To my fellow homeschoolers,

It’s counter-intuitive, but true: Our children will do better in math if we *delay teaching them formal arithmetic skills*. In the early years, we need to focus on conversation and reasoning — talking to them about numbers, bugs, patterns, cooking, shapes, dinosaurs, logic, science, gardening, knights, princesses, and whatever else they are interested in.

In the fall of 1929 I made up my mind to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite – my new Three R’s. And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language.

— L. P. Benezet

The Teaching of Arithmetic I: The Story of an experiment

The children in these rooms were encouraged to do a great deal of oral composition. They reported on books that they had read, on incidents which they had seen, on visits that they had made. They told the stories of movies that they had attended and they made up romances on the spur of the moment. It was refreshing to go into one of these rooms.

A happy and joyous spirit pervaded them. The children were no longer under the restraint of learning multiplication tables or struggling with long division. They were thoroughly enjoying their hours in school.

…

One of our high school teachers was working for her master’s degree at Boston University and as part of her work he assigned her the task of giving tests in arithmetic to 200 sixth grade children in the Manchester schools. They were divided fairly evenly, 98 from experimental rooms and 102 from the traditional groups, or something like that. These were all sixth graders. Half of them had had no arithmetic until beginning the sixth grade and the other half had had it throughout the course, beginning with the 3-A.

In the earlier tests the traditionally trained people excelled, as was to be expected, for the tests involved not reasoning but simply the manipulation of the four fundamental processes. By the middle of April, however, all the classes were practically on a par and when the last test was given in June, it was one of the experimental groups that led the city.

In other words these children, by avoiding the early drill on combinations, tables, and that sort of thing,had been able, in one year, to attain the level of accomplishment which the traditionally taught children had reached after three and one-half years of arithmetical drill.— L. P. Benezet

The Teaching of Arithmetic I: The Story of an experiment

Read all the posts in the Delayed Arithmetic Series.

For more ideas about teaching math informally, check out my book Let’s Play Math: How Homeschooling Families Can Learn Math Together, and Enjoy It!

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Thank you SO much for writing this and showing me this guy’s stuff. This is key to what I’ve been telling my husband about math teaching. (I’ve sworn to not give K8 a math book until she BEGS for it.)

Hi, Bon!

I’m glad you enjoyed the links. I go back and forth between this sort of natural learning and a more directed style of teaching. I

definitelybelieve in delaying formal, algorithmic math — the step by step procedures that haunt so many elementary textbooks.But I enjoy math books so much that I can’t resist them. For instance, I wanted to play with Miquon Math

myself, and giving the books to my daughter gave me an excuse to buy them.Of course, now that Kitten is in 8th grade, I no longer have the excuse, but that didn’t keep me from buying Beast Academy. It just meant I had to use my personal budget, not the school fund…

Very very true but a hard one to sell to non mathematicians! Excellent article.

Pingback:How Can I Teach Math If I Don’t Understand It? « Let's Play Math!Pingback:Monthly math roundup: Math Teachers at Play 53 - fun tips | Motion Math - Play with numbers!Pingback:Math Circle Topics, Math Advice, and Math Lawyer | Talking Stick Learning CenterPingback:How to Recognize a Successful Homeschool Math Program | Let's Play Math!Pingback:Homeschooling High School Math | Let's Play Math!My 5.5yo son has picked up a lot of math, formal and informal, from apps on my phone, games on the computer, story books, etc. I think it doesn’t hurt to introduce formal math at a young age, so long as you keep the child in mind. We sometimes do multiplication tables while waiting for his school bus in the morning, for example (I have a variety of apps for that). I bribe him with buying the next multiplication rap app if he memorizes one of the other ones and can answer all of the randomized questions in about a minute and a half.

I have never done worksheets of math with him, and I do use lots of variety, but a lot of it’s still formal math (the rest obviously is informal math). I think in some ways it might be easier to get kids to memorize all their math facts at a young age, while you can still do it playfully, without the stress of having to learn them *now* or facing a bad grade.

I also just finished Life of Fred: Apples with him, although more as a way to get him to listen to stories (his verbal IQ is 75).

An app that seems fun but that is still a bit hard for my 5.5yo is Dragonbox Algebra (a definitely *informal* way for learning the algebra rules).