How is my child thinking about maths
January 14, 2019 4:43 AM Subscribe
My daughter has just turned 8. We live in Scandinavia at the moment and so she didn't actually start school until she was 7. She's an extremely articulate, thoughtful and sensitive little soul. She's inclined to listening to story tapes, being read to, playing with her lego etc. Just to give you some background. Nothing about the way we interact or converse with her as her parents gives me any cause for concern.
However, she's doing at the very bottom of her class at school for maths. Obviously all of this is quite new to her, the concept of addition and subtracting was only introduced to her a year ago. I've been practicing with her at home a little bit, and she has what I see as unusual methods for attempting the exercises in the workbook we've been using.
Say there's a page of additions to work through, there will be perhaps four houses, then a split in the picture, then six houses on the other side of the split. My daughter can't easily keep either one of those numbers in her head and 'abstractly' come up with the answer. If we use our hands, she'll start counting from '1' - i.e. she doesn't start from the known quantity of four, then add on six. If we gently correct that, so that we start from 'four', then use our hands to count up and stop at ten, my daughter doesn't easily sort of realise why we might stop counting and reach our total.
Finally, I THINK in her mind, she is literally visualising houses, not able to treat the "four houses" thing as merely an aid to not losing interest in stark figures.
Anyone able to chime in with their own experiences? Could all this add up (!) to something like dyscalculia or is it just one possible temporary outcome of having a lovely, somewhat dreamy child?
Please note I will also (and have already) asked my child's teacher for feedback and his thoughts. I'm just curious what the hive mind thinks.
My child's teacher reported back that my daughter is having extra one-on-one help but they're in no way worried or labelling at this stage. I should maybe also note that my child isn't yet reading or writing. Others in the class are further ahead with this but there are others further 'behind' as well.
However, she's doing at the very bottom of her class at school for maths. Obviously all of this is quite new to her, the concept of addition and subtracting was only introduced to her a year ago. I've been practicing with her at home a little bit, and she has what I see as unusual methods for attempting the exercises in the workbook we've been using.
Say there's a page of additions to work through, there will be perhaps four houses, then a split in the picture, then six houses on the other side of the split. My daughter can't easily keep either one of those numbers in her head and 'abstractly' come up with the answer. If we use our hands, she'll start counting from '1' - i.e. she doesn't start from the known quantity of four, then add on six. If we gently correct that, so that we start from 'four', then use our hands to count up and stop at ten, my daughter doesn't easily sort of realise why we might stop counting and reach our total.
Finally, I THINK in her mind, she is literally visualising houses, not able to treat the "four houses" thing as merely an aid to not losing interest in stark figures.
Anyone able to chime in with their own experiences? Could all this add up (!) to something like dyscalculia or is it just one possible temporary outcome of having a lovely, somewhat dreamy child?
Please note I will also (and have already) asked my child's teacher for feedback and his thoughts. I'm just curious what the hive mind thinks.
My child's teacher reported back that my daughter is having extra one-on-one help but they're in no way worried or labelling at this stage. I should maybe also note that my child isn't yet reading or writing. Others in the class are further ahead with this but there are others further 'behind' as well.
(Just adding that Bedtime Math is not like a workbook -- it's designed to be like reading a book to your kid at night, only math, if that makes sense. It doesn't feel like "work.")
posted by heavenknows at 4:52 AM on January 14, 2019 [2 favorites]
posted by heavenknows at 4:52 AM on January 14, 2019 [2 favorites]
Cuisenaire rods are as old fashioned as all hell but I credit them with forming the bedrock of my own numeracy.
posted by flabdablet at 4:52 AM on January 14, 2019 [12 favorites]
posted by flabdablet at 4:52 AM on January 14, 2019 [12 favorites]
Sleeping Queens is a card game invented by a 6-year-old girl. It practices addition and subtraction, and I've personally seen a child who does not care how many houses are on the page in the workbook, care a lot about waking up the queens.
posted by Former Congressional Representative Lenny Lemming at 4:59 AM on January 14, 2019 [11 favorites]
posted by Former Congressional Representative Lenny Lemming at 4:59 AM on January 14, 2019 [11 favorites]
Great suggestions. In addition, there are so many games and day to day activities that can fall under the heading ‘applied maths’, which may help make all a bit more relatable. I struggle to think of many card and board games that don’t at least involve counting and adding up, many also require you to take away. And if she likes to help baking, cooking and food shopping all are applied maths problems.
posted by koahiatamadl at 5:57 AM on January 14, 2019 [1 favorite]
posted by koahiatamadl at 5:57 AM on January 14, 2019 [1 favorite]
Could all this add up (!) to something like dyscalculia or is it just one possible temporary outcome of having a lovely, somewhat dreamy child?
I was a lovely, dreamy child with a very late diagnosis of dyscalculia and this sounds exactly like me. I spent lunch every other day with my lovely, lovely maths teacher at my lovely, progressive, no pressure primary school and it made essentially no difference to me. I did not succeed at maths at all until we got to geometry.
Had this been a learning disorder people were looking for in 1980, they would also have noticed that I couldn't read an analogue clock until I was 13, that my rote number memorisation was dreadful, and that the only way I can organise cardinal directions is by reciting "Never Eat Shredded Wheat" which I still do at 46.
The good news is that if this is a diagnosis she acquires, while meeting scholastic maths requirements may be difficult, her adulthood need not be difficult if the difficulty is medium to mild. I can use a spreadsheet and a till, and navigate with google maps, and live in a world where hepatic feedback makes using my phone easy.
posted by DarlingBri at 6:03 AM on January 14, 2019 [12 favorites]
I was a lovely, dreamy child with a very late diagnosis of dyscalculia and this sounds exactly like me. I spent lunch every other day with my lovely, lovely maths teacher at my lovely, progressive, no pressure primary school and it made essentially no difference to me. I did not succeed at maths at all until we got to geometry.
Had this been a learning disorder people were looking for in 1980, they would also have noticed that I couldn't read an analogue clock until I was 13, that my rote number memorisation was dreadful, and that the only way I can organise cardinal directions is by reciting "Never Eat Shredded Wheat" which I still do at 46.
The good news is that if this is a diagnosis she acquires, while meeting scholastic maths requirements may be difficult, her adulthood need not be difficult if the difficulty is medium to mild. I can use a spreadsheet and a till, and navigate with google maps, and live in a world where hepatic feedback makes using my phone easy.
posted by DarlingBri at 6:03 AM on January 14, 2019 [12 favorites]
If we use our hands, she'll start counting from '1' - i.e. she doesn't start from the known quantity of four, then add on six. If we gently correct that, so that we start from 'four', then use our hands to count up and stop at ten, my daughter doesn't easily sort of realise why we might stop counting and reach our total.
Not quite sure how you're describing this, but does she count to four on her hands to get to four, then count an extra six, then count how many fingers she's holding up in total? Or do you mean instead of doing 4 + 6, she starts at one and just adds six?
My 6yo has been doing maths for a couple of years (in the UK), and it took him a long time to be able to add in his head (and then only because they learn by rote "number bonds", i.e. pairs of number that add up to ten). He will still do some sums by counting out the first number on his fingers and then adding on the second number, so if that's what your daughter is doing I think it's common.
posted by EndsOfInvention at 6:11 AM on January 14, 2019 [2 favorites]
Not quite sure how you're describing this, but does she count to four on her hands to get to four, then count an extra six, then count how many fingers she's holding up in total? Or do you mean instead of doing 4 + 6, she starts at one and just adds six?
My 6yo has been doing maths for a couple of years (in the UK), and it took him a long time to be able to add in his head (and then only because they learn by rote "number bonds", i.e. pairs of number that add up to ten). He will still do some sums by counting out the first number on his fingers and then adding on the second number, so if that's what your daughter is doing I think it's common.
posted by EndsOfInvention at 6:11 AM on January 14, 2019 [2 favorites]
In addition to the extra help and the great suggestions of using an abacus and a card game, look into ideas for passively transmitting lessons, like placemats under her breakfast/lunch/dinner plates. They make them for everything, not just math. Just get the ideas in front of your daughter and let her explore.
It's way too early to worry about dyscalculia.
posted by Cool Papa Bell at 6:39 AM on January 14, 2019
It's way too early to worry about dyscalculia.
posted by Cool Papa Bell at 6:39 AM on January 14, 2019
You also mention LEGO toys. There are many lesson plans available that use LEGO as a teaching tool.
posted by Cool Papa Bell at 6:42 AM on January 14, 2019 [3 favorites]
posted by Cool Papa Bell at 6:42 AM on January 14, 2019 [3 favorites]
Bedtime Math is a fabulous book and not at all like a textbook. It's engaging and funny. HIGHLY recommend.
We also did a lot of adding and subtracting at mealtime. "Hey kid, you had four blueberries on your plate and you just ate one! How many do you have left? Yeah, three! Four minus one makes three! You just subtracted! Let's see what happens if you subtract another blueberry." Or, "How many blueberries do you have now? Four? OK, let's see what happens if we add six more. (count out six) Now how many are there? Right! Ten! Because 4+6=10!"
For those pages with the pictures of the houses, have you tried putting a lego on each picture? It might be easier for her to have something that she can physically manipulate.
At this stage, I think beefing up her connection between math and everyday life, so she understands viscerally what addition and subtraction MEAN, will help in getting her over the hump in figuring out abstract calculations.
posted by telepanda at 7:03 AM on January 14, 2019 [5 favorites]
We also did a lot of adding and subtracting at mealtime. "Hey kid, you had four blueberries on your plate and you just ate one! How many do you have left? Yeah, three! Four minus one makes three! You just subtracted! Let's see what happens if you subtract another blueberry." Or, "How many blueberries do you have now? Four? OK, let's see what happens if we add six more. (count out six) Now how many are there? Right! Ten! Because 4+6=10!"
For those pages with the pictures of the houses, have you tried putting a lego on each picture? It might be easier for her to have something that she can physically manipulate.
At this stage, I think beefing up her connection between math and everyday life, so she understands viscerally what addition and subtraction MEAN, will help in getting her over the hump in figuring out abstract calculations.
posted by telepanda at 7:03 AM on January 14, 2019 [5 favorites]
A lot of the techniques suggested here would be refferred to as using "math manipulatives" by elementary math teachers. Physical objects like Lego and cuisenaire rods can help make abstract ideas more concrete.
For the house problem specifically i'd take little scraps of paper and draw the same houses on them. I'd lay them on their corresponding images in the homework book and then encourage the child to touch and move and count them. I'd probably work up to lego and other objects too using scripts like telepanda's above. But i'd start with the papers. Remember, for a child the process of answering random questions about random objects can be abstract in itself.
Similarly, the idea of counting on your fingers and starting from a point you already know (in your example that's the four) can be a new and strange concept. It's a "shortcut" and before your daughter can learn the shortcut she needs to know what adding actually is.
As an elementary teacher, I wouldn't be worried about a child at your age with her behaviours. I would consider it a typical stage of development. The goal now is to make sure she understands what's happening mathematically before she just memorizes tricks to doing the math. Many children benefit from math manipulatives at this stage. Others can pick it up from conversations and explanations. You know your child best. I'd just make sure her teaching team is helping her to work it out too.
posted by eisforcool at 7:24 AM on January 14, 2019 [7 favorites]
For the house problem specifically i'd take little scraps of paper and draw the same houses on them. I'd lay them on their corresponding images in the homework book and then encourage the child to touch and move and count them. I'd probably work up to lego and other objects too using scripts like telepanda's above. But i'd start with the papers. Remember, for a child the process of answering random questions about random objects can be abstract in itself.
Similarly, the idea of counting on your fingers and starting from a point you already know (in your example that's the four) can be a new and strange concept. It's a "shortcut" and before your daughter can learn the shortcut she needs to know what adding actually is.
As an elementary teacher, I wouldn't be worried about a child at your age with her behaviours. I would consider it a typical stage of development. The goal now is to make sure she understands what's happening mathematically before she just memorizes tricks to doing the math. Many children benefit from math manipulatives at this stage. Others can pick it up from conversations and explanations. You know your child best. I'd just make sure her teaching team is helping her to work it out too.
posted by eisforcool at 7:24 AM on January 14, 2019 [7 favorites]
The specific examples you give are related to a skill called subitizing. This is the ability to quickly and without counting recognize a quantity. Subitizing is pretty foundational for math.
Luckily, there are lots of fun ways that you can help a child practice subitizing. Rolling dice and calling out the numbers, playing dominos, etc are examples, but there are a lot more. You can purchase materials to help kids practice subitizing, but it's also easy to just create activities out of what you have at home. Pre-K Pages has some good ideas.
Ten Frames build on the subitizing skill to help children develop more advanced concepts like addition and subtraction. I couldn't find a good link summarizing how ten frames work, but if you google around you will find lots of resources. There are lots of ten frames templates you can print out and play with at home. Feel free to fill them with something more interesting than dots! You can also buy ten frame materials, though I wouldn't think that would be necessary.
Another important thing you can do is just talk with your child about math in the course of your daily lives. If you are with your daughter and you have three cookies, ask her how many will be left you each eat one. If you and your daughter are getting together with another family, ask how many people will be there altogether. Bringing math into daily conversation will help your daughter practice and will also demystify the process of thinking about numbers, making it less scary.
posted by Winnie the Proust at 8:31 AM on January 14, 2019 [3 favorites]
Luckily, there are lots of fun ways that you can help a child practice subitizing. Rolling dice and calling out the numbers, playing dominos, etc are examples, but there are a lot more. You can purchase materials to help kids practice subitizing, but it's also easy to just create activities out of what you have at home. Pre-K Pages has some good ideas.
Ten Frames build on the subitizing skill to help children develop more advanced concepts like addition and subtraction. I couldn't find a good link summarizing how ten frames work, but if you google around you will find lots of resources. There are lots of ten frames templates you can print out and play with at home. Feel free to fill them with something more interesting than dots! You can also buy ten frame materials, though I wouldn't think that would be necessary.
Another important thing you can do is just talk with your child about math in the course of your daily lives. If you are with your daughter and you have three cookies, ask her how many will be left you each eat one. If you and your daughter are getting together with another family, ask how many people will be there altogether. Bringing math into daily conversation will help your daughter practice and will also demystify the process of thinking about numbers, making it less scary.
posted by Winnie the Proust at 8:31 AM on January 14, 2019 [3 favorites]
Manipulatives, yes! The stuff on paper is unreal to her. Use anything available, pieces of fruit, legos, toy cars. Use arithmetic with her in daily life, not related to school. Like cooking, shopping, telling time.
Other books that kids enjoy are Mathstarts. They cover basic arithmetic concepts through stories. They come in three levels, with level 1 the simplest, I think.
posted by mareli at 8:32 AM on January 14, 2019 [1 favorite]
Other books that kids enjoy are Mathstarts. They cover basic arithmetic concepts through stories. They come in three levels, with level 1 the simplest, I think.
posted by mareli at 8:32 AM on January 14, 2019 [1 favorite]
It sounds like she is also having trouble abstracting from the pictures of houses to counting on fingers to the abstract idea of "4" or "10". I would do some experiments to get a better sense of where her numerancy (sense of numbers) is at.
Start super basic and see what parts make sense. How many things can she tell you "how many" at a glance - one? Two? Three? Can she tell at a glance which is more and which is less if the difference is more than 50%?
How high can she count just saying the names of numbers in a row? How high can she can by touching objects? If you give her one more, does she know how many without starting over? If you take one away? If you have two or take two? (do this physically). In other words, if she knows how many she has, can she count up and down from there?
Then I would try combining. Start with numbers that she can count at a glance. If you have two and I have three, how many do we have if we put them together? Count and find out. What if I have two and you have three? If we have five, and I take one, how many are left for you? (do it and count) Let her make questions. Try it again with bigger numbers.
If she can get that, then doing the picture math might start to make more sense if you match a token to each picture.
There are lots of ideas for how to do this is a fun way but I want to make sure you are doing it at her level.It does sound to me like there is a little switch that hasn't flipped for her yet. I don't know if it is a problem or just needs time but in the meanwhile, you need to help her build her intuitive sense of what numbers mean - often a slow process with lots of repetition until it clicks.
Also, check to see if she recognizes the numbers as symbols. If I say "two", can you show me two blocks?" If I print a "2" does she know that is called "two"? If I print "2" can she show me two blocks? If she's not reading or writing, she may not have this part down either. If she is starting to, then when you go a verbal/tactile problem, write it down using the symbols so she can see that "you have two and I have three so we have five together" looks like 2+3=5. And i take one away, we have four is written as 5-1=4.
posted by metahawk at 1:16 PM on January 14, 2019
Start super basic and see what parts make sense. How many things can she tell you "how many" at a glance - one? Two? Three? Can she tell at a glance which is more and which is less if the difference is more than 50%?
How high can she count just saying the names of numbers in a row? How high can she can by touching objects? If you give her one more, does she know how many without starting over? If you take one away? If you have two or take two? (do this physically). In other words, if she knows how many she has, can she count up and down from there?
Then I would try combining. Start with numbers that she can count at a glance. If you have two and I have three, how many do we have if we put them together? Count and find out. What if I have two and you have three? If we have five, and I take one, how many are left for you? (do it and count) Let her make questions. Try it again with bigger numbers.
If she can get that, then doing the picture math might start to make more sense if you match a token to each picture.
There are lots of ideas for how to do this is a fun way but I want to make sure you are doing it at her level.It does sound to me like there is a little switch that hasn't flipped for her yet. I don't know if it is a problem or just needs time but in the meanwhile, you need to help her build her intuitive sense of what numbers mean - often a slow process with lots of repetition until it clicks.
Also, check to see if she recognizes the numbers as symbols. If I say "two", can you show me two blocks?" If I print a "2" does she know that is called "two"? If I print "2" can she show me two blocks? If she's not reading or writing, she may not have this part down either. If she is starting to, then when you go a verbal/tactile problem, write it down using the symbols so she can see that "you have two and I have three so we have five together" looks like 2+3=5. And i take one away, we have four is written as 5-1=4.
posted by metahawk at 1:16 PM on January 14, 2019
Manipulatives, yes! The stuff on paper is unreal to her.
Just jumping in to say that while all of these suggestions are great, if your child actually has dyscalculia, this will probably make absolutely no difference. I spent at least 70% of those lunches I mentioned with Lincoln Logs (rather than Legos) and felt pies in quadrants and 8ths and those bend math sticks there the 5s are half as tall as the 10s, etc. None of it helped.
The only thing that helped me was support in doing arithmetic the only way I could work it in my brain. I also got a lot of positive support for the things I could do well and I never, ever felt stupid.
posted by DarlingBri at 1:36 PM on January 14, 2019 [4 favorites]
Just jumping in to say that while all of these suggestions are great, if your child actually has dyscalculia, this will probably make absolutely no difference. I spent at least 70% of those lunches I mentioned with Lincoln Logs (rather than Legos) and felt pies in quadrants and 8ths and those bend math sticks there the 5s are half as tall as the 10s, etc. None of it helped.
The only thing that helped me was support in doing arithmetic the only way I could work it in my brain. I also got a lot of positive support for the things I could do well and I never, ever felt stupid.
posted by DarlingBri at 1:36 PM on January 14, 2019 [4 favorites]
The Montessori method uses a lot of hands on manipulatives.
Also sumblocks seems to be pretty neat.
Difficulties with mathematics may be indicative of other learning difficulties besides dyscalculia (e.g. issues with working memory, attention).
posted by oceano at 1:46 PM on January 14, 2019 [1 favorite]
Also sumblocks seems to be pretty neat.
Difficulties with mathematics may be indicative of other learning difficulties besides dyscalculia (e.g. issues with working memory, attention).
posted by oceano at 1:46 PM on January 14, 2019 [1 favorite]
I haven't seen a mention of plain old card games like Crazy Eights and Go Fish and dice games using two dice. In addition to the math concepts, this also provides your time and attention, which is always a bonus.
Also if the games are continually frustrating rather than fun for your child it may clue you in to possible learning difficulties.
posted by Altomentis at 7:16 PM on January 14, 2019 [1 favorite]
Also if the games are continually frustrating rather than fun for your child it may clue you in to possible learning difficulties.
posted by Altomentis at 7:16 PM on January 14, 2019 [1 favorite]
The above suggestions are great, but I wanted to chime in and say that I distinctly remember learning addition in 2nd grade (at 8-9 years old), and it was absolutely bewildering to me. "How many apples do you now have?" But you never had any apples in the first place, they were just drawings on paper! And even if they were real, why would you want to do this number stuff with them when apples are for eating?
The thing that seemed to help was my mom explaining that this is just some mental exercises that the teacher wants you to learn, and the apples aren't the point. Like, she had to explain the idea of abstract thinking to me.
After I got it (and it took a while), I was just fine at math. Did well in pretty much every math class since, went to a top-tier college, majored in a hard science. All I'm saying is that as you suggest, this may well be temporary.
Also check out this article and MeFi discussion about why playing with algebraic and calculus concepts—rather than doing arithmetic drills—may be a better way to introduce children to math.
posted by danceswithlight at 4:38 PM on January 15, 2019 [1 favorite]
The thing that seemed to help was my mom explaining that this is just some mental exercises that the teacher wants you to learn, and the apples aren't the point. Like, she had to explain the idea of abstract thinking to me.
After I got it (and it took a while), I was just fine at math. Did well in pretty much every math class since, went to a top-tier college, majored in a hard science. All I'm saying is that as you suggest, this may well be temporary.
Also check out this article and MeFi discussion about why playing with algebraic and calculus concepts—rather than doing arithmetic drills—may be a better way to introduce children to math.
posted by danceswithlight at 4:38 PM on January 15, 2019 [1 favorite]
Probably a tangent, as it might not be relevant for dyscalculia specifically, but I loved this book by Alexander Zvonkin on teaching math to young children. It lists many games and exercises he used to illustrate concepts.
posted by taltalim at 3:40 AM on January 16, 2019
posted by taltalim at 3:40 AM on January 16, 2019
This thread is closed to new comments.
Sorry, not sure if this is helpful, but perhaps worth trying! For what it's worth, this does not sound like something to worry about if the teachers aren't. (And it's lovely not to have the pressure of school until 7!)
posted by heavenknows at 4:50 AM on January 14, 2019 [4 favorites]