Written by Jamie Martin of Simple Homeschool and Steady Mom
Two weeks ago I began a short series on math by explaining how our family decided to approach this subject in a non-traditional way.
If you missed that post, I’d recommend reading it first before continuing this one.
Today I want to continue by serving up more math inspiration. Several “out of the box” math links follow, which I hope will help you come to your own unique conclusion on this topic.
Many of these fueled our personal decision on when and how to teach math.
You can read the entire post I reference by clicking on the title link. I’ve also written a short overview as well as included excerpts. Enjoy!
David Albert shares the story of 9-12 year-olds who learned all K-6 math in just 20 hours of study. He also shares his belief that an average teen who is actually motivated to learn math, and wasn’t held back by math anxiety, can learn all the K-12 math that he hasn’t naturally picked up in life in approximately eight weeks of study.
“So, do the math. If you figure the actual math time at 30 hours a year for 8 years (accounting for the wasted time in the early years), it totals 240 hours. Lo and behold – if, at age 15 or so, you wanted to learn all the math K-12, weren’t inhibited by math anxiety, and were willing to spend 30 hours a week at it, it would take you…8 weeks!”
In this 25 page article (later expanded into the book above), research mathematician Paul Lockhart makes the case that math is an art form, and that the way we currently study it prevents kids from falling in love with and seeing it through the lens of imagination that the other arts inspire.
“If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done–I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”
“You want to train them to calculate 427 plus 389? It’s just not a question that many eight-year-olds are asking. For that matter, most adults don’t fully understand decimal place-value arithmetic, and you expect third graders to have a clear conception? Or do you not care if that understand it? It is simply too early for that kind of technical training. Of course it can be done, but I think it ultimately does more harm than good. Much better to wait until their own natural curiosity about numbers kicks in.”
This article shares (in thorough detail) how math has been taught historically through the ages–a fascinating study! The author then suggests waiting until around age ten to begin formal math lessons.
“So to wait until age ten to teach arithmetic is actually, from an historical perspective, to advocate an “early start.” It is only from a decidedly modern perspective that waiting until age ten would appear to be a “late start.”
“Depending upon the child, upon the method, and upon the subject matter covered, there exists the potential for developmental harm from the formal teaching of arithmetic before age ten.”
“Small children cannot understand many arithmetic concepts at an early age. We can teach them to perform the process, but we cannot make them understand the concepts. The child “learns” to hate “learning.” The child’s understanding develops along the wrong lines. He may actually develop mental “blocks” to arithmetic – actual physiological blocks in the brain.”
How can someone actually begin the formal teaching of math at age ten?
Laurie Bluedorn suggests one possibility in her follow up article to the above – Delayed Formal Math Approach:
“At age ten we start the child in formal math with a 6th grade math textbook. I give the child two math grids, and they are allowed to use them when doing their math lessons.”
At age eleven I take away the addition/subtraction grid. The child should have the addition/subtraction facts memorized by then. If I think that he doesn’t have them memorized then we would drill on them till he does have them memorized. At age twelve I take away the multiplication/division grid.”
Louis P. Benezet’s study…as told in Free-Range Learning
In 1929 Louis P. Benezet, the Superintendent of Manchester, New Hampshire schools, tried an experiment within his system. He trialed having some of his classes wait until seventh grade to introduce formal math study. Before that time he encouraged naturally occurring math learning in the classroom, but had teachers make reading, writing, and reasoning the focus in the early years.
“I feel that it is all nonsense to take eight years to get children through the ordinary arithmetic assignment of the elementary schools. What possible need has a ten-year-old child for knowledge of long division? The whole subject of arithmetic could be postponed until the seventh year of school, and it could be mastered in two years’ study by any normal child.”
“Due to pressure from some school principals, children were started on a math book in the second half of sixth grade. All sixth-grade children were tested. By spring of that year, all the classes tested equally. In other words, those children exposed to traditional math curricula for part of the sixth-grade year had mastered the same skills as those who had spent years on drills, times tables, and exams.”
What we do in our family
In some ways it’s difficult to explain exactly what we do in our family–because it is, has been, and no doubt will continue to be completely different for each child. There’s no formula, but we have followed the advice mentioned above about waiting to introduce formal math.
This decision comes from our deep belief in the importance of our young children having a full and thorough Core Phase, which does not include a focus on early academics.
Two of my three children are now in the second phase of learning, Love of Learning, and recently math emphasis has crept into our lives more regularly. But it is still highly individualized and based on each child’s needs and strengths.
I have one who is naturally gifted with numbers, who has “played” with them over the years and by doing so has picked up quite a lot. I have two children who learn very differently to the traditional classroom style and who appear to have their geniuses (at this stage) in other areas. Of course this doesn’t mean that math won’t be a part of their lives, but it means that I introduce concepts when I believe maturity and readiness are present–so I can set them up for success.
If you decide to get out of the box when it comes to math, what can you do in the early years to prepare and play with numbers instead? I’m glad you asked!
Come back next week for a list of specific resources so you can create your own math playground.
“Mathematics should be taught as art for art’s sake. These mundane “useful” aspects would follow naturally as a trivial by product. Beethoven could easily write an advertising jingle, but his motivation for learning music was to create something beautiful.”
~ Paul Lockhart
Are there any helpful or surprising aha moments you have when reading any of the above articles? Do you find yourself feeling excited, skeptical, scared, or some other emotion while reading?