Trivium Pursuit

Delaying Formal Math

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I just received your book Teaching the Trivium: Christian Homeschooling in a Classical Style a couple of days ago. I’ve been reading the article on math because that’s the area of my children’s schooling that seems to be least successful. My 12yod never was mathematically inclined, but my 2nd child, an 8yod, has always been mathematically-minded. I expected the older to not be crazy about math and to have to go to great lengths to find a program that fit. However, the one that is a natural at math is starting to dislike math. Left on her own (before kindergarten and 1st grade) she was adding in her head. Once I started her on a program, all self-initiated math ceased. After 2nd grade was over this year, although not right away, she began to do multiplication orally/mentally on her own, even though she was disliking math and struggling somewhat with simpler problems. Now, it may seem obvious what I should do — drop the curriculum. But, leaving her on her own won’t necessarily cover all that she ought to cover (for testing). It won’t be systematic, consistent. Any advice would be greatly appreciated. Should I just bite the bullet and put away the curriculum? And what should I do with my 12yod? She still struggles with the four simple operations. She is advanced in every other area, just in case you’re wondering if there is something biologically wrong. Also, about all the quotes concerning how math was not a subject in the grammar school… I might not know history well enough where math is concerned, but math as a science was still being developed, wasn’t it? So it wasn’t even at the point of being teachable, was it? Also, if children can understand an abstract symbol system like alphabets and reading, why can’t they understand an abstract symbol system of numerals and arithmetic? Trying desperately to understand. Thank you for your time. Gail S.

We get more questions about math than any other, and you will find that the subject of math comes up quite often. When we do our seminars, at one point we ask, “How many of you did not like math in school?” Every time, no matter which state we are in, about half of the people raise their hands. Why is it so many people dislike math?

If you read the article on the history of teaching math you noticed that until the 20th century, math was not taught in a formal way to children before age ten. Before the 20th century, children under age ten learned math (actually arithmetic) informally, and began to study math formally, in schools or at home, around age ten. A man named Pestalozzi changed all that at the turn of the century by introducing some new ideas about education.

Some highly developed concepts of mathematics have been developed in the last few centuries — such as calculus. But none of that is the subject matter of elementary mathematics.

When you teach a child that the letter “a” stands for the sound aay, you are right to say that it is an abstract concept. But when you teach a child that the digit 2 stands for the number two, you must also go one step further and teach him that the digit 2 and the number two stand for “two things.” It seems to me that math is somewhat more abstract than the teaching of reading. There is one more step to learn in the study of math.

The symbols of the alphabet are phonetic, linked to the auditory-speech mechanism which the child has been experiencing and practicing with since his goo-goo-gah-gah days. The numerical and operation symbols of arithmetic are further abstracted one or more steps from this. The more complex combinations of abstractions are physically more difficult for the young brain to handle. The child’s brain will store the information where it can best use it AT THE TIME — in a linear file. Unfortunately, at an early age, because of the lack of physical development of the brain to handle such abstractions, that information is stored in a place which is less accessible to the brain after it has become more highly developed. At a later age, the brain will develop multidimensional arrays, and this information is more accessible when so stored.

But, leaving her on her own won’t necessarily cover all that she ought to cover (for testing).

I would avoid testing young children at all costs. There are only a few states where testing young children cannot be avoided, and if you live in one of those states you might have to be satisfied with lower test scores in math during the younger years. Actually, everywhere we have traveled and discussed this topic we have heard plenty of evidence that children DO do well on math tests even though they are following the so-called “delayed formal academics” approach.

I would suggest dropping the study of formal math with your younger child and study math informally with her (see our book for ways to study math informally). When she turns ten she can start a systematic and consistent study of math. You will have plenty of time to work through grades 6 – 12 in math (including calculus, if needed) before she is 18 years old.

With your older child, I would go back and start studying math at the point where she is beginning to get confused. There is nothing wrong in going back a grade or two in math. We’re not out to produce college math professors, are we? The goal is to produce children who understand and enjoy it. What I usually find when mothers talk to us about how their children dislike math is that the mother also disliked math in school. I’m wondering if parents are somehow communicating this fear and dislike to their children. Maybe we did hate math when we were in school, but homeschooling parents don’t have to be afraid anymore. This is our second chance to learn it again and learn it better. Repeat after me, “I love math; it is my favorite subject.”

Some people mistakenly believe that we were the ones who originated the idea of delaying the study of formal math till age ten. Not at all. This idea has been around for a very long time. In addition, it was Raymond and Dorothy Moore who reintroduced this idea to American education in the 1970’s (read Better Late Than Early: A New Approach to Your Child’s Education). Some people read what the Moores and we write concerning delaying the formal instruction of math till age ten and conclude that we are opposed to teaching any math to any child before the age of ten. Not so. When the child asks questions, answer them. If he asks for a math workbook, buy one for him. But this is different from systematically working through a math curriculum with a child every year from age five through age nine, doing every page, teaching every concept according to a preset schedule/”scope and sequence”/”typical course of study” developed by World Book or A Beka. There is a more thorough discussion of this topic in our book.

The mathematician Blaise Pascal was homeschooled by his father after his mother died. His father didn’t think any subject should be taught until the child could easily master it, so he removed all the math books until the children were at least sixteen years old. At twelve years old, Pascal studied math (in secret) and figured out that the sum of three angles in any triangle is 180. His father was so impressed that he allowed him to study Euclid, and by age sixteen the boy was the first to prove some new geometry theorems which he presented to, among others, Descartes. His work has influenced philosophers and scientists including Descartes and Isaac Newton. This is a good example of delaying formal math.

Learn more about Blaise Pascal:

A Piece of the Mountain: The Story of Blaise Pascal
Works of Blaise Pascal
Pascal’s Wager: The Man Who Played Dice with God

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3 Responses to “Delaying Formal Math”

  1. Hélène Says:

    I am advanced in all areas. I was in school also. Except for math.
    UGH
    I detested it.
    Some ppl ain’t mathematically inclined.
    Keep trying to automate the 4 operations. And get the 12yo a manipulative based curriculum. That will work wonders.
    Now after 30+ yrs of HSling and learning how God shines thru in numbers and patterns, establishing rules and order in the universe — I do like math.

  2. Hélène Says:

    Waiting, for me, would have done no good. In fact, the earlier exposure to numbers and patterns and using manipulatives would have helped me.
    In my house, my very abstract (Math major) mother did all math in her head. My dad did no math beyond construction needs, even tho he was a 6th grade teacher for his formal job. Math was not part of my world; words were. Words were my whole world. I read and wrote from age 5. My mom asked me the spelling of words.
    I needed math early on too. Not formal, not hurried, not pushed…but numbers.

  3. Jessica Says:

    Years ago I read your book and put away the formal math. I have a 15 year old that started on formal math at 10 but now he’s behind where he should be if he wants to go to college for an engineering degree (which he does). You mentioned above that “You will have plenty of time to work through grades 6 – 12 in math (including calculus, if needed) before she is 18 years old.” Could you elaborate on this? Do you just plug a 10yo into 6th grade math? How are all the math subjects covered between ages 10 and 18? We are currently working through pre-algebra.

    ——————

    What has he worked through so far (in math)? Laurie

    ——————

    We use Math-U-See and he started at the beginning with Alpha and has worked his way up to Pre-Algebra. Next, will be Algebra followed by Geometry, Algebra II, PreCalculus and Calculus. I don’t expect him to reach Calculus in high school though. He’s a good student and self-teaches himself in math and most other subjects. He rarely has math questions and tests A’s and B’s.

    I have 7 other kids after him, so I really appreciate your thoughts.

    Warmly,
    Jessica

    ———————–

    This is generally what we suggest:

    age 10 — 6th grade
    age 11 — 7th grade
    age 12 — 8th grade (pre-algebra)
    age 13 — algebra 1
    age 14 — algebra 2
    age 15 — geometry
    age 16 — advanced math
    age 17 — calculus

    An average student is capable of starting with 6th grade math at age
    10. I’m wondering if your son has been going through the math
    curriculum too slowly. I suggest re-assessing the situation to see if
    he could safely skip some of what he’s doing now. Laurie

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