safety and well-being (complete with an analogy to the backyard fence to help her understand the word boundaries). Then we started brainstorming ways she can have a little more autonomy.

She already has some autonomy such as deciding what to wear, what books to read, when to take a bath, and whether she will actually eat dinner (any other families feel that pain?!). We also encourage overall responsibility, such as contributing to household chores and taking care of her clothes and toys.

Even so, my daughter was expressing her desire to have a little more control over her daily life. I know that developing her autonomy will help her see herself as a competent person and someone who can take on tasks and challenges as they arise.

How We Increased Autonomy At Home

So here is what we brainstormed:

I would set the guidelines for what kinds of foods need to be packed in her lunch. She needs some protein, some carbs, some fat, and some fruits / veggies. But she can pick what those are and make her own lunch.

Because of the increased amount of screentime with virtual school, we had said no TV during the school week. She negotiated to have 30 mins on Wednesdays because her school is asynchronous that day.

She has to clean her room once a month for safety and hygiene.

And the kicker... she can now bike across two streets to go to the neighborhood park all by herself.

She was ecstatic about these new choices she could make on her own. Although when she got back from the park, I asked how it felt and she said, "It was weird to not have a grown up there. Weird, but good".

Before this whole process, I would have said that my daughter had a lot of choices as most of her play is child-led, but now I realize she was seeking more ways to try out her capabilities. As a parent, letting go can be a little scary. What choices will she make? How will those choices affect her and the rest of the family? How will I scaffold her through the consequences (positive and negative) of those choices?

How To Increase Autonomy At School

We sometimes see this same issue come up in classrooms, especially with younger children. Children may either not be encouraged to have roles and responsibilities in the classroom, the roles may not be meaningful to children, or they aren't given the chance to really do the job. For example, a teacher may call on a child to lead calendar time, but tell them where to point or hold the pointer for them.

Just like parents, it can be scary for teachers to find ways for children to have more autonomy in the classroom. Children might make mistakes (or messes), tasks can take more time, and taking care of all the other tasks needed to teach a classroom full of preschoolers can be overwhelming. However, when children are given opportunities based on their abilities and readiness, teachers may be surprised at what children are capable of and how it affects the classroom as a whole.

If you are interested in increasing children's autonomy in the classroom, here are some questions for your reflection.

What roles do children have? Can they make all of the decisions related to that role? If not, why? How could they make more decisions and take on more responsibilities?

Example: If they are watering the plants, can they complete all of the steps, including cleaning up the water that spills, or testing the soil to see if the plant needs to be watered?

Example: If they are in charge of handing out the napkins for snack time (in a non-COVID world), can they figure out how many napkins are needed and where to put them? Can they fix the mistake if they miscalculate?

How could the children be included in making classroom decisions?

Example: Make an emotional charter that outlines how they want to feel in the classroom and how to make that happen.

Example: Make a group plan for how the children want to spend their time in the block center.

How meaningful are the choices in the classroom? What will change in their experience based on the choice? Does it enrich their experience or not make much difference?

Example: Children can choose how to create a crown rather than being given a crown to color and only allowed to choose which color they want.

Example: Children are allowed to pick out their own books in the library rather than having the teacher select the book based on what she thinks the child might like.

One Size Does Not Fit All

It is important to note that there are important cultural differences in how much autonomy is desired, when and how it is appropriate for children to demonstrate a desire for more autonomy, and how to scaffold a child's growing sense of autonomy. This example is one family from one cultural background and is not meant to be prescriptive. Teachers and parents should guide the children in their care according to their context. However, I hope that this recent lesson in my life can help other parents and teachers to take a step back and think about who makes the decisions, in what way might a child become more involved in the process, and what the overall outcome may be.

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How to Increase Children's Autonomy in the Classroom

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In the CLASS® dimension Regard for Student Perspectives, there is an indicator called Support for Autonomy. This means the ability to self-govern or make your own decisions about what, how, and why you do what you do. I recently have had a life lesson in autonomy. My oldest daughter just turned 7.

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Hello Teachers,

You are all invited to be part of the Concept Development Overview. We will explore and discuss strategies to promote higher-order thinking. Stay tuned, more information will be shared.

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Materials: CLASS Manual Prek

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As you know, CLASS is a tool that captures teacher-student interactions. When it comes to the dimension "Concept Development" the focus is on the method the teacher uses to provide instruction in the classroom. While the interactions are what get measured with CLASS, as a teacher you can plan for Concept Development to be present throughout your lessons.

Let's look closer at how to do this.

When planning for Concept Development, it's helpful to list out the indicators of the dimension on a supplemental lesson plan sheet. You can find these indicators in your Dimensions Guide.

Create one plan for each interest area currently present in your classroom, as well as one for each major component of your day, such as: small groups, whole group, snacks, and meals.

For instance, I may have a small group planned called "Comparing Size." My materials for the activity are three picture cards-one is a small tennis ball, one is a soccer ball, and the last one is a beach ball. The guidance provided in my curriculum book may say something like this:

1. "Display pictures of the balls. Ask which is biggest, and which is smallest."

2. Next, "Place the cards in order by size. Point to them and label small, medium, large."

3. Then, "Have children compare sizes of other sets of three objects."

There are some hints of comparison in here, but we can take this same activity and brainstorm ways to make it go a little deeper in Concept Development:

Activity: "Comparing Sizes"

Indicator

What to Say

"I have three pictures here. How are these pictures the same? How are they different?"

"How else could we figure out if things are small, or medium, or large?"

"I have three cards here with pictures on them. What could I do with these cards?"

"I see there are many other objects on the table. What could we do with these objects?"

"This is reminding me of yesterday's story, The Three Bears! Why is it reminding me of that story?"

"What other things do we have in our room that are small, medium, and large?"

"The mixing bowls in our house are small, medium, and large."

"The measuring spoons that we used to make playdough yesterday fit inside of each other too-there was a big tablespoon, a medium teaspoon, and a small ½ teaspoon."

"What things do we have at our houses/parks/stores that are small, and medium, and large?"

This lesson-planning strategy is just a first step, of course. The most important part is engaging the students in the activity using your strategies on the lesson-planning sheet.

Hopefully, you will find this small example of a structure that supports the process is helpful. Remember, Concept Development is not something you are either "good at" or "bad at," but rather, a learning process for grown-ups too. Improving takes planning and practice.

If you try this strategy out, you may discover it gets easier over time to analyze the activities you have planned, and embed more Concept Development into them.

BONUS MATERIAL: Click here to download a free, blank Concept Development lesson plan.

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The Best Way to Incorporate More Concept Development in Your Lessons

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As you know, CLASS is a tool that captures teacher-student interactions. When it comes to the dimension "Concept Development" the focus is on the method the teacher uses to provide instruction in the classroom. While the interactions are what get measured with CLASS, as a teacher you can plan for Concept Development to be present throughout your lessons.

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Most parents, teachers, and children would agree-there is something special about story time. I can recall the thrill I felt at seven years old, sitting on the primary-colored carpet of my elementary school's library, listening intently as the school librarian read us The Widow's Broom or Alexander and the Terrible, Horrible, No Good, Very Bad Day. Some of my fondest memories include my mom reading me passages from The Secret Garden before bedtime, or my dad curling up on the couch with me to read Tales of a Fourth Grade Nothing, or my absolute favorite, Curious George.

For me, the best part about reading books was being able to relate to the characters-and it still is to this day! When my parent or teacher made a direct connection between the book and my own life, the conflicts in the stories became real to me. I felt deeper empathy for the characters and imagined what I might do in similar circumstances. Now that I have been studying the CLASS tool for several years, I've realized that what I loved about reading as a child was aligned with interactions related to the Concept Development dimension-connections to the real world.

Creating Connections to the Real World through Stories

Concept Development can be a tough dimension for teachers to build in to their day; it involves providing children opportunities for higher-order thinking. It may sound daunting, but the good news is that reading stories to children almost consistently affords teachers opportunities to help children connect concepts from books to their own lives. To make learning come alive for children, teachers can plan questions that encourage children to connect concepts from the story to their world. Almost every book contains a central conflict or concept for children to consider in their own lives.

Encouraging Children to Make Connections

Here are some questions you can ask to get children to make these important connections:

How would you feel if this happened to you?

Has anything like this ever happened in your life? What did you do?

If this happened in school, what would you do about it?

How do you think the character feels? Tell me about a time you felt that way.

Have you ever been to a place like this? What was it like?

Making real-world connections is important. Not just because it is an indicator of Concept Development, but also because it can help foster a love of learning for years to come. I'm living proof of it!

How do you make learning come alive for children? Share your experiences and tips below!

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Teacher Tips: Making Real-World Connections Come Alive at Story Time

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Most parents, teachers, and children would agree-there is something special about story time. I can recall the thrill I felt at seven years old, sitting on the primary-colored carpet of my elementary school's library, listening intently as the school librarian read us The Widow's Broom or Alexander and the Terrible, Horrible, No Good, Very Bad Day.