Favorite Comments '12: Deirdre Mundy, Barry Garelick, ChemProf, Julie in GA, and Catherine Johnson

On Explaining your answers when there's nothing to say

Deirdre Mundy said...

This morning I realized that there IS a place for 'discovery math'-- But it's individual, not group based, and you need a good underlying curriculum to support it.

I use Saxon with my daughter. But I'm also really lazy and don't always check to see if they're introducing a new concept--so I just give her the worksheets, let her go to town, and then step in a 'teach' if it turns out there's something she can't handle.

On her own, she 'discovered' that 4*10 is just like 4 dimes, and that multiplying is really just adding over and over, really quickly. No tables, no group work, no guesstimating....

The same sort of thing has happened with the fractions in second grade Saxon, and with almost every concept that has come up. (I had to step in to explain the meanings of 'symmetry, oblique, horizontal and vertical' Everything else, she just figures out when she hits it.

In a sense, this is what 'discovery' math is supposed to be--kids teaching themselves and wrestling with new concepts until they understand them--- The problem is that Discovery Math in the classroom is often about 'fun!!!' instead of learning. However, I'm seeing that 'guide on the side' DOES work..

If:
1. You have a very small number of students
2. The students are fairly bright

and

3. Your curriculum has a good, orderly structure.

Barry Garelick said...

Discovery can be done right and wrong. And as you've "discovered", it can also happen during homework, when students are working problems by themselves. Some books structure the problems so that some discovery does occur in the course of doing them.

ChemProf said...

"Balanced math" is the same idea as "balanced literacy" in reading, where in theory they are blending more traditional math assignments with discovery based assignments. In practice, the problem is usually that the traditional assignments become homework because the poorly designed discovery assignments take up all the class time. Be suspicious.

Julie in GA said...

"Balanced math" is exactly as ChemProf described it. My first grade son's classroom instruction consists of 90 minutes of group activities using manipulatives, playing "math games" and having calendar time. At the last conference, I asked his teacher how the math instructional time is allocated (group activities, teacher instruction, independent work.) She told me that she spends about 10 minutes showing students how to play the game or use the manipulatives, about 45 minutes in groups of 4 (collaborative learning)playing the games & using the manipulatives, and the rest of the time is spent working with pairs of students if they need extra assistance. She actually admitted that sometimes she isn't aware that a student hasn't understood the concept until long after they've moved on. Ridiculous!

My son has struggled all year with math -- his weekly math homework consists of a packet of worksheets, which we realized is where any and all direct instruction is occurring, in the form of me teaching him. He has also decided now in first grade that he "isn't good at math" and that "math is too hard."

Catherine Johnson said...

One is the notion that, regardless of how much your math skills exceed your verbal skills, if you can’t communicate your mathematical thinking then that thinking must be deficient.

I've just recently discovered, via Barak Rosenshine's article in American Educator, the idea of 'elaboration' in learning, and it makes perfect sense to me. In fact, it's more or less the 'missing piece' in my own thinking about all this.

Elaboration means (as I understand it) that we learn best when we .... manipulate or develop or grapple with the content we're trying to learn (remember) in some way.

That's what writing does for me: I learn via writing because it is through writing that I 'elaborate' on the content I'm trying to master.

That's also got to be what a good class discussion does; a good class discussion allows everyone to elaborate on the novel or poem or history text etc. they are studying.

"Elaboration" also goes a good long ways towards explaining why watching a video of a lecture doesn't work. In a real lecture students interrupt and ask questions or make remarks, or the lecturer self-interrupts and asks questions, or the lecturer simply sees from the looks on student's faces that he/she needs to take another tack, etc.

I'm thinking that progressive educators may have confused "explain your reasoning in words" with "elaborate upon the content you are trying to learn."

Because we all speak English, for most of us 'elaboration' is probably verbal -- or, at least, language is the medium in which we engage in shared elaboration (via class discussion, writing papers, etc).

But offhand, I don't see any reason why elaboration in math wouldn't take place IN MATH.

I don't know what the relationship of math to language is for math specialists; a lot of the 'math people' at ktm seem to be pretty verbal. I'm guessing that 'math people' can engage in useful elaboration via language --- BUT elaboration per se does not mean 'put into words' as far as I can tell.