Preschool quantity actions

© 2008 – 2023 Gwen Dewar, Ph.D., all rights reserved

Preschool quantity actions usually contain counting, however counting alone – naming numbers in the fitting order – isn’t sufficient. Youngsters additionally must develop “quantity sense,” an intuitive feeling for the precise quantity related to a given quantity. The place does quantity sense come from, and what can we do to ensure youngsters actually be taught the idea of quantity?

Experiments counsel that even 6-month-old infants can inform the distinction between 4 cookies and eight. And 14-month-old infants appear to understand that counting tells us one thing about amount (Wang and Feigenson 2019). In order that’s a begin. What’s wanted — as youngsters become old — are hands-on experiences.

When ought to we start educating youngsters about numbers?

It’s potential to begin as quickly as your baby has developed the power to be taught a string of phrases, however it’s necessary to know that the method is gradual.

For instance, in the USA, youngsters usually start to observe verbal counting across the age of two. However they may want a lot of observe to keep away from making errors (equivalent to skipping a quantity, or getting the order incorrect). And these early learners don’t actually perceive the which means of quantity phrases.

When does this understanding lastly come collectively? It normally takes a 12 months or two after they start collaborating in quantity actions. Via repeated publicity and observe, they progressively be taught what precise portions are indicated by the phrases “one,” “two,” “three,” and “4.” Then – finally — they work out they’ll use counting to find out the numerosity of any set (Wynne 1990; LeCorre and Carey 2007; Carey and Barner 2019).

How can we assist youngsters find out about numbers?

Analysis is fairly compelling on this level: Children profit once we actively train them – introduce them to the ideas and terminology, and provides them loads of alternatives to work with numbers.

The next evidence-based quantity actions encourage youngsters to consider a number of key ideas, together with

• The secure order precept (quantity phrases should be recited in the identical order)
• The precept of accelerating magnitudes (as we rely increased, the numbers signify larger numerosities)
• The one-to-one precept of numerosity (two units are equal if and provided that their gadgets may be positioned in excellent, one-to-one correspondence)
• The one-to-one precept of object counting (every merchandise is to be counted is counted as soon as and solely as soon as)
• The cardinal precept (the final phrase counted represents the numerosity of the set)

In addition they give youngsters observe naming numbers – recognizing the verbal labels, and connecting them with the right, symbolic (Arabic) numerals.

As your baby engages in these preschool quantity actions, bear in mind this recommendation (from my information to preschool math classes):

• Begin small. It’s necessary to regulate the sport to your baby’s consideration span and developmental stage. For novices, this implies counting duties that concentrate on very small numbers (as much as 3 or 4).
• Ensure it’s enjoyable. If it’s not playful and enjoyable, it’s time to cease.
• Be affected person. It takes younger youngsters a couple of 12 months to learn the way the counting system works.

Proof-based preschool quantity actions

Your baby’s first counting actions

As famous above, most children are prepared to start verbal counting by the age of two, and one basic strategy is to recite collectively – in unison – for enjoyable.

However there are additionally methods to include counting into video games. For instance, researchers counsel that you could play “Cover and Search,” the place gamers should be taught to attend for a rely earlier than starting a search. “One…two…three…right here I come!” (Levenson et al 2022). Different concepts for combining counting with play embrace:

• a dancing sport, the place gamers should freeze till somebody has completed a short rely;
• strolling up a stair case, whereas counting every step
• shifting ahead in a room, or outside, whereas counting every step

Your baby gained’t essentially be taught what portions are related to every quantity. However they are going to be studying the secure order precept – that there’s an accurate sequence to observe. And verbal counting will pave the best way for deeper classes.

Image book-based actions for educating youngsters about utilizing counting to find out the quantity in a set

I discussed above that youngsters finally make a breakthrough of understanding: They notice that they’ll use counting to find out the precise amount of any set. For instance, in the event you ask them to pick out precisely 6 toys from a field, they may be capable to do it. “Oh…I simply must preserve amassing toys till I’ve attain a rely of six.” They’ve found out the cardinal precept.

However this breakthrough doesn’t simply occur. Research counsel that it relies upon, partially, on youngsters first gaining a concrete feeling for the quantities specified by “one,” “two,” “three,” and “4,” and being proven how we are able to use counting to examine.  And a staff of researchers – lead by Kelly Combine – have give you an fascinating strategy that folks can use at residence when they’re studying to their preschoolers.

It really works like this. Suppose you might be studying a storybook together with your baby, and also you come throughout three bears. Name consideration to the variety of bears you see, after which information your baby by way of a rely of them. “Look, I see three bears! Are you able to say it with me? Three bears. Let’s rely: One, two, three.”

Subsequent, ask your baby to repeat the method on his or her personal. “Now it’s your flip. What number of bears are there?”

Encourage your baby to carry out each components of the quantity process – counting the bears once more, and labeling the whole quantity within the set. Right here’s the suggestions you may present to ensure this occurs:

• In case your baby merely says that there are three bears, however doesn’t rely them, say, “Proper! There are three bears. Are you able to rely them?”
• In case your baby accurately labels the whole variety of bears, however makes an error whereas counting, say “Proper! There are three bears, however watch: 1, 2, 3.”
• In case your baby counts the bears accurately, however fails to label the set, say: “Proper! 1, 2, 3…So, what number of are there?”

Kelley Combine and her colleagues examined this strategy in a randomized experiment on youngsters who have been 3 ½ years outdated, together with some different strategies – like merely asking youngsters to rely objects (e.g., “Let’s rely the bears!”) or just telling youngsters about amount (“Look! This web page has three bears. Are you able to say it with me? Three bears…).

After 3 weeks of day by day coaching, the youngsters who had been randomly assigned to the mixture strategy (label first, then rely, and ask youngsters to do the identical) made important good points of their capacity to grasp and rely units bigger than 5. In truth, they have been the solely youngsters who skilled important enhancements. The researchers conclude that youngsters made progress in understanding the cardinal precept (Combine et al 2012).

Preschool quantity actions for educating the one-to-one precept of numerosity

Matching gadgets one-to-one is a surprisingly necessary mathematical idea. It’s how we show that two portions are equal. Two units comprise the identical variety of gadgets if the gadgets in every set may be matched, one-to-one, with no gadgets left over. Researchers name this the “one-to-one precept of numerosity,” and you may assist youngsters grasp the idea with these easy, preschool quantity actions.

Free play utilizing “objects with slots”

Think about a muffin tin with 6 slots, and a set of balls that match inside – one ball per opening. If youngsters play with one thing like this, will it assist them be taught to consider matching gadgets one-to-one?

Dr. Kelly Combine thought this may work, so she examined it in a randomized experiment on 30 preschoolers (3-year-olds). Half the kids got “objects with slots” to play with (e.g., 6 balls and a 6-slot muffin tin). The remaining youngsters got a double set of toys with out a container (e.g., 6 balls and 6 frog toys). The dad and mom have been instructed to encourage youngsters to play with the toys at residence, after which, 6 weeks later, the researchers examined youngsters to see if they’d improved their understanding of one-to-one matching. Children in each teams noticed enhancements, however those that performed with “objects with slots” made greater good points general (Combine et al 2011).

Recreation: Duplicate a set utilizing small tokens or counters 

Can your baby assemble a set of two gadgets? Three gadgets? Extra? To play this quantity sport, arrange two, adjoining zones on a desk high or different flat floor (equivalent to the ground). You need to use two placemats or ground mats to outline your areas. Alternatively, you might draw chalk boundaries round every zone (on a pavement), or mark the borders with colourful tape (on a carpet).

Subsequent, place a small variety of tokens in a single the zones, and ask your baby to refill the opposite zone with the identical variety of tokens. You possibly can say one thing like, “Are you able to make one other set of tokens like this one? In order that it has the identical quantity?” After your baby has made an try, rely the members of every set to see in the event that they match, and label the units as described within the earlier exercise (e.g., “1, 2, 3, 4, 5. There are 5 tokens!”)

For a variant of this sport, create a set of index playing cards, every card displaying a distinct variety of dots. Choose a card to problem your baby with, and ask her or him to create an identical set of tokens. Comply with up in the identical manner, asking your baby to rely and label the set.

Tip for beginning out: Start with very small numbers. It might probably take nearly a 12 months for a two- or three-year-old to essentially perceive how the counting system works, so don’t be stunned if youthful youngsters have bother counting past “1-2-3.” Assist your baby with counting if wanted, and increase set measurement progressively as your baby’s abilities develop.

What do you have to use for tokens? For youngsters below the age of three years, it’s necessary to decide on one thing that gained’t pose a choking hazard. In line with the U.S. Shopper Product Security Fee, a ball-shaped object is unsafe for youngsters below 3 years if the merchandise is smaller than a 1.75″ diameter golf ball. Different objects are unsafe if they’ll match inside a tube with a diameter of 1.25″ inches. Items out of your toddler’s constructing block set may do the job.

Additionally, attempt to use plain-looking tokens. You may assume that little toy frogs or spiders would make counting extra enjoyable. However researchers have discovered that younger youngsters are inclined to get distracted by these particulars. Children really be taught extra from math actions once they manipulate easier, extra summary gadgets (Petersen and McNeil 2012). Plastic chips — like these used for poker or bingo — are a good selection for youngsters aged 3 and up.

Sharing on the tea get together: Dividing up tokens into equal parts

Right here is one other exercise to assist youngsters observe one-to-one matching, impressed by the analysis of Brian Butterworth and his colleagues (2008).

Select three toy creatures to play the a part of get together attendees, and have your baby set the desk for them. Then give your baby a set of “goodies” (tokens or actual edibles) to share with the get together friends. The full variety of goodies must be a a number of of three, so your baby can distribute all of the gadgets equally and don’t have any leftovers.

In case your baby makes a mistake and offers one creature too many tokens, you may voice the a part of one of many different characters and complain. It’s also possible to take turns taking part in the function of the tea get together host and intentionally make a mistake. Ask on your baby’s assist. Did somebody get too many tokens? Or not sufficient? Have your baby repair it.

Actions for educating the precept of accelerating magnitudes

For these preschool quantity actions, use playing cards like these described the earlier part. You need to use them in 3 ways.

Recreation: Guess the fitting order

To play this sport, shuffle the playing cards, after which ask your baby to put them, aspect by aspect, in a sequence of accelerating magnitude.

For youngsters who haven’t but discovered to rely, use playing cards that change by a considerable quantity, e.g., 3, 6, 10, and 15. For youngsters with rising counting abilities, use playing cards that differ by a single dot, and have youngsters guess first, then examine their solutions by counting. 

What’s the purpose of all this guesswork? Experiments present that even infants can spot variations this huge, and working towards these duties could assist youngsters hone their estimation skills — skills that are important for future arithmetic achievement.

For instance, in a single research, researchers examined five-year-olds with computer-based variations of those preschool quantity actions. The youngsters weren’t given sufficient time to rely; they merely took a fast look and answered primarily based on their intuitive, visible impression. Children who practiced making progressively tougher discriminations — getting correct suggestions after every try — skilled subsequent enhancements of their capacity to unravel issues utilizing symbolic numbers (Wang et al 2016).

Recreation: Guess which card has extra dots?

To play this sport, choose two playing cards, every displaying a distinct variety of dots, and present them to your baby. Which card has extra dots?

Be sure you begin with playing cards that differ by a ratio of no less than  2:1. For example, strive 1 vs. 2, 2 vs. 4, and a pair of vs. 5. It’s also possible to strive bigger numbers, like 6 vs. 12.

As your baby will get observe with these easy-to-discriminate variations, you may current her with more and more tough decisions (like 6 versus 8; and even 9 versus 10).

For a extra playful variant of the sport, you should use tokens as an alternative of playing cards, and fake they’re one thing enjoyable, like muffins. Dole out totally different quantities between you and ask, “Who has extra?” Make sure you give your baby suggestions concerning the appropriate reply.

And as youngsters turn into extra skillful, you should use your playing cards in a aggressive sport known as, “Quantity Battle” (Scalise et al 2017). See my article, “DIY Preschool math video games that assist youngsters develop ‘quantity sense’” for a full description of the principles.

Recreation: Massive guys eat extra

To play, use your playing cards, in addition to three animal toys or dolls of various measurement — small, medium, and enormous. Fake the toys are get together friends, and the gadgets on the playing cards are treats. Subsequent:

1. Line up the three toys so as of measurement.
2. Current your baby with three playing cards, every card depicting a distinct variety of dots.
3. Ask your baby to present the best variety of treats to the most important toy, the second-greatest quantity to the second-largest toy, and the smallest quantity to the smallest toy.

After your baby has distributed the goodies, present nice, encouraging suggestions.  “That’s proper!” (for an accurate response), and “That’s not proper…are you able to strive once more?” (for an incorrect response).

In case you choose, you may play the sport with tokens as an alternative of playing cards. And as soon as your baby has began to learn and perceive quantity symbols, you should use playing cards that show solely Arabic numerals. This may assist youngsters observe quantity recognition.

When researchers examined related preschool quantity actions, they discovered that each dot-based and numeral-based video games helped youngsters develop higher intuitions about amount. However youngsters who performed the Arabic numeral model of the sport skilled larger progress in fundamental arithmetic abilities (Honoré and Noël 2016).

Fake play actions for educating youngsters about quantity symbols

What else can we do to foster studying about quantity symbols – just like the Arabic numeral “3”? Of their evaluate of instructional math video games for preschoolers, Julie Sarama and Douglas Clement (2009) remind us that even unstructured, fake play can flip into quantity recognition actions.

As an instance, they cite an instance of two preschoolers engaged in fantasy role-playing a couple of “Dinosaur Store.” One participant acted because the store keeper (providing toy dinosaurs on the market). The opposite participant, the shopper, had cash (a deck of playing cards, with every displaying a distinct, Arabic numeral, a corresponding variety of dots). The client would buy quite a lot of dinosaurs by handing over a card: Give the store keeper a card with the quantity “5” on it, and it’s best to obtain 5 dinosaur toys in return. Then gamers may rely to verify an correct transaction.

So video games of shopping for and promoting could assist youngsters find out about quantity symbols. And so, too, may these role-playing video games:

• Making pizzas. Utilizing cardboard disks and paper toppings, ask your pizza chef to make pizzas to order: Give the chef a quantity card, and have the chef create a pizza with the corresponding variety of toppings. When the pizza is completed, the chef and buyer can examine for accuracy by counting the toppings and evaluating this with the numeral on the cardboard (Clements and Sarama 2009).
• Delivering the Mail. Arrange a “avenue” with a sequence of various “houses” arrayed alongside it. Mark every residence with a “resident” (a toy or doll), in addition to a quantity card displaying the specified handle. Ensure the addresses are lined up in numerical order (1, 2, 3…). Then ask your baby to ship the “mail” – letters and packages marked with the specified addresses.

A puppet sport for educating the one-to-one precept of counting objects, and the precept of cardinality

Right here’s one other “one-to-one” precept — this time the one-to-one precept of counting objects. Children must be taught that every merchandise in a sequence is counted as soon as and solely as soon as. In addition they must be taught the precept of cardinality, the concept that the final phrase in our rely represents the numerosity of a set.

Youngsters be taught these concepts by way of observe. However they could additionally be taught by correcting others who make errors. In a single research, researchers requested preschoolers to observe–and assist–an incompetent puppet rely a set of objects (Gelman et al 1986). The puppet would sometimes violate the one-to-one precept by double-counting (e.g., “one, two, three, three, 4…). He additionally generally skipped an object or repeated the incorrect cardinal worth.

Children ranging in age from 3 to five have been fairly good at detecting these violations. So your baby might need enjoyable correcting your personal goofball at residence.

What in case your baby doesn’t discover an error? Right the puppet your self. And both manner, ask your baby to elucidate what went incorrect. In one other, related research, researchers discovered that preschoolers didn’t make conceptual progress until they have been requested to elucidate the puppet’s errors (Muldoon et al 2007). For a dialogue of how self-explanation could make preschool quantity actions and different instructional experiences extra invaluable, see this Parenting Science evaluate of the proof.

One other puppet-based sport which may assist preschoolers develop intuitions about addition and subtraction

Younger youngsters have a protracted solution to go earlier than they’re able to carry out fundamental arithmetic calculations like “2 +3 = 5,” or “7 – 3 = 4.” However we would be capable to construct their intuitions about addition and subtraction by asking the fitting questions. A method to do that is by taking part in a sport.

You start by pretending that somebody (a puppet or toy character) has baked some “muffins” (a set of tokens). Ask your baby to rely the muffins (serving to your baby with this if wanted).  

Subsequent, have the puppet bake yet another cake and add it to the set. Are there extra muffins or fewer muffins now? Ask your baby, and supply her or him with appropriate suggestions afterwards.

You possibly can strive the identical factor with subtraction by having the puppet “eat” a cake. And fluctuate the sport by including or subtracting different small quantities, like two or three.

Ought to we count on youngsters to give you correct solutions? Not obligatory — particularly not if they’re below the age of three years (Izard et al 2014). However the expertise of predicting and checking is effective, and even when youngsters get the exact quantity incorrect, they do an excellent job developing with cheap guesses. When researchers requested 3-, 4- and 5-year-olds to carry out these duties, they discovered that 90% of the guesses have been in the fitting route (Zur and Gelman 2004).

Board video games that train preschoolers concerning the quantity line

As your baby begins to grasp the primary few quantity phrases, you may also check out this DIY board sport for educating preschoolers concerning the quantity line. Together with full directions for creating this sport — a sport examined by researchers — additionally, you will discover a dialogue of whether or not youngsters can profit from taking part in the normal sport, Chutes and Ladders.

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References: Preschool quantity actions

Butterworth B, Reeve R, and Lloyd D. 2008. Numerical thought with and with out phrases: Proof from indigenous Australian youngsters. Proceedings of the Nationwide Academy of Sciences 105(35): 13179-13184.

Carey S and Barner D. 2019. Ontogenetic Origins of Human Integer Representations. Traits Cogn Sci. 23(10):823-835.

Clements DH and Sarama J. 2009. Studying trajectories in early arithmetic—sequences of acquisition and educating. Encyclopedia of Language and Literacy Improvement (pp. 1–7). London, ON: Canadian Language and Literacy Analysis Community.

Gelman R and Gallistel C. 1978. The kid’s understanding of quantity. Harvard College Press.

Gelman R, Meck E, and Merkin S. 1986. Younger youngsters’s numerical competence. Cognitive Improvement 1(1): 1-29.

Honoré N and Noël MP. 2016. Bettering Preschoolers’ Arithmetic by way of Quantity Magnitude Coaching: The Influence of Non-Symbolic and Symbolic Coaching. PLoS One. 11(11):e0166685.

Izard V, Streri A, Spelke ES. 2014. Towards precise quantity: younger youngsters use one-to-one correspondence to measure set identification however not numerical equality. Cogn Psychol. 72:27-53.

Le Corre M and Carey S. 2007. One, two, three, 4, nothing extra: An investigation of the conceptual sources of the verbal counting rules. Cognition.  105:395–438. 

Levenson ES, Barkai R, Tirosh D, Tsamir P. 2022. Exploring adults’ consciousness of and strategies for early childhood numerical actions. Educ Stud Math. 109(1):5-21.

Combine KS, Moore JA, and Holcomb E. 2011. One-to-one play promotes numerical equivalence ideas. Journal of Cognition and Improvement 12(4): 463-480.

Combine KS, Sandhofer CM, Moore JA, and Russell C. 2012. Acquisition of the cardinal phrase precept: The function of enter. Early Childhood Analysis Quarterly 27(2): 274–283. 

Muldoon KP, Lewis C, Francis B. 2007. Utilizing cardinality to evaluate portions: the function of social-cognitive battle in early numeracy. Developmental Psychology 10(5):694-711.

Park J and Brannon EM. 2013. Coaching the Approximate Quantity System Improves Math Proficiency. Psychol Sci. 2013 Oct;24(10):2013-9.

Petersen LA and McNeil NM. 2013. Results of Perceptually Wealthy Manipulatives on Preschoolers’ Counting Efficiency: Established Data Counts. Little one Dev. 84(3):1020-33.

Sarama J and Clements DH. 2009. Constructing Blocks and Cognitive Constructing Blocks: Taking part in to Know the World Mathematically. American Journal of Play. 1: 313-337.

Scalise NR, Daubert EN, Ramani GB. 2017.  Narrowing the Early Arithmetic Hole: A Play-Based mostly Intervention to Promote Low-Earnings Preschoolers’ Quantity Abilities. J Numer Cogn. 3(3):559-581.

Wang JJ and Feigenson 2019.  Infants acknowledge counting as numerically related. Developmental Science 22(6): e12805.

Wang JJ, Odic D, Halberda J, Feigenson L. 2016. Changing the precision of preschoolers’ approximate number system representations changes their symbolic math performance. J Exp Little one Psychol. 147:82-99.

Wynn Ok. 1990. Youngsters’s understanding of counting. Cognition. 36(2):155-93.

Zur O and Gelman R. 2004. Younger youngsters can add and subtract by predicting and checking. Early childhood Analysis Quarterly 19: 121-137.

Content material of “Preschool quantity actions” final modified 3/2023. Parts of the textual content derived from an earlier model of the article, written by the identical creator.

Picture credit for “Preschool quantity actions”

title picture of toys with plates and cups copyright Parenting Science

photos of provides for preschool quantity actions copyright Parenting Science

experimental picture of bears and baggage from: Honoré N and Noël MP. 2016. Bettering Preschoolers’ Arithmetic by way of Quantity Magnitude Coaching: The Influence of Non-Symbolic and Symbolic Coaching. PLoS One. 11(11):e0166685. Picture seems right here courtesy Creative Commons Attribution License

picture of puppet copyright Parenting Science