Teaching Teachers - A Cautionary Tale

Teaching is a great field to be in. Like every job, there are positives and negatives, trials and tribulations, difficulties and successes. Teaching has its stars and its plodders, champions and minions just like every other business. Find the good ones and try to avoid the bad ones.

I just wish so many teachers weren't so damned frustrating.

The tagline for one particular blog is "Burn The Textbooks, Shred The Worksheets, Teach Math," which is a sentiment I can follow, albeit cautiously. There is certainly nothing sacred about a textbook if you are replacing it with superior material, ideas and learning. Some things seemed childish, as if they were geared towards a young audience, but that's all right. I like to see what elementary students are learning, to get a sense of the state of the art in the lower grades, so I kept looking.

This guy, though, strikes me at first glance as a pretentious moron and I find myself wondering how I got to this one in the first place ... whose blogroll contained him? He seems to always be pitching his lesson plans for sale and that rubs me the wrong way. I can forgive if the quality is there, but then he posts this kind of thing (Learning the Number System with Maps) and you wonder ...

Anyway, I threw his blog into Google reader a week or so ago and I think he just earned his way into the joke folder.

My college students were offered extra credit for producing a hands on math project on one of the following themes. 1) The Real Number System 2) The Commutative, Associative or Distributive Properties

And then I looked at the pictures posted with it.

1.	2.	3.
4.	5.

As a project for college students, they are poorly thought out and suffice only as examples of their own math illiteracy. As extra credit, I'd consider them as negative value work in that I'd actually reduce grades for trying to pass this off as worthy of a child's time. If these people are supposed to become teachers, I shudder at the implications for their prospective schools. Do they truly know so little? Is this their best work or merely a toss-off handout meant to glean a couple of points from a gullible and not-too-attentive professor? Does the professor not know the problems?

Now, I understand that I may have misunderstood the purpose of the assignment and that these students may have intentionally written incorrect examples, confusing or obfuscated instructions, or created Venn diagrams and graphic organizers that intentionally make incorrect mathematical points.

Nothing in the post or in the pictures above, however, makes that clear or explains why such dreck is worthy of extra credit, a concept with which I rarely agree.

On its face, extra credit is a silly idea.  Doing something unrelated to fractions in order to improve a grade on fractions seems antithetical to the idea of a grade being a numerical representation of a student's understanding and knowledge. Show me later that you understand this work better than you did the first time and I'll increase your grade on it. Doing something like washing teachers' cars for extra credit is outright bribery -- ethically, it's equivalent to accepting cash.

If anyone reading this is a teacher prospect and is wondering what I find so problematic about the above images, let me be clear that I am making these comments without knowing any more than the post and the images.

1. The butterfly graphic organizer bothers me. Before creating this, the teacher must be clear in his mind exactly what color, shape, represents what type of number and know the definitions of each. If a rational number, $\sqrt{100}$ is placed in a green region as are the irrationals like $\sqrt{19}$, students will assume that irrationality is exclusively determined by a square root. Does the teacher candidate not realize that 10 is rational.  Secondly, if there are no irrationals without radicals, will the viewer understand the nature of π or φ? If the teacher does not know himself ...

By my count, 5 of the greens are rational but I may not have found them all. Finding them would make a good lesson but it's one that seems to have been lost on the constructor.

2. This one is just odd. The instructions are unclear: "Do not feed the alligators unless the #'s are the greatest."  Why superlative rather than comparative? Why state this as "Do Not ... Unless"? Are there too many other options to list?

How about "The alligator eats the larger number"?   Maybe "The point is small and the other end is large so it points to the smaller number"?

I have no idea what "Order Property" means or why "Food" is listed on strips.  Where are we going with that? Is the top list greater than the smaller list? Is every element of the first list being compared to those in the second list or is it intended to mean that place in the list matters? If this is truly a lesson for children, then we have to assume that the children are having trouble with the concept - this does nothing to simplify it.

3. First, the picture is of the associative property.

Second, the story is ridiculous and has nothing to do with either mathematical property.

Third, a child who is reading something written in this font style should be focused on the idea of the property without bothering with the name of it.

Fourth, stop pretending that a child wrote this.

4. A nice idea, but flawed in the execution.  Start with the map of the world.  Irrational numbers are Australia and rational numbers are the USA ... that's pretty goddam funny and possibly backwards, but who's making a GOP joke? Me, actually. What's the rest of the world?  If it's not rational, it's irrational by definition. To make this work, the USA would be rational and the rest of the world irrational and I can't stop giggling at that either.

The USA is divided up in a better fashion in that there are vastly more non-integral rational numbers than integers but I doubt that the designer knows that.

The Virginia split? Apparently the whole numbers are just Frederick County meaning the rest of the state is negative integers. Seems unbalanced somehow since, other than zero, there are equally many positive as negative integers, but that's a nitpick.

Speaking of zero, if the Town of Winchester is the Natural numbers and Frederick is the Whole numbers, then what does that say about the rest of the county? Yup, it's the zero.

I know, I know. Area shouldn't matter in a graphic organizer but when you use a visual that explicitly has such a meaning then the reader will make the wrong inferences based on those meanings.

5. What can I say? 75% of the examples are wrong and 75% is less than 100% but that's no reassurance either because 100% wrong is a lesser problem than 75% wrong because the former is a misunderstanding of the notation and easily solved, but the latter shows both a misunderstanding and a mistake based on that misunderstanding.

2 is less than 1? No shit.

Forget the "Feeding Instructions." Could someone please explain what "Please put food of the lower number into its mouth" is supposed to mean, because my English skills are lacking and my mathematical side seems to remember it the other way around. The only correct problem listed, 5 < 6, along with the improper instructions, gives me the distinct impression that the last example was actually a double negative.

Oh well, the South won the Civil War, too.
God Bless Virginia.