On Tuesday I visited a friend, and I wound up helping her daughter with homework. She goes to a school with block scheduling, so Monday had been her first day with her new 90-minute subject classes — including history and geometry, two of my favorite things.

In high school, I got low Bs and Cs in every math class I ever took — except Geometry. Spatial relationships appealed to me, and I “got” a lot of the systems intuitively. So will she, eventually. She has that kind of mind.

But she was a little concerned about Geometry, so we worked through fifteen problems together. I thought the homework was a little long, especially for the second day, and given how many steps some of the later problems had. But it was relatively simple stuff — the Additive Line Segment postulate.

As she did the homework, and I watched her write out the answers to the problems, I had a chance to see what I imagine, but rarely actually see, every day. Here was a student doing her homework at home. She was sitting on the floor, her notebook and worksheet on a coffee table, and working under a bright light in an otherwise-dark room.

Here at school, students work in their own rooms at a desk or in a large room together during study hall each evening. Boarding students work entirely differently than day school or public schools, I guess.

Anyway, back to the homework. I realized, watching her, that the habits she set now for Geometry would have a lot to do with how successful she was in the rest of the term. But the teacher hadn’t provided any guidance about how to do geometry problems, or how to show your work. Which was D-U-M-B: dumb. We put kids through years of addition, subtraction, fractions, decimals, and parentheses, and train teachers and students alike to show their work algebraically.

But this is Geometry. There’s a completely different notation, a completely different set of assumptions, and a much better set of tools (like graph paper, blank paper, a ruler, a compass and more). So, first I set her up with a notebook (not for tonight’s homework, but for the future), with graph paper on one side and blank paper on the other. A friend of mine brought it to me from Germany; it’s fancy paper for engineers, I think.

And then I talked her through drawing lines and lettering points.

Now. You may ask (especially as a mathematics teacher) why bother doing this sort of work on the first day? Just measure the lines, record the length of the lines in millimeters as it says, and move on to the next problem.

Oh, but poor little girl! She’s never taken geometry before! The way to learn geometry is to learn how to visualize lines and figured. The easiest way to visualize these is to draw them and then follow those lines to logical conclusions.

Only, she wasn’t going to draw the lines. The geometry teacher didn’t teach them that.

So I taught her. Dumb math teacher, I thought, doesn’t know to teach his kids how to draw lines from day one on their homework, so they get into the habit of thinking “it’s geometry, I can solve the problem if I draw it and look at it.”

Then I thought, hey! If it’s the first day of school, she has her homework from the world history teacher, and I can see his day-one handouts and papers. So I asked my friend’s daughter to let me see them, and she did.

Oh.

Did you ever have one of those moments when you realize that another teacher has shown you up, badly, by doing things you never thought of doing? Her history teacher did that to me. I was blown away by his day-one works. Why?

He had — a list of earlier historical research papers, and a worksheet for the students to fill out saying what they wanted to research this term and why — along with a little checklist on how to tell if you’ve chosen the right topic for yourself. There was a list of about 60 historical lenses, based on the six basic concepts of Technology, Politics, Environment, Social, Cultural, and Economic viewpoints. There was a list of the six basic types of Historical Questions, along with examples of each and a written description of each question.

In short, a lot.

I intended to spend most of the evening grading papers, but instead I wound up making my own versions of his documents, and making them into PDFs for my class wiki, and putting them into the wikitext.

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