Living Stones Academy

Educating by atmosphere, discipline, and life

New math, old math

on April 12, 2011

Do not allow a child to count by ones to find how many objects there are in a group, but teach him to recognize the group as a whole. — Teach what three means by repeatedly combining two and one, and one and two, into groups of three apples, three blocks, three marbles, three books, three pencils, three lines, three dots, etc., etc., and then immediately separating these groups again into their component parts, two and one, or one and two, apples, blocks, etc. When the group three instantly suggests the idea three to the entire class, teach four in the same manner by combining and separating one and three, three and one, and two and two objects. Make all the possible combinations and separations of integers forming each number, using as wide a variety of objects as possible.—From “Eclectic Manual of Methods” for McGuffey Readers and Ray’s Arithmetic

Today I witnessed a very good reason for not teaching children strictly how to read numerals—the physical representations for number 1, 2, 3, etc. Also why you want to be careful with what comparison words you use. For some reason we believe that small children are  both unbelievable sponges yet at the same time not too bright, so we throw information at them, but dumb down some of it. I know we’re guilty of saying “This number is BIGGER than this number” instead of “This number is MORE than. . . .” It’s not technically wrong, but if all they know of numbers are the written numerals then they have no concept of why it is more, and start to think in terms of size of the numerals.

Saw this firsthand this morning. Caleb and Isaac were playing with the foam number blocks—you know those interconnecting mats you can get? I heard Caleb say loudly, “So, Isaac”—by the way, he loves to pretend to teach like mommy –“is 6 bigger than 0?” Both said in unison, “NOOOO!!!”

Obviously I had to jump in—forget the laundry—and correct this right away! I went to the room, pushed aside the large numbers, and collected 6 plastic beads (the large baby kind). I told both boys to hold out their empty hands and tell me how many they had.

The trouble I then ran into is that Isaac cannot operate without his imagination (hence his tendency to make up stories about dragons when the Pastor asks him about the Bible, be scared of the dark—Caleb never was until Isaac convinced him it was scary; etc). Instead of looking at his hands and saying, “None” or “Zero” or “I don’t have any”, he kept grinning and saying, “One!” “Two!” “Six!” I finally gave up and told only Caleb to answer. Sometimes Isaac is MOTO (Master of the Obvious) and other times he’s MOTI (Master of the Imagination). Caleb is usually literal, if not always accurate or obvious.

Having decided which boy was best to talk to, we commenced with the lesson. I think we spent 5 minutes on it.  And we corrected the comparison words by working on saying “Three is MORE THAN two; zero is LESS THAN 6” instead of saying bigger and smaller. It worked to a point. Currently they are practicing (read: playing) on their own, but not using the foam letters: using the same beads I did.

I’m now changing my scope and sequence for math for next year to include those things I saw missing today.

I’m following Benezet’s Story of An Experiment as a basis for my scope and sequence, though it needs some tweaks. For instance, he doesn’t speak at all about recognizing quantity, and immediately wants children to recognize written numbers, which I’ve just said I don’t agree with. However, it is so far the best I’ve seen as far as what should not be covered in early years. Like telling time. Why on earth does a 5 year old need to read an analog clock? At 7 they start to have more responsibilities and so yes, then it is time to teach. But in kindergarten?? Also, counting money. When is your first grader going to be handling more than $1 on his own at the store? Yet everything I see out there—from Living Math to Stiller’s to MathUSee—has all these things covered in the very early years. Even Ray’s, who’s manual I quote above, has quite a bit of this scheduled in the first 3 years. Though they mostly discourage text work, which is what I love about the experiment, they still insist on all these ideas and more being introduced to a child that is still trying to get his brain around more and less than.

So I’m going to be using a hybrid over the next 6 years: Benezet, Ray’s, Receptive Math (free online lessons), and some living books on math (such as Number Stories of Long Ago, A Single Grain of Rice, etc). By the time we start delving into higher math like algebra, I hope to have children that are excited about finally seeing in text and on paper the things they know, and hopefully love, so well.

For another mom experimenting with textbook-free math see this blog.

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3 responses to “New math, old math

  1. Wow, so obvious, yet I managed not to notice, lol. Math lesson plans will be changed for today just to make sure that my little ones understand that it is not size but QUANTITY!

    • Good to know it’s not just me and I wasn’t making a generalization about others! LOL Glad to share. 😀 I’ll be checking out your blog, love to know what other homeschoolers are doing.

  2. […] just read a great article, “New math, old math“, posted on Sixsmoothstones blog.  Be sure and take a peak, it is simplistic but incredibly […]

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