This is the last (for a while) of a series of posts I have made dealing with math anxiety. Before turning to the technical side, I want readers to understand both things we are dealing with. The first is students, and how they learn. The second is arithmetic and algebra, and it has a simpler conceptual base than most realize. The focus of this post is on the student.
As a 20 year veteran of the math classroom, a former homeschooler, and a counselor to homeschoolers, I think it is vital that we understand how age, readiness, and motivation are the keys to learning. Violate any of those, and all of our best teaching is for naught. Work with those, and the student often learns with minimal help from us. That is just the way it is. So whether we are a parent or a teacher, the following stories should be instructing, encouraging, and freeing.
I include stories about reading because good reading is fundamental to all but the most basic math. The required abstract skills are similar.
aberlehome.com/hear-from-homeschool-moms-who-delayed-formal-education
Every child is unique and learns differently. My eldest are quite academic and were reading independently by the time they were 5, I gave a little input and they picked it up really quickly because they were interested. My third had to attend school for a year when he was 4 (whilst I cared for my father) and after that year of ‘formal teaching’ was still unable to even recognize letters. The school wanted to put him back a year. I pulled him out of school and within 5 weeks of gentle teaching at home he was reading independently. My 4th child showed no inclination towards reading so I allowed him to follow his interests and play. I read to him lots but didn’t really do any formal teaching with him. Then one day when he was about 7 and a half I noticed him snuggled up on the sofa ‘reading’ a novel. When I asked if he wanted to read to me he read perfectly! He had picked reading up from his environment and taught himself.
howtohomeschoolmychild.com/teaching-math-to-kids-case-studies
Hunter was six years old when I decided to take him off formal math studies. He didn’t do math workbooks, or math curriculum until he was 11 or 12 years old. Within a year or two, he completely caught up with all the grades that he missed.
aberlehome.com/hear-from-homeschool-moms-who-delayed-formal-education
Children are really so different. By 18 months my oldest was walking around car parks reading the license plate numbers, and by 4 she’d essentially taught herself to read, whereas my second wouldn’t even look at letters till she was almost 7, then she picked up a book and started reading it. The beauty of home education lies in the ability to respond to individual needs, rather than do things by an age-based time table. My second child never needed anything formal, because she was processing in her own way, whereas my first enjoys the challenge of more formal lesson plans. Just follow their lead, and they’ll surprise you.
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We unschool and only do real world math. My daughter didn't learn how to take change back until she worked concessions then she downloaded some apps and had us work with her plus her experiences at the register and she did just fine. Trust me after 9 years of homeschooling, I've learned if they need it they will learn it. I am comfortable learning anything with my kids. I'm not a forensic science person but my daughter loves it and she is very knowledgeable about it. My learning abilities are not her limits, if they want to know something I don't, there are tons of resources I will help them find whether people, classes, books or anything else. If they do want to learn it schoolyourself.org is an excellent resource for upper level math like algebra.
aberlehome.com/hear-from-homeschool-moms-who-delayed-formal-education
I don’t do formal lessons for my kids until later. I find it more effective to let them casually play with learn-to-read apps and games until they’re pretty good at reading on their own, which tends to naturally happen around 7. At that point, I start formal lessons for all subjects.
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When my oldest (now 6 1/2) was 4, I attempted to teach him to read. While he showed interest at first, he soon began to protest, and so I stopped. Just after he turned 5, he started asking me to teach him, and instead of jumping on it, I *tried* to talk him out of it. He insisted that he wanted to learn, and so we started. It was semi-slow going for a year or so (and I didn’t push it very hard), but he made definite progress. One morning shortly after he turned 6, I heard him sitting in his room reading aloud the steps to a science experiment he wished he could do. From that day on, his reading skills improved dramatically and quickly. Now, 6 months later, he reads all the time and (aside from 20 minutes or so of reading curriculum each day), without coercion. I am definitely a believer in allowing it to progress naturally!
howtohomeschoolmychild.com/teaching-math-to-kids-case-studies
Losing her love of learning happened with my middle daughter, Gentry. By the time she was 10 years old, she hated math.
At that time, I took her off formal math. I wanted to change her attitude towards math, so we started with a “break” from math curriculum.
I don’t know if she ever fell in love with math, but she did tolerate it better.
When she started her math curriculum again, I gave her a times table and said, “Here is your times table, use it any time you want.”
During those early years, I bought every contraption there was so Gentry could learn multiplication facts. I discovered she would learn her times tables when she was ready or had a need to learn them.
Fast forward a few years . . .
By Algebra, she was fine. She knew all those times tables. I think she got tired of looking up the answers on the chart, so she eventually memorized them on her own. I also think she is not naturally a math person, so it took her longer to learn math.
The irony in this case study is Gentry helped her friends in college math classes. She could figure out a way to solve the problems, and would share that with her friends. Gentry made an A in both freshman math classes, without tutoring help.
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My only child who is uncomfortable with math is also the only one who attended public school and who had a teacher who was uncomfortable with math. He entered loving math, and left (after second grade) with severe math anxiety. He’s only now at 15 beginning to overcome it.
My husband is a genius-level mathy guy (and uses it regularly for work and in our lives) and our other kids seem to have inherited his ease with it. We do a lot of Gameschooling, they think numbers are fun and have remarkable number sense, and it’s never been anything but a beautiful, satisfying sort of puzzle to them to learn more about how they work.
I’ve never had anxiety around it, although I do around approaching it with my oldest because his panic is so intense. I don’t have the inherent skill with it that my husband and younger kids have, but I’m good with patterns and find it fun enough.
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I’ve recently come out the other side of this anxiety tunnel.
We didn’t do structured maths, my son would do Maths Seeds in the early days before we decided to unschool. We applied maths through life but nothing structured.
He decided last year at nearly 11 that he will need maths for his future so asked to learn it. He goes to a tutor one hour a week and is now at the stage that his schooled peers are. I understood the unschooling theory, but I still felt panicked in case it didn’t work. Thankfully it did and he really enjoys it.
One more story—long, but good!
This is from Daniel Greenberg, author of Free at Last, The Sudbury Valley School. The school has no rigid schedule. Classes are offered only at the request of the students. Now in his words:
Sitting before me were a dozen boys and girls, aged nine to twelve. A week earlier, they had asked me to teach them arithmetic. They wanted to learn to add, subtract, multiply, divide,
and all the rest.
"You don't really want to do this," I said, when they first approached me.
"We do, we are sure we do," was their answer.
"You don't really," I persisted. "Your neighborhood friends, your parents, your relatives probably want you to, but you yourselves would much rather be playing or doing something else."
"We know what we want, and we want to learn arithmetic. Teach us, and we'll prove it. We'll do all the homework, and work as hard as we can."
I had to yield then, skeptically. I knew that arithmetic took six years to teach in regular schools, and I was sure their interest would flag after a few months. But I had no choice. They had pressed hard, and I was cornered.
I was in for a surprise.
My biggest problem was a textbook to use as a guide. I had been involved in developing the "new math," and I had come to hate it. Back then when we were working on it — young academicians of the Kennedy post-sputnik era — we had few doubts. We were filled with the beauty of abstract logic, set theory, number theory, and all the other exotic games mathematicians had played for millennia. I think that if we had set out to design an agricultural course for working farmers, we would have begun with organic chemistry, genetics, and microbiology. Lucky for the world's hungry people that we weren't asked.
I had come to hate the pretensions and abstruseness of the "new math." Not one in a hundred math teachers knew what it was about, not one in a thousand pupils. People need arithmetic for reckoning; they want to know how to use the tools. That's what my students wanted now.
I found a book in our library, perfectly suited to the job at hand. It was a math primer written in 1898. Small and thick, it was brimming with thousands of exercises, meant to train young minds to perform the basic tasks accurately and swiftly.
Class began — on time. That was part of the deal. 'You say you are serious?" I had asked, challenging them; "then I expect to see you in the room on time —11:00AM sharp, every Tuesday and Thursday. If you are five minutes late, no class. If you blow two classes — no more teaching." "It's a deal," they had said, with a glint of pleasure in their eyes.
Basic addition took two classes. They learned to add everything — long thin columns, short fat columns, long fat columns. They did dozens of exercises. Subtraction took another two classes. It might have taken one, but "borrowing" needed some extra explanation.
On to multiplication, and the tables. Everyone had to memorize the tables. Each person was quizzed again and again in class. Then the rules. Then the practice.
They were high, all of them. Sailing along, mastering all the techniques and algorithms, they could feel the material entering their bones. Hundreds and hundreds of exercises, class quizzes, oral tests, pounded the material into their heads.
Still they continued to come, all of them. They helped each other when they had to, to keep the class moving. The twelve year-olds and the nine year-olds, the lions and the lambs, sat peacefully together in harmonious cooperation — no teasing, no shame.
Division — long division. Fractions. Decimals. Percentages. Square roots.
They came at 11:00 sharp, stayed half an hour, and left with homework. They came back next time with all the homework done. All of them.
In twenty weeks, after twenty contact hours, they had covered it all. Six years' worth. Every one of them knew the material cold.
We celebrated the end of the classes with a rousing party. It wasn't the first time, and wasn't to be the last, that I was amazed at the success of our own cherished theories. They had worked here, with a vengeance.
Perhaps I should have been prepared for what happened, for what seemed to me to be a miracle. A week after it was all over, I talked to Alan White, who had been an elementary math specialist for years in the public schools and knew all the latest and best pedagogical methods.
I told him the story of my class.
He was not surprised.
"Why not?" I asked, amazed at his response. I was still reeling from the pace and thoroughness with which my "dirty dozen" had learned.
"Because everyone knows," he answered, "that the subject matter itself isn't that hard. What's hard, virtually impossible, is beating it into the heads of youngsters who hate every step. The only way we have a ghost of a chance is to hammer away at the stuff bit by bit every day for years. Even then it does not work. Most of the sixth graders are mathematical illiterates. Give me a kid who wants to learn the stuff — well, twenty hours or so makes sense."
I guess it does. It's never taken much more than that ever since.
Conclusion
A case is not a statistic, but a collection of stories is enough to point us to something statistically significant. I hope you felt the tension in your head and neck relax as you read the real life stories from real life parents and a teacher. Even if you feel stuck in your classroom curriculum, you can take heart from these stories because your care for students will help them far more than the stress you might feel about meeting arbitrary standards.
All real learning is natural, organic. A student will work hard when they are ready, when they are willing. That means, when the topic becomes relevant to them. Preparing for college calculus is not very relevant to a kindergartner. Therefore, starting with this summer, relax! They have a few years to prepare.
