Comments for sursumcorda.salemsattic.com/post/another-article-on-teaching-mathematics-or-not

Comment #1766

2008-04-18T22:13:44Z

Heather came through: Here's the post with Jonathan reciting Psalm 1.

Comment #1765

2008-04-18T20:41:36Z

Perla, your English is wonderful. My Spanish is nonexistent, or I'd appreciate still more of your blog. I do think you mean "profitable" or maybe "expedient" instead of "convenient."

Ruth Beechick's booklet (An Easy Start in Arithmetic) is indeed a very good one; thank you for bringing it to my attention. I love most of her ideas for exploring and practicing math concepts, especially because she includes a favorite game of our family's called Bang. She offers a simpler version and calls it Zap, but the idea is the same.

I do quarrel with her reliance on Piaget; the division of learning into Manipulative, Mental Image, and Abstract Modes seems useful, but I find these categorization too restrictive as well as inaccurate in my experience. Perhaps my prejudice comes from having had a child who could easily handle all three modes before she even entered school, and from our frustration at what the school had -- or more accurately, didn't have -- to offer her. That was another reason we chose to begin homeschooling. If she had had to wait until Piaget's recommended age 12 for abstract thinking, we would have both gone mad. And she probably would have given up on math altogether.

One of homeschooling's great advantages is that we don't need to rely on experts and their research. We can learn from them, but in the end it's the "individual and personal experiences" with our own children that matter most.

She hasn't spoken up here yet, but you might be amused to know that the same mathematical child I'm speaking of would probably agree with you more than I do, since she is very much an unschooler and favors natural learning whenever possible. Yet as a child those math workbooks and worksheets were just another type of delightful puzzle to her.

Comment #1764

2008-04-18T17:39:15Z

Hello Linda:‎

Well, as the Bluedorns said in the second article of my post “On Early Academics”, the ‎research until now shows that delay formal arithmetic instruction give better result in the ‎long term. ‎

They wrote about the delaying of formal math:‎

‎ …We very much want to learn if there is any contrary research or historical evidence. ‎Everything which we encounter on the question continues to confirm this common sense ‎view on the matter…‎

We can take decision based in our personal believes or in individual and personal ‎experiences, or we can take decision based in research which are based in historical ‎investigations and studies that use the scientific method with hypothesis and analysis of data, etc.‎

Until now, while we do not find another study that invalided the previous research, we do ‎not have a reason to believe the research false.

As you know, all is allowed to us, but not all is convenient. I think the workbooks and ‎flash cards styles of learning for yound children are of those kinds of things that are not convenient. At least ‎not have prove to be convenient.

Bye, bye

Ps: Sorry my English, as child I only study English in textbooks.‎And thank you for your words. I visit your blog sometimes, but my english is not in the level of understand all what you wrote, I am working on that :)

Comment #1763

2008-04-18T14:36:07Z

By the way, I highly recommend visiting Perla's Classical Mommy site. Even though we don't agree on everything -- as I've said before, I don't even agree with myself on everything! -- she's a remarkable woman and has assembled an enormous collection of resources.

Comment #1762

2008-04-18T14:23:41Z

Hi, Perla! Thanks for commenting. I can tell from your work with Octavio that you are not opposed to teaching math as a subject, and have changed my first sentence to one which I hope you will find more accurate.

The superintendent, however, was more extreme, and I especially quarrel with his contention that any formal instruction in arithmetic should be delayed till at least sixth grade. Certainly I do not believe that workbooks are the best way to learn math -- before age ten or at any other age. But I do believe that teaching logic and giving a good, foundational base in practical experience should not preclude the rote learning of arithmetic facts. Scales are not music, but knowing the scales upside down, backwards, and standing on his head in a cold shower allows the musician to concentrate on making music. Phonics isn't reading, but knowing the rules so well you no longer have to think about them facilitates true reading fluency. Knowing arithmetic facts won't make one a mathematician, but can smooth the way for higher thinking. Workbooks, computer games, flash cards, educational songs, and even skip counting while bouncing on a trampoline (as our children did) are all useful tools; the problem, I believe, comes when they are allowed to take up too much time, or become an end in themselves.

I agree wholeheartedly about the puzzles, by the way. Jigsaw puzzles, logic puzzles, word puzzles -- even those that seem to have no direct connection with math seem to stimulate the mathematical part of the brain.

I'm sure I would agree more with your position (as I understand it; I may still be wrong) if I thought this were and either/or choice. I see no reason why we can't have it all. :)

Comment #1761

2008-04-18T13:28:54Z

Hello Linda:‎

Just to clarification, ‎

I never said that children must do not learn arithmetic before age ten. Please, read my ‎post again.‎

What I did said is that in the first ten years is better to teach math in a practical way, as the ‎suggestion of An Easy Start in Arithmetic by Ruth Beechick, or Math on the Level. ‎Maybe if you check those books, you will agree with me.‎

I did say that workbooks (math drill in paper) are not the only (and are not the best, better ‎avoid them) way to learn math, those are modern ways that had being probe not to be ‎very efficient in the early ages.

Real life experience, solve real life math problems in the ‎daily life, reasoning, puzzles, table games, counting money, learn to use measurement ‎instruments, etc. are better ways to learn math than drills in paper that usually are ‎disconnected of the reality.‎

Again, if you read my suggestion (basically Mrs. Beechick’ s book ) , I think you will ‎agree with me

Now, if your postion is: "workbook are the best way to learn math before age ten", well in this case, yes disagree :) , because my posture is about workbooks,not about arithmetic or math in general.

Bye, bye