Math Foundations for Preschoolers

Updated on February 23, 2019
Clare R Okyere profile image

Former teacher and elementary school principal who is currently leaning into motherhood and homeschooling her preschool-aged daughter, Zoe.

Whether you love or hate math, you have the power to ensure your child loves and excels in this content area. Watch out world: the next engineers, doctors, and investment bankers are on their way up!

Mathematics for Preschoolers

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Love of Math Starts in the Early Years

As a teacher, I lost track of the number of fifth and sixth grade students who hated math and felt inadequate in this subject area. As a principal, I continued seeing this pattern. In addition, I saw teachers who didn't feel comfortable teaching math past a certain point, stating it was their weakest content area. This doesn't need to be! Math is logical and predictable, and you can help your preschoolers develop all the skills they need to love math and feel confident both when they enter school as well as the work force.

Developing Math Foundations Through Number Puzzles

While a great deal of our math instruction happens organically (counting stairs as we climb, counting the number of strawberries in our bowl, comparing who has more goldfish crackers...), I do like to include more formal instruction as well. These number puzzles are a great tool, and we work with them at least once a week.

There are a few steps I follow when working with these number puzzles:

1. Exploratory Play

2. Independent Learning Time

3. Instructional Activities

4. Free Play Time

Free explore time is critical in developing curiosity, independent thinking, and a love of learning. Today, Zoe chose reading a number book to "help her" with her number puzzles.
Free explore time is critical in developing curiosity, independent thinking, and a love of learning. Today, Zoe chose reading a number book to "help her" with her number puzzles. | Source

Free Explore Time

Any time we take out a new material (new for a preschooler often means they haven't seen it today!), I start with a few minutes of free explore. Our most important goal is always to instill a love for learning. I never want our more specific content goals to hamper this objective.

Free explore is just as it sounds - allow your preschooler to engage with the materials as they sit fit. We've used these math puzzles before, so Zoe initially started with some guess-and-check matching as well as a little counting. She then proceeded to pull out one of her favorite counting books looking for pages that would "help her" match her puzzle pieces. It is often difficult not to intervene during this segment as there are always so many teachable moments, but try your best to resist. I distracted myself with folding some laundry as Zoe explored. Win-win! When I heard her move on to her drum set, I knew she was done with her free explore. I gave her a few minutes on the drums while I arranged the materials for our next segment: independent learning time.

When children have a skill they can accomplish independently, they should be given the time and space to do so.
When children have a skill they can accomplish independently, they should be given the time and space to do so. | Source

"Practice doesn't make perfect. Only perfect practice makes perfect."

— Vince Lombardi

Independent Learning Time

Nearly all materials can support or inhibit learning, depending on how they are used. Based on Zoe's current abilities (watching and listening closely is critical here), I sort the materials into three piles:

  • Puzzles 1-5
  • Puzzles 6-10
  • Puzzles 11-20

Puzzles 1-5 are the only ones I currently use for independent practice. There are a few reasons for this.

Independently, Zoe can:

  • easily identify these numbers
  • accurately count the quantities without getting overwhelmed
  • still has to think to complete this task (it is not so easy for her that it has become mundane)

Remember, "Practice doesn't make perfect. Only perfect practice makes perfect," Vince Lombardi.

I want to be sure Zoe is able to accurately complete a task she is given independently, and she is actually practicing the target skill. Even though these are self-correcting puzzles, meaning they will only attach if correctly matched, I still want to be intentional in how I present the materials. If all she is doing is guessing, she is working on her fine motor skills, but she is not working on one-to-one correspondence and quantity.

Therefore, Puzzles 1-5 are in their own pile, and I call Zoe over to match them. I am close enough that I can see and hear, but I am not involved in supporting. She excitedly counts the quantities and matches them to the correct number. I notice she can do Puzzles 1-3 without even counting; she has already memorized these quantities. They will soon become mundane and move out of independent practice. She correctly counts and matches all five puzzles. This piece takes less than five minutes.

Providing intentional instructional support helps your learner acquire and become independent with new skills.
Providing intentional instructional support helps your learner acquire and become independent with new skills. | Source

Instructional Learning Time

The instructional sweet spot is just past what a child can do independently. Educators have a fancy term for this - the zone of proximal development. For Zoe, there are two instructional goals I have for today's instructional Number Puzzle session:

  • counting quantities between 6-10
  • identifying double-digit numbers to 20

For this session, I sit very close to Zoe. I listen and watch as I want to be sure she is not developing any bad habits or misconceptions about the topic. I still let her guide to some extent (i.e. select which quantities to count first, attempt the initial count independently), but I quickly intervene, correct, and model as needed.

I notice Zoe can count the quantity of six independently and accurately. This will move to our "independent" pile in our next session.

The main error that emerged was double counting objects. I repeatedly modeled my thought-process and strategies for this with Zoe:

"There are a lot of marbles here Zoe. Mommy needs to count them. I am going to start on the top, and snake my way down to the bottom (I trace the path I will count). Remember, I will only count each marble one time. Ready? Count with me."

I then use the hand-over-hand strategy and physically move Zoe's hand as we count the objects. Or, she will place her finger on top of mine. As I move my finger, hers moves as well. We count the objects together. This intentional instructional practice will help her move toward independence with these larger quantities.

We work through Puzzles 6-10 in about 5 minutes.

The instructional sweet spot is just past what a child can do independently. Educators have a fancy term for this - the zone of proximal development.

Instructional Time

The second instructional objective for Zoe is identifying double-digit numbers to 20. How did we select this goal? Zoe can rote count to 20, although she consistently skips the number 15. She can accurately identify all single digit numbers with 100% consistency, and accurately identifies the number 10 nearly all of the time. She cannot accurately name numbers 11-20, however, unless she is continuing in order on a number line.

For this instructional objective, I use Puzzles 11-20. During this time, I do not expect Zoe to count the quantities. She is still developing proficiency of quantities 6-10, so counting numbers larger than this would be in the "frustrational" not "instructional" zone.

For this session, I count the quantities out loud. I am still modeling this skill, but I am not using physical manipulation (i.e. hand-over-hand or finger-on-finger) to have Zoe count along. Rather, after I have counted, I ask Zoe to find the number that matches the quantity. In this way, her focus is on identifying the double-digit numbers.

Again, I watch closely to see how much she can do independently and where she needs support. We like to make a game out of this, as she tries to find the number faster than I can. We spend about 5 minutes to match the remaining number puzzles.

Instructional Time

As I model counting larger quantities, Zoe likes to take a turn as photographer.
As I model counting larger quantities, Zoe likes to take a turn as photographer. | Source

Free Play Time

I like to end the session the same way we started: with play. Zoe is only 2, and I want her to love learning. Having a positive association with numbers and math will benefit her for years to come.

Today, she wanted to line up all the Number Puzzles to make a road. She crawled back and forth on her road, playing with the puzzles as she saw fit. She did this for just over five minutes before she was ready to clean up.

Associating numbers and math with play and fun is just as critical as teaching counting and quantity
Associating numbers and math with play and fun is just as critical as teaching counting and quantity | Source

Number Puzzles are one tool we use for formal math instruction. We'd love to hear all the formal and informal ways you help your child solidify a love for math!

Share your comments, photos, and questions in the comment section below.

In learning,

Clare & Zoe

Questions & Answers

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      • Clare R Okyere profile imageAUTHOR

        Clare R Okyere 

        2 months ago from Arizona, USA & Ghana, West Africa

        I am glad you enjoyed it!

      • bhattuc profile image

        Umesh Chandra Bhatt 

        2 months ago from Kharghar, Navi Mumbai, India

        A good article for teachers to encourage kids towards Maths.

        Nice reading. Thanks.

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