Posted in wwlw

learning to love math

Rondel never took to the “3 R’s” of education quite as naturally as Limerick (most people don’t, honestly), though he is an information sponge for the things that interest him, which have throughout his life been mostly science-related. We’d tried a couple of different approaches to learning and practicing math before I came across the Life of Fred curriculum (and I don’t even remember where, or I would definitely send them my thanks!).

Life of Fred is very, very different from any other math curriculum I’ve used. Every math concept is introduced in the context of a story about Fred Gauss, a five-year-old math professor (yes, it’s strange, but you have to just roll with it), and the end of each short (ridiculous, hilarious, bizarre) chapter has a few practice questions that work in both new and old concepts. So kids reading through the stories begin to see math as something useful, lovable, and even beautiful as it snakes its way through Fred’s everyday life (and his very odd adventures). And the stories will have kids laughing out loud along the way, if they are at all like Rondel (and myself!).

The elementary series for Life of Fred starts with Apples and Butterflies, which are both kindergarten level, and goes from there – through decimals, fractions and percents, through pre-algebra and algebra, and all the way through calculus (which was actually the first book the author wrote, oddly enough). While the books are published by Polkadot Publishing, I couldn’t find a way to purchase directly through them and ordered from ZTwist Books instead (free shipping!).

We are just beginning Cats now, having spent an average of 3-4 weeks each on the first two books. Rondel has been asking me to read Life of Fred all the time – more than I can right now with my lingering sore throat, and more than Aubade has patience for at times – and I can see his confidence with math growing week by week (we’ve been using the books for over two months by now). He will now tell people that math is his favorite because of Fred; he doesn’t get overwhelmed by basic addition and subtraction problems; he is starting to understand analog time-telling; he is getting better at remembering the days of the week and months of the year; he will skip-count for fun; and he is learning to notice patterns and sets in the things around him. The practice problems force him to focus as he has to recall information and use concepts in new contexts, but there are never so many in a set that he can’t make his way through them all.

In short, I am so glad we found these books and highly recommend them for anyone else, particularly those kids who are struggling with a traditional approach to mathematics.

Posted in wwlw

what we’re learning wednesday: episode 4

Rondel and Limerick are very different academic beings. Rondel’s first love is stories – he tells them, he listens to them, he invents them, he demands them, he constantly (since before he could talk) brings us books so he can hear their stories too. He soaks up facts about animals, and then populates his worlds with monsters generated from conglomerations of the different animals he loves. Limerick, on the other hand, has always been intrigued by symbols and patterns. He knew all (and could write most) of the letters and numbers by 18 months, spent a good 6 months nearly inseparable from a Duplo pattern board he created, and currently puts a lot of energy each day into creating symmetrical designs and exploring the world of numbers.

When we introduced Cuisenaire rods (a really great math manipulative, by the way – I grew up using these with the Miquon math curriculum and have always felt that they gave me a strong conceptual foundation in mathematics) for the first time this week in preparation for more kindergarten-type activities, this difference in their inclinations was immediately evident.

Limerick went through each color rod, noticing how long each one was as compared to the small white unit blocks. When he reached the longest rod, he began to line up the smaller rods next to it, to see how he could split it up. Ten is ten groups of one, he realized, and five groups of two, but when you try to split it into groups of three you end up with one empty space.

We made squares (one group of one, two groups of two, three groups of three, etc.) and talked about the difference between the perimeter of a shape (how long all the edges are, put together) and its area (how many white unit squares could fit inside it).

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Meanwhile, Rondel was using different sizes and color of blocks to retell the story of the Three Little Pigs with house-building fleas and a predatory lion (I think he chose fleas because they are too small to see, and he didn’t have any prey animal toys on hand to use with the lion figurine). He went through all the steps of the story with sound effects and drama, creating and destroying as necessary, completely immersed in his imagined world.

When the boys play together, I see these inherent differences leading to growth in each of them. Rondel’s love of imagination draws Limerick along with him into wildly creative and unrealistic pretend games, while Limerick’s fascination with numbers and patterns motivates Rondel to learn the vocabulary and concepts of math also. It makes me glad all over again that they have each other to grow up with.

So what are we learning, this Wednesday? We are learning about how numbers work together, how they split apart and recombine in consistent ways. We are learning about the trial and error it takes to finally build a house that can keep out a powerful lion. And we are learning about each other, and how we can help each other learn in grow in different ways.

Posted in wwlw

what we’re learning wednesday (episode 2)

Limerick is currently in love with numbers.

He counts everything he can, comparing amounts and sizes: he counted all the straps on the plastic pool chairs at the public pool Saturday afternoon, at least ten times in a row; he makes long chains of flakes and counts them over and over again as he builds to find out how long they are and which color is the longest; he counts the number of bites or slices on his plate and recounts each time he eats one. Essentially, he is spending time with the numbers and quantities, becoming friends with them, getting to know how they interact with each other and discovering their unique qualities.

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Limerick figuring out how many sticks could fit on the length of our big wooden cutting board – I think it was somewhere around 40.

He will break numbers down into their component groups: if he builds a tower with fourteen wooden blocks, he will tell me proudly that it is two groups of seven. When he expanded his tower to eighteen blocks, I asked if it could split into two equal groups and he lined them up into two equal lines and counted each one to make sure that they both contained nine blocks. When I then asked if it could split into three groups, he made many little groups of three blocks and found out there were six of them – so, six groups of three and three groups of six. Since he’s been doing this on his own anyway, I introduced the vocabulary of “even” and “odd” to him.

“See this group of seven? I can’t break it into two groups of the same size – one of them is always bigger than the other. Numbers like that are called odd.”

Limerick pondered, then declared, “But eight is two groups of four!”

“Exactly! Numbers that can be split into two groups of the same size are called even!”

“Nine would be five and four,” Limerick told me with a slight frown, “but ten would be five and five!”

“So nine is odd, and ten is even!”

We’ll see if he remembers – he tends to hold a new word to himself for a week or so after he learns it, before he brings it out for everyday use.

Emboldened by all the math talk going on, I pulled out one of my favorite math tools from my own childhood (one that I believe my mom created, and that she now uses in her job as a remedial math professor at the community college):

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It’s a physical representation of place value – the numbers on the cards in front show what the number would look like written down, while the buckets hold the appropriate number of craft sticks. In this picture, there are three single craft sticks in the box on the right, six bundles of ten craft sticks each in the middle box (the tens place), and nothing in the box on the left (the hundreds place).

We pulled out some huge foam dice and decided to take turns rolling and adding the number we rolled to the number already in the buckets:

Sometimes the boys knew right away what the answer would be; other times they would line up all the sticks to count them to make sure, and to bundle up the new ten-pack if needed.

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Limerick verifying that the three bundles of ten sticks in the tens place bucket really did equal 30 total sticks! I liked how he lined them up in groups of ten instead of just all in one big pile.

Before this we hadn’t done much with written numbers – the boys know all the digits, but they didn’t understand double digit numbers. So it was a bit confusing at first for them, but by the time we stopped I think they were beginning to understand what the numbers meant and looked like, which is really cool!

Math tools and games like this aren’t necessary for learning math – Limerick has certainly been picking up on concepts ranging from quantitative comparison to division (with even a touch of fractions) just from everyday conversations about the numbers around us – but they are definitely helpful for illustrating a specific concept, challenging the mind to use a concept in a new way, or just having fun together with numbers! And since all you need for this particular tool are buckets, sticks, and paper, it doesn’t get much easier 🙂