An Education Lesson Gone Awry...

[MineralMan]

A number of years ago, I volunteered to give clarinet lessons to the 11-year-old daughter of a good friend. She was a very bright, motivated kid, who learned quickly and had a good analytical mind. The clarinet lessons went very well, and she was soon sitting in the first chair in her grammar school band. As time went on, she ended up doing the same in middle school and high school. But that's not the point of this OP, except to point out that she was bright and motivated.

After each clarinet lesson, we'd chat for a little while. I asked her about school and other things. One day, she told me that she was having the most difficult time getting the hang of arithmetic that involved fractions. Uh oh! I thought. First, I asked if I could look at her text book, which turned out to be using one of the newer method of introducing fractions. I recognized it, but can't remember the name of the particular book or method. She wasn't getting it. I knew that, because she said so. I asked if the teacher was helping students who were having difficulties by approaching fractions in a different way so they could jump the comprehension hurdle. The answer was that the teacher was not doing that.

Remember, this is 5th grade arithmetic. They were just starting that subject, and the current deal was adding and subtracting fractional numbers. So, I asked her if she had a ruler. She pulled one out of her backpack and handed to me. In about 15 minutes, I showed her how to think about adding and subtracting fractions. She got it almost instantly. Now, we only got to sixteenths, because that was as small a division that was on her ruler, but that was more than adequate for her current stage. We went on to understanding common denominators. After that, I asked her to hand me a piece of music she was learning on her clarinet. We'd gone over the musical notation before, but she looked at it and said..."Hey! Half notes, quarter notes, eighth notes. Fractions!" So we doubled up on the lesson with musical knowledge she already had.

On another day, I showed her how to multiply and divide with fractions, using the old standard techniques, rather than the awkward newish math methods used in her textbook. I told her not to bother showing this stuff to her teacher, unless she wanted a lecture on improper techniques. She got her A in arithmetic.

Now, I know the reasons for using different math teaching methods. I learned all of those while I was in college and thinking about becoming a teacher. I know the theories and why these systems are used. For this 11-year-old, though, they were not useful, but an obstacle. She ended up understanding what was being taught, but learned how to solve the problems before she understood the theory. A ruler. A sheet of music. Practical arithmetic.

So, she went on with her education, and ended up becoming a elementary teacher. She's now teaching whatever arithmetic method that's currently being played with. I saw her a couple of years ago, and she told me that she also teaches using the traditional arithmetic methods like the ones I taught her for fractions. She said that it was more important that the kids learn how to do the problems than how to "understand" the problems. They get the theory pretty quickly once they understand how to solve the problems. She's right.

Not every new arithmetic theory is effective. Not every educational theory works for every student. Sometimes, a little creative thinking is all that's needed to get a student over a small obstacle in the learning process. It's a pity that that thinking isn't as much a part of education as it once was.

I'm not a teacher. Well, I am, but not professionally, and only with adults these days. I can, however, take a bright 11-year-old through adding and subtracting fractions in half an hour. Once they get it, it's gotten. Of that I'm certain. Whatever works for the individual student. There's always another way of looking at the problem and, sometimes, really old-fashioned methods still work the best.

[LWolf]

1. A perfect illustration to why differentiation is key, and

scripted curriculum should be banned. Unfortunately, under current law, the worse a school is doing, the more scripted their curriculum becomes. When they can't make AYP and reach the stage of mandated "improvement plans," those plans inevitably include scripted curriculum.

Under any high-stakes testing program, teachers are pressured to stick to adopted curriculum. In some places using other methods or materials are "discouraged." In others, they are outright banned and grounds for being "written up."

[MineralMan]

2. Worse, many young teachers do not even know how to

teach differentially. They have their curriculum and the methods they were taught, and have no clue about other approaches. I know this because I have talked about the subject with newly-graduated teachers. There is an entire generation or maybe two of teachers who cannot teach using alternative methods when the scripted method is not working, as so often happens.

This is not true, of course, of all young teachers, or old teachers for that matter, but it is true of many. It's a damned shame, and many of the parents of elementary students didn't get this stuff either. So, it's the blind leading the blind.

I'd estimate, knowing that person who was an 11-year-old stumped on fractions, that she has an IQ of about 130. That's based on her other accomplishments. If a method cannot get a bright kid past such a simple concept, what hope is there for those who don't have that potential?

There is much to be said for the ancient standard methods. Yes, they used some rote crap that we all hated, but they also taught some subjects in practical ways that most of us learned and still remember. An old standard method made almost instantaneous work of teaching one kid how to do fractional arithmetic. She got it immediately.

How many kids get through school without even being able to read a ruler? I know it's a lot, because I've had to teach otherwise adequate young adults how to use a ruler and use fractional measurements. This is a failure of method. Anytime such basic material is not learned, the method has failed. It is that simple.

[demmiblue]

5. I disagree.

If anything, new teachers abhor the way they are forced to teach.

The majority of teacher education is based on how a child learns. Multiple intelligences, culture, life experiences, psycho-social needs (yes, Maslow), etc. These ideas, among others, are common in teacher education classes. I wonder where these people that you know went to school.

[LWolf]

6. Differentiation began in specialized subsets:

teaching the gifted and the learning disabled. For way too long, the standard practice was to remove them from the room, from what the rest of the room was doing. Efforts to differentiate core curriculum IN the classroom started with gifted education, and moved to special ed. It's only been in the last several years that it's begun to move into the mainstream.

It takes time to move new methods into any large system, and our public ed system across the nation is massive. Part of it, of course, is overcoming the standard, traditional ways people have done things. Differentiation is intimidating to teachers that haven't been taught and supported in their efforts. It means more work, and more time, when we already put in more hours than we are paid for. So we offer training, we offer mentoring, and we offer encouragement, and little by little, it becomes part of classroom practice.

We've got a long way to go. As someone who was in that population of teachers of the gifted, who took extra certification from UCLA in gifted education, and who spent some years helping develop gifted programs at the district level, and doing professional development about differentiation for all students for two different districts, I know that the best of us can only differentiate within the limits of time, support, resources and class size we are given. We could move faster with more resources, which, in this economy, are just not there.

The good news is that teachers are hearing about it on a regular basis, which sets us up to incorporate it as we can.

[MineralMan]

14. I grew up in a small town in California in the 1950s.

My HS graduating class had just 106 students. There was no gifted program whatsoever. What there was were a number of dedicated teachers who spotted the students who were far ahead of the class through self-learning. In several instances, those teachers singled me and others like me out and diverted us into self-study. Class sizes were about 30 or so throughout my 12 years. At least half a dozen times, a teacher would notice me and a few others who were spinning wheels in their classes.

In first grade, for example, I was already reading at the sixth grade level. My first grade teacher, Miss Setzer, spotted me the first week of class, and moved me to the back of the room and gave me books at my actual reading level to read during reading lessons. No Dick and Jane. It was done subtly and without any of the other kids even noticing what was going on.

In fourth grade, the teacher assigned me to help three other students, who were falling behind in their math skills. We spent the time that math was being taught in the back corner of the classroom, where I helped them catch up with the rest of the class...very quietly. Nobody noticed. Nobody cared. They caught up.

Later, in High School, my Senior year English teacher, who gave the class an hour-long test to assess language skills the first week of school, simply dismissed me from the class for the rest of the year and directed me to the city library, across the street from the school, where I was free to explore as I saw fit. No assignments. Nothing. I was done with High School English. Also in my Senior year, the college prep math teacher discovered that I had learned Trigonometry over the summer, with the help of a surveyor friend of my father. So, he gave me an introductory level Calculus text and turned me loose, with permission to ask him questions in non-class time if I had trouble with anything. I took him up on it a number of times, and learned Calculus.

These teachers had no constraints on their teaching techniques. There was no program for kids who were ahead, so the teachers improvised something for individual students that suited their needs. In so doing, they avoided having bored kids who were likely to behave badly in class, and could focus on the students who would benefit best from normal teaching methods.

That was how the small schools in that small town coped with me and a few other students who needed more challenge, but lacked the staff to provide it. They improvised. We improvised, and learned at our own pace. It probably kept me sane, and gave me as much challenge as I wanted to accept.

I can't imagine anything like that happening today. I really can't.

[LWolf]

17. It's much more difficult, and therefore

less frequent, that's for sure.

The shift from flexible teaching to standardized teaching is a part of the standards and accountability movement that gave us so many standards that one study tells us we'd need to continue through grade 21 to teach them all, and high stakes testing as a weapon to control what we were doing in class.

That's when the scripted curriculum, the narrowing of curriculum, the obsession with "grade level" instead of "student's level" took off. And we won't see the end of it as long as high stakes testing is driving everything we do.

[zipplewrath]

3. I'm writing just such a text

Okay, so far it's all in my head. But the working title is "You're not bad a math". I've never actually met anyone who is "bad at math". We all struggle with some concepts once and a bit. I struggled with long division because I was sick the day they started teaching. It took forever for me to get my head around trigonometric calculus. But once the switch flipped, I was off and running.

I've worked with innumerable kids over the years whose parents "didn't know math real well". To a person it was just a case of trying to figure out what their mental block was. I find it everytime. Your ruler is a good tool. I often use money "What's a quarter" kind of thing. "Why do we call it a quarter?". My wife was struggling with currency exchange on one trip, I finally said "just think of it as a 30% off sale". She knew how to calculate a sale price.

I also often take the "numbers" out of problems. Numbers represent quantities. Get a bunch of coins, or marbles or cookies. Start pushing piles of them around to "add" them or "divide" them. People instinctively understand manipulating piles of things. They understand "3 squared" real fast when you make a sqaure out of cookies that are 3 wide by 3 high.

[demmiblue]

8. As an aside...

I saw Danica McKellar on some talk show discussing her new book: "Math Doesn't Suck: How to Survive Middle-School Math Without Losing Your Mind or Breaking a Nail."

Danica= Winnie Cooper on "The Wonder Years."

Kind of refreshing!

[MineralMan]

16. Danica McKellar is actually a pretty cool person.

You don't hear much about her any more, but she's interesting as an adult.

[MineralMan]

11. I finally threw in the towel in Differential Equations. The professor

was Indian, and his English was almost incomprehensible, and he had no patience with anyone struggling with the subject. It was about then that I switched majors from Electronics Engineering to English. 1964.

My experience with this young girl was informative to me. She was very smart, but the way the subject was presented to her didn't click. So, I simply gave her another approach that she understood immediately. It made me wonder how many others in her class simply never learned that particular part of arithmetic, which is what it is, not math. The system that was being taught, which I understood just fine, was almost guaranteed to flummox a lot of kids. Too bad, that.

Not having had children of my own, I wasn't exposed to teaching practices on a regular basis at that time. So, this was an isolated incident, as far as I know. But, I do wonder. And I have no idea what techniques are currently being used in our elementary schools. I think I'll go get a textbook list for the fifth graders in my district and have a look.

[damntexdem]

4. Yes, different people learn different ways.

It's not a question of which method is best. It's a question of what method is best for a given student.

Many educators often get into ideological quarrels over which method is the best one. Then they don't have to worry about how to fit the instruction to the pupil.

[DirkGently]

7. +1 Teaching is an interactive undertaking and a conversation.

Not something a teacher applies to a student like a coat of paint. Given permission to be flexible, and a reasonable class size and load, people with the gift and the motivation to teach can do wonders.

Given instead an overwhelming emphasis on standardized tests, overflowing classrooms, and students and parents primed more for lawsuits than learning, and it becomes nearly impossible.

[JuniperLea]

9. Brilliant!

I remember being stuck in long division... back in the day when Mom would give me a ride to school on the Brontosaurus... and a teacher of mine tried several different ways to frame the discussion. I remember seeing her look for a sign of understanding on my face; when it didn't come, she said, ok, let's try this... and went on to something else. She was a peach, and I'll always remember her.

I hated the rote stuff with a fiery passion! But I can name the planets in our solar system, and all of the Great Lakes, because of her funny tricks.

Oh, and Schoolhouse Rock... well, it ROCKED! It was the only thing that got me to memorize the multiplication table.

[MineralMan]

15. Ah, multiplication tables.

No problem when I was a kid, but an interesting thing happened to me in my 40s. I caught viral encephalitis, and was in a hospital, semi-comatose for almost two weeks. When I finally came around and was beginning to recover, I found out what had laid me low. The neurologist who was handling my case told me that I might have some deficits and the recovery might be a long one.

So, when I was alone, recuperating, I started to see if I could identify any of these possible deficits. For a while, I couldn't. I could still use my computer just fine, and write as well as I ever had, and had no problems with speech or reading. Then, while assessing, I discovered that I couldn't multiply or divide numbers. Uff da! I was used to being able to do pretty complicated operations in my head, so this came as quite a shock to me. What to do?

Well, I started building a new set of multiplication tables in my head for myself, drilling myself over and over on them. I created them by adding, since I had no problem with that. In about a week, I had relearned the multiplication tables to the point where I didn't need them any longer, which also restored my ability to divide numbers automatically.

The neurologist just looked at me funny when I explained how I had done this. He just shook his head and said I was done with my recovery.

Our brains are amazing organs. Fortunately, mine wasn't badly damaged, and I had enough of my wits about me to reteach myself that simple stuff I had learned in grammar school. The oddest thing, though, was that my computer programming skills improved dramatically after that illness. I still don't understand that one, but the difference was a major one.

[JuniperLea]

18. Great story, MM!

Amazing what the human brain can do... as your story illustrates.

[ljm2002]

10. What a great story, and thanks for sharing!

There certainly are different learning styles, and different ways of teaching any subject. All of this plays into whether a given student can overcome the initial learning hurdle. Kudos to you for seeing it and intervening for that young lady.

[MineralMan]

12. It's pretty easy to do, one on one. Harder in a classroom.

Still, I wonder how many kids who may have had fewer intellectual resources than my young friend fared under that teacher. It gives me pause to this day.

[madinmaryland]

13. Oh man! My daughter got stuck with a fifth grade teacher that was using

the "new math" methods. Even me, as an electrical engineer with two years of calculus found it extremely confusing. She has had no problems since then with math, even if it is not her favourite subject.

[Scurrilous]

19. Thanks MineralMan.

K & R :thumbsup: