Tuesday, September 30, 2008

Free Printable Graph Paper, Rulers and More

Those of us in the teaching business never have enough graph paper, rulers, and various types of lined paper. Previously I've spent a lot of time and effort creating my own graph paper, but no more. Here's four excellent resources I learned about via Lifehacker and a growing list of others I've been collecting:
  1. Print Free Graph Paper - Creates a PDF based on your size and format specifications that you can save or print. I'll use this when we start working on linear equations.
  2. Printable Paper - This site has a lot more variety: print a Cornell Notes template, Isometric Graph paper or anything from their teacher resources page!
  3. Graph Paper by Konigi - This site's templates are best suited for drawing; for example art classes could easily use this for storyboards, perspectives or rough drafts.
  4. Printable paper rulers - It's ridiculous how quickly and easily students manage to tag, mangle and/or break rulers. This may be the ultimate solution: accurate paper rulers that you can reuse, recycle or replace easily!
  5. Free Online Graph Paper / Grid Paper PDFs - Fully customizable graph paper (set the size and grid spacing) and tons of other options like number line and notebook-style paper.
  6. Graph Paper for High School Math - This site features good trigonometric graph paper and TI-style graph screens as well as more versions of everything else you could want.

[Last updated 3/29/09]

Sunday, September 28, 2008

Parent & Student Guide to Getting the Teachers and Classes You Deserve

At this point in the school year, students probably have a good idea about whether their teachers are any good. Kids know when they're getting screwed, but they don't always know how to maneuver the roadblocks put in front of them to prevent them from switching out of a class. You know how you always hear about schools and districts putting adults ahead of children? This is an example of what they're talking about. Schools avoid changing students' classes whenever possible because they don't want to do the work involved.

There are ways to improve your chances, but it will take a lot of planning and mutual support between parent and student. One note before we get into it: if you know that the principal must approve every schedule change at your school, skip right to Level Two. Otherwise, here we go:

Level One: Student Action
Students need to prepare to present their case in a mature, responsible way. Parents and trusted teachers can certainly help with this. You need to be ready to approach counselors in a way that will get those adults to want to do things for them.

This means providing legitimate reasons for wanting to change your class. "The teacher hates me," or "I hate the teacher" won't get you anywhere. "That class is boring" or "stupid" won't work either (even if it's true). Legitimate reasons might sound like:
  • "I'm having trouble understanding the way [Mr/Ms X] teaches. I ask questions and go for extra help, but I still don't get it."
  • "I learn better with [a certain style of teaching], and my friend is in [another teacher's] class and told me that's what they're doing in that class."
Counselors want to hear that you're doing everything you can to make your current class work. Asking questions, coming before and/or after school, getting help from other students (or at home), are all things that a responsible student would be doing to keep their grades up. You're approaching them in a way their not used to--counselors hear a lot of complaining and deal with many immature students and teachers all day. You have to be a breath of fresh air.

Your chances of success will also go up a lot if you also provide a solution to your problem. Bringing up your concerns in a responsible way is good, but taking it one step further makes it easier for people in power to say yes. This means you have to do some research:
  1. Find out about the other teachers from friends, relatives, and trusted adults. It would be a good idea to go talk to the teacher you think you want and ask them if they would be okay with you switching into their class. You could even ask them if they would be willing to talk to the counselors on your behalf (which could help you avoid Level Two). In the end, you need to find the class where you'll have the best chance to learn and be successful. After all, you wouldn't want to have to go through this again later, would you?
  2. Figure out how to fit it into your schedule. Your first priority should be to see if the teacher you want has a class at the exact same time as your current class. The more changes counselors have to do to your overall schedule, the less likely they are to say yes. If there's no way to make it simple, you have to at least try to figure out a new schedule that would fit both your desired new class and different periods with your same teachers for everything else. Ask trusted teachers for help with the schedules of other teachers so they can help you lay out something that will impress the counselor you bring it to.
Why do you have to do all this, you might wonder. As with anything in life, if you do most of the legwork, it's easier for people to help you when you need it.

If all your hard work results in the counselor stalling, not answering your questions, or just a flat out refusing, it's time to move to Level Two.

Level Two: Parental Action
If you've presented both legitimate reasons and possible solutions without success, it's time to bring in one or both of your parents/guardians. Most school administrators (and of course the districts themselves) are so afraid of angry parents complaining to the press, getting them fired/demoted/reassigned or suing that they will do whatever the parents want with little hesitation.

First, go back to the counselor with your adult supporter. They must make it clear to the counselor that they support your very reasonable, very well thought out request. They also have to make it clear that they will go to the principal if they aren't satisfied with the result of this meeting. It would probably be good to get the counselor to commit to a timetable, telling you exactly when the changes will be made, and when you can start your new class(es).

If the counselor is still obstinate or won't give you a clear answer, you need to set up a meeting between you, your parents and the principal. Again, while it is okay to be upset in this situation, your adult supporter needs to refrain from yelling at the principal, as that will make them less likely to want to help you either.

I think you, as the student should first explain (without losing your cool) what you're trying to accomplish, and what you did to try to make it happen. Keep it short and simple. You have to do this because the principal will probably have no idea why you're there until you get there. Then it's your parents' turn. Again, they should explain that they support their student's position and tout all the hard work you did up front. They should also explain that in spite of this, the counselor wouldn't or couldn't do what you requested. If the counselor was at all rude or unreasonable with you, tell the principal.

This is a key as well: If the teacher whose class you're trying to get out of is doing or saying inappropriate (or illegal) things in the classroom, you should use that information now (generally it would be a waste of time to bring that kind of information to the counselor first). The principal is the one person at the school most directly connected to the higher-ups in the school district. Whatever their teachers might be doing, they're going to be held personally responsible.

Any threats that you might be forced to go to over the principal's head will almost certainly result in one of two things:
  1. The principal immediately acquiesces to your demands, fearing the wrath of the school district (and beyond).
  2. They will think you're bluffing and refuse your request, forcing you to leave empty handed.
Either way, you're looking at the end of the meeting. In most cases, things won't have to get this far. If, however, you're still not satisfied, you have one last option.

Level Three: Friends in High Places
You and your parents have the right to bring your request to an administrator in the school district, probably the person with a title like Assistant Superintendent for Curriculum and Instruction. You would repeat your case and what happened when you brought your concerns to the administrators at your school.

It's hard to go too much farther at this level if your parents don't have any connections to district officials, the school board, the superintendent, city council members, the mayor, or anybody with political clout where you live. If they do, they should call in a favor. I guarantee you that no matter what the school thinks, if someone at that level starts throwing their weight around, you will get your way very quickly.

Similarly, connections to the local media would be really helpful as well. Again, it's hard to imagine most school districts letting an issue get that far in the first place.

Success and Failure
If you've exhausted all of your options to no avail, then you'll just have to suck it up and deal with your terrible teacher. Just remember that if you hate that teacher, refusing to do work, getting in trouble all the time, or otherwise disrupting their class will only hurt you, not the teacher. In that position, you need to work twice as hard so that you'll pass the class and give them no reason to make the class any worse than it already might be.

Remember that time is not on your side, and the longer you wait to make a change happen, the more difficult it is going to be. If you need to switch out of a class, you need to start the ball rolling this Monday if you haven't already!

Saturday, September 27, 2008

How to Improve the Combining Like Terms Card Game

I recently received this comment on my original post Sample 5e Lesson Plan: a Card Game for Combining Like Terms:
Please help me understand how do I make the scores MEANINGFUL to the students at the end (other than saying that we just learned how to combine like terms). cchou1@lausd.net
This is a completely valid concern, one that I haven't addressed well enough. One possibility is to make the game a short one, playing one round only and stripping down the structure to the bare minimum. Then you immediately start doing straight practice of combining like terms during the very same class period, telling students only to follow the grouping rules used in the game, and that their answers will look like their "scores" for the game.

Of course, I don't see the world through rose-colored glasses, and I realize that idea may not be the most meaningful way to wrap up this activity. The other most obvious answer is to assign numerical values to a, b, and c and have students plug in those values after simplifying their respective expressions. I think most Algebra I teachers cover evaluating expressions for a given variable just before they move on to combining like terms, so it could be a good way to tie those two topics together. Students get a tangible numerical score, and it could help them understand the concept of variables as well.

I worry though that the evaluating approach would confuse or distract students from what they can combine and how they do so because they would be wrapped up in calculating a numerical result. Perhaps the solution is to keep the original "scores" intact and follow the game with a simple graphic organizer that reviews what they learned and connects it to the big picture. For example [with prospective student answers in brackets and italics like this]:
In this game, we learned that:

An "a" could only be combined with... [ a].
A "b" could only be combined with... [ b ].
A "c" could only be combined with... [ c ].
An "a2" could only be combined with... [ a2 ].
A "b2" could only be combined with... [ b2 ].
A "c2" could only be combined with... [ c2 ].
Numbers without a variable could only be combined with... [other numbers without a variable].
When I had a group of 3 or 4 cards, combining them meant that I had to... [add up the coefficients].
Like terms are terms that have the same [variable] and the same [exponent].
if I have like terms in a problem, I have to... [combine them]!
Finally, one last perspective on the original question. I think there's a lot of inherent meaning in this activity as is. I created the game because I wanted my students to remember what combining like terms looks like, and what a simplified expression might look like. This is why I've never assigned values to the variables. To a typical student, it is a weird, cryptic thing, all these letters and numbers arranged in this way. Our job is to demystify and decode these expressions so that our kids are not confused or intimidated by them, especially considering that they get more complex as we progress through the subject. The fact that they combine their terms mostly independently, and could complete all the statements in my sample graphic organizer above, is infinitely more meaningful and memorable than it would have been if I had done a traditional, straightforward lesson on the topic. The game, and the resulting "scores" they get are very meaningful for everything that comes afterward.

If you think you might want to use some form of this card game, please be sure to read two other follow-up posts I wrote about the game designed to make it work better in your classes:

Follow-Up: Combining Like Terms card game
Combining Like Terms Card Game Revisited

Alternative Assessment Idea: New Version of "Students Become the Teacher"

Last week I replaced my usual weekly quiz with a new version of an idea I shared both here on the website (Slope-Intercept Project, Teacher for a Day) and in my book Ten Cheap Lessons, (Idea #8 "Students Become the Teacher"). In my new school there is less of a focus on teaching to the test, so I use very few multiple choice questions on my assessments. This was a central part of the original version of the lesson, requiring quite a bit of reflection and revision.

I've been very impressed by the progress of my classes this year, and I think their fundamental skills coming in are far beyond what I was expecting given the reputation and results of the school districts here. So I've been giving a lot more open-ended problems, which gives me a much better picture of where students are as we progress. It also means I had to scrap much of the original idea and create a framework to guide students in creating a much different kind of quiz.

The purpose of this kind of assessment is two-fold:
  1. Student create a quiz with an answer key, proving they can answer questions about whatever it is you've been studying.
  2. It promotes higher order thinking as students determine what type of questions to include, what they might look like, and the relative level of difficulty involved. This is especially true if they have to write word problems.
In addition, students may realize that being the teacher isn't the easiest job in the world (even if you don't explicitly mention that part). That's good for your classroom culture.

I decided to use this in both my Algebra I and II classes (for different topics of course), and to give students a clear rubric in the form of a checklist. The list tells them:
  • How many of each type of problem to include
  • In Algebra I, I asked students to include some negative numbers, fractions and decimals to insure a higher level of difficulty on their quiz (those kind of basics are things we struggle with constantly)
  • To include a complete, correct answer key, directions, and a heading as any assessment must have
  • An extra credit question (as teachers like me are known to provide frequently)
What I had thought about providing, but didn't, was an example of a completed quiz as a model. I did give a few examples of what each problem might look like, and strategies for coming up with problems, but neglecting a complete model left many students lost. The class period wasn't long enough to complete the assignment either. This made the turn in rate really low, and is purely my fault.

On the other hand, I've learned over the past month that my students want a more traditional, straightforward approach in my teaching. This is mostly due to a complete lack of stability in the math department at my school--they've had eight different teachers over the course of 2 years, with varying degrees of effectiveness in their respective tenures. In Texas, I often had to use the kinds of alternative strategies I share because my students didn't get the material the first time around. Now, my students tend to get more of the material in less time, and appear to have an insatiable appetite for challenging material. It's a very interesting dynamic to deal with.

In any case, here's the two versions of the checklist via Google Docs. They are designed to fit two to a (landscape-oriented) page to save paper. The back of each half page would be a good place to put a full sample quiz or examples of appropriate questions.