# Maths for tiny people?

August 13, 2011 8:32 AM Subscribe

How to teach math to a 3.5 year old?

Posting for a friend:

A friend of mine has asked me to give maths lessons to his 3.5 year old son, and I'd like to help - but I don't know where to start.

What sort of "math" is it reasonable to try to teach to someone so young? And what would be the best way of teaching it? Are there maths games I could use?

Thanks in advance!

Posting for a friend:

A friend of mine has asked me to give maths lessons to his 3.5 year old son, and I'd like to help - but I don't know where to start.

What sort of "math" is it reasonable to try to teach to someone so young? And what would be the best way of teaching it? Are there maths games I could use?

Thanks in advance!

"Here are five cheerios. How many are there if we eat three?" That sort of thing is always fun for small children, and you just add complications as they understand better. Sorting and grouping is a start, and then you can begin showing them the foundations of multiplication. (With patterns and groups. "How much is three groups of five?")

Blocks, toys, and other colored manipulatives are wonderful for this sort of thing.

posted by RedEmma at 8:48 AM on August 13, 2011 [1 favorite]

Blocks, toys, and other colored manipulatives are wonderful for this sort of thing.

posted by RedEmma at 8:48 AM on August 13, 2011 [1 favorite]

I'm a former math major and parent of a 4 year old, though I have no particular expertise in child education.

3.5 is about the right age to learn how to count, including the numbers up to 20 or so and maybe beyond. Songs are good for this. Playing with Lego is also great fun, and gives the child a hands-on sense of different numbers and sizes. I don't think you need to make explicit lessons out of it; just play and they will be learning things through their hands.

Names of shapes and shape sorting are also appropriate, though for whatever reason my own daughter hasn't shown much interest in them compared to numbers and counting.

posted by mbrubeck at 8:48 AM on August 13, 2011

3.5 is about the right age to learn how to count, including the numbers up to 20 or so and maybe beyond. Songs are good for this. Playing with Lego is also great fun, and gives the child a hands-on sense of different numbers and sizes. I don't think you need to make explicit lessons out of it; just play and they will be learning things through their hands.

Names of shapes and shape sorting are also appropriate, though for whatever reason my own daughter hasn't shown much interest in them compared to numbers and counting.

posted by mbrubeck at 8:48 AM on August 13, 2011

Reader Rabbit Preschool - the variety pack has math lessons and is available in a variety of formats.

Also, Cuisenaire rods are fun because they are like little blocks, but designed to teach fractions and such.

You might want to look at the requirements for kindergarten. They ask that children know their ABC's, how to count to 10, etc. And then make that your goal but some kids just don't have the attention span at that age. Making it a game helps, as long as they're fed and well rested.

posted by Marie Mon Dieu at 8:48 AM on August 13, 2011

Also, Cuisenaire rods are fun because they are like little blocks, but designed to teach fractions and such.

You might want to look at the requirements for kindergarten. They ask that children know their ABC's, how to count to 10, etc. And then make that your goal but some kids just don't have the attention span at that age. Making it a game helps, as long as they're fed and well rested.

posted by Marie Mon Dieu at 8:48 AM on August 13, 2011

Great suggestions already, so I'm just gonna add one: Try to point out math in every day life situations - numbers on signs, tv channels, simple recipes (like jello simple at 3.5 years, how many cups of water?), types of measurements.

Showing your child how important math is (similar to a parent reading/modeling reading to show how important reading is) will help the child develop an appreciation for it.

posted by NoraCharles at 9:05 AM on August 13, 2011 [1 favorite]

Showing your child how important math is (similar to a parent reading/modeling reading to show how important reading is) will help the child develop an appreciation for it.

posted by NoraCharles at 9:05 AM on August 13, 2011 [1 favorite]

Great suggestions! I would add, especially since you have no training in this area, that you read "How Children Fail" by John Holt. I'm sure you could get it from/through your local library. He was a math teacher, and spent a lot of time observing how children learned -- and didn't learn -- from standard math teaching. The reason I suggest the book is that he talks in detail about how the teacher's attitude decides whether the child focuses on the numbers themselves or on getting the right answer for the teacher. It was an eye-opener for me, and I still have to be careful when I try to "teach" something. Even to a toddler.

Numbers are great to fool around with. You don't have to worry about their feelings, they don't depend on somebody's interpretation, they just dance around, completely themselves. (At least until you get into the mystical parts....)

posted by kestralwing at 9:27 AM on August 13, 2011 [5 favorites]

Numbers are great to fool around with. You don't have to worry about their feelings, they don't depend on somebody's interpretation, they just dance around, completely themselves. (At least until you get into the mystical parts....)

posted by kestralwing at 9:27 AM on August 13, 2011 [5 favorites]

Maybe you could try counting as high as the child can, and then count backwards from there, and then count by 2's and by 3's, etc.

posted by losvedir at 9:30 AM on August 13, 2011

posted by losvedir at 9:30 AM on August 13, 2011

Big second to NoraCharles' suggestion about math in every day situations. My two-and-half year old loves games like run-to-and-count-the-diamond-paving-stones as we walk from the car into the store.

I know mine isn't ready for counting backwards, but at three and half that might not be unreasonable.

From my (albeit brief) experience teaching ESL to small kids, I think key thing (especially for a boy kiddo) is that it needs to be physically active. Moving his whole body from object to object - big silly gestures with each count (stomping on the item being counted, whacking it with his butt, etc). I think little girls have more patience for sitting in-once-place activities like coloring or organizing tangram pieces. (I'm not trying to force any kind of gender role thing here - I'm pretty certain these kinds of differences in what activities maintain focus are well researched).

posted by colin_l at 9:48 AM on August 13, 2011

I know mine isn't ready for counting backwards, but at three and half that might not be unreasonable.

From my (albeit brief) experience teaching ESL to small kids, I think key thing (especially for a boy kiddo) is that it needs to be physically active. Moving his whole body from object to object - big silly gestures with each count (stomping on the item being counted, whacking it with his butt, etc). I think little girls have more patience for sitting in-once-place activities like coloring or organizing tangram pieces. (I'm not trying to force any kind of gender role thing here - I'm pretty certain these kinds of differences in what activities maintain focus are well researched).

posted by colin_l at 9:48 AM on August 13, 2011

I'm sorry the 3.5 year old has been put in the context of having "lessons." From my experience that's sort of like putting your cat down in front of you and expecting them to pay attention.

There's two questions here: HOW to teach and WHAT to teach.

For the HOW: you can either spend your time trying to teach him/her to sit still and pay attention or you can basically play with them i.e. babysit.

For the WHAT: I've found kids this age are naturally curious about numbers and counting. So, any situation, ask "How many" and then count with them. Until they can count confidently addition and subtraction are not going to mean much to them. For fun you could spend some time pointing out different shapes: square, circle, etc. The idea is to build awareness rather than a specific skill.

Honestly, getting number sense can take awhile and I would have little interest in trying to force a 3.5 year old to count if it wasn't interesting to them... so, good luck. Again, it takes years of training before kids are able to sit still and pay attention to a teacher (honestly, many kids in the US never get that far.) This can be a good thing or a bad thing, but a 3.5 yr old will not have this skill and is not going to have this skill overnight or even in a few weeks.

I would be worried about your friend's expectations from these "lessons."

posted by ennui.bz at 10:13 AM on August 13, 2011 [3 favorites]

There's two questions here: HOW to teach and WHAT to teach.

For the HOW: you can either spend your time trying to teach him/her to sit still and pay attention or you can basically play with them i.e. babysit.

For the WHAT: I've found kids this age are naturally curious about numbers and counting. So, any situation, ask "How many" and then count with them. Until they can count confidently addition and subtraction are not going to mean much to them. For fun you could spend some time pointing out different shapes: square, circle, etc. The idea is to build awareness rather than a specific skill.

Honestly, getting number sense can take awhile and I would have little interest in trying to force a 3.5 year old to count if it wasn't interesting to them... so, good luck. Again, it takes years of training before kids are able to sit still and pay attention to a teacher (honestly, many kids in the US never get that far.) This can be a good thing or a bad thing, but a 3.5 yr old will not have this skill and is not going to have this skill overnight or even in a few weeks.

I would be worried about your friend's expectations from these "lessons."

posted by ennui.bz at 10:13 AM on August 13, 2011 [3 favorites]

Lots of excellent suggestions here, especially all the games you can play with counting and sorting objects. I would ask the parent what goal of these lessons is. Is it to prep the child for kindergarten, or does the parent have some specific skills in mind? For kindergarten prep I think in a public school just counting to ten is all that is required. Try and figure out if the parent's goals are realistic for a 3.5 year old.

posted by Joh at 10:35 AM on August 13, 2011

posted by Joh at 10:35 AM on August 13, 2011

Old fashioned drill works better than you might think. My elderly aunt, a former one room school teacher, used to be infuriated that a school could leave a child behind. She claimed that any kid could be taught to read, write and compute at an early age. Having seen her at work, I believe her. Drilling and repetition until the basics are second nature -- I've seen her make it work at a surprisingly early age. A 2-ish-year old can be taught to count confidently.

She was so damn certain that her methods work that her kids believed it too. She'd ask my 2-year old nephew's son arithmetic questions, he'd get them wrong or sit silently confused and she'd gleefully tell him that he knew the answer already and just needed to remember how it was done. Two cheerios here plus three cheerios there? One, two, three, four, five! You've got it! It was like watching a live-action reenactment of Plato's

You may need to

posted by justsomebodythatyouusedtoknow at 10:47 AM on August 13, 2011 [4 favorites]

She was so damn certain that her methods work that her kids believed it too. She'd ask my 2-year old nephew's son arithmetic questions, he'd get them wrong or sit silently confused and she'd gleefully tell him that he knew the answer already and just needed to remember how it was done. Two cheerios here plus three cheerios there? One, two, three, four, five! You've got it! It was like watching a live-action reenactment of Plato's

*Meno*. She'd do that over and over, day after day until it became true. The tyke became a confident counter before he'd actually learned to count.You may need to

*be*my aunt to pull this off. Her genuinely cheerful, singsong tone made drill sound like a game despite the fact that it was nothing of the sort. She used to hold my 2-year old nephew's son firmly in her lap to keep him still while she chanted numbers with him (at him), and somehow made it more like a hug than like a prison. Perhaps that was the most valuable lesson she was teaching, a habit of paying attention that would serve the kid through all future schooling. Sit still, concentrate, learn.posted by justsomebodythatyouusedtoknow at 10:47 AM on August 13, 2011 [4 favorites]

Good suggestion to find out what the parents expect at this age. In preschool they talk about "pre-math" skills. I would make sure everything is a game and fun for that particular child. Like monkeytoes suggested, pattern blocks are good, lacing beads to make patterns, you can sort anything (legos, beads, m&ms). I'm thinking the child is a bit young, but games like Chutes and Ladders and Cariboo teach counting. Cooking together can teach math. Also, this is a bit more advanced but having a measuring tape and measuring things. But again, I would only do the activities that the child feels motivated to do and that feels like play.

posted by hellochula at 10:59 AM on August 13, 2011

posted by hellochula at 10:59 AM on August 13, 2011

"Old fashioned drill works..."

Searching for "rote" on this page will save me from typing out the usual problems with it. It works -- it gets them to memorise it. But at a cost. "Such a textbook-driven curriculum may contribute to students' falling behind, failing to see how math relates to their lives, and depending upon rote memory rather than reasoning. By contrast, beginning a lesson with a real-life situation, continuing with guided exploration of various mathematical techniques, and culminating with students applying those techniques to achieve solutions will capture students' interest and attention."

Nth using real-life situations. Manipulatives... Cuisenaire rods. My mother had a little thing where she'd give me a jar of pennies, and little cards with numbers 1-to-? on them; I had to place the right number of pennies underneath each card, and if I did it right,

I taught my nearly-4yo larger numbers in part via supermarket flyers. What shall we buy? Oh? And how much do they cost? (This also leads to a discussion of weights and measures, of course.) I also ask her to tell me what page the story/chapter she wants out of a book is on in the table of contents. Fractions should come out of everyday life, too. "I'm going to cut this in half -- or should I cut it in quarters?" stuff.

Lauri makes wonderful stuff and if you want something to reinforce real-world math you could do worse than this Lauri Toys Early Learning Center Kit- Math Discovery

I agree that the "lessons" idea at 3.5 is a bit dodgy -- which is not to suggest that I completely disagree; clearly I am thrilling to getting my own kid into math. But I have been doing it strictly on the sly. Now she enjoys it and likes to boast "I know math!" whenever she figures out something new; I have not done any 1+1=2 1+2=3 1+3=4 dry stuff with her, and she seems to be figuring out the rudiments of addition and subtraction quite organically, which I find quite exciting. A book or two on "unschooling" is nice to read for reassurances and tips on how to guide that sort of 'organic' learning along. (If the parent is dead set on strict lessons with drills, Under Pressure: Rescuing Our Children from the Culture of Hyper-Parenting has some very good chapters on education that may be of interest to parent.)

posted by kmennie at 11:05 AM on August 13, 2011 [1 favorite]

Searching for "rote" on this page will save me from typing out the usual problems with it. It works -- it gets them to memorise it. But at a cost. "Such a textbook-driven curriculum may contribute to students' falling behind, failing to see how math relates to their lives, and depending upon rote memory rather than reasoning. By contrast, beginning a lesson with a real-life situation, continuing with guided exploration of various mathematical techniques, and culminating with students applying those techniques to achieve solutions will capture students' interest and attention."

Nth using real-life situations. Manipulatives... Cuisenaire rods. My mother had a little thing where she'd give me a jar of pennies, and little cards with numbers 1-to-? on them; I had to place the right number of pennies underneath each card, and if I did it right,

*the pennies were mine.*This was very exciting at the time...I taught my nearly-4yo larger numbers in part via supermarket flyers. What shall we buy? Oh? And how much do they cost? (This also leads to a discussion of weights and measures, of course.) I also ask her to tell me what page the story/chapter she wants out of a book is on in the table of contents. Fractions should come out of everyday life, too. "I'm going to cut this in half -- or should I cut it in quarters?" stuff.

Lauri makes wonderful stuff and if you want something to reinforce real-world math you could do worse than this Lauri Toys Early Learning Center Kit- Math Discovery

I agree that the "lessons" idea at 3.5 is a bit dodgy -- which is not to suggest that I completely disagree; clearly I am thrilling to getting my own kid into math. But I have been doing it strictly on the sly. Now she enjoys it and likes to boast "I know math!" whenever she figures out something new; I have not done any 1+1=2 1+2=3 1+3=4 dry stuff with her, and she seems to be figuring out the rudiments of addition and subtraction quite organically, which I find quite exciting. A book or two on "unschooling" is nice to read for reassurances and tips on how to guide that sort of 'organic' learning along. (If the parent is dead set on strict lessons with drills, Under Pressure: Rescuing Our Children from the Culture of Hyper-Parenting has some very good chapters on education that may be of interest to parent.)

posted by kmennie at 11:05 AM on August 13, 2011 [1 favorite]

I work with kindergarteners, one of whom is 3.5. Barring his ability to pay attention to anything for a long period of time, I work with him on counting to 20, writing and identifying numerals, using manipulatives like little toys to count to a certain number, and understanding cardinality.

Put everything in terms of food and you'll be golden.

posted by These Birds of a Feather at 11:30 AM on August 13, 2011

Put everything in terms of food and you'll be golden.

posted by These Birds of a Feather at 11:30 AM on August 13, 2011

When my grandmother used to take care of me as a small child, we would do lots of different puzzles. We would do sorting games. Sort blocks by color. Look at the groups you've formed. Now sort the blocks by size. Look at those groups. Stuff like that. I now have a PhD in mathematics, and my grandmother likes to brag that it was her actions with me while I was young that set me on that path. =)

G.H. Hardy once said "A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with

posted by King Bee at 11:53 AM on August 13, 2011

G.H. Hardy once said "A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with

*ideas*." Play with physical objects and make patterns. Do not try to teach arithmetic to the child. Not only might it be detrimental to the child who might not have fully grasped the concept of abstract numbers yet, it will be painful for both of you if he fails. It will be like trying to train bananas to clean your toilet for you.posted by King Bee at 11:53 AM on August 13, 2011

"Drill...It works -- it gets them to memorize it."

I agree that the old methods fail more often than they work. For that reason, I don't think I could recommend them. However, I've seen that a skillful teacher can make them work, producing genuine understanding. Agreed, memorizing numbers is useless, but building habits of paying attention is golden.

The idea of modern methods is to start with stuff that kids find interesting and stretch that interest to abstract subjects, correct? Yeah, that works, but such methods can also be misapplied. Abstract mathematics is artificial and unnatural. Learning it requires reshaping the mind, and we should not assume that a kid's natural interests will drift them into it.

No method is perfect. The ability of a teacher to pass on a passion for the subject matter is probably more important than the curriculum used.

posted by justsomebodythatyouusedtoknow at 12:17 PM on August 13, 2011

I agree that the old methods fail more often than they work. For that reason, I don't think I could recommend them. However, I've seen that a skillful teacher can make them work, producing genuine understanding. Agreed, memorizing numbers is useless, but building habits of paying attention is golden.

The idea of modern methods is to start with stuff that kids find interesting and stretch that interest to abstract subjects, correct? Yeah, that works, but such methods can also be misapplied. Abstract mathematics is artificial and unnatural. Learning it requires reshaping the mind, and we should not assume that a kid's natural interests will drift them into it.

No method is perfect. The ability of a teacher to pass on a passion for the subject matter is probably more important than the curriculum used.

posted by justsomebodythatyouusedtoknow at 12:17 PM on August 13, 2011

I just started reading a book called Teaching Needy Kids in our Backwards System (based on another AskMe suggestion...) that may help. He talks about designing a preschool math curriculum for inner city children. He actually manages to teach kids abstract mathematical concepts far beyond the preschool curriculum. He does a lot of direct instruction and uses the ploy of, "Oh, there's no WAY you guys can master this! It's too difficult for you!" and they say, of course, that they CAN do it, etc. He gets some awesome results.

It's not so much a how-to, but he describes his process.

posted by guster4lovers at 12:30 PM on August 13, 2011

It's not so much a how-to, but he describes his process.

posted by guster4lovers at 12:30 PM on August 13, 2011

Many (many) moons ago, my mother taught me basic math with solitaire games using playing cards, and I found them very entertaining and educational. One name I remember is Pyramid, in which you take away cards in groups totaling 13; there were numerous others for which I no longer recall the names or precisely how they are played. A basic book of Hoyle or the software should offer up many such games, though, as I'm sure she didn't make them up.

posted by DrGail at 12:57 PM on August 13, 2011

posted by DrGail at 12:57 PM on August 13, 2011

when we put the kids to bed every night, we would pretend they were in a rocket ship and count down from 10, at which point they would blow the light out (because this all started on a night when we had no power). Over the years, this count down became more complex, going in twos and threes, and part numbers.

When we went shopping, we would ask them to grab one or two of a product (or three or however many we needed), and as they got older we had them doing the math for unit conversion - if this item is $1 for 250grams, and this is $1.50 for 500g, which is cheaper?

When they were little, there was a lot of plastic cups and water. A young child will identify a tall thin cup as holding more water than a wide large one, and can be blown away by tipping water between. Great fun in the bathtub or wading pool.

Putting away toys can involve counting, grouping and patterns. Driving in a car gives an opportunity to identify the same, how many buses, dogs, traffic lights.

I would totally not do flash cards or formal lessons, only because I tried them and annoyed the fuck out of my kids. Oh and my boy achieved the highest grade on a nationwide test on math, when he'd disengaged in high school and his grades weren't wonderful. It was nice to see that the ability to think logically stuck.

posted by b33j at 2:27 PM on August 13, 2011 [1 favorite]

When we went shopping, we would ask them to grab one or two of a product (or three or however many we needed), and as they got older we had them doing the math for unit conversion - if this item is $1 for 250grams, and this is $1.50 for 500g, which is cheaper?

When they were little, there was a lot of plastic cups and water. A young child will identify a tall thin cup as holding more water than a wide large one, and can be blown away by tipping water between. Great fun in the bathtub or wading pool.

Putting away toys can involve counting, grouping and patterns. Driving in a car gives an opportunity to identify the same, how many buses, dogs, traffic lights.

I would totally not do flash cards or formal lessons, only because I tried them and annoyed the fuck out of my kids. Oh and my boy achieved the highest grade on a nationwide test on math, when he'd disengaged in high school and his grades weren't wonderful. It was nice to see that the ability to think logically stuck.

posted by b33j at 2:27 PM on August 13, 2011 [1 favorite]

Don't think of the child as a 3.5 year old. That will do you no good.

What are the kids current math skills. I have 2 kids. The older one at age 2 could add and subtract. The younger one at 2, just learned to count to 15. Totally different math skills...at the same age.

Find out where they are...and go from there.

Use M&Ms...or raisins or nuts, or whatever...it'll keep the kid interested. And its a great way to show that 3 + 2 =5 M&Ms

posted by hal_c_on at 4:08 PM on August 13, 2011 [1 favorite]

What are the kids current math skills. I have 2 kids. The older one at age 2 could add and subtract. The younger one at 2, just learned to count to 15. Totally different math skills...at the same age.

Find out where they are...and go from there.

Use M&Ms...or raisins or nuts, or whatever...it'll keep the kid interested. And its a great way to show that 3 + 2 =5 M&Ms

posted by hal_c_on at 4:08 PM on August 13, 2011 [1 favorite]

We found measuring fluids and putting them in different sized containers and cutting fruit/pie/cake in to halves and quarters etc to be excellent starting points.

Measuring and weighing for baking is also pretty helpful. For them, not you.

posted by taff at 4:37 PM on August 13, 2011

Measuring and weighing for baking is also pretty helpful. For them, not you.

posted by taff at 4:37 PM on August 13, 2011

My daughter learned to count well (in order and all), because for months on end, we counted the steps every time we walked up them together. I suggest finding little ways for parents to work math into everyday life. I'm not sure someone else coming in to teach for a formal lesson will work for a preschooler. But repetition and fun things to do together are recommended.

posted by Margalo Epps at 9:33 PM on August 13, 2011

posted by Margalo Epps at 9:33 PM on August 13, 2011

I agree with counting suggestions. Count to 5, count to 10... Once he can count to 20. Have him count by twos, by threes, by fours, by fives. Then count backwards. Then memorize the primes. He doesn't need to know what a prime is or why the number is prime. He's just memorizing it. Praise and memorization... Cookie Monster and The Count.

Developmental psychology 101 tip: Kids at that age have trouble with fractions. There's a neat trick you can do with kids that age.. Give him one cookie and take two for your self and ask if that's fair. (they will say no, of course not I want another cookie!) And then you take their cookie, break it in half and give it back and ask if it's fair now.

at 3 and a half, the kid will most likely agree that it's fair now. I tried it once on my friends little brother once and we laughed hysterically when it worked.

I think that trick only works in a pretty narrow age window, but it's a good way to test if they're ready to understand fractions.

posted by j03 at 11:58 PM on August 13, 2011 [1 favorite]

Developmental psychology 101 tip: Kids at that age have trouble with fractions. There's a neat trick you can do with kids that age.. Give him one cookie and take two for your self and ask if that's fair. (they will say no, of course not I want another cookie!) And then you take their cookie, break it in half and give it back and ask if it's fair now.

at 3 and a half, the kid will most likely agree that it's fair now. I tried it once on my friends little brother once and we laughed hysterically when it worked.

I think that trick only works in a pretty narrow age window, but it's a good way to test if they're ready to understand fractions.

posted by j03 at 11:58 PM on August 13, 2011 [1 favorite]

This thread is closed to new comments.

You might also try pattern forming ("Now, can you put down three red buttons and then three black buttons? What do you think comes next?")

My little one loves pattern blocks, so she can feel the shapes that go with the names. She also likes making the blocks fit the printed pattern. Manipulatives (we have a farm set and a vehicles set) have also been a big hit and have been good for teaching counting, grouping, and sorting by color and size.

posted by MonkeyToes at 8:42 AM on August 13, 2011 [1 favorite]