Actually, you get only one chance when teaching anything.
I was in an internal adult training class for corporate websites. In the middle of a discussion one student said, “How about if we each take something about Sharepoint that interests us, research it and report back to the group?”
Great idea, right?
The instructor put her face in her hands, breathed deeply, ran her fingers back through her hair and said, “Well, I want to make sure you get the things you need, so hold off on that.”
CRUSH.
End of learning.
Game over.
What are your thoughts on this? Share them in the comments below.
In a previous post, we learned that you don’t have to use a LCM (least common multiple) to find a common denominator to add fractions. In another post, we learned that you can use primes instead of the GCF (greatest common factor) to reduce fractions.
And now I’m going to demonstrate that finding the LCM and GCF of two numbers is still pretty cool.
Apologies for the glare on the video. I tried a different method and clearly it is inferior to the other method.
Do you have an especially difficult student? Does one kid stand out as just not getting it?
The answer lies not in your approach, but in their perception of their own capabilities.
My Former Drug Dealer Student
I was teaching Oilfield Math at a large oilfield services company to a group of new hires. One guy had particular difficulty.
Because I set myself up as approachable, he came to me to explain his plight. He was an ex-con and had spent 10 years in prison for drug dealing.
As soon as I heard this, I knew my way in. I watch much more drug-related TV that I should, so I knew that fractions were involved in drug dealing.
I asked him to explain some of the prices and measurements. Since he would have to work against time calculating cost, weights and prices, he was exceptionally good at fractions.
When I pointed out how good he was in math he was upset. “I’ve left part of my life behind me” he told me. “Yes,” I said, “but it shows that you could be just as good at legal fractions.” This Oilfield Math’s got nothing on drugs-on-the-street math.
His life turned around that day.
If you have a struggling student, find out where they already do math. Show them that they have the talent already. Let them see their abilities.
I’ve discovered many ways of teaching math through the years and the most interesting one was the addition of numbers with opposite signs. I learned this from a teacher who said that he never understood the rules – so he made up his own method.
He “breaks” the bigger number into two pieces so it can be cancelled. Here it is:
What do you think? Can you teach it this way? Share your thoughts in the comments.
We had a lively discussion at last week’s homeschool math chat about teaching algorithms versus allowing a discovery learning process.
What I can’t help but think about when I reread this discussion is how this compares to teaching a child manners.
Teach kids manners early. Very early.
I know someone who elected to wait until their child understood the concept of appreciation before teaching them how to say thank you. The child is now eight years old and doesn’t say thank you unless prompted.
Daughter, at 18 months old, is being taught please, thank you, ma’am and sir. She has no concept of being polite. Her frontal lobe is about as advanced as the local neighborhood chimpanzee’s. Her favorite phrase these days is, “No. Mine.” I correct this with, “No ma’am.”
At some point it will become habit. Or at least the ritual of, “No,” from her and my “No ma’am” response will become habit.
And at some point shall make the connection that using these polite words will gain her something. She’ll be looked upon favorably, considered one of the “good kids,” or smiled at a little more.
And then she’ll connect it. She’ll see that the concept of politeness is directly tied to the “algorithm” of saying polite words.
Teach kids algorithms early. Very early.
I love the idea of teaching concepts before algorithms in math. But sometimes algorithms have to come first so that the rhythm and habit are in place when the brain is ready to understand the concept.
Each child’s brain is different. One of the beauties of homeschooling and private tutoring is that you can focus on a child and know when they’re ready for algorithms and ready for concepts. As a classroom teacher, it’s a little bit more difficult, but still can be done.
In the classroom you can teach algorithms at the same time as concepts. If you cycle them back and forth, you can catch each student as they are prepared to accept the learning.
But this is reality. And I have two issues with David’s opinion.
The conversation points for each focus is different.
He compares questions like “What is your grade?” with “What did you learn?” If a child takes a test, the question, “What did you learn?” is goofy. You can learn while taking a test, but the intent of the test is to prove what you have already learned.
Grades are specific measurements, learning is a general unmeasurable concept (not mathematically). You would do just as well switching the question, “How far is it to your house?” with “Do you like your commute home?”
The logistical questions about homework and report cards are a trained response for parents. Parents need hear this only once, 20 minutes before the bus ’rounds the corner: “OH NO! I FORGOT TO DO MY MATH HOMEWORK!” Yeah, try telling a mom to switch “What’s your homework?” with “Did you have fun today?”
Sometimes grades are all a kid’s got.
Occasionally there’s no energy around learning a subject. A good student will turn to the competition of the grade to get the job done. Either way, the kid gains some knowledge.
I did this with history. It’s not my bag. I did have a great history prof in college who made things come alive. But I still just wanted to get through. Focusing on the grades got me there. And I learned lots.
If a student doesn’t love math, that’s cool. They can focus on the algorithms to get the job done and measure that with the grades. If it keeps their confidence up, maybe they’ll run into something someday that gets them excited about math. And maybe they won’t.
And that’s okay.
Parents should use both types of conversation points.
David’s intention is pure, though. We should focus more on the learning. But to think that we’ll stop with the grades altogether is crazy. It’s against human nature. We always want to know how we measure up. Kids want to know. And parents want to know. So it’s okay to focus on grades.
As long as where it matters, we focus on learning.
For some reason I have trouble adding 5 to the larger digits (like 7, 8 and 9). I noticed at some point that the last digit of that addition is the same as if you subtracted 5 from that number. Like this:
7 + 5 = 12
7 – 5 = 2
and
8 + 5 = 13
8 – 5 = 3
and
9 + 5 = 14
9 – 5 = 4
So now when I add them, I merely subtract them and slap on a 1 at the beginning!
(Oh, yeah, and there is a good reason this happens – it has to do with 5 being half of 10. And 10 is the base of our number system. Maybe one of the other math blogs can do a proof of this using base n…?)
I was in the 4th grade. We were studying geometry. Mrs. Wilburn was the teacher.
I read the definition of a square in the textbook:
A square is a polygon with four equal sides and four equal angles.
I read the definition of a rectangle:
A rectangle is a polygon with four sides and four equal angles.
I thought, “Okay, then a square is also a rectangle.”
Hoping to be validated and praised, I went to Mrs. Wilburn and asked, “So a square is also a rectangle, right?”
“No,” she said, “a square is a square and a rectangle is a rectangle. A square is never a rectangle.”
So I went back to my desk and read the definitions again. And I thought about it. And I read the definitions. I went back to her desk because now I was thoroughly weirded out.
“But the book says that a rectangle has four sides and four equal angles. A square has four sides and four equal angles. So isn’t a square also a rectangle?”
“No, a square has four equal sides and four equal angles. A square isn’t a rectangle.”
This was the turning point in my math life.
I had two choices:
The blue pill: Believe Mrs. Wilburn and thus believe I wasn’t competent to do math because my logic was clearly faulty.
Swallowing the blue pill, choice 1, would mean that for the rest of my life I would hate math. I would say things like, “I’ve never been good at math,” and “I switched my major in college because what I really loved required too much math.”
But if I took the red pill, it would mean that I would become a math vigilante. Regardless of the topic in math, I would know that I could figure it out no matter what anyone else said.
I would believe and quote a favorite professor, Dr. Fitzgibbon (aka Fitz) when he said: “Once you realize we are all idiots, only then can you do math.”
And I would start a math blog.
I chose the red pill.
I’ll put money on it that 90% of people have similar stories to tell.
They might not have such outwardly facing results like a blog, but some do.
They might not have become math vigilantes or math incompetents – these are the two ends of the spectrum. My extremist personality causes me to swing wildly and severely in one direction.
But I’ll bet that anyone with a story like this, took a turn in their math learning.
Teachers have an incredible power to affect students.
With this power comes the responsibility to talk to our students. Really listen to them. And learn from them. It’s okay to be wrong. It’s okay to be confused. Our job is to facilitate learning, not know everything.
We should welcome questioning. Welcome the alternate method. Welcome the new viewpoints.
Remember, we’re all idiots – we all have to think, be confused and sort things out. Even the PhD math professors.
The difference between a student and us is that we don’t let questions or confusion stop us from struggling through to the solution. Even if it’s a different solution that what we’re used to.
Instill that confidence in your students and you’ll be successful in teaching them.
What do you think? Join the discussion by commenting.
Do you keep struggling to teach common denominators? Do your kids just not “get it”?
Well, it’s time to quit.
Yep! You can teach (and do) fractions without ever finding a common denominator.
The key is in the definition of addition for rational numbers. If you have two numbers and the sum of them is .
Granted there is the technical issue of reducing, but using a little prime factorization will get you there without an issue. (And you don’t really HAVE to reduce, which I will discuss in a later post.)
Here is an example:
Here’s one with an obviously easy common denominator that works just fine with this method. In it I explain a little about why you would want to do it this way:
You might argue that finding a common denominator is an important learning experience. And you’re right. In the same way that learning about death through the loss of a pet is an important learning experience. But if you can avoid all that pain, why wouldn’t you?
If you teach this method first, kids will get annoyed with having to do so much reducing and discover the common denominator method for themselves. And that’s really what learning math is all about.
What do you think? Can you teach fractions this way? Share your thoughts and experiences in the comments.
Thanks to @padgets for our conversation about teaching fraction on #mathchat a few weeks ago. You inspired this post!
