By Lynna Sutherland of Homeschool Without Training Wheels
My parents’ generation were among the pioneers of homeschooling. They believed that yes, they could educate their own children in their own home. They were homeschooling long before it was cool.
Their curriculum choices were limited. My mother recalls that her two main options were both companies that designed textbooks for private Christian schools.
In our generation, homeschooling is gaining steam and increasing in popularity. Though we might still get funny looks at the grocery store or funny comments from extended family members, most folks are aware of homeschooling as a legal educational option.
If the challenge of the last generation was to believe that we really can take the child out of school and educate him at home, the challenge of this generation is to believe that we really can take the school out of the home without harming his education.
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Math: the Last Holdout
I know plenty of families who have shed the idea of grade levels and no longer feel the need for textbooks in most of their subjects. They read historical fiction or biographies together for history. Science includes nature walks and hands-on experiences where all the siblings learn together.
Yet in most families, math is still a textbook-per-kid-per-grade kind of subject.
I want to say right now that I’m not anti-textbooks. By all means, use the tools that facilitate the goals of your homeschool and reduce the work you have to do from scratch to provide what your children need to further their learning goals.
However, the math-by-textbook approach is often symptomatic of the philosophy that lies behind the method.
What if They Get “Behind”?
We are used to thinking of math as a sequence of ideas that must be learned in a certain order. We are used to thinking of those ideas as divided into “grades” of math and expect that each grade worth will take about a year to master.
For example, if, for some reason, your child did no math at all during second grade, we assume that he’d need to spend third-grade doing second-grade math, fourth-grade doing third-grade math, etc. Or perhaps he’d need to “cram” two years of math into one so that he could get back on track.
It’s true that he might “get behind” or need to “cram” if “learning math” is synonymous with completing a textbook. After all, textbooks are designed to take a whole year to complete. They are made for schools who need the students to have about 180 lessons to do each year.
But have you ever stopped to consider whether this idea of learning and mastery meshes with how we think of learning in other subjects?
My general plan with potty training is to wait until my kids are three and are able to communicate well about bodily functions. I have friends who start potty training at eighteen months.
If you begin potty training at eighteen months and I don’t begin until age three, does that mean that my child is a year and a half “behind”? Will it take him eighteen months to potty train and “catch up” with other children?
No. In fact, the whole reason I wait is so that what might be a long, drawn-out, parent-intensive process with a smaller child can be a simpler process with an older child who has greater mental maturity.
Does That Work with Math?
But maybe you’re thinking, “Sure, that’s true with potty training, but math isn’t like that.” I’d like to gently point out that the reason we think of math so differently is actually the “schooling” mentality we’ve all grown up with and haven’t realized we absorbed.
When my fourth child turned eight, her older sisters decided to buy her a wristwatch. An analog wrist watch. For “educational purposes” they said.
She opened the gift, was delighted with it and then turned to me and said, “Mama, can you teach me how to tell time?” Yes, she was eight and hadn’t learned to read an analog watch.
In a traditional system, kids start learning to tell time at age five. In Kindergarten, they identify the hour hand and the minute hand and tell time to the hour. In first grade, they tell time to the half and quarter hour. In second grade, the learn to tell time to the five minute and minute intervals.
So, since we hadn’t started yet, shouldn’t it have taken about three years for my daughter to learn to tell time? Well, it didn’t. It took about five minutes.
She already understood time, hours, and minutes – she’d been marking her day on a digital clock for years. All I had to do was to take the concepts she already understood and match them with a bit of new information about this device and she was good to go.
She was attentive and eager to learn because she asked and wanted to know. And I promise you, her life was none the less rich and fulfilling because she spent the first eight years of it unable to read an analog watch.
Louis Benezet and His Experiment
One of the things that bolstered my confidence in a common-sense approach to math learning was reading about Louis Benezet and the work he did in the New Hampshire school district where he was superintendent in the 1930s.
You can read more about his work and observations here, but the summary version is that he delayed formal math instruction for a group of immigrant students. He found that within one year, they were able to catch up with and even exceed their peers who had experienced a traditional math program.
I feel that it is all nonsense to take eight years to get children thru the ordinary arithmetic assignment of the elementary schools. What possible needs 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.
How Much Math is There?
Another discovery that encouraged me to let go of a traditional grade-level approach to math was the Math on the Level program. Carlita Boyles, a homeschool mother of three, knew there had to be a better way to learn math and to experience it through real-life learning.
She combed the table of contents of traditional arithmetic textbooks and listed all of the topics that were covered from Kindergarten through Pre-Algebra. Do you know how many there are?
There are fewer than 150 concepts.
So why do we assume that it will take eight or nine years to learn these concepts? It really has more to do with a division of labor and a trend towards early academics.
The reasoning goes something like this. Kids need to learn all this stuff in order to be ready for algebra. So, let’s take all the information and divide it into eight chunks so that each grade level teacher can teach a bit of it.
When schools discover that students aren’t as strong in math as they’d hoped, they tend to try to do more, earlier to keep them from getting “behind”. But this actually makes the problem worse.
Studies show that students who are “behind” by first grade rarely “catch up” and are rarely ready for college at the end of high school. These studies are often used to drum up motivation for earlier and earlier academic intervention. After all, if you don’t get them fully on track by first grade, their futures are ruined, right? Time to panic?
Here’s a quote from the above-linked article:
The lesson is that the needle of academic achievement moves slowly, because essentially you are building knowledge and skills that develop over time. It’s one of those pieces of research that when you tell people, they say, ‘We knew it all along,’ but they don’t know it, because if they did, and they acted as if they knew it, they would be much more focused on early interventions.
Ironically, because the problem is misdiagnosed, the “solution” actually makes the problem worse. The numbers don’t lie. But the interpretation of the study is off.
What the study actually shows us is that if students’ learning needs are not accommodated by the system in first grade, things are not likely to improve as they proceed through the grade levels. As Albert Einstein said,
The definition of insanity is doing the same thing over and over again, but expecting different results.
A child who is not mentally or developmentally prepared for academic seat work in first grade will develop negative associations with that activity and also develop a sense of self in relation to his struggles and failures in that area.
Heaping more book work on him, and taking him to after-school tutoring in the subject which he most dreads but in which he needs to “catch up” do nothing to address these underlying problems.
Lighting a Fire
One of my favorite illustrations of fostering a love of learning is that of lighting a fire. Durenda Wilson, author of “The Unhurried Homeschooler” says …
We carefully lay the fuel to get the fire burning. It starts out small, but as we encourage and feed the flame, it grows. Sometimes we blow on it, and sometimes we add more fuel a little at a time. If we add too much of anything all at once, we extinguish the fire. And that’s true for learning as well. Learning thrives with gentle encouragement.
There are so many ways to gently add fuel to the fire of math learning. Board gaming. Baking. Shopping. Even poetry.
Don’t be afraid, mama! Don’t make fear-based math decisions. Homeschool families have the ultimate freedom and privilege to pace the learning to the child’s developmental needs and use a wide variety of approaches.
If you’d like more information about how we do math (especially in the elementary years) in our homeschool, check out my post about Family Math. For more encouragement, watch this Facebook Live called “Is your child behind in math?” You might also enjoy my free eBook “5-Myths that are Killing Your Multi-Age Homeschool“.
Be sure to download the Elementary Math Topic Cheat Sheet, so you never have to wonder what your child needs to know for higher level math!