Q&A #4: Is it safe to delay math learning?

0:00 [Music] foreign hello and welcome to today's q a episode of the your parenting Mojo podcast which is on the topic of whether it's okay to delay math education so here is listener Lindsay with the question hi Jen my question is how safe is it to neglect maths education until your child shows some kind of interest

0:30 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 maths 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 maths ability like there is for language thanks Lindsay originally emailed this question and added some additional detail that I think is also relevant so

0:58 I'm going to add that here too 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 yay capitalist system

1:20 also a child's Learning Journey doesn't happen in a vacuum and delaying maths 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 so I want to start by telling you a little bit about my history with math is this context for this so I don't remember the very very early years but in the later years in Primary School my

1:45 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

2:07 off on our own doing pretty much whatever we wanted and 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 was some there were a lot of conversations about great inflation so

2:31 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 their a grade and so as far as school is concerned I am a good math student right I I did as almost as well as I could have done and I would say I don't really understand math what I am really good at doing as I've mentioned before in the show related to things like writing

2:58 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 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 I call prerequisites which is the

3:27 classes that you need to do to be able to make that transfer into the full University and I called the advisor in the Department of Forestry and said what is the least amount of math that you will accept and still take me and the advisor laughed and said pre-calculus and and pre-calculus 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

3:50 like great I can do pre-calc and so I did that and I got into Berkeley and then once I was in Berkeley obviously didn't have to do much 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 Rey's National Seashore and we dug up uh soil with an appropriate permit in different areas of the park looking for a different organic content

4:19 of the of the soil and so this this other student had access to the Machinery to do that 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 and math at Berkeley and then when I got into Yale there was

4:43 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 um and so I know just about enough of Statistics to do what I hear what I do here on the podcast so I I know the things that I'm supposed to be looking for and what levels I'm supposed to be

5:10 looking at but I really don't know any more than that so um 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

5:37 of Forestry and environment and so I passed that no problem and then I took the GMAT to see if I could get into the School of Management as well and I ended up I 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

5:58 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 learn 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

6:19 they get tutoring to 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 was an option and or that I was needed and and that I wanted even to go to the School of Management and so I didn't uh go through that process of um of getting the the tutoring because I'd miss the boat already on the deadline to apply so um so as far as school goes as long as

6:43 you don't count that quote-unquote 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 uh 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

7:07 gonna 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 charis's math learning so one of the ideas that I think is super super important and what Lindsay asked which is the uh the idea of a critical period for Learning and this idea originated I think it was in the late 60s from animal research when uh

7:34 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 then it's going to imprint on me and it's going to follow me around instead a similar period was found in a chaff inch if a chaff inch Hears A

7:54 traffic song within its 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

8:25 who has been spoken to since the very early days um has is able to develop language 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 quote unquote normal speech and of course what we're assuming is that's our goal that to appear normal to communicate in a quote-unquote normal way is the goal of

8:50 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 a 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

9:21 language acquisition and unfalsifiable embarrassment question mark 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 a massive variation there there were even problems with the idea of you know what is what is speaking like a native mean some of them are saying this is not about vocabulary it's

9:48 not about syntax this is about sort of an attitude and an identity that 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 and then another wrench was thrown in

10:19 the works with a massive study so some researchers put this this uh 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 end up taking this test and they the researchers found that the learning rate for syntax declines by 50 percent right huge huge Cliff there

10:46 around the age of 17.4 which is massively massively later than the preschool to age eight period that many researchers have thought that this critical window ended so um so if if we can say that the 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 never mind first language acquisition never mind math where that concept really doesn't seem to exist right if I

11:18 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

11:43 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 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

12:09 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

12:34 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 from teachers about their math ability through things like grades so there is data from children like I guess let me back up on that let's not

13:03 call it data let's call it anecdata from children who have attended Sudbury school which is in Massachusetts um 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 kind of show up and they can learn whatever they want to learn um 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

13:31 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 and so it seems as though one of the reasons why math is so hard and it takes so long

14:02 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 they could a whole lot faster and so those teachers sorry the students are 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

14:27 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

14:55 this is wanting to give our children the best possible start in life and we can't ever know that we're doing that we may force them to 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 feel safer to do something that everybody else is doing it but if our

15:23 overall goal is to uh 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 this also there's also a layer here of this uh 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

15:48 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 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

16:17 you can do about that right and 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 uh if they're looking around and seeing that everybody else is 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 when my child points out you know that child's really good at that or not good at that we can

16:42 also kind of you know counter balance so yeah this child's good at this and 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 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

17:07 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 homeschooler 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 so her mom pulled her out of school and after that she really

17:34 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 and there was just this kind of big period of relaxation which you know for a freshman in high school I think is is typically not a period when we're talking about relaxation being the primary thing we're spending our time on and then eventually this person decided she wanted to be a math major

17:56 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 her oh she's she's learning it because she wants to learn it because she wants to go deep into this and 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

18:20 interested in but it's connected to something they want to do at 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 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

18:42 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 then 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

19:08 they are and I guess there's an illustration of that I would say you know the biggest problems that I've faced in life are not because I didn't know enough math the biggest problems 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 um and so I I would I guess I would

19:30 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 but I guess having said that there is a vast Gulf I guess between um sort of forced math curriculum you

19:58 know we're going to 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 with out formal lessons and of course I'm sure everybody's familiar with the idea of cooking using math and and so to build on that idea listener

20:18 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 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

20:43 Charis was learning to count and she would count you know 10 11 12 13 16 sorry 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's saying okay she doesn't learn this now she's never going to learn that 15 is a thing I knew that it

21:05 was 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 a 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

21:31 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 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

22:00 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

22:26 check I get the a at the end and I haven't understood the connection between the two uh the the problem in the first place and the result at the end 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

22:53 learning math and and we can go through this with our children at 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 and how old they are now right because there's a big there's a leap there as you as you cross over the year

23:12 2000 and then you're dealing with the odd number at the end um how 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 um and 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 they they have they have a hard time uh figuring something out and then a sibling says oh

23:38 you could do it like this and and a friend says oh you could try it like this and it becomes this kind of collaborative uh event where you don't have to be the uh the expert 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 quote-unquote teach using this method but you can also use it in a super unschooly way to answer questions that

24:05 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 going to use fractions in cooking right this is this is a very uh much a middle ground here that I have become much more

24:27 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 and so I guess sort of as an upshot to all of this you know where 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 the math is going to come uh if we're

24:50 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

25:23 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 that we're going to teach them how to do it 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 thanks so much for asking this question

25:46 and if you have a question of your own that you would like me to answer you can go to your parentingmojo.com there is an astronaut 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 your parentingmojo.com thanks so much and I'll see you soon