Preschool math lessons: A developmental guide for the science-minded parent

© 2008 – 2022 Gwen Dewar, Ph.D., all rights reserved

Preschool math lessons don't take to be irksome. They don't even take to focus on counting.

Here I review the highlights of research about early mathematics education, along with specific tips for creating mathematical experiences that are playful and stimulating. I also nowadays some opens in a new windowresearch-inspired number activities and opens in a new windowmath games designed to assist preschoolers hone their opens in a new window number sense.

The payoff? By sharing these experiences, you become to watch your child's listen at work. And your child gets to learn about numbers through play and exploration.

It'due south approach that works. When researchers used opens in a new windowfun lath games to teach preschool math concepts, children made lasting improvements in their mathematical ability (Whyte and Bull 2008; Ramani and Siegler 2008).

Such improvements may bode well for future accomplishment. An analysis tracking thousands of English-speaking students found that kids who entered kindergarten with a stiff grasp of

• counting
• relative magnitudes, and
• ordinality (sequencing magnitudes)

achieved better math scores in the later years.

Moreover, these preschool math skills were more predictive of full general scholastic accomplishment than were language, attention, or social skills (Duncan et al 2007).

That doesn't mean that preschool math lessons cause improve scholastic achievement. Just it suggests that preschool math power is an important bellwether of a child'south scholastic training.

So let's get downwardly to business organisation. How tin we create preschool math lessons that are stimulating for kids and their teachers?

Empathise that number sense is distinct from a cognition of counting

Preschool math lessons oft emphasize counting, and for proficient reason. Agreement the counting arrangement is a prerequisite for learning nigh the number line. Information technology likewise helps kids grasp the concept of improver.

Just it's important to realize that number sense doesn't depend on linguistic communication.

In a way, this shouldn't surprise united states. After all, even nonhuman animals take reason to keep rail of quantity.

Which tree bears more fruit?

If three predators hide behind a rock, and one walks away, how many are left?

Studies show that all sorts of non-linguistic animals-—birds, rats, monkeys—-tin can solve such problems (Dehaene 1999).

And inquiry also suggests that human children can perform bones mathematical tasks without knowledge of number words.

Case in signal: Recent research conducted by cognitive neuroscientists on kids who speak simply Walpiri or Anindilyakwa, two native Australian languages (Butterworth et al 2008).

These languages include number words for but 3 numerosities–"1," "two," and any imprecise quantity that is "more than than ii."

Yet 4- to seven-year old speakers of these languages performed besides or better than English speakers when they were asked to

• briefly examine a pocket-size ready of tokens and then assemble an identical gear up of tokens from retentivity

• listen to a series of up to 7 taps and and so place the corresponding number of tokens on a mat

• spontaneously subdivide a set of 6 or 9 items into three equal sets when they were told to "share" these items amid three toy bears

• briefly observe ii small-scale sets of tokens and get together a third set of tokens that represented the sum

Again, these kids knew no words for specifying precise quantities of more than two.

The implications?

Kids can larn a lot about numbers without knowing how to count. Preschool math lessons tin extend to activities that don't require counting at all.

In fact, enquiry suggests that kids demand to acquire a lot about numbers earlier they begin to label specific quantities with counting words. We can apply this information to blueprint a variety of interesting preschool math lessons.

Assist your kid develop a stiff sense of "numerosity" and other basic math concepts

Numerosity

How many cats are in your backyard? How many hours are left before bedtime?

Psychologists use the term "numerosity" to denote the number of things in a set.

Numerosity is the conceptual bedrock for about basic math skills. Kids who don't grasp numerosity—as an abstract concept and equally an intuition well-nigh the meaning of specific magnitudes—have trouble understanding the counting system. They likewise have more difficulty with arithmetics and making measurements (Booth and Siegler 2006; Siegler and Booth 2004).

How tin we help kids learn about numerosity? Recent experiments on American beginning graders suggest that approximation activities are helpful. Show kids two sets of objects and ask them to judge which is bigger — without counting (Hyde et al 2104).

Such activities might help preschoolers, too. But very immature children take a lot more to learn. They demand to know that specific numbers signify, or map onto, specific quantities. And this understanding may improve with applied, easily-on experience with real sets (Dehaene 1999; Hirsh-Pasek et al 2003).

Consider, for instance, how everyday games can assist children acquire these crucial concepts (Butterworth 1999):

• The "1-to-one principle." How exercise y'all know if two sets have the same numerosity? Your kid tin check by matching upward the members of each set in one-to-1 correspondence. If they tin do this with nada left over, the numerosity is the same. How many? Assist you kid count when you're done. Y'all tin likewise pose a simpler, but related task to your child: Take a tea party in which each attendee (human being, stuffed animal or action effigy) gets one of each item—plate, cup, spoon, cookie, etc.
• Numerosity tin can apply to sets of annihilation . Y'all can bulldoze this signal dwelling house by having kids work with a variety of objects every bit well as intangible things, similar the number of times they hear you lot clap.
• The numerosity of a set can exist changed by add-on or subtraction. Games similar Hi Ho Red-O assist kids put this concept into practice. What happens to your tree of cherries when y'all add one cherry? Or accept ane away?

Counting

Counting skills depend on a child's grasp of numerosity, including an  agreement that (ane) each number word picks out a specific numerosity, and (ii) each item to exist counted is counted once and simply once. In improver, equally cognitive psychologists Rochel Gelman and Randy Gallistel take noted (1978) kids as well need to learn:

• That number words must be recited in the same social club (aka the "stability principle")

• That later number words in the counting sequence refer to bigger numerosities

• That the concluding word counted represents the numerosity of the set (aka the "cardinality principle")

For help teaching these concepts, see my opens in a new windowinquiry-inspired, play-based preschool math lessons and these opens in a new windowinstructions for creating your own experimentally-tested preschool board game.

---

Start preschool math lessons the right way past building on what your child already knows

Call up the birds and rats I mentioned above? Pre-linguistic humans have some math savvy, too, which means your preschooler isn't a blank slate.

Elsewhere, you tin can read more than about opens in a new windowwhat babies know nigh numbers. Only, for now, here are the highlights:

Even babies know something about very pocket-size numbers.

Experimental studies advise that 14-month one-time infants can proceed precise track of quantities upwards to 3—remembering, for instance, if a box contains 1, 2, or three balls (Feigenson and Carey 2003).

Babies too know something most the judge, relative value of different numbers. Testify babies a serial of visual displays—each featuring an array of dots—and their brains volition answer differently depending on what they see. A baby who is used to seeing displays of iv dots will perk up when you lot show her a display of 8 dots (Izard et al 2008).

In that location are limits to these abilities. For instance, babies don't understand the pregnant of counting words. And babies don't make fine distinctions between number sets. Ten-month sometime babies, who can distinguish between sets of 8 and 12 objects, do not discriminate between sets of eight and 10 objects (Xu and Arriaga 2007).

But the of import point is this: Past the time your child is 2-3 years onetime, he already knows something about tracking very pocket-sized numbers, and he understands something about "greater than" and "less than."

These findings indicate a skillful starting point for preschool math lessons:

• The starting time three numbers. Focus on learning the words for numbers 1-3 and you'll be working with your child's pre-existing number sense.
• Relative magnitudes. Y'all can assist kids sharpen their intuitive sense of "how much" a number represents by encouraging them to compare and conform sets of objects in order of relative magnitude.

Be patient

It'south ane thing to go along track of 3 objects, some other to empathise that the number term "3" refers to all sets of iii things. If your child is just starting to learn almost numbers, expect slow progress.

Enquiry suggests that a 2- or 3-twelvemonth old kid who has learned the meaning of "i" volition accept another six months to learn about "2" and three months beyond that to learn about "3."

Birthday, information technology can take kids virtually a year to really sympathize how the counting system works (Wynn 1992).

Exist set for a faster pace subsequently your child has mastered numbers upwardly to iv

One time your kid really "gets" the outset 4 numbers, he will probably notice information technology much easier to tackle college numbers (Wynn 1992).

Don't push. Learning should be spontaneous and fun.

Granted, there is some contend about whether or not information technology's a good idea to push button an academic curriculum on young children. At present, I can't find any experimental studies addressing the question. So the jury is yet out.

But I recollect it's meaning that the vast majority of human societies don't await children to sit however for formal education until they are between 5 and 7 years former. This may reflect a universal trend of brain development. The frontal lobes—-which permit us to reflect, reason, and control our impulses-—don't begin to mature until children are around 5-half-dozen years old (Eliot 2000).

Formal educational activity before this historic period may therefore be an exercise in futility, or at least frustration. And fifty-fifty if kids larn something this mode, is it worth it?

Some researchers are concerned that an overly-regimented approach to early babyhood teaching could backfire, making restless young children develop negative attitudes about school (Blakemore and Frith 2005; Diamond and Hopson 1999).

As I've written opens in a new windowelsewhere, some school kids are developing math feet as early as the commencement grade. The results can be intellectually crippling, because anxious kids are more likely to avoid math do and fall behind.

Given these concerns, I think information technology makes good sense to play it safe and avoid preschool math lessons that feel like lectures or drills. Learning about math should exist fun, and—-ideally-—should reflect your child's own spontaneous interest.

Don't presume that school is the best place to larn almost math

Some schools might practise a slap-up job presenting preschool math lessons.

Only a contempo British study suggests that even loftier-quality preschools may non foster long-term achievement in math.

According to this research, the amend predictor of long-term math achievement is the quality of a preschooler'south opens in a new windowhome learning environment.

Help unfocused, distractable kids set for kindergarten math by improving their self-control

A contempo study tracking 228 American children reports a link between early math skills and cocky-control. Three-twelvemonth-olds who scored low on executive command — the ability to regulate one's impulses and attention — had poorer math skills in kindergarten (Clark et al 2012).

Does this hateful that every preschooler with weak executive command is headed for problem with mathematics? No. But given the evidence that we can assist kids develop amend self-command, information technology seems a proficient idea to place struggling kids and invest some effort in boosting their executive control. For more data, check out my evidence-based article about opens in a new windowteaching self control.

---

References: Preschool math lessons

Blakemore SJ and Frith U.. 2005. The learning brain: Lessons for teaching. Malden, MA: Blackwell Publishing.

Booth JL and Siegler RS. 2006. Developmental and individual differences in pure numerical estimation. Developmental Psychology 41: 189-201.

Butterworth B, Reeve R, and Lloyd D. 2008. Numerical thought with and without words: Evidence from ethnic Australian children. Proceedings of the National Academy of Sciences 105(35): 13179-13184.

Clark CA, Sheffield TD, Wiebe SA, and Espy KA. 2012. Longitudinal Associations Betwixt Executive Command and Developing Mathematical Competence in Preschool Boys and Girls. Kid Dev. 2022 Sep 24. doi: 10.1111/j.1467-8624.2012.01854.x. [Epub ahead of print]

Dehaene S. 1997. The number sense: How the heed creates mathematics. New York: Oxford Academy Press.

Duncan GJ, Dowsett CJ, Claessens A, Magnuson K, Huston AC, et al. 2007. School readiness and subsequently achievement. Developmental Psychology 43(vi): 1428-1446.

Diamond MC and Hopson J. 1999. Magic Trees of the Mind : How to Nurture Your Child's Intelligence, Creativity, and Healthy Emotions from Nativity Through Adolescence. New York: Plume.

Eliot Fifty. 2000. What'south going on in there? How the encephalon and heed develop during the showtime five years of life. New York: Bantam.

Feigenson L and Carey Southward. 2003. Tracking individuals via object-files: Evidence from infants' transmission search. Developmental Scientific discipline, 6: 568-584.

Gelman R and Gallistel R. 1978. The kid's understanding of number. Cambridge, MA: Cambridge University Press.

Hirsh-Pasek K, Golinkoff RM and Eyer D. 2004. Einstein Never Used Flashcards: How Our Children Actually Larn–and Why They Need to Play More and Memorize Less. Emmaus, PA: Rodale.

Hyde DC, Khanum S, Spelke ES. 2014. opens in a new windowBrief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Noesis. 131(1):92-ten.

Izard V, Dehaene-Lambertz G, and Dehaene S. 2008. Singled-out Cerebral Pathways for Object Identity and Number in Man Infants . PLoS Biol 6(2): e11.

Ramani GB and Siegler RS. 2008. Promoting broad and stable improvements in low-income children's numerical knowledge through playing with number board games. Child Evolution 79(2):375-394.

Siegler RS and Booth JL. 2004. Evolution of numerical interpretation in young children. Child Evolution 75: 428-444.

Whyte JC and Bull R. 2008. Number games, magnitude representation, and bones number skills in preschoolers. Developmental Psychology 44(2):588-96.

Wynn K. 1992. Children's acquisition of the number words and the counting system. Cognitive Psychology 24(2): 220-251.

Xu F and Arriaga RI. 2007. Number bigotry in 10-calendar month-old infants. British Journal of Developmental Psychology (25)1: 103-108.

Content of "Preschool math lessons" terminal modified 2/14

Image of boy toddler: opens in a new windowLudmila27/wikimedia commons

farquharyesectood.blogspot.com

Source: https://parentingscience.com/preschool-math-lessons/