It's 8:05 P.M., Your Homework is Late!

Following up on my previous post on how I want to stop grading, I thought it would be good to provide some notes from the field as we head in to our second full week.

• I sent out a "Math Checkup" using a Google Form. This was a pretty quick and easy diagnostic assessment that I made using NYS Testing Program multiple choice questions. A few students had trouble opening the form either in their e-mail or through a hyperlink, but after a few days most everyone had figured it out. I now know a rough estimate of each student's proficiency and could figure out the value-add at the end of the year if I give a similar exam. I also know a few topics to cover early on that I may have skipped over. Oh, and did I mention that I can skip collecting exams, grading the answers and entering the data into Excel?

• We have started to do nightly homework assignments also using Google Forms. When I gave out a quick survey at the end of this past week, I got the following results:

"The one thing that should change about this class is..."
"The homework" (1)

"The one thing that should NOT change about this class is..."
"The homework" (2)

Ever seen kids answer a survey and say that they didn't want the homework to change? And that one student is getting a paper copy printout tomorrow.

• While the students are completing their homework in Google Forms, I come home from school everyday and check my Google account after dinner. I always get to see who has completed the assignment already and can think ahead to what we need to review in class the next day.

The next steps for this project:

1. Reliability - This is an issue. Some kids have been reporting trouble opening the email or submitting their finished work. I think a few more test cases should help solve this.
2. Confirmation - Everyday students have come in to class asking "Did you get my homework?" It's music to my ears! However, I'd like for them to know that I received their work before then so there is no anxiety. Currently, I've customized the confirmation note, but even this leaves them wondering if it even worked.
3. Feedback - One possible solution to #2 is to give the students permission to view the results. This would be great because it could give them instantaneous feedback on whether they got it right or not. However, currently this would mean they could see everyone's answers. I need to make sure they can be trusted not to use that information for evil. I want to trust them, but we need to discuss this and maybe build up our group norms a bit. There is also the risk that they could cheat by seeing the answers then sending them to a friend. But that's why I love that time stamp feature that is built in. I wouldn't mind students submitting, checking and resubmitting. In fact, that would be the best. Video games good.

No Wonder They Don't Like Math

I started reading Polya's "How to Solve It" this morning and found some tasty gems immediately:

• "Thus, a teach of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking."

• "... overhearing Polya's comments to his non-existent teacher can bring that desirable person into being, as an imaginary but very helpful figure leaning over one's shoulder."

• "Mathematics, you see, is not a spectator sport. To understand mathematics means to be able to do mathematics."

• "... to teach mathematics well, one must also know how to misunderstand it at least to the extent one's students do!"

• "Experienced mathematicians know that often the hardest part of researching a problem is under standing precisely what that problem says. [...] 'If you can't solve a problem, then there is an easier problem you can't solve: find it.'"

Duelling With Math

In my history of mathematics course, we are reading William Dunham's Journey through Genius, which I highly recommend for those who can admire a good proof.

The thing that has got me so excited about this class though isn't the beautiful theorems we're reading about. Far from it. It's the sense of storytelling that you can create by including some of the history of math into your teaching.

I was blown away with the historical perspective I gained in reading the following passage (p.134-135) about mathematics in the Renaissance:

"[A]cademic appointments were by no means secure. Along with patronage and political influence, continued service depended on the ability to prevail in public challenges that could be issued from any quarter at any time. Mathematicians like [Scipione] del Ferro always had to be ready to do scholarly battle with challengers, and the consequences of a public humiliation could be disastrous to one's career.

"Thus a major new discovery was a powerful weapon. Should an opponent appear with a list of problems to be solved, del Ferro could counter with a list of depressed cubics. Even if del Ferro were stumped by some of his challenger's problems, he could feel confident that his cubics, baffling to all but himself, would guarantee the downfall of his unfortunate adversary.

"Scipione apparently did a good job of keeping his solution secret throughout his life, and it was only on his deathbed that he passed it along to his student Antonio Fior."

I was so taken with this idea that I came up with some slides for a game that I'd like my students to play: Math Duel. (see slides below)

I've seen teachers have students generate their own questions for each other, but how about setting it up within the historical context of famous men and women in the course subject. I've got to give a lot of credit to Dunham for writing such a thrilling history of a subject that gets a bad reputation as too dull and black and white.

Grading Regents

I had my first experience grading state regents exams today. It felt like a terrific rite of passage, like jury duty. Only I was disappointed to see firsthand what Diane Ravitch described in The Death and Life of the Great American Education System, including how a student can receive a passing grade for scoring about 1/3 of the possible points.