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### 10 Math Skills Your Kids Can Master Before Kindergarten

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by Patrick Greenwood, Founder of Kontu

This guide is here to reduce the overwhelm and add to the fun. Whether you are a self-proclaimed math nerd or vowed you would never go near algebra again, this article prepares you to guide your little one through early math. You are your child’s first teacher. But don’t stress...your child is curious and will learn so much just through play. Here we will explain the big ideas and concepts that your preschooler will master during their early years. Many of these skills will build on each other. Other skills may seem to develop “out of order”. And that’s ok. All children learn at their own pace and time. It’s your job, as their guide, to identify the path, and where they are on it. Keep this guide as your math reference for the preschool years. Refer back to it as they grow, and mentally check off their progress. As they begin to master one idea, then you can introduce new ones. They may take off down a new road, or detour in an unexpected way. Or go back to an earlier skill. All of this is ok. Through play, your child’s innate curiosity will take off. Early math learning will come naturally. And that is amazing.

One of the first numeracy skills a child learns is rote counting. Rote counting is reciting a memorized sequence of numbers. For example, a two-year-old may be able to count from 1 to 10, or even 20, but does not yet understand what these number words signify. This is similar to a young child who can sing the ABC song but does not yet recognize letter sounds. Rote counting is linked closely to memory and language skills rather than math skills. That said, it is still an important skill for children to learn. This early counting cements a sequence of numbers in their mind that they will reference in later learning. You can promote this skill by singing all of the Number songs. Five Little Monkeys, Hickory Dickory Dock, The Ants Go Marching, and Here is the Beehive are all great choices. Even better, most of these fun songs will get your kids up and moving. Be silly with them, jump around, or add in finger play, and soon your child will be counting along with you.

Where Rote Counting is reciting a sequence of words, Rational Counting involves knowing that the number words spoken refer to quantities of things. To develop a strong understanding of quantity, and eventually how to manipulate these quantities, children need an abundance of counting experiences! When a child can count rationally, they are said to have developed One-to-one Correspondence. Rote counting and one-to-one correspondence are very different. If rote counting is memorizing the lyrics, one-to-one correspondence is understanding what those lyrics mean. One-to-one correspondence is happening when a child touches each object in a set only once and says the corresponding number word out loud. This is a much more complex skill than rote counting as it requires more than memory and knowledge of language (Platas, 2017). You can find many opportunities in your child’s daily life to illustrate one-to-one correspondence. They can place one sock inside one shoe. They can count out one napkin for each member of the family. You can ask them how many berries they would like and then count them out loud as you place each berry in the bowl (Petreshene,1985). Every time you count something together, tap or touch the objects as you count. Once a child understands this relationship, they can begin to count with true understanding.

It is during the preschool ages that children connect number words to number symbols. They begin to understand how a quantity (for example, four blocks) relates to the number word “four” and to the written numeral “4”. It is an exciting mental leap when your child realizes that numbers and letters are symbols with meaning. As your child plays counting games, you can bring these ideas together by pointing to a number line, number chart, or written numeral. Encourage your child to see written numerals as symbols. These symbols help them to express what they are thinking to others. For example, writing the symbol “5” is much quicker than drawing five blocks (Reid & Young 2017).

Cardinality refers to the quantity or the total number of items in a set. It can be determined by subitizing (for small sets) or counting (Clements, 1999). While subitizing allows a child to perceive the cardinality of small sets, counting requires them to understand that the last number in the counting sequence represents the quantity of the set. This is the end game of counting via one-to-one correspondence, and it is an important skill to develop. This is best practiced by counting. When counting, emphasize the total number of objects. “One, two, three. There are three cars here!” After success with small, easily counted sets, children will begin to generalize this knowledge and become successful with more difficult counting tasks (Fosnot & Dolk, 2001).

The concept of Conservation of Number sounds fancy but it is actually quite simple. It refers to the fact that if I have three avocados in the grocery bag and I remove them and place them on the counter, I still have three avocados. The quantity hasn’t changed just because the location has. This is a concept a child must learn. Until a child understands this, they will need to recount the items each time they move. Snack time is the perfect opportunity to explore this concept. Count out the crackers, apple slices, or cheese cubes from the bag to the countertop. Then count them as you place them onto a plate. We started with five crackers, and now all five are in the bowl! Let’s eat!

To subitize is to glance at a set of items and quickly perceive the quantity without counting. Generally, humans can subitize a group of seven randomly placed items. Young children can often subitize up to two or three items without being taught to do so. Pictured below is a group of dots. Quickly glance at the dots before continuing on. Ready? GO! How many dots did you see? How long did you need to look before a number came to mind? If you have ever played a board game, you likely had the correct number in under a second. Even if you’re not a game player, I bet the answer came to you quickly. This skill is called Subitizing (soo-ba-ti-zing). To practice subitizing, help your child see patterns. Play board games or dominoes together. Count out two animals, two people, and two cars and talk about how each set contains two items. Their brain will soon learn what two looks like, and subitizing will come naturally as a result.

Ordinality is just a fancy word for first, second, third, and so forth. Use these words during day-to-day activities and your young child will quickly catch on. Once my daughter learned what first meant, she couldn’t get enough of being first. “I got to the front door first!” Use this excitement to also explore what comes AFTER first. If they are first through the door you can ask, “If you were first, then what was I?” They might giggle and say, “You were last!” Haha. Encourage them to learn the corresponding ordinal as well. “You were first and I was second!” If you have a large family, you have even more learning opportunities!

Composing and Decomposing numbers describes the ability to recognize that numbers, or sets of objects, can be combined or separated to make new numbers. This is a great early step into fractions. Children learn that a whole is made up of smaller parts and that those parts are each smaller than the whole. For example, if there are 4 paintbrushes and 3 are being used, only 1 paintbrush is left. Your child begins to recognize that smaller numbers are “hiding inside” larger numbers. In our example, 1 and 3 are hiding inside 4 (Reed & Young 2017). Kontu’s magnetic STEM Blocks are a great way to illustrate this idea. Take a full 4-tray and an empty 3-tray. Hold the empty tray above the 4-tray, and clack! Three blocks magically move to the new tray, leaving one behind. You can then place each block back in the 4-tray, counting on from one to four.

Much of what we’ve covered so far centers around counting. But early math is so much more! Spatial Reasoning is an important skill, critical for building a structure, navigating our world, or sculpting a work of art. Spatial abilities include thinking about how objects look from different angles and how objects fit together. Spatial language is used to understand how objects relate to each other. You might say “the car is inside the garage” or “the bird is in the tree behind the fence, not the one in front.” (Eason & Levine, 2017). How can you help your child learn spatial words? Use them! Kids love spatial play: puzzles, stacking, and building blocks! You can tell your child to put all of the small objects in a large bowl or have them go under the bridge. You can also set up a scavenger hunt with clues using plenty of spatial words. By encouraging both boys and girls to play with blocks and puzzles from an early age, and by providing spatial language, parents can support their child’s spatial thinking (Casey, 2008).

The CPA (Concrete-Pictorial-Abstract) approach was developed by a Singaporean Mathematics Professor for teaching early math. He suggested three steps necessary for students to develop a complete understanding (Leong, 2015). This approach digs deeper into the “why,” giving the child a path to fully comprehend mathematical ideas. The concept of Kontu was inspired by the CPA approach. The three steps are illustrated by Kontu’s wooden blocks, cards, and activities. First, the CPA approach introduces concepts in a concrete and tangible way. This step is learning by doing. Manipulatives, or math toys and tools, are the perfect choice during this stage. Kontu’s magnetic blocks invite playful exploration. They prompt questions that encompass the skills featured in the guide. Using tangible, everyday objects gives math meaning and purpose. All while keeping it fun and engaging. Next is the pictorial stage – the visual part of the approach. In this stage, a child makes the psychological association between the physical objects and the numbers themselves. What does three look like? What is the “three-ness” of three? Kontu’s trays and bits provide a visual way for children to understand how 2 + 1 makes 3. Once the cards are introduced, the tactile knowledge they have gained with the blocks is represented again, this time in purely visual form, with iconic pictures of the trays and bits. Finally, there is the abstract stage. This is where a child can learn to use the digits and operational symbols (ex.1, 2, 3, +, -, =). On the opposite side of the Kontu cards are the corresponding numeric symbols, representing quantity in abstract form. The activity cards then help cement this knowledge. Using Kontu, you and your child can explore all three stages of the CPA approach in a fun and engaging way. With Kontu, math comes to life!

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Casey, M. B., Andrews, N., Schindler, H., Kersh, J. E., Samper, A., & Copley, J. The development of spatial skills through interventions involving block building activities. Cognition and Instruction, 26, 269–309. 2008. Clements, Douglas H. Subitizing: What Is It? Why Teach It? Teaching Children Mathematics. 1999. Eason & Levine. Spatial Reasoning: Why Math Talk is More Than Numbers. dreme.stanford.edu/news/spatial-reasoning-why-math-talk-about-more-numbers. 2017 Fosnot, C., & Dolk, M. Young mathematicians at work: Constructing number sense, addition, and subtraction. Portsmouth, NH: Heinemann. 2001. Leong, Y. H., Ho, W. K., & Cheng, L. P. (2015). Concrete-Pictorial-Abstract: Surveying its origins and charting its future. The Mathematics Educator, 16(1), 1-18. Retrieved from http://math.nie.edu.sg/ame/matheduc/tme/tmeV16_1/TME16_1.pdf Platas, Linda M. Counting on Counting, prek-math-te.stanford.edu/ counting/counting-on-counting. 2017. Reed & Young. Play Games, Learn Math! Explore Numbers and Counting with Dot Card and Finger Games. www.naeyc.org/resources/pubs/tyc/ oct2017/play-games-learn-math-explore-numbers. 2017. Petreshene, S. S. Mind joggers! 5 to 15-minute activities that make kids think. West Nyack, NY: The Center for Applied Research in Education, Inc.1985.