Math curriculum for toddlers?

[Chris Wright]

Keri - I have always thought that finding math books that can be read as stories would be a particularly good way for the parents who may not be comfortable with math to spend some time with their children enjoying math together. I looked briefly at the snippets that Amazon has of the Adventures of Penrose the Mathematical Cat. The chapter on binary numbers was amusingly introduced, but it seemed awfully brief for someone (child or parent) seeing it for the first time. Do you find you need to augment the topics a lot, or is there more background in the book in places that I didn't happen to see? I would love to see more titles from your favorite math story reading list.

Mandabplus3 - Thanks for the welcome. Thanks for considering buying my books - I make about the same amount of money pretty much any way you buy them - they are available from Amazon, AoPS, or from Rainbow Resource, or from me. I only handle bulk orders (I'm not really set up for handling orders for the most part). Rainbow Resource has a considerably better price on my books than anyone else (not sure how their business model works). My daughter, also my webmistress, makes a little bit of money if you buy the books through my web site (www.drwrightskitchentablemath.com), but it's no big deal.

I'm afraid I don't have much more to say about one-to-one counting than what I wrote in section 1.1 of my first book. In that section, which I think is excerpted on Amazon, I mention that learning to count involves at least five ideas - 1-to-1 (that numbers can be associated with things in a 1-1 fashion), the numbers are ordered, the last number when counting is how many things there are, counting is universal (it doesn't matter which objects you are counting and it doesn't matter if the collection is a mixture of things), and it doesn't matter what order you count things in. I found these ideas being discussed in a math education book and tried to distill them in my book. To answer your question - I would say almost all of the discussions in my books are higher level than that particular discussion - I was talking about these ideas at the start of book 1 because I wanted to make sure that parents understood how much a child had to learn, and I also wanted to emphasize to them that they had to wait for their child to get to the right point in their development - that these particular topics mostly could not be hurried (though obviously by doing things like counting in front of your child you are providing them with experiences which will fuel their development). In other places in the books I do talk about what makes certain topics tricky or what some of the stumbling blocks are, but those discussions aren't as oriented toward development steps as that discussion in 1.1. By the way, I am a bit astonished that anyone would suggest that the idea of 1-to-1 correspondence wouldn't usually be mastered before age 6. However, people have also said that Algebra shouldn't be done before sometime in Middle School because children are not able to think in terms of abstract quantities before then - clearly that is a rule that doesn't hold for every child.

As for memorizing facts... What you wrote "Most of the parents decided to teach both and reinforce any weak understandings later." sounds okay to me, though I suppose it depends on just how much the children are simply memorizing something that is meaningless to them. The danger of memorizing alone is obviously that the child will have no idea what they are talking about (as in, no feeling for the results) and also that it could become a grind (and therefore a turn-off concerning math). If both of those pitfalls are avoided, then I don't think there is a problem. In KTM1 I try to take a very structured approach to learning the math facts, and I think that method has two advantages in general - it helps the child see math relationships and thereby gain an appreciation that cool things are going on with the numbers, and it makes learning the math facts more of a puzzle and less of a straight drill. To take an easy example, in teaching multiplying by 5's one can push the importance of knowing how to multiply by 10 (and its relationship to place value) and knowing how to take halves of things - not only might that make learning the 5's easier, but by making a task easier it inspires the child to consider the relationship of 5, 10, and half as something useful (rather than as just another random piece of information).

- Chris

[Mandabplus3]

Thanks! Looks like I can go shopping bound to learn something!

[sonya_post]

Nee,

Regarding AoPS and why I like them: Most of that has to do with my philosophy of education and why I chose home schooling in the first place 17 years (or more) ago. The rest has to do with being pragmatic.

Plato felt that the purpose of education was to train someone to love what is lovely. That is a paraphrase, but it is essentially the  point. I pretty much ascribe to the philosophy that education should be the pursuit of the good, the true and the beautiful. I present a standard to my children but my job is, more importantly, to get them to love the standard.  I had managed to find a way to make school a beautiful pursuit in all subjects except math. Think of it this way: we love to garden. I have flower gardens and food gardens. I installed a strawberry bed this spring adn the rabbits ate all 75 plants. So we did it again after  relocating some rabbits. Ahh, they found their way back and there went another 75 plants. I am about ready to put more plants out - this time I have a fence around the garden. It is strong, not bad looking ( I hate ugly in the garden), it blends into the landscape. But it is not my garden and it would be foolish to mistake the fence for one.

Before we found AoPS all the math curriculum I had found were merely fences. Saxon (don't mean to harp but it is the one I have most experience with), is a fence. A strong fence, better looking than most, nearly a fortress when it comes to pests.  My problem, our problem, was that I didn't even know a math garden existed. So, I mistook the fence for the garden. AoPS is the garden. My son got excited about math for the first time ever. I had to start restricting the time he spent on math. It doesn't just teach you to solve equations - it breaks them apart, explains what is going on and why and application. And, in the last 2 years I've come to realize that application is everywhere. So, AoPS has made it possible for math to fit into my home schooling philosophy. It started with Dr. Wrights books,.Well I got them after starting my son on AoPS but he introduced me to a way of thinking about math that I hadn't encountered before. If you want to really develop a love for math I'd recommend for parents - not kids - getting some of the math related material from The Teaching Company, in the US you can find them at libraries. I loved: The Joy of Math; Mathematics in the Visual World; Great Thinkers, Great Theorems; Mathematics, and Philosophy and the Real World. I am slogging my way though The Shape of Nature right now. It is slow going but I love it. You certainly don't need to get these courses, they just got me excited and pushed me on the journey of the beauty of math. My son will be a life long learner when it comes to math and will have much more to offer my grandchildren that I had to offer him.

That was on the philosophical end: Practical. AoPS will help you child understand the whys and what fors of math. They aren't easy texts at all. My son might end up spending 45 minutes to solve 1 problem. But in doing so he developed a whole treasure chest of tools to use when approaching future math problems. That is what appealed most to my son. He began the understand the underlying principles that guide math and he learned to apply them in various situations. He learned to approach problems from different angels. Plus they have a forum for the kids to join, then your child isn't the only math geek out there. The classes are taught with kids from multiple age ranges which appeals to me as a parent. There was always someone smarter than my child or at least on his level that he could compete with (which we hadn't found previously) so he had a challenge. Then there is alcumus, just in case you think your kids aren't getting enough practice in. Plus, customer service is outstanding. Send an email and they respond with book length responses. More than enough information to satisfy even the most curious of us on here.

This is not to say that AoPS is the only answer. For many parents, the cost of taking classes will be more than they can afford. But the books are reasonable and Alcumus is free - as are the forums. AoPS is designed for gifted kids. If you don't have a mathematically gifted child or child who just loves math, these might be too difficult or prove to be frustrating.

My personal thoughts on this is that you are going to need both a fence and a garden. You cannot do without either. Many programs are attempting to just do the garden part with exploration and having kids "discover" answers on their own when what they should be doing is building a fence. Think of how much easier math is going to be for Ella and others, So much of the basic "stuff" of math is second nature to them at 4. They get regrouping, bundling, can do rapid mental calculations, the 4 basic functions are down with very few mistakes. WOW. What a head start. Fences are nearly built, these kids are going to need to start planting gardens.

@ Kerlianne - nice review of KTM. I think that is what I'd say about it too. Those books were to teach me how to teach. I don't know who on here recommend Dr. Nebel's book Building Foundations of Scientific Understanding. It is kind of the same thing, It is a book to teach you to teach your kids. Yes, there is a plan but the main point is that it is a book for parents.I remember reading through all of them and at the end thinking I was a terrible mother for what I'd done to my child and was grateful that I didn't have to repeat it with my newborn baby - there were options. All of this was before I found early learning.

[Korrale4kq]

Wow Sonya. I just got that science book for kindle. I am impressed. It is the kind of book that I have been wanting. We do science haphazardly through non-fiction book reading and observation of the world around us. But I love having something a little more systematic for reference. I will surely supplement as we go through the book. But i like it!

[Korrale4kq]

Has anyone here read Einstein Never Used Flash Cards? I vaguely remember DadDude (I think) mentioning that it breaks down the order or the when of a child being able to understand something. Kind of reminds me of what I am reading about KTM above.

[sonya_post]

Korrale.

You need to join the yahoo group for the science books, It isn't super busy but there is a lot of good ideas that come down through the ranks and some very educated folks on there. As far as I can tell not too many EL however.

I think Kerlianne mentioned that math just becomes part of the da - little chunks here and there. That is what we are doing with science also. I"ve kind of picked up some basic concepts that need to be taught and then we just talk about them. At 25 months my son has a pretty good grasp of living/non-living. We didn't do worksheets or anything, just go outside. We do a lot of sorting/categorizing. Everytime we put the toys away we sort them differently. Sometimes we put all the cars, critters, balls etc into different bins. Sometimes we sort by color, sometimes by shape. Sometimes we just make a mess of it and them we get frustrated when we can't find what we want- but that is a good thing to learn also. We don't make a big deal out of stuff. We blew up balloons and I said full. Then I let the air out all over my son's face and he grabbed the balloon and said empty. He has the idea that air takes up space. He knows that air moves. I really like the book a lot. His recommendations for books are great!

[Korrale4kq]

Any idea how to find this yahoo group. I havent really had much to do with the yahoo groups.

Keri has given me a lot of ideas for books. And I go to our library for most books. We absolutely love the usborne behinners books. James learns so much from reading them over and over. But they are not comprehensive in all catergories. I love the science sections in the What Your _Grader needs to know series also. But I felt that it was lacking in its entirety. I really just wanted one all in one book. And I am absolutely smitten with the flow chart in the Buillding Foundations For Scientific Understanding book. I have plans to recreate that for math.
I still plan to do math haphazardly. I make up a lot of games and activities as I go along. And I borrow from a variety or curriculum and do sheets from various workbooks.   But I want to have a focus each day so that I am not skipping things or jumping ahead too much.

[Kerileanne99]

Chris-
I shall have a look through our collection and pull out our favorites to make you a nice list..i actually have a booklist somewhere that organizes them by topics taught.  We began with the MathStart books by Stuart Murphy, and they have nice lists of further activities for reinforcement. They are also by topic and are leveled, which makes it helpful. although, there again, minimally so!  Marilyn Burns has some really nice ones, Alex adores one called The Greedy Triangle that always wants to add just one more side and one more angle...Alex can instantly recognize up to a pentadecagon...in fact she kept asking me for a 'something?gon' but I couldnt uderstand her.  Finally she said, no, "I want a 'centi-gon' and made the ASL sign for hundred! She was DEVESTATED to learn that it is actually called a hectagon She still insists this is not correct...We have quite a range as well, from picture books to Penrose books to Life of Fred Apples, which she adores...for the harder ones she requires a lot more background and we read them again and again, at her insistence...I think she gleans just a bit more each time.
I do know that it causes her to think about the world differently.  She was just a little more than two when I came into a room and she was sorting some bath blocks with numbers she hadn't even glanced at in ages.  She was sorting them into an even and odd pile (when questioned, she knows that even-numbers can all be 'shared fairly between her and her stuffed hen'.
Definitely, the integration of math into picture book reading, daily activities, everything we do (especially science) has done this.  At this age it is so much fun to teach a toddler what literary concepts like Onomatopoeia is in a picture book about math, whilst we buddy read (she reads the even pages and I read the odd!)

Sonya-
I absolutely second the BFSU book, and that is exactly how we use it as well, combined with the Handbook for Nature Study and a ton of supplements...I actually find that the integration of science, math, and reading all fall into place naturally, especially just incorporated into the day!

I recently posted a How to Teach your Toddlers Science thread, and Taniket first mentioned BFSU then. I bought it immediately and have been thrilled!
Here is the thread, and I actually found a free ebook version of the Handbook of Nature Study, the link is also posted in the thread.
http://forum.brillkids.com/teaching-your-child-other-topics/how-to-teach-your-child-science/

And if nothing else, take a look at the Rookie Readers! Your LO is just about the right age and they tackle concepts like mass, density, gravity, atoms, etc, as well as a geo set and life science set as well

[sonya_post]

FYI - I'm taking my science thoughts over to the science thread. Korrale - I'll see you there.

[nee1]

FYI - I'm taking my science thoughts over to the science thread. Korrale - I'll see you there.

Me too! See you there.

[Korrale4kq]

Good idea!

[sonya_post]

Cross - posting this from the math supplement 3 y/o thread

Just wondering if anyone has seen or used this. Obviously we are not ready for it but thinking of ordering it. I found this on the Hoagies Gifted Website and it comes with rave reviews. The website is terrible. You have to wade through a mess to get to his material. Anyway opinions?

http://www.mathman.biz/

[sonya_post]

BTW-  did you know you could go broke buying school books?

[Kerileanne99]

Sonya- we must be reading each others minds I recently bought the package after sending him an email! I will post in the advanced 3-year old forum as others have asked as well!

[sonya_post]

I picked up Marshmallow Math from the library today. It is a fine enough book. But I think I will take notes but not purchase it.  It has great ideas but I liked and got more from KTM than Marshmallow. However, the KTM series is considerably more expensive.

The other thing that you guys might want to think about is picking up a Saxon 2 teachers manual and use it as a spine. Not the books for kids. It covers everything and is scripted. So it says, "say this.Then wait for a response and then say this.....Do this......

I really did like the way that Saxon taught stuff in the early years. I'm betting you can get them cheap on Amazon or Ebay or homeschoolclassifieds.com. It is going to give you that solid foundation and you can adapt the lessons as the kids move to larger numbers. It will be a book for you and you will really get a feel for the spiral approach that Saxon uses. You really don't need the student books as it is just straight math and you can get worksheets all over the internet.

You can use that with MEP or something else. And there is this resource: http://www.schoolhousetech.com/  I purchased the old version about 10 years ago, which I am still using. It is a much better product and will take a child through high school. I used it less as my son got older. But we used it to make time tests and a bunch of other stuff. i also used it to make tests when I couldn't find the test kits from Saxon.

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