Archive | March, 2009

## Much: a great way to make multiple versions of a test

Last year, I finally resolved to end the “wandering eyes” problem during tests. It seemed like there was no way to ensure that nobody would sneak a peek during tests, and when kids had the same test they would easily be able to cop an answer from their neighbor and it would be really really hard for me to catch/notice. Nobody wants to go around accusing kids of copying especially when it’s as flimsy as I saw you look at X’s paper. So, I figured, there must be an easier way.

Solution 1 instead of writing one test, I wrote two. It temporarily fixed the problem but it sucked my time to write two versions especially if there were going to be roughly equal in difficulty but tough to copy from with quick glances.

Solution 2 employ some software to write multiple versions for me. See an example inspired by Kate’s Perfect Challenge. I wrote 20 questions on a quick quiz for the kids to memorize the perfect squares from 1 – 20. Using a sweet piece of open source free software I then generated 20 different versions of the test. Now I can give them a different test for as long as it takes until they have it all mastered. (Obviously 20 is hopefully overoverkill, but it seems like a good demonstration of how easy it is to create multiple versions).

Googling this was not so straightforward, but I ended up with “much”. I love much. I have a test template that I use over and over again. All I must do to write a test is make a set of test questions – 1 per file

question
.

if I want them to be multiple choice they are formatted

question
.
.
fakeans 1
.
fake ans 2
.

Up to 6 possible answers work I believe. Much can shuffle around the order of the questions, and on multiple choice tests it shuffles around the order of the answers. If you make a strictly multiple choice test you can even use an output file that lists the correct answers.

Implementation I’ve been the best at keeping this thing updated for my Algebra 1 class, here’s a shot of the folder with all the questions.

The perfectsquares folder contains all the source files necessary to generate the exam.pdf test file with all the tests.

The fine print for this is that it can be hard to get comfortable with all the technology behind it. But if you know LaTeX, and are willing to dabble in commands from the command line, it’s a pretty quick process. I’ll outline the steps below in case it’s helpful to anyone (The much page has all the relevant info, and I taught myself from it, so head there if this isn’t so helpful)

1. Write a set of questions with some sort of standardized naming scheme, i.e. if I want to have 5 questions on linear equations name the files lineq-1, lineq-2, and so on.

2. Create a file named “test-info” also copy the “exam.tex” file into the current directory. These files are provided as part of the much download, here’s the test-info file I used for the perfect squares quiz and here’s my exam.tex.

3. In the “test-info” file copy the exact formatting, and set the number of tests you want to generate, and then define what goes on each test. For example, if I wanted 2 of the 5 linear equations questions on each test I’d add the line:

use 2 from "lineq-*";

To tell the computer to insert two questions with the file name beginning “lineq-” and the * indicates that any ending is acceptable. If I had a file named lineq-toughproblem5 it might potentially be chosen as one of the 2 lineq-* questions.

3. Once your test-info file is set up with all the questions you’d like on the test, use much to prepare the tests by typing much create test-info at the command line, once you’ve navigated to the folder with all your test files and test-info file.

4. Command line: pdflatex exam

## Law of Cosines

I just lost a couple of hours to the law of cosines. It kicked my. So now, with my newfound knowledge I feel ready to have a go at class tomorrow. Thanks to the kind folks at the math forum I set it up with geogebra, schemed off about 5 pieces of scrap paper, and have a fool proof, coordinate proof-inspired strategy for explaining it. I also, however, have a bucket of lemons for the text book which presents the law, for the sake of presentation, I assume. I hope that it’s not common knowledge that cos(x)^2 + sin(x)^2 = 1 at this point in their careers. I also cannot think of how any of the other ways of deriving the law would make sense at this point in the game. I imagine that a few years off I will either not teach this or will present it in more of its glory, but for tomorrow, having an explanation is better than nothing at all. Mine looks like this.

Picture the triangle with A at the origin, B at the point (c,0).

Knowing the angle A, b, and c, we can find a (the length of the side opposite the angle at the origin). First we find the coordinates of C by drawing the altitude from C to the x-axis. C = (c cos A, c sin A). Then using the points (c, 0) and (c cos A, c sin A) we apply the distance formula as follows.

$\inline a^2 = (b-c \cos A)^2 + (0 - c \sin A)^2 \\ &= b^2 - 2bc \cos A + c^2\cos A^2 + c^2\sin A^2\\ &= b^2 - 2bc \cos A + c^2(\cos A^2 + \sin A^2)\\ &= b^2 - 2bc \cos A + c^2 \hfill \mbox{ note: } \cos A^2 + \sin A^2 = 1\\ a^2 = b^2 + c^2 - 2bc \cos A$

Having figured out how to use the law of cosines, we have the opportunity for a sweet detour into a little calculator programming. I bring you, the law of cosines in LCOSSSS – which will find all the interior angles, given the sides of a triangle.

The SAS version allows you to find the side opposite an angle given an angle and the two adjacent sides.

And the SAS version – given an angle and the two adjacent sides, find the side opposite the angle.

## This class would be better if “it were less verbose and boring”

Wrote a student on the survey I handed out today. It’s fun to read the little thoughts kids have about class. Any ideas on being more to the point and engaging?

## Teaching Dimensional Analysis

I’m on attempt #3, and finally had some success. First, I had kids take two guesses.

1. 8ft = ? cm (I drew 8 ft and 1 cm on the board)
2. 15 mi = ? cm (Made them picture some local 15 mi distances)

Then we did 58 hands to fingers to people type conversions.

$58\mbox{ hands} \cdot \frac{5\mbox{ fingers}}{1\mbox{ hand}} \cdot \frac{1\mbox{ person}}{10\mbox{ fingers}} = 29\mbox{ people}$

I would joke with kids about how 58 hands isn’t really equal to 29 people – like if you had a bunch of hands they wouldn’t be able to talk. But purely the numbers like 29 people, 58 hands come from the same thing. This is also useful in discussing the answers for real conversions like 8 ft = 96 in. The number (96) has to be greater because we are describing the same thing with smaller units. I had them follow along with a few examples, and asked them to explain where the numbers from the conversions I had done for them came from. (There are a few smart board vids of the process – I’m a fan of anything to allow things to appear that offers me the freedom of not being in the front of the room).

I made a few worksheets for more practice.

I also spent some time making a nice conversions handout (“ho-” in my ‘ol naming scheme) for kids to use when doing conversions. The pdf might be useful.