It was an actual mini-lesson on interpreting -- and more importantly, on using -- the five-point rubric my teammates and I adopted.

Here is my version of the rubric (as a PDF): Rubric handout - Algebra.pdf

WHAT I DID

After the syllabus and the course requirements, I handed out the rubric and had the kids read the bulleted description of each element of a full-credit five-point answer.

We discussed each element, most of which were familiar to all students, but then I really stayed with the topic of "presenting one's work in a neat, organized, and logical manner according to the standards recognized by mathematicians around the world."

My kids are from very varied backgrounds, so we talked about how mathematics has become a lingua franca in our modern world -- so much so that a math teacher in Russia or in Egypt or in India or in Italy could easily read and assess the essence of a math problem written out by a well-trained student who does not speak the same language they do. We marveled at this for a bit (they're very smart and curious middle schoolers!).

Then this was the piece that really pinned the whole thing home.

**HAVE**

*ASSESS A WORKED PROBLEM USING THE FIVE-POINT RUBRIC*__THE STUDENTS__I wrote a very elementary prealgebra problem on the board and told them that the solution I was about to show them was presented on a math assignment turned in by one Hermione Granger. I told them that they were going to have to

**Hermione's work on the problem and**

*assess***their score using the rubric we had just reviewed.**

*justify*Now, of course, being Hermione, she was very meticulous in solving problem #4, showing every step of her work, spacing her work out on the page so that it was easily readable, lining up the equals signs so that equivalence was as visually obvious as it was algebraically.

Then I asked them to give this work a score.

I was really excited by how engaged they were in assessing Hermione's work. One student gave it a five, and then another agreed, citing each of the criteria in the rubric in turn. Then one of the eighth-graders said, in summary, that this made sense because she had shown both that she understood what she was doing AND that she understood that

**she presented her work was important in communicating to others that she understood the value in communicating clearly, logically, and neatly.**

__how__Needless to say, I was dumbfounded.

I then showed how Ron Weasley had approached the same problem. Unfortunately, Ron started by labeling his paper from 1 to 22, and squashed in problem #4 to fit the meager space he had left on the page, writing smaller and smaller until he had to have his solution creep up the right-hand margin of the page toward where the paper was dated in handwriting so cramped it verged on mental-patient scribblings. He circled his answer near the top of the page.

Then I asked them to assess his work using the rubric.

The students had a hilarious time criticizing the insane-looking presentation of the work. Much hilarity was had at poor Ron's expense, which was fine, since he is a fictional character without actual human emotions.

**CONSOLIDATION OF LEARNING**

To drive my point home, I took Dreikurs' strategy of using natural and logical consequences as a framing device and asked the class about the different choices Hermione and Ron had made in how they presented their work and their answers.

Everybody agreed that Ron had made lazy, poor choices because even though he had arrived at the "correct" answer, he had done so in a way that sabotaged his own efforts to do well in the class.

There was a lot of repetitive, reinforcing discussion of this point and we concluded that in a situation where you have control over choices (such as how to present your work), it would be foolish and short-sighted to sabotage your chance to have your learning be recognized by a scorer just because you're feeling a little inconvenienced.

And THAT was exactly the point I was hoping they would discover for themselves. Low-cost, high-impact point made.

And

**I'm really going to bed.**

*now***UPDATE: 14-Sep-11**

I created a completely generic downloadable version of my 5-point rubric as a PDF which you are welcome to use / steal. It's on the Math Teacher's Wiki at: Rubric-5-point-generic.pdf

Genius! I think this was a really clever first lesson. Maybe you would consider sharing Hermione's and Ron's solutions, too, as a resource for others?

ReplyDeleteI just made up a problem (which happened to work!) to demonstrate their work habits. And I just wrote it all out on the whiteboard.

ReplyDeleteThe problem was 2 (x + 2) = 24 .

Hermione went through each step and wrote it out neatly:

problem #4

2x + 4 = 24 (distributive property)

2x + 4 - 4 = 24 - 4 (subtraction property of equality: subtract 4 from both sides)

2x = 20

(2x)/2 = 20/2

x = 10

Of course this was all lined up, written neatly, and answer circled.

Ron started by numbering his paper down the left-hand side, then he squashed his work into the available space for problem #4 (it crawled up the right side of his paper and looked terrible):

2 ( x + 2) = 24

[something written, then scratched out in a messy way]

2x = 24 - 4

x = 10

I wanted to emphasize that, even though Ron happened to get the correct answer at the end, he had done so by taking great risks with his understanding, communication, and even his score (they're always point-obsessed, why fight it) (though of course, he might very well check his work by plugging his answer back into the initial equation.

I also reminded them of Mr. Shah's Fabulous Math Motto: "Don't be a hero."

ReplyDelete(they're too young for the "Calculus Above All" motto, so we say "Algebra Above All").

Lovely!

ReplyDelete