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01:10 Listener Lindsay asks the question, “How safe is it to neglect math education until your child shows some kind of interest in wanting to do it?” 01:48 Jen gives her academic history in math and admits to applying problem-solving strategies without full comprehension. 07:44 The critical period for learning seen in animal research also applies to children with severe language deprivation during early months. 08:51 The critical period for language development and second language acquisition is questioned in relation to math learning. 12:58 Sudbury School's anecdotal evidence suggests children can learn math quickly when motivated, sparking questions about early teaching, fostering a love of learning, and the impact on future opportunities. 15:54 Emphasizing intrinsic motivation over forced comparisons in math fosters self-awareness, more vital for a fulfilling life than specific skills. 19:31 Cognitively Guided Instruction values children's math knowledge, encourages pattern exploration, and validates individual methods, fostering a deeper understanding of math concepts. 22:09 Fostering children's intuitive understanding of math through collaborative learning and self-developed algorithms is a powerful approach. 24:01 Don't worry about formal math instruction; children will naturally develop their own strategies and algorithms when provided with a supportive learning environment.References
Singleton, D., & Lesniewska, J. (2021). The critical period hypothesis for L2 acquisition: An unfalsifiable embarrassment? Languages 6(3), 149.Transcripts
Hi everyone, I am Denise, a longtime listener of Your Parenting Mojo. I love this podcast because it condenses all the scientific research on child development, comparisons with anthropological studies, and put it into context of how I can apply all of this to my daily parenting. Jen has a wealth of resources here. So, if you're new to the podcast, I suggest you scroll through all her episodes, I'm sure you'll find one that will help you with whatever you're going through, or one that just piques your interest. If you'd like to get new episodes in your inbox, along with a free infographic on 13 Reasons your child isn't listening to you (And what to do about each one), sign up at YourParentingMojo.com/subscribe. Enjoy the show.
Jen Lumanlan:
Hello, And welcome to today's Q&A episode of The Your Parenting Mojo podcast, which is on the topic of whether it's OK to delay math education. So here's listener Lindsay with the question:
Lindsay:
Hi, Jen. My question is, how safe is it to neglect math education until your child shows some kind of interest in wanting to do it? Because I have heard anecdotes that I've found online about for example, a 12 year old starting from zero could catch up to their typical grade level in math in like two months or less. But do we have any evidence for this kind of thing? And also, do we know whether there's a critical window for math ability like there is for language? Thanks.
Jen Lumanlan:
Lindsay originally emailed this question and added some additional detail that I think is also relevant. So I'm going to add that here too:
Jen Lumanlan:
So Lindsay said, "There's a lot more to say around this topic, for example, while math skills are relevant to plenty of careers, the main reason I'm concerned about it for my child is that it's a required hoop to jump through in order to get entrance to university (at least where I live!), and so not having it cuts off a lot more options than just the ones that actually use maths. Yeah, a capitalist system. Also, a child's learning journey doesn't happen in a vacuum, and delaying math education past what is typical could affect their belief in their own learning ability, for example. But really, I'm most interested in the first part of the question.
Jen Lumanlan:
So I want to start by telling you a little bit about my history with math has its context for this. So I don't remember the very, very early years. But in the later years in primary school, my friend Claire, and I worked ahead of everybody else in the math books. And so what that basically meant is we were all going through at our own pace, reading the explanations in the book and doing the exercises and checking the, the answers in the back. And so Claire and I worked on the orange books, everybody else was on the blue books. And I think maybe the people in the blue books, got some more teaching. And we were sort of off on our own doing pretty much whatever we wanted.
Jen Lumanlan:
And that worked pretty well for me because I was independent. And I enjoyed the process of kind of getting to do whatever I wanted basically. In high school, when I finished high school, I got an A in math. And that's actually not a perfect grade when I was in school, not sure things have changed. But there were a lot of conversations about grade inflation. So they added an A star grade at the top, which was the highest grade. I didn't get the a star. But I did get the A grade.
Jen Lumanlan:
And so as far as school is concerned, I am a good math student, right? I did as almost as well as I could have done. And I would say I don't really understand math. What I am I really good at doing, as I've mentioned before on the show related to things like writing prompts, what I can do with math as well is see the kind of problem that is on the test. And I can know what is the strategy that I'm supposed to use to produce the result. But I don't necessarily And I would say even often understand what I'm doing.
Jen Lumanlan:
And then this continued as I transferred from community college into the University of California, Berkeley. And when I was getting ready, I was doing what are called prerequisites, which is the classes that you need to do to be able to make that transfer into the full university. And I called the adviser in the Department of Forestry and said, "What is the least amount of math that you will accept and still take me?" And the adviser laughed and said precalculus.
Jen Lumanlan:
And so this, this other student had access to the machinery to do the analysis. And she was also really good at math. And so she did the math portion of the paper. And she was not so strong in writing. And so I did the writing portion of the paper. And I'm pretty sure we both got a very good grade. So I didn't have to do much more in math at Berkeley.
Jen Lumanlan:
And precalculus is a lot of algebra and algebra was actually one of the things that made more sense to me than many other types of math. And so I was like, "Great. I can do freak out." And so I did that and I got into Berkeley, and then once I was in Berkeley, obviously didn't have to do much math related to my English degree. For the forestry aspect, there was an applied sampling project and I remember working with another student. We actually went out to Point Reyes National Seashore and we dug up soil with it appropriate permit in different areas of the park looking for a different organic content of the soil.
Jen Lumanlan:
And then when I got into Yale, there was a statistics component of the Master of Environmental Management. And so essentially, I went back to my old strategies from high school, where I'm getting deeper into being able to complete procedures without really being able to understand them. And so I know just about enough of statistics to do what I hear what I do here on the podcast. So I know the things that I'm supposed to be looking for, and what level is I'm supposed to be looking at. But I really don't know any more than that. And so I also was interested in doing an MBA. I found out fairly late in the game that I could combine my Master of Environmental Management with an MBA at Yale, and get two degrees in three years. And so I had passed what's called the GRE, which is a test to get into grad school that's really more kind of language focused, to get into the school of forestry and environment. And so I passed that no problem.
Jen Lumanlan:
And then I took the GMAT, to see if I could get into the school of management as well. And I ended up I wouldn't say I failed it, but I didn't do very well, I certainly didn't do well enough to actually get into the business school. And the reason for that is not that I couldn't do the math, but because when you're doing the GMAT, the whole point of it is that you're supposed to know these tricks to be able to do the problems fast enough to be able to get to the advanced problems that really show your competence. And I knew the math, but I didn't know the tricks. And apparently, the tricks are the things that you often learned in high school in the US. And because I hadn't gone to high school here, I didn't know the tricks. And of course, what many people do is they get tutoring, to understand the tricks to learn the tricks so that they can apply them in the exam. But I found out too late that that that was an option and or that I was needed, and that I wanted even to go to the School of Management. And so I didn't go through that process of getting the tutoring because I'd missed the boat already on the deadline to apply.
Jen Lumanlan:
So as far as school goes, as long as you don't count that "failed GMAT", I did, I did well in math, right, but I don't understand it. I would say overall, the topic doesn't really make sense to me. And I would even say it potentially scares me a little bit. So I've always been a little bit uncertain about how I'm going to support my daughter's learning in math. And over the last few months, I've become a lot more confident about that. And so I'm going to go through and address Lindsay's questions. And towards the end, I'll start talking about some of the things I've been learning that are making me much more confident in my ability to support Carys's math learning.
Jen Lumanlan:
So one of the ideas that I think is super, super important, in what Lindsay asked, which is the idea of a critical period for learning. And this idea originated I think it was in the late 60s from animal research, when scientists found out that there's a critical period for ducklings to imprint on their mother. So duckling little duckling pops out of its egg. And the first thing it sees it thinks is his mother. And so as long as it is, its mother, we're all good. If it's me that it sees that it's going to imprint on me, and it's gonna follow me around instead. A similar period was found in a chaffinch. If a chaffinch hears a chaffinch song within the it's critical period, it will learn its song. If it doesn't, then it won't. And so scientists assumed from that, that there's a critical period for learning language. And this rather large leap, I have to say, was based on studies of children who were severely deprived during childhood. So we're talking about children who are basically not exposed to language in their very early months. And yes, they come out to not being able to speak in the same way that somebody who has been spoken to, since the very early days has is able to develop language.
Jen Lumanlan:
Another sort of corroborating point on that is, for children who are born deaf. If they have a cochlear implant in the first six months or so of their life, they will probably develop "normal" speech. And of course, what we're assuming is that's our goal that to appear normal to communicate in a "normal way" is the goal of having that cochlear implant. And so a big problem with this research is that there's really, I mean, I would say, no agreement on what the critical period is. And then secondly, when we're talking about language development, this critical period was only ever intended to be relevant for second language development, not for first language development. And so there was a paper published in 2021, called "The critical period hypothesis for L2 meaning second language acquisition, an unfalsifiable embarrassment?" And so this paper reviewed a wide set of ranges when different scientists thought that the window ended and so some of them think it ends very early in the preschool period. Others are looking around eight or nine. So massive variation there.
Jen Lumanlan:
There were even problems with the idea have, you know what is what is speaking like a native mean? Some of them are saying this is not about vocabulary. It's not about syntax. This is about sort of an attitude and an identity that is really more associated with being a native speaker. Some late second language learners perform at a native-like level, which, of course, messes up the data. And there's a huge variance in the amount of opportunity for speaking in the first or the second language. And all of that impacts the speaker's ability to learn, and that impacts the outcome.
Jen Lumanlan:
And then another wrench was thrown in the works with a massive study. So some researchers put this method together that allowed people to test online if they could speak like a native speaker. And of course, this thing went viral. And everybody wants to know, "Can I speak my second language like a native speaker? 600,000 people ended up taking this test. And they the researchers found that the learning rate for syntax declines by 50%, right,(huge, huge cliff there) around the age of 17.4, which is massively massively later than the preschool to age 8 period, that many researchers have thought that this critical window ended.
Jen Lumanlan:
So if we can say that the critical window kind of isn't really even a critical window for second language acquisition, which is where this concept was meant to be relevant, nevermind first language acquisition, nevermind Math, where that concept really doesn't seem to exist, right? If I do a search of critical window math, there's nothing there's nothing relevant that comes up. So if we can accept that there is no critical period to learn math, then we start to ask different questions, like, "Why do we want to make sure our children learn before they're motivated to learn it?" And I guess, I would say that one potential reason why we might choose to do this is if we think we will put them back in school or they will choose to go into school at some point, it would potentially be easier to not have to catch up. And then of course, we get to the question of well, can they catch up (whether or not they go back into school)? And of course, there's really no research evidence on the aspect of this, that's really interesting to us.
Jen Lumanlan:
So any research on this topic is going to be done on children who are not doing well in school, particularly who are not doing well in math, who have probably already internalized the idea that they aren't good at math. And this has happened through you know, I'm getting failing grades, I'm being told by the teacher I need to pay more attention, that I need to do more work, and so on. And so I've been identified as a failing student, and then you know, I get more time more attention being taught in the same ways, using the same methods. And I'm not coming out with much of an improvement, right. And that's not the environment we're talking about here. What we're talking about is an environment where we are deciding how much math to expose our children to, and whether it's okay to delay that outside of an environment where they're getting messages from school or from teachers about their math ability through things like rights.
Jen Lumanlan:
So there is data from children, I guess, let me back up on that. Let's not let's not call it data, let's call it anecdata from children who have attended Sudbury School, which is in Massachusetts, you may remember hearing about that from Dr. Peter Gray when we talked with him. It's basically a school in name only where the children can show up and they can learn whatever they want to learn whenever they want to learn it. And there is information online that I'll link to in the references, where teachers have documented teaching six years worth of math in 20, contact hours. And in doing that using a math primer written in 1898, which had none of the teaching methods, right. There's nothing in there explaining how to do things. All it is is, you know, endless set of practice exercises. And the children are able to learn this quickly, because the material isn't very complicated, firstly, And secondly, because they're motivated.
Jen Lumanlan:
And so it seems as though one of the reasons why math is so hard, and it takes so long to learn it in school is because we are trying to teach it before the child is potentially ready to learn it. And before they're motivated to learn it. And then if we were to wait and do it later, when they are motivated to learn it, that they could learn it a whole lot faster. And so their students are begging the teacher to teach them. And the teacher is telling them, you know, if you're late, or if you don't do the homework, we're done. I'm not doing this anymore. And so they showed up on time, they did all the homework, and you know, they learned all this math in a very short period of time. So so that sort of provides some anecdata as it were for the idea that even if our children are get very little exposure to learning related to math, that when they are motivated, they can very quickly catch it up. And I think a bigger question related to this is wanting to give our children the best possible start in life and we can't ever know that we're doing that.
Jen Lumanlan:
We may force them to see sit down and learn math either in school or out of school, and they might come out hating it. They might come out scared of it. They might come out thinking they can't do it. It is the safer thing to do. It's always the feels safer to do something that everybody else is doing it. But if our overall goal is to instill this lifelong love of learning, to instill this idea that math is useful and interesting And exciting, and it can really help us to understand things, then it may not work out in the way that we hoped. And of course, there's also a layer here of this, you know, it's, it's a necessary step to get into university. And this is very much coming from a scarcity mindset, right. There's a limited number of opportunities available, and our child should be able to get one of them. And we want to make sure that we aren't withholding from them skills, or abilities, or anything else that could enable them to get one of these limited opportunities.
Jen Lumanlan:
And that really gets us deep into a comparison mindset, the idea that everybody else should do things at the same rate, and we should compare ourselves to other people to see how we're doing. And I think there's a lot you can do about that, right. And this also speaks, I think to Lindsay's idea about well, the child could develop some sort of negative self-image related to their math, if they're looking around and seeing that everybody else is "better" at it than than they are. And so I think one of the ways that we kind of counter that is that when my child points out, you know, "That child's really good at that, or not good at that." We can also kind of, you know, counterbalance, so yeah, "This child is good at this. And you're good at this. And they're different, or, yeah, that child's really not good at that. Well, yeah." And they're also really good at this, right.
Jen Lumanlan:
So everyone has unique strengths. And by not forcing our child to do math, we're not creating an environment where they can't succeed later. And it's possible, that in doing that, we may actually increase the likelihood that they will dive deep into math, and really be interested in it and really want to understand it. And as another kind of anecdata point, I interviewed a parent for the Confident Homeschooling course, who started unschooling as a freshman. She actually did a project in school on what unschooling is. And as she's doing this project, she's thinking, "Wow, this is really cool. Why am I not doing this? Why am I in school." And her mom pulled her out of school. And after that, she really didn't do very much for six months. And so she read a little bit, her mom would bring her books wouldn't ever force her to read them. And there was just this kind of big period of relaxation, which you know, for a freshman in high school, I think is typically not a period when we're talking about relaxation being the primary thing we're spending our time on.
Jen Lumanlan:
And then eventually, this person decided she wanted to be a math major. And she learned the math. And she majored in math. And now she specializes in data science, and data analytics and modeling. And so of course, all of this is her own choice. And she's learning it because she wants to learn it, because she wants to go deep into this. And I think that comes back to the motivation factor, right that when our children are motivated to learn something, and even if it's not something they're intrinsically interested in, but it's connected to something they want to do out the other end, then they will be willing to do the thing, even if it's just a stepping stone to get to where they want to go.
Jen Lumanlan:
And I think this, again, kind of brings us back to the idea that we can never know how our children will turn out. And yes, we want to do our part to smooth their path. I think that's sort of a cultural expectation of us at this point. But it's possible, right? The idea that I'm trying to seed here is what if the process of doing that which almost always involves getting them to do something that we want them to do that they may not necessarily want to do, could undercut their intrinsic motivation to learn the thing by themselves. So not just that, but also their ability to be with us in a way that enables us to truly see who they are. And I guess as an illustration of that, I would say, you know, the biggest problems that I faced in life are not because I didn't know enough math. The biggest problems that I faced in life are because I didn't know how to understand my needs. I didn't know how to advocate for my needs. I didn't know how to see other people's needs, and to meet them as well. And so I guess I would argue that anything that we can do that is helping us and our children to understand that more, is going to have a much, much, much bigger impact on their life than any unique skill or ability that we try to equip them with, which frankly, they can do for themselves in a very short period of time if they want to do it.
Jen Lumanlan:
But I guess having said that, there is a vast gulf, I guess, between sort of forced math curriculum, you know, we're gonna sit down, we're going to do this lesson every day because I say so. And completely hands off, okay, then we're not going to do anything. We're not we're just not going to talk about math. We're not going to think about math at all. There's so much that we can do without formal lessons. And of course, I'm sure everybody's familiar with the idea of cooking using math.
Jen Lumanlan:
And so to build on that idea listener Elisa recently introduced me to Cognitively Guided Instruction. And so I created a module on this in the Learning Membership. And so we're going to start digging into that very soon. And what's really cool about Cognitively Guided Instruction is it builds on the knowledge that children already have about math, rather than the correcting the thing that they're doing wrong, so that we can see all the things they're doing right. And as an example of that, I think back to the time when Carys was learning to count, And she would count, you know, "10, 11, 12, 13, 14, 16." And so she'd miss 15. And, of course, you know, me as a parent who didn't know any better is, "You missed 15!" And I wasn't worried about it in any way, right? There was no, there's nothing in my mind that saying, okay, she doesn't learn this. Now, she's never gonna learn that 15 is a thing. I knew that it would come. But what I was missing, there was everything that was going right in that, right? She's learning, she's already learned that there's a one to one correlation between the things that she's counting and the number that she's saying. She already knows that the last number that she said corresponds with how many things there are in the set. And I was completely not seeing all of those things, because I was only seeing the mistake that she was making. So when we can start to see those things, then we can see the math learning that our children are already doing and have already done. And I think that that enables us to potentially relax a little bit and to know that they're already doing so much of this anyway.
Jen Lumanlan:
A lot of Cognitively Guided Instruction focuses on exploring patterns and relationships with numbers. And doing this not necessarily using the sort of textbook provided ways of doing these things that you would get in in a regular math textbook. But seeing that the ways that children devise themselves, of working with these numbers, is just as valid as traditionally taught methods. And what it enables children to do when they use the methods they devise themselves, is to make sense of it, right. And that's the piece that I was missing. I can follow the process in the textbook and get to the result. And I get the check, I get the A at the end. And I haven't understood the connection between the to the problem in the first place And the result at the end.
Jen Lumanlan:
But when children are allowed and enabled and encouraged to develop their own algorithms, their own ways of thinking about these things, then they intuitively see and understand the relationship between the numbers in a way that I never did. And so that, I think, is an incredibly powerful way of learning math. And we can go through this with our children the same time, right? We don't have to be the expert on Cognitively Guided Instruction to be able to do this. We can ask them to explain to us, you know, "How did you figure out that this person was born in 1953? And how old they are now?" "There's a leap there as you as you cross over the year 2000, and then you're dealing with the odd number at the end? How did you go about figuring that out?" And then you can have them walk through the process that they are using to do this. And that I think recognizes the enormous skill that children are bringing to this. And maybe they can't do it in the first place, right. And they have a hard time figuring something out. And then a sibling says, "Oh, you could do it like this." And a friend says, "Oh, you could try it like this." And it becomes this kind of collaborative event where you don't have to be the expert.
Jen Lumanlan:
And so of course, Cognitively Guided Instruction is geared for teachers, right? It was developed by professors to help teachers teach, so you can teach go to her teach using this method. But you can also use it in a super unschooling way to answer questions that interest your child. And so I think this is one of the coolest tools I've seen, to help us to bridge that gap between thinking that, you know, it's math workbooks, and it's making sure they get the grade, and they have the knowledge at the right grade level. And nothing or even slightly more than nothing, we're gonna use fractions in cooking, right? This is this is a very much a middle ground here, that I have become much more comfortable with over the last few months, in terms of my ability to see it when it's happening, and to be able to support it in my child as well.
Jen Lumanlan:
And so, I guess, sort of as an upshot to all of this, you know, where are we? Where are we leaving this? How are we thinking about this topic as a whole? I would say try not to worry about the math.
Jen Lumanlan:
The math is going to come. If we're not actively teaching children, the algorithm, the strategy that you're using to solve this problem is wrong, they will continue to develop these algorithms themselves. We can support them in doing this using tools like Cognitively Guided Instruction. But what our real focus should be on in my opinion, is creating an environment where they can be their whole selves, where they can learn what's really important to them, not just related to the world around them, but about themselves as well. And explore ideas that they're interested in, and have us join them along that path as their partner in learning, rather than as somebody who has this sort of set of knowledge and skills that they need to have, and then we're going to teach them how to do it.
Jen Lumanlan:
It's a really different way of being in relationship with children. And I would say it's a whole lot less stressful, and it's a whole lot more joyful as well.
Jen Lumanlan:
Thanks so much for asking this question. And if you have a question of your own that you would like me to answer it, you can go to YourParentingMojo.com. There is an Ask A Question button on the website. And if you would prefer to submit a video, which we always love, we always love to see your faces as well. You can do that by sending your video to support@YourParentingMojo.com. Thanks so much and I'll see you soon.
Denise:
I'm a Your Parenting Mojo fan, nd I hope you enjoy the show as much as I do. If you found this episode, especially enlightening or useful, you can donate to help gem produce more content like this. Just go to the episode page that Jen mentioned. Thanks for listening.