12.09.2009

Professional Goals

On my way to an evaluation team meeting today (I want to write more about that...but don't feel I can confidentially...one bad thing about being myself online and not having a blog pseudonym), I had a bit of a heart to heart with my boss (principal).

You might think, "on the way" isn't very long...but picture 100+ outdoor stairs from the school building to the admin building where the meeting was being held...lol.

Anyway, he was asking me how things were going, if I could believe that the year is already almost halfway over, and how time has flown in the 1.5ish years I've been in VA. He also mentioned that I have 30 more years to go before retiring. After that comment, he asked about my professional goals: When you're getting ready to retire, what do you hope to have accomplished/done?

At first, I didn't know how to respond. I'm not much for long-term planning. I'm lucky to know and have decided that I indeed will be staying in VA for at least one more year...to think 30 years down the road and wonder about what I hope to have achieved/accomplished?! That's way out of my comfort zone. Not on the horizon, even. I did answer him, however. I said that I want to get my Master's. The program I want might be closing, so I need to do more research, but I would *love* to do something along the lines of math/science instructional design/curriculum or, like the program I originally wanted, Deaf Education with a focus on math and science instruction.

I guess as a long range goal after that, it would be neat to be a tech facilitator (like @msgregson is studying to become), or a math specialist. I think I would like to be a consult or resource for the elemetary teachers (at least in my current school) with ideas and maybe even push-in math-specific services. There currently is no such position at my school, but I think it would be neat.

Just thought I'd share what my current thoughts are about long-term goals...any thoughts?

12.06.2009

Thanksgiving Observations

Over my week-long Thanksgiving Break, I spent 1 1/2 days doing observations of other math classrooms. A bit of background: my major in college was Special Education - Deaf Education with minors in math and english. Basically, though, I was treated as an Elementary Education major, with the addition of some ASL classes. All of my observations and practicums, as well as my internship placements, were in elementary classrooms. I *did* observe in a public middle school program for d/hh students at one point, but other than that, all of my exposure was to elementary teaching methods.

Tune into now, my 2nd year as a high school math teacher. I realized that the only high school math teachers I have ever observed were my own, and that was long enough ago that I don't remember specifics about what they did (let alone, while I was in high school I didn't really think I would ever be a high school math teacher...I started college majoring in music education with a minor in math thinking I could maybe teach middle school math if the band directing thing didn't work out).

Needless to say, I thought it might be a good idea to observe some other teachers at work with my "teacher goggles" on, looking at things like classroom management and structure, lesson organization, how to handle notes/homework, and just generally what other people's classrooms look like.

I went to Wisconsin School for the Deaf to look at Bilingual/Bicultural teaching philosophy, as well. I was able to observe a HS geometry, HS simulated budgeting, middle school, and several elementary classrooms. I was a little disappointed that my schedule wasn't exactly as it had been planned, but it was good to see what was happening at another school for the deaf. One of the major things I took away from those observations are ideas that I hope to bring to a personal finance class in the future. The simulated budgeting program that they have is very detailed and organized, and gives students real experience! I'd love to see something like that at my school. Something that surprised me, though, is that I only saw one student all day write anything on paper (as in, notetaking) other than their homework assignment. I spend a lot of time making guided notes and "worksheets" to allow the students to work through problems and then keep them as a reference in the future. The classes I observed did not do that. Problems were "through the air" or students worked them out on the board.

I also went to see @JackieB for a day! It was really fun to meet her in person, as I've been learning from her blog and tweets for about a year now. I got to see her integrated classes of freshmen and seniors, and her Algebra 2 class, as well as an AP Calc AB class. We also had the opportunity to go out to lunch and talk math. If only we could change the world...and the system...and kids' motivation to learn math. Something that I learned from Jackie is to highlight *every* opportunity to connect equations, graphs, tables and situations. In certain types of problems, I just forget to look at one of those 4, I now realize that the connections that can be made across the board might make at least a little easier for students to build connections and understanding of concepts. She asks really good questions, and makes her students squirm sometimes by refusing to tell them if their answer is right or wrong, but continuing to ask them questions like, "why?" and "how did you get there?" Keep it up, Jackie, and thanks again!

Contrary to popular belief (my friends and grandparents in the Chicago area), I am not looking for a job for next year. I'm just looking to get ideas of how I can improve my teaching, what I can do differently, and affirmation of some of the things I am already doing well. I wish I could take more time to go observe at different schools for the deaf across the country. There *has* to be someone out there that is having success teaching math to students who are d/hh. I want to steal every bit of wisdom I can!

11.19.2009

Humbling

I'd forgotten how humbling it is to make something and then send it to another person for feedback. As I was making my derivatives test yesterday, Sam mentioned that he would like to see it to compare with his. As I was writing the test, I was adding specific questions to target certain skills, but I also became highly aware that someone whose teaching I highly respect would be looking at this test very soon. It made me nervous! I'm in the very early stage of my career so I feel like I don't have anything to offer these teachers who have been at it for years. I become self-conscious.  But I sent it anyway, despite my insecurities, and hopefully he'll have some feedback on how it could be better. *smile*

Thanks for making me strive to be a better teacher.

11.15.2009

Running headfirst into a brick wall...

...is what it felt like in my Algebra 1 class on Thursday. We had been making major progress Monday and Tuesday looking at function machines, finding outputs when given inputs and a rule, finding a rule and predicting outputs when given several input-output pairs. Then Wednesday we didn't have class because of standardized testing being done at school (Stanford Achievement Test-10...it has Deaf/Hard of Hearing norms so we use it every year to see how our students are improving with respect to their same aged d/hh peers). Thursday it was as if Monday and Tuesday had never happened.

While one student was trying to figure out the rule (2-step) for the table he had completed, two other students were struggling trying to complete the table. I had felt confident after Monday and Tuesday because this year I was actually talking about the functions and talking about the rates of change of the input and output, how they were related to the equation, how they related to each other, etc. (side note: last year I don't think I even talked about rate of change at all...I know that's terrible...but I didn't think the students had the grasp of the language *or* the concept, so we were in major survival mode when it came to slope, functions and graphing). Granted, the problem we were tackling on Thursday wasn't simple, but I was bamboozled when 2 students, half of my class, couldn't fill out a table given inputs and a rate of change!

The hardest thing to do in this class is differentiate. I have one very high student that needs to be challenged, and two fairly low students that need my support and guidance/hand-holding for much longer than other students need. Problem is, when I challenge the one student that is ahead, he needs my assistance to get going and to guide him along the way, then the other two are either lost or they go ahead and try their best to work independently and end up making errors along the way.

10.30.2009

Catapults and Algebra 2

In a previous post, I talked about how I used Sean Sweeney's catapult lesson in Calculus. I also used it in Algebra 2, as an enrichment project for two students while the rest of the class was gone for a sports event. I also talked here about how I introduced the project without actually being there.

Unfortunately, time for the actual project was cut short by an assembly that ran long. From what I could gather from sub notes and the notes that the students left, they enjoyed it. Unfortunately, with the short amount of time that Algebra 2 gets (and it keeps getting cut shorter when the kids leave early for sports games!!), they never finished it. It might be something I resurrect once the pressure of the SOL test is finished. There is just so much material to cover and I want to be able to take the time to actually *teach* the material instead of just showing it to them last minute.

Maybe it'll work better next year...?

p.s. this post was started on October 13th...it's now October 30th. Where does the time go?

10.22.2009

On Catapults and Calculus

I stole Mr. Sweeney's catapult project and tweaked it (more like, added to it) for Calculus class.

It was fun! We not only calculated the equation of the parabolic motion of the projectile, but at the end we talked about how fast it was going using the limit definition of the derivative at different points during its flight. It was a really great discovery point of how the velocity is zero at the maximum height. We were also able to then talk about why that "makes sense".

The next goal was for my calculus student to help my Algebra 2 students with the project while I was at a conference...stay tuned to hear how that went!

(I started writing this post 1 1/2 weeks ago...and the other one has been started, too...just waiting for some TIME to finish up!)

10.13.2009

Discouraged

Last week was a definite high. Things were going great! My observation went well, I was excited for the projects that I was leaving for while I was going to be out, and the substitute teacher that was scheduled to cover for me knew the language *and* the math! It was all looking good!

I arrived back at school to find my plans weren't completely followed. I know this is not unusual, but in preparing I thought I was ready for everything that could happen and that I had thought of everything...organized, etc. I guess not.

My Algebra 1 class that was solving 2-step equations like crazy on Wednesday bombed a quiz that they took on Friday (which they were supposed to take Thursday...but that's another story entirely). I felt like I needed to start from scratch again, and that everything from the week before was lost.

I had no Algebra 1 class today, so no chance to redeem. Tomorrow is a new day, though. We're going to correct the quizzes and then move on. We can't be solving 2-step equations forever, but we need it as a foundation!

10.08.2009

Encouraged, Again

Last Monday I was feeling overwhelmed. I go through these phases when I plan ahead, get a few days worth of lessons/notes put together, and then I get through one day and realize I'm not really ready for the next day at all because things didn't go the way I planned. These phases often leave me frustrated and irritated that I spent time up front that seems to be wasted. In the long run the time spent is not wasted, but it's still frustrating to *think* you're ahead and then *realize* that you're just as far behind as you normally are, despite the extra time you put in.

Anyway, that's how I was feeling Monday. And Tuesday I was supposed to get observed for the first time this school year. "Great," I was thinking, "just great." I had a less-than-stellar lesson planned, introducing graphing one-variable inequalities and solving one-step inqualities. Not something normally covered in Alg1 (it's a middle school concept), but that's what my kids need. I sent my lesson overview to my principal the day Monday and continued brain-storming ideas on how to make it more interesting.

I arrived Tuesday morning, less frantic than Monday (did I metion that I slept through my alarm on Monday morning, too...talk about a rough start to the week), and prepared myself mentally for the lesson and observation. Class started and I knew it was going to be a good day. I picked my best class for this observation. To provide some sort of closure from the day before and transition to the new topic, I had 2 students present problems from earlier (one- and two-step equations).

I was blown away as they were presenting. Without my prompting, they were explaining why the balance method for solving equations worked.
ex. 4x-7=9. I first added 7 to both sides because it's the opposite of the negative 7 that you have right now. I can cancel out the -7 and +7 because they equal zero. Then 9+7 is 16. I pull down the 4x = 16. Next I need to divide because it's the opposite of the multiplication that's happening now. I end up with x = 4
This type of reasoning and explanation never happened voluntarily in my classes last year. It's something I really have been working on with the students by asking a lot of "Why?" and conceptual questions. While the student was presenting, I kept thinking, "He's answering every question that I would have asked him!"

Later in the class, I found a way to make a boring part interesting by having the kids move around a bit. They needed to decide whether or not to flip the inequality. If it needed to be flipped, they stood up. If it could stay, they stayed sitting. One student made a mistake and stood up when the rest were still sitting. He felt silly at first, but his neighbor looked at him and explained why it didn't need to be flipped. He even gave an example of a situation (using the same numbers) where it would need to be flipped.

I was astounded. I love my job because I get to see things like that happen. I get to see kids grow and learn and teach each other. And I get to sit back and just watch sometimes! LOVE it. *smile*

10.04.2009

Really excited for this week!

I'm getting really excited for this week. Plans include catapults with Calculus and Algebra 2, complete with video instructions (really hoping that technology is my friend this week) and peer mentoring.

The goal for catapults is to work through the project in Calculus on Monday and Tuesday. We'll be taking it a bit more in depth than Mr. Sweeney's Algebra 2 project, talking about velocity and position relating to the initial discussions of derivatives. Then, on Thursday, Algebra 2 student will make a catapult from my model, and begin his investigation. Friday, Calculus student will join Algebra 2 student to help with the "math" of the project. All this will happen without me being there, which is why we need video directions!

I'm really excited for this, and the excitement easily turns into anxiety and thinking of all the ways it could completely bomb and blow up in my face when I return. But, it's worth a shot, right? Two-thirds of my Alg2 class is going to be gone Thursday and Friday anyway at a volleyball tournament, so here's my time to throw in a project for one of the more advanced students in my class.

Any words of wisdom?

10.03.2009

GSP meets Algebra 1

I was pleasantly surprised when my ITRT (read: tech person) at school emailed and said she found out we had a lab license for Geometer's Sketchpad (GSP). Last summer I took an online course from KeyPress to learn how to use GSP and more specifically, how it can be used in Algebra classes. I was very excited to learn more about this software and to be given examples of how it can apply to the concepts we teach in Algebra classes.

Earlier in the year, I used GSP to demonstrate adding and subtracting integers. I was using it as a demonstration tool at first, projected on my SMARTBoard. One problem I found using it that way, was that the sketch itself was too small for the students to see, and I ended up having one student sit at my computer and do the manipulating. I tried to make it work, and to let students take turns doing the manipulating, but it just didn't work the way I wanted it to. It was good, however, introducing the basic concept of what I was trying to develop: adding and subtracting integers on the number line. We then took that concept/idea and went back to paper and pencil methods.

This time, I took the students to the lab. We are solving equations, starting with the basics and moving forward to multi-step. I started the unit asking them to find the missing number in some simple equations, to see what methods they intuitively used. Next, we talked about working backwards, doing the opposite of what is currently being done to the variable, in order to get the variable alone. Finally, I wanted them to be able to explore the balance method of solving equations. I found a sketch with a balance, using positive and negatives. Gave the students a guided worksheet to explore what happens when you do different things to the balance. Was looking for the students to discover some properties about balancing equations (i.e. adding/subtracting the same number from both sides keeps the equation balanced, a positive and negative "cancel" each other, whatever you do to one side you must do to the other).

The students (as could be expected) struggled with the software. It was the first time they used it and the sketch had too many other things they could explore. They were curious and excited to play with it. I was able to ask some higher level questions, and the students responded well because they could support their ideas with the sketch. Their reading level caused them to struggle, even with the simple worksheet I created. I spent a lot of time going from student to student explaining what to do next.

Hopefully I'll be able to use this program again with this class, because I think they will be more comfortable with it and it'll probably be more successful the more they use it. Just thought I'd share my experience. Any suggestions are welcome.

**Note: I can't figure out how to upload the GSP files, so if you want a copy, leave a comment or email me**

Becoming more Human

Wednesday I gave a test in Calculus. It was covering limits at a point, at infinity, one-sided limits, continuity, etc., even some free fall questions leading into our next unit on differentiation. The day before the test, I was nervous that the test was not going to go well. Review, things that should have been easy, was like pulling teeth. I was starting to doubt myself and my teaching.

During the test, I was looking through some stuff in my classroom and I happened upon my limits test from when I was in high school. I got a B+, and there was a calculator and no-calculator portion. I instantly thought, "Arg! I should've made a no-calculator portion!" Instead of dwelling on that, though, I just looked it over and found my mistakes...very interesting ones. Since the class finished the test with time to spare, I decided to show my test, and look at my mistakes. Looking at the problems I answered incorrectly, I asked the student to decide where I went wrong and what the answer should be.  We went through the whole test like this, and even on some of the questions I answered correctly, I asked why that is the right answer.

This little exercise was a time-filler, yes. I think it made my student view me as a co-learner and as someone who has gone through what he is going through. I'm not just a teacher, I'm a student and learner too. I make mistakes in the classroom all the time, so it's not that my students view me as perfect and error free, but I think showing my old test and what was expected made a stronger bond between us. While I don't have all of my tests from calc, so I won't be able to do this frequently, I do plan to share from my experiences in calc during high school, and I hope to bring in some of the activities that we used (and some others!)

9.28.2009

Encouraged

Calc class today:

Limits review...he was actually on it! Material that I thought was going way over his head last week was processed and we had some really good conversations about different types of problems. Great questions were asked, showing that he's actually thinking about what he's doing and why, too. (There are, of course, still some trouble areas like knowing when to factor/rationalize and what numbers will "help" in the simplification process, but it's a process, right?).

Then, we did some free fall problems, applying limits and previewing derivatives. It was so great to actually apply what we've been talking about to a real situation and make it mean something. Here's the problem we spent time looking at, and some of the humor that came out of it...

A construction worker is working on a building that is 1000 feet tall. (side note, we took a tangent to see how many stories that would be, because 1000 ft is just an strange number to envision). Suppose the construction worker accidentally drops his wrench. If he immediately yells "Look out below!" (or something similar), how long will the person standing on the ground below him have to get out of the way before the wrench hits the ground?  What will the speed of the wrench be at that time?

We took a tangent to talk about finding speed (using the limit definition of derivative, but he doesn't know that yet) at 5 seconds, and then at the time the wrench would hit the ground. We also had a good conversation about why the velocity is negative. When we found the velocity (-160ish ft/sec at 5 seconds, -252ish ft/sec at impact), we talked about how fast that really is, relating it to a football field. He couldn't believe the wrench could fall that fast.

When we had spent a lot of time talking about speed. He asked, "Wait, we didn't answer our question yet, can the person get out of the way in time?" *GRIN*

ASL is so visual with these kinds of problems...I love it.

9.27.2009

Panic Mode

Last week was the official Mid-Quarter marker for my school. This meant that mid-quarter grades were due, as well as updates on all IEP goal progress. It made for a busy week for all at school, learning a new grading program (I <3 PowerTeacher) and keeping up with *all* of the IEPs. (For those of you that don't know, every student I teach has an IEP...though not all have math-specific goals).

At the mention of Mid-Quarter, my heart started fluttering a little. It means that the school year is 1/8 finished. It also means that my semester-long Algebra 2 class is 1/4 finished. When I was looking at the state Standards of Learning for that class (there are 20) and thinking about what my students know and are able to do at this point, I entered what we will call "Panic Mode".

Algebra 2 is a tough course. There is so much to cover that is built upon Algebra 1 skills, more indepth and some entirely new concepts. I'm trying to remediate skills from Algebra 1, and cover new skills from Algebra 2, but they aren't getting it! The days that I have had great success and the students "got it", are the concepts that on a quiz 2-3 days later, the students missed the boat completely.

This is my fault for assuming that because they "got it" the first day, it didn't need to be revisited the next day. The "one and done" approach is not effective, but it is so difficult for me to think that it can be different in such a packed course.

Questions for the PLN:
  • How do you handle the pressure of time and breadth of courses while still covering concepts rather than procedures? 
  • How much of your class time is spent allowing students to practice new skills/concepts on their own or with a partner as opposed to watching you demonstrate examples, group problem solving, or the like?

9.20.2009

Planning and Time Management

I've been a bit frazzled lately. I feel like I'm constantly running around at school and I don't have time to get my head on straight. When I sit down to work on planning the next day's lessons, or creating materials, I get sidetracked by other things that I *know* must be done while I am at school. I then leave the rest of the planning and creating for time over the weekend or at home. I'm not really liking that strategy.

I know that, as a teacher, it is almost innate within me to bring work home and to think about work when I am not actually working. I seriously think it's in our genes or something. What I don't like, though, is that I feel ineffective in the time I do have at school. Does anyone have any suggestions for how to manage planning time more effectively? How to use resources available online and from textbooks to develop lessons without feeling like you're recreating the wheel every time you make notes for a new topic?

I'm at the beginning of year number 2, and of the 4 classes that I teach, 2 are new to me (one is new to the school). I'm trying not to rely on the textbook so heavily, and trying to develop more activities and less worksheets to teach concepts, but it's a process. I'm also trying to go from primarily guided notes in Algebra 1 to a mix in Algebra 2, and teaching my calculus student how to take notes himself (this whole process is made much more difficult in a signing environment, because students cannot listen and write at the same time).

9.19.2009

Hello!

Well, I've entered the math 'blog-o-sphere."  Don't set your expectations too high ("the best math teacher blog EVER"?  not quite). My goal is to post at least once/week...but I'm not exactly sure how it's all going to work out. Be patient with me and if I get quiet, feel free to bug me on twitter or in comments. *smile*