I think what intimidates us most about teaching math to our children is our own ignorance of the subject. Knowing how it is approached dissipates confusion and frustration. I’ve created a video that helps explain (but this post has all sorts of other goodies and links you don’t want to miss out on, too):
Here are some great links to things I mentioned in the video that may be of great help to you:
Besides all that, here’s a free downloadable chart to give you an idea of how math is typically structured:
But wait, there’s more! Here is a republish of a post I wrote on the subject not too long ago:
First, what math instruction was….
Before the 20th century people didn’t care much about mathematics.
Beyond basic figuring most folks never gave it much thought.
Math instruction was very different back then. Most school masters couldn’t “cipher” for themselves. Students did nothing more than copy and memorize rules. No logical, gradual introduction, no practice problems. Some students learned how to figure for the merchant trade, but few pursued higher math.
Then some rare men changed all of that. One of them was Dr. Joseph Ray, a schoolmaster who not only loved math, but loved teaching math to children. He not only presented rules and theories to be memorized, but offered practice problems and examples of application. The books he wrote in the 1830’s made learning math logical and interesting. These texts were popular for almost a hundred years, selling 250,000 copies between the years 1903 and 1913 alone!
Regular folk still failed to see the use of math except for common trading, but times were changing. The years during which Ray’s arithmetics were sold were years of amazing invention and innovation. As technology increased, so did demand for those who could do higher math. Eventually books were published for teaching scientists and engineers.
Then two movements changed the way we look at arithmetic.
The first was the Progressive Education Movement.
Folks like John Dewey were in charge of this one. Western society was becoming more secular, even humanistic. Instead of relying on the strength of individuality, social engineers looked at children in groups and manipulated them like commodities on the stock market. Education was about manufacturing, not about learning.
Common sense approaches such as Ray’s Arithmetic were forced out, and in their place were books that were “modern” and treated children as mere calculating machines (one of Dr. Ray’s fears).
The second movement was the Space Race.
This began when the Russians leaped ahead by launching Sputnik in 1957. It wasn’t just about space, it was about the threat of communism. Folks believed our destiny was tied to our ability to compete in a technological age. The entire American education system was overhauled. The new curriculum put math center-stage and anyone who couldn’t measure up was left in the shadows.
Next, what math instruction is…
The pace has only picked up since the 1950’s, but it seems as though we are falling farther and farther behind.
It is almost as if we have gone back to the time in our history when arithmetic was considered irrelevant. Our children are drilled and tested more than ever, but they know less than previous generations.
Survey of 23 industrialized countries ranks United States at 21 for numeracy, just in front of Italy and Spain…The main problem identified by the data…was with younger American workers, who lagged in nearly every category.
Graduates these days lack basic arithmetic skills, or what is referred to in the quote above as “numeracy.”
A numerate individual has the confidence and awareness to know when and how to apply quantitative and spatial understandings at home, at school, at work or in the community.
We’re turning out rocket scientists who can’t tie their own shoes.
Finally, what math instruction should be…
It should be logical.
There should be a gradual progression that makes sense and is easy to follow without a lot of jargon attached. None of this fuzziness, forget the complicated explanations that make children feel lost.
It should stimulate the imagination.
Math is not just a subject in school. Our days are precisely 24 hours, each one divided by 60 minutes which are divided by 60 seconds. Even our heart beats point to rhythmic order. Some have said that we exist in a hologram built out of numerical order.
(If you have a few moments, watch this video and be amazed!)
It should have personal value.
“Story problems” are not enough. Children need to be immersed in the huge laboratory called life so they can find out how delicious fractions are when they bake a cake or how exhilarating algebra is when they are flying around on a roller coaster.
It should be short and sweet and leave time for natural exploration.
An hour a day of actual operational math is more than enough, and even less at younger ages. My ten-year-old does about 20 minutes, my seven-year-old less than that.
It should start later rather than earlier.
Numbers are not concrete, they are abstract. Small children have not run around in this world long enough to have a grasp of what that means. They need time playing with cups in the bathtub, watching the arc as they swing back and forth, building with Legos, estimating the exact time to mash the brakes on their bicycle, engaging in language and reasoning.
I cannot do this idea the justice Denise Gaskins has in her delayed arithmetic series.
Here is an excerpt:
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.
Gaskin refers to a math teacher who tested his theory of delayed math instruction by the name of L. P. Benezet. You can read an article about his findings here.
I have found this to be so very true with my own children. Delaying formal math has not hurt them, it has helped them. The ones who started later moved forward faster and stayed interested longer than those who began early and learned to hate the whole process.
Today the ones who struggled early-on are handling businesses, coding websites for colleges, and keeping out of debt via careful budgeting.
Professor Ray had it right. Children who find math logical, interesting, and life-enhancing have no trouble learning it. When done right, homeschooling does not put children behind, it gives them a head start.