I discovered long ago that I did not have many clever and creative ideas. However, I also discovered that if I paid close attention, I could steal wonderful ideas from some of the greatest minds around.

I was reminded of this recently. One of the readers of this blog sent me a link to a great article on the teaching and learning of math. She said that she thought I would find it interesting because I was always curious about education. And, she was absolutely correct. It is well worth reading and pondering.

http://opinionator.blogs.nytimes.com/2011/04/18/a-better-way-to-teach-math/

Several parts of this article really caught my attention. They are the parts that I’ll probably steal in the future. In fact, here are five thoughts that I plan to steal (borrow) and apply to my own teaching.

(1) – The subject of the story has an absolute certainty that students can learn math. In fact, he says so “’Almost every kid — and I mean virtually every kid — can learn math at a very high level, to the point where they could do university level math courses,’ explains John Mighton.”

I wonder what would happen if we all walked in each day and had that same certainty about our own students.

It is amazing to me how quickly I begin mentally classifying my students as “excellent,” “average,” and “poor.” Do I start treating those students in that way? Do I ask harder questions of the “excellent” students and dumb down the questions for the students I perceive as “poor?” What kind of subtle messages am I sending them? Perhaps in that way, my perceptions become a self-fulfilling prophecy. I know I say to my students often “you can ALL learn this.” Is that my true sentiment or just lip service that I spout because it sounds good?

In the future, I’m going to try to do a better job of helping everyone to excel. Maybe, as he says, I am forcing my own students early in the semester to choose to think of themselves as either smart in accounting (my subject) or dumb in accounting. And, maybe it is that choice that then serves as a driving force for the rest of the semester. If I can change that mindset, can I get better results? Can I convince them that they can all learn accounting and, if so, how will that change them over the rest of the semester?

(2) – I loved what he had to say about “extensive practice.” I get the feeling in education that we show students how to do something once, maybe twice, and then expect them to be experts from thereon. When I was growing up, we would work extensively on math facts in school: 56 divided by 8 is 7, 20 percent of 15,000 is 3,000. We did hours and hours of that type of practice. Sure, it wasn’t exciting. But, as I have said here before, every student in my fifth grade class in 1959 knew more about basic math than every student that I taught this past year in college. Why? That is easy – students today are trained to use calculators and have never really practiced math facts. The next time you are in a college class, ask a student to multiply 12 times 9 without a calculator and you’ll see pure panic and dread. In 1959, every hand would have been raised (in the fifth grade).

Practice really is necessary for learning.

Maybe we all want to avoid the possibility of boredom so we eliminate extensive practice from the learning process. Then, when we get to a test, we (as teachers) are surprised that the students cannot handle the questions we give them. Perhaps what they really need is just more practice. Few things can be learned by doing them merely once or twice.

(3) – “Studies indicate that current teaching approaches underestimate the amount of explicit guidance, ‘scaffolding’ and practice children need to consolidate new concepts.” I really like the idea of “scaffolding” or building a structure that allows students to see new material within a logical framework. Often, professors have worked with their material for so long that they have no need for a structure. To them, the material is virtually self-explanatory as it stands alone. However, students do not have that wide-ranging knowledge as a basis for understanding new material and how it ties in with other material. To me, a course is a large puzzle where every day you introduce new pieces and then work to fit them into the rest of the puzzle so that—by the end—it all makes sense; the total picture becomes clear.

(4) – “’No step is too small to ignore,’ Mighton says. ‘Math is like a ladder. If you miss a step, sometimes you can’t go on. And then you start losing your confidence.’” Once again, we—as teachers—always understand where the process is headed. We know the end of the story before we set out the beginning. In teaching, we may lose track of why we need to explain every minute step along the way. To the student, one missed step can bring the whole learning process to a screeching halt. Some students get lost easily. Of course, we prefer students who can make giant leaps from one concept to the next but, in truth, those are the people who have the least need for a teacher. If you really want to be a teacher, you have to want to help those people who experience the most trouble in making the connections. That is where the real teaching comes in. You have to recognize when a student can only take small steps and then break the process down so they can successfully see the connections.

(5) – “The foundation of the process is building confidence.” If you have taught for more than one day, you will have experienced the student who loses confidence. It is a real shame but those students will come to believe that they are simply not smart enough to understand the topic at hand. Often, after that, no degree of work can win back that student. They are lost. They assume they will do poorly and they do. If you are going to turn all your students into winners, you have to recognize immediately when a student starts to struggle and then work to break the process down into more manageable pieces for that student. You need to constantly work to build confidence.

Yes, teaching can be real work but no one ever said it would be easy.

Thanks for sending the article along to me!!! I definitely managed to steal (borrow) a lot from it.

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