Carolyn Morgan on how to teach

This is a comment by Carolyn Morgan on the WillinghamOnLearningModalities thread: it's a beauty, so I'm posting it.

Things I note about her teaching approach:

• It's actually multimodal! She's talking, she's getting the kid to write AND draw his own pictures, she's doing whatever it takes to get the kid on track.
• It's feedback-driven: she switches gears in midstream if the kid isn't getting it.

Carolyn's post:

SteveH is correct. Whatever you do, you must bring all students to UNDERSTANDING. And this is what students really do want. "Understanding" or "not understanding" are the reasons students "hate" or "love" math.

A good math teacher learns how to "approach" a student having difficulty. The teacher has all of these ideas (hopefully) stored away back there some place, ready to be pulled out when needed. But a teacher's most important job is determining where the student's understanding fell apart, identifying where there might be gaps in reasoning, and knowing how to bridge those gaps. This is where choosing the right approach comes in. It might involve reteaching, reviewing a step that is being omitted, or helping a student reason through a difficult story problem.

So a hand goes up, and a student says, "I need help."

(Those are my favorite times of the math hour because it means I get to find the puzzle piece that is needed to make this all fit together in his/her head and give understanding to what I've just taught or to what's needed to solve this problem.)

So I have some choices, but I always look to see what the student has already done or tried. That tells me what to do next.

I then start by having the student read the problem to me (if it is a word problem).

Then I make a choice:

I might say, "OK, draw Bill's house. Now write 'B' on it for Bill. Now, draw the schoolhouse; now write 'S' on it. Now, draw the road from the house to the school. Now, look at the problem again to see how far it is to the school (and the student answers outloud 4 1/2 miles). OK, write that number on the map you've just drawn."

I could have drawn that little map for the student, and might do it under certain conditions, but having a student draw the map involves his sight and his movement (and mouth from speaking and ears from hearing his own voice) and it involves more importantly his BRAIN. (I've got to make sure his BRAIN is working and focused on the problem so he can "understand".)

So I would continue, "Start at Bill's house with your pencil; now walk to school. OK how far did Bill just walk? ('4 1/2 miles') OK, write that down. Now, he's at school, but he wants to come home, so have Bill walk back home. How far did Bill walk to get home? OK, write that down under the first number. How would you know how much he walked to school and back on that one day? ('add the two numbers together.') Good, do that. OK, but that is just one day. Now, let's read the problem one more time and let's see what the questiion was. (How far does Bill walk in a week going to school and back?) OK, now how could we figure that out?"

Many times the problem just works itself out in the student's brain as they begin to draw out a picture of the problem.

Or, if I've checked over his work and seen that he's added 4 1/2 miles 5 times for the 5 days of the week, I can see that he's overlooked a part of the question. So I have the student reread the question. Many times, the student will catch his own mistake when he hears his voice repeat the words "to school AND BACK". If not, I have him read just that part again.

Something really important: for some students it's just a matter of not knowing "how or where to get started". There are gaps in processing the information and gaps in understanding.

Not only does he need to know where to start, but he needs to know that where he is starting will get him going in the right direction and will help him get the right answer. This is very important to a student's confidence. If a student doesn't know "where to start" or isn't sure "if he's going about solving it properly", a teacher's trying to find the right modality isn't necessarily the answer.

This is where an "constructivist" approach is so devastating to the student. That student wants to be able to KNOW what to do to get the right answer.

It's terribly upsetting and deflating to a student not to know "where to start" and "if they're taking proper steps to solve the problem correctly." To leave this student to come up with his own idea isn't helping him.

Hopefully, though, a teacher will NOT just repeat the instructions that were given initially (if any were given). If a student didn't get it the first time, at least try a different approach.

One of my former students said of another teacher, "Why should I ask her for help? She always just repeats the same instructions that didn't make sense the first time." This student, smart as a cookie, just wanted to understand the entire process and to know how to work to get the right answer.