Yes, teen numbers are very opaque (plus you run out of fingers at ten), so it makes sense that your son hasn’t yet carried his new addition knowledge into the teens. In the other decades (twenTY, thirTY, fourtTY, etc) the place value is more clear in a sense of a set number of tens and clear directionality. FourTEEN has a sense of ten but is backwards in that the four part of it comes first, making kids want to write 41. And twelve has no sense of ten in the morphology at all, though the tw hints and its “two-ness.” Eleven loses all sense of ten or one more for kids and has to be memorized without any morphological clues. Without explicit instruction, kids with phonological difficulties are likely to also miss the morphological patterns in those more transparent numbers - another link to phonological difficulties affecting math learning!
Also, I think it’s worth quantifying the comment that “plenty of kids” who have reading difficulties don’t have math difficulties. Depending on the study, about 70% of kids with reading difficulties will also have math difficulties. Yet between the cultural acceptance of math difficulty being normal and the myth that dyslexia only affects reading, I consistently hear from parents that their child was diagnosed with dyslexia and schools would only address the reading difficulty, despite clear math difficulty, telling parents to “wait and see” with math. And as you noted, phonological difficulty gets in the way of some really crucial & foundational math learning, causing the “wait and see” approach to just leave those kids further behind. As an interventionist, I just wanted to advocate for that point to readers since I so persistently hear that schools think dyslexia only affects reading, but yet math difficulty its clearly associated with dyslexia for a majority of students. And math difficulty is actually a greater predictor of poverty, incarceration, and health difficulty than reading difficulty according to one study I saw from the UK.
Thanks for this. I am Michael's Aunt and the parent of a child (now a PhD and and a math professor) who had dyslexia. We had multiple struggles with our public school system regarding educating our son in math (he failed Algebra multiple times) because much of math education, especially in a progressive public school district, is very language based. Although our son had no problem with mathematical concepts his slow processing and weak short term memory would trip him up and he would find himself unable to keep up with classroom instruction and then he would fall behind and then the teachers who could tell he was gifted in math would accuse him of being lazy and the whole thing ended up being a cycle of failure. Eventually our son got instruction about how to learn how to learn given his brain and was able to pull through. But those years of failure were heartbreaking for him. I am glad there are interventionist like you who understand that learning when there are learning differences is not always linear.
Thank you so much for sharing! I love this point! Just because a child struggles with language, processing speeds, or working memory doesn’t mean they can’t be good at math, but they need instruction that works for those needs. And learning how to work with their brain, rather than against it, is huge! I can see how that background would make your son an excellent math teacher. People who always found math easy sometimes make terrible math teachers because they just expect kids to figure out way too many pieces on their own.
Great connection! I don't have the research at my fingertips, but I think there may be a parallel foundational aspect for mathematical development of number counting using fingers (alongside the language you point to here)
Very interesting! This reminds me of the book Mathsemantics: Making Numbers Talk Sense by Edward MacNeal and also the discussion of the “Chinese advantage” in Keith Devlin’s book The Math Gene regarding the shorter, easier words for numbers in Chinese making it easier to learn to count.
That's why I always counted beyond thirteen (and back down) when teaching my little one to count (plastic animals on the side of the bath every night). The "nonsense poem" MUST be familiar up to the point where the pattern re-emerges (eleven twelve thirteen - FOURteen), and only then can the pattern be extended through the twenties. Grouping the animals enabled conversations of 4 birds and 3 cats - how many altogether to cement additive reasoning, similarly with subtraction. This "game" has been a foundation to his subitising and general number understanding... now approaching 7, he's been thoroughly confident with all number challenges, and we're playing pontoon (summing to 21) AND introducing probabilities with the need to decide whether to "twist" another card or not!
Very fun to read this after all of our chatting about this topic in the Science of Math group! I will share with my team!
Thought you might like this and related research links: https://ece.umd.edu/news/story/the-brain-makes-sense-of-math-and-language-in-different-ways
Yes, teen numbers are very opaque (plus you run out of fingers at ten), so it makes sense that your son hasn’t yet carried his new addition knowledge into the teens. In the other decades (twenTY, thirTY, fourtTY, etc) the place value is more clear in a sense of a set number of tens and clear directionality. FourTEEN has a sense of ten but is backwards in that the four part of it comes first, making kids want to write 41. And twelve has no sense of ten in the morphology at all, though the tw hints and its “two-ness.” Eleven loses all sense of ten or one more for kids and has to be memorized without any morphological clues. Without explicit instruction, kids with phonological difficulties are likely to also miss the morphological patterns in those more transparent numbers - another link to phonological difficulties affecting math learning!
Also, I think it’s worth quantifying the comment that “plenty of kids” who have reading difficulties don’t have math difficulties. Depending on the study, about 70% of kids with reading difficulties will also have math difficulties. Yet between the cultural acceptance of math difficulty being normal and the myth that dyslexia only affects reading, I consistently hear from parents that their child was diagnosed with dyslexia and schools would only address the reading difficulty, despite clear math difficulty, telling parents to “wait and see” with math. And as you noted, phonological difficulty gets in the way of some really crucial & foundational math learning, causing the “wait and see” approach to just leave those kids further behind. As an interventionist, I just wanted to advocate for that point to readers since I so persistently hear that schools think dyslexia only affects reading, but yet math difficulty its clearly associated with dyslexia for a majority of students. And math difficulty is actually a greater predictor of poverty, incarceration, and health difficulty than reading difficulty according to one study I saw from the UK.
Thank you for all this! I know enough at this point to know that I've only skimmed the surface of the math/language relationship.
The other thing about the teens -- thirteen/fourteen/fifteen is just a brutal sequence of phonologically similar words.
Thanks for this. I am Michael's Aunt and the parent of a child (now a PhD and and a math professor) who had dyslexia. We had multiple struggles with our public school system regarding educating our son in math (he failed Algebra multiple times) because much of math education, especially in a progressive public school district, is very language based. Although our son had no problem with mathematical concepts his slow processing and weak short term memory would trip him up and he would find himself unable to keep up with classroom instruction and then he would fall behind and then the teachers who could tell he was gifted in math would accuse him of being lazy and the whole thing ended up being a cycle of failure. Eventually our son got instruction about how to learn how to learn given his brain and was able to pull through. But those years of failure were heartbreaking for him. I am glad there are interventionist like you who understand that learning when there are learning differences is not always linear.
Thank you so much for sharing! I love this point! Just because a child struggles with language, processing speeds, or working memory doesn’t mean they can’t be good at math, but they need instruction that works for those needs. And learning how to work with their brain, rather than against it, is huge! I can see how that background would make your son an excellent math teacher. People who always found math easy sometimes make terrible math teachers because they just expect kids to figure out way too many pieces on their own.
Great connection! I don't have the research at my fingertips, but I think there may be a parallel foundational aspect for mathematical development of number counting using fingers (alongside the language you point to here)
Very interesting! This reminds me of the book Mathsemantics: Making Numbers Talk Sense by Edward MacNeal and also the discussion of the “Chinese advantage” in Keith Devlin’s book The Math Gene regarding the shorter, easier words for numbers in Chinese making it easier to learn to count.
That's why I always counted beyond thirteen (and back down) when teaching my little one to count (plastic animals on the side of the bath every night). The "nonsense poem" MUST be familiar up to the point where the pattern re-emerges (eleven twelve thirteen - FOURteen), and only then can the pattern be extended through the twenties. Grouping the animals enabled conversations of 4 birds and 3 cats - how many altogether to cement additive reasoning, similarly with subtraction. This "game" has been a foundation to his subitising and general number understanding... now approaching 7, he's been thoroughly confident with all number challenges, and we're playing pontoon (summing to 21) AND introducing probabilities with the need to decide whether to "twist" another card or not!
I'd love it if you could share a link to that research please