Fish eyes by lois ehlert 

Written in response to a question on the LivingMathForum.

Question:  One of the books we found was Fish Eyes. Do I just read this book, or is there more to it?  Btw, the kids I'm reading this one to are 5 and 8.

A book like Fish Eyes would be on my lap to read with about 4-5 others of similar length, or with one or two that are longer. That particular book is more for the younger children, I suppose being more specific might help in that it's pre-multiplication age, but my 8 y/old loves the artwork and listens in. That author/illustrator has a beautiful living science book called Feathers For Lunch I just found recently as well, if you like the artwork.

It's an addition book, even though it may not look like it, for the very young, anticipate that 2 1 equals 3, 3 1, equals four, and so on, there's a pattern. So as I read, I read the last part "plus me makes . . ." and leave it up to my girls (4 & 6) to fill in the blank. My 6 y/o has gotten used to letting the 4 y/o answer the easy ones like this, or they take turns. As the text doesn't exactly repeat each time, they get that the math is the pattern. There is also visual stimulation with the adjectives and artwork - some pages are very mixed up, but some are symmetrical. Whenever I see a page that has some symmetry, I ask if there is a pattern, or can we count by 2's, or 5's, etc. (similar to the Greg Tang books but w/out the script!).

If you have the book you can see on the page before the 1 fish, there is a neat little line of green fish - count have them count those by 2's (2, 4, 6, 8 etc.) with 2 fingers each. You then might count the light green fish, and the dark green fish, noticing the alternating pattern. On the 7 page there are four little fish that have 2 stripes each, count the little fish, then count the stripes by 2's - multiplication. We do this technique with so many books it becomes natural, and reading in a group they vie for their turn to do it. On the 10 page, my 6 y/o might be the one to count the blue fish and the green sea horses, adding 5 5 to get the total of 10. I really like this book because it is predictable in some ways, but not in others. I have it listed as not necessarily engaging for the middles, so your 8 y/o may not go for it, but mine listens in on ALL our readalouds if he can. And tag lines like "If you could truly have a wish, would you wish to be a fish?" I read with a lot of feeling, looking right at my 4 y/o, then my 6 y/o, usually rewarding me with a huge grin and a "Naahhh." Have fun and keep it lively.

Julie Brennan
June 18, 2004

The Old Lady Who Swallowed A Fly

Question: The Lady Who Swallowed the Fly -I know that, we have sang that since I was a child.  Are these books suppose to be math related and obvious about it?  

When you realize that mathematics is much more than arithmetic, you start to see math in many more places than you realize.

The Old Lady Who Swallowed the Fly deals with a cumulative pattern with a limit. It is, quite mathematically: 1 = 1, 1 1=2, 1 1 1=3 and so on. And it is further mathematical in that you recount the cumulative addition in the story backwards, in exactly the same sequence as it is built up. Each item is not only bigger than the previous one, but has a logical relationship in consuming the prior item, again reinforcing the cumulative "counter" going on in the story.

There is absurdity of course in the limit - how many things can she swallow and still live?? But for a young child, there is a thought process going of volume and increase to a limit. The funny part is how extreme that limit is - of course we could not swallow a dog and a cat - but we can swallow a fly and spider. At some point, mentally the child is calculating limits and entering into the absurd, which is size, space and volume thinking. When I read books like this I stop all the time and ask questions to the 4 y/o especially like, "Do you think YOU could swallow a cat??" She'll grin and say "No!!" And we'll agree that it is silly. The question though puts the story in her world, what would that feel like? Obviously a cat would be too big . . . size, space and volume.

Another more unusual book that does a different twist on this is Mother, Mother I Feel Sick, Call for the Doctor, Quick, Quick, Quick. Many folklore tales from ancient times have this kind of a theme - some are cumulative like this one, others are more sequential, like our modern If You Give a Mouse A Cookie . . . Some end up in a different place, others loop around in an endless circle. These are like mental geometry with language and develop mathematical thinking, especially if read repeatedly and my children do read these repeatedly. A toddler that cannot read can pick up these books having had them read to them and "read" them to themselves with the pictures forming the anchors for the stories. This is why I think picture books are superb for early math.

All the books on my library page are ones I actually own and use, I have been collecting these for years from Chris Brock's used book list, library sales, and I'll invest in a new one now and then. I don't buy much curriculum, so this is where my budget goes. We used the library for years, but my late fees often would have paid for a new book and caused me to search out the used books instead. If you are very good at managing library books, though, many are available.