Kiss My Asymptotes

Moved to WordPress.com

2009-01-20T18:29:00.000-08:00

Sorry, everyone! I've moved my blog over to WordPress.com.

http://kissmyasymptotes.wordpress.com/

For the very few readers out there, hope to see you there! :)

The Art of Procrastination (Part II: How to)

2009-01-18T10:01:00.000-08:00

[Wow, this blog post is much longer than I anticipated, and I still didn't cover everything there is to my method of procrastination. I may continue a Part III sometime in the far future (kind of like The 8th Habit came after the first 7 in a separate book), but for now, I'll leave you with this. Enjoy! -JT]

The Art of Procrastination (Part I)--an attempt to explain why procrastination is not necessarily a bad habit, but rather an art mastered by lazy people to become efficient, productive, and quality producers.

Now, procrastination is not the only way, nor is it the best way of getting things done. As Jackie commented on my previous post, she is definitely not a procrastinator, but she works very much like one by moving up her deadlines. However, Jackie is not lazy. Lucky her.

On the other hand, Part II is my "how to" guide for lazy people. Unfortunately, there are two types of lazy people: those who do stuff and those who don't. It would be great NOT to have a lazy mentality, but think about all the greatness that have come from possibly very lazy people trying to make life easier--Lazy Boy recliners, calculators, power tools, cruise control, and even electric toothbrushes. Okay, I made that stuff up; but I wouldn't be surprised if the people who thought of those ideas were in fact lazy people.

Lazy != Non-productive. Okay, enough intro stuff. Here's the guide...well, more like tips. You can follow them, or you can not, but if you follow them, procrastination is much less stressful.

1. Know your limits and prioritize--As much as I love to procrastinate, I know my limits and my capabilities. For example, I would not start a 20-page research paper at 5 a.m., when I know its due that same day at 9 a.m. That's insane.

I also know what tasks complete first. Just because things have an earlier deadline, it doesn't necessarily mean its more important. At the same time, it doesn't mean that the most important need to be completed first. Assess your projects and see which ones are the most important. See if other less important ones can assist you in the more important ones.

Lastly, try to assess the people who are giving you assignments and see which deadlines you can fudge. I'm not saying to push back deadlines when possible, but if you find that you've gone past your limit, well, something has got to go!

2. Work while you're not working--HUH? Now that sounds like a contradiction. No, but really. Play video games, take a shower, go out and party, go clean your house, find random YouTube videos, read my blog. Do whatever you do when you procrastinate! But while you are doing whatever it is you choose, always keep your project(s) in mind.

A lot of people try to relax by forgetting everything they have on their plate. That may be nice to do sometimes, but you would definitely be setting yourself up for a load of stress in the future. I enjoy my time when I'm not working, but at the same time, I am constantly brainstorming. People sometimes look at me weird when I drift off into my own world, and end up asking random questions. It's not because I'm ignoring them (well maybe a little), but rather because something may have been mentioned that sparked an idea that I want to continue to explore.

Brainstorming and exploring ideas at all times (whether your working or not) is the key to procrastinating effectively.

3. Get started early--I know what you're thinking. What?? I thought procrastination means to put things off until the last minute! True, I'm full of contradictions. But think about it this way. When you first get a project, it's fresh on your mind, and you may have ideas already spinning inside your head. Get those out early on, even if you only spend 10-20 minutes on it. If anything at least read the guidelines of what you need to get done.

By starting early, I can relieve any stress by just thinking, "Oh! I already got started on that project." Further, starting early primes your brain to begin the brainstorming process. If you put your work out of sight and out of mind right from the start, then it's difficult to follow #2 when you have no idea what you're even supposed to think about.

4. Take on side projects--Be a consistent and constant learner. I always tend to pick up so many side projects, more things to procrastinate on. Do I finish all of them? No. Do they contribute to completing a project, not really. But at least I don't feel like I'm 100% lazy. No, I'm joking, sort of.

When we procrastinate, we often look for something to do other than what we're really supposed to do. Take for example, my blog. I really should be lesson planning, working on BTSA stuff, creating a rubric ([check] done!), etc., but instead I take joy in writing other crap instead. Surprisingly, though, blogging has actually benefited my teaching and my entire lesson planning process.

When taking on side projects, try things that may interest you, but at the same time may in fact make your life easier. As I said in Part I, the laziest people are also the most efficient. Waste time on projects that will help you free more time to waste more time. That's a doozy of a sentence. And if not, you never know when a side project will assist you in completing a real project in the future.

I'm sure Project Euler will one day be useful to me. My photography has already helped me in numerous projects. Same with designing web pages, writing and reading blogs, spending time on Twitter and Facebook, cutting snowflakes, surfing the web, spending time with friends, going out to eat, playing World of Warcraft (this has helped more than you know, but I quit now), going to class, reading books and magazines, rearranging my room...wow, too many things to list. Just do something! But the trick is, don't forget about them either! You never know when they'll come in handy.

***The first four steps are very much focused on preparing yourself to complete a project. If you didn't read them, then basically brainstorm, brainstorm, brainstorm, constantly, in whatever you choose to do. And apply everything you've learned while procrastinating to your project.

The next steps are focusing on how to do deal with a project once you've gotten to the point where you need to work.***

5. Be rested--If you plan to produce quality work, then you must not work past the point that you are too tired to think. If I'm working into the early morning hours and notice I can no longer think clearly and quickly, I close my laptop, and go to bed. If you don't have time to do that, then you didn't follow #1 and waited too long. If I fall asleep at around 2 a.m., I will set my alarm for around 5, then probably continue snooze-button sleep until 5:30-5:40. At that point a shower will wake me up and energize me enough to keep going with a fresh mind.

6. Don't think too hard--Again, if you prepared correctly, most of the difficult thinking should be done and waiting in your mind, ready to be produced. If you are thinking too hard about what to write/do next, then you are wasting time. Just go with your first instincts and follow the plan that's already in your mind.

7. Adapt to your environment--Personally, I love to work at Starbucks or Panera (I'm actually at Starbucks right now). Unfortunately, those places aren't open 24 hours. When I'm not procrastinating, those are the only places I can get stuff done. Once its crunch time, I have to be able to work wherever is available, whether its home or Denny's. I hate working from home or my classroom, but when time counts, I can't waste time trying to find the perfect place to work.

8. Have backups already in place before you even think about getting started!!--You don't want to be the person who doesn't complete an assignment, or have the test ready for students because you didn't have a place to print, or because your computer crashed. I laugh at people who don't know how to recover from problems. I can list a number of places I will go to print (whether at home, school, work, etc) if my printer fails.

Have a flash drive, and web-mail accounts ready to go, and make sure you save it in different formats. As soon as I finish something on my laptop, I send it to myself on gmail and copy it onto my flash drive. You never know what methods (or software) you'll have available when you need to access your files on your desktop or laptop. Oh, and if possible, PDF versions of your files are awesome too, when you need to print.

9. Don't be afraid to be innovative--I know I've talked a lot about not thinking and letting things flow because of your great non-working time brainstorming. However, if a new idea comes up, then go with it! You start to become a true procrastinator when ideas and innovations come more often, and you learn to more easily incorporate them into your projects.

Side projects, school courses, conversations with friends, ideas from blogs, or random experiences--you're not a true procrastinator until you can really learn from ALL of your experiences and be ready to apply and synthesize on the fly.

By the way, all those people who complain or have complained about the general education/breadth courses in college? They will never be truly successful procrastinators because they aren't learning and applying. Don't be one of them!

10. Get "in the zone"--I can't really explain this one, but it is hands-down the most important skill. You probably already know what I'm talking about, too. And again, hopefully if you follow the preparation stages of procrastinating, getting "in the zone" is becomes much easier to reach.

Getting in the zone is the culmination of all the skills developed by procrastinators, coming together to create a powerhouse worker who understands all, knows all, does all. The more you procrastinate, the easier it becomes.

You reach the point where you just sit down at your computer and everything just flows from your brain to your hands to your computer (or whatever platform you are using to complete your project). Unexpected problems are solved in a matter of minutes, or even seconds. You are so focused on completing your task that time actually slows down for you. It's an amazing feeling once you've reached that point.

Focused, determined, motivated, everything that a non-procrastinator is, but 100 times more intense. Normal distractions, for you teacher/student ADD people, are no longer distractions, but beautiful compositions of musical elements that increases your cognitive and physical abilities.

Practice procrastination, and you will eventually reach that point. And I will leave you with that.

Sandy the Superintendent

2009-01-15T20:27:00.000-08:00

The Principal and Superintendent came around to every classroom today. I dread when the Principal drops by my classroom. I always feel like I'm being judged. However, when our Superintendent visits, it is a bit of the opposite feeling.

Mrs. T was the principal during my first year as a student at my high school. Now, I'm back, but I don't think she really remembers me. Anyway, whenever she comes in, she gives me a big hug and tells me how proud she is of me.

I'm know she does that with everyone, but whenever she comes in, I feel like such a little kid getting praised by a nice lady. I love it!

Some of the other teachers don't like being hugged, and truthfully, I'm not big on the whole touchy-feely thing. But it just really lifts my spirits when she comes in and acknowledges my teaching.

The Art of Procrastination (Part I)

2009-01-14T22:06:00.000-08:00

Procrastination is often looked down upon as a bad habit, or poor time management. I, on the other hand, disagree--mostly.

As I've said before, I am a huge procrastinator, and I have been all my life. I believe that if done correctly, procrastinators can definitely reach the same level of success as those who plan their time "wisely", while building new use skills and enjoying life, simultaneously. Part I focuses on these skills gained while learning to procrastinate.

I know what you're thinking. Sure you can enjoy life, but what skills can you possibly learn by procrastinating? Well, in my opinion, procrastination is an art, and if you're able to master this artform, then you must have demonstrated an ability to understand and apply a number of key principles and skills.

Decision making. I've tried the step-by-step, take-it-a-bit-at-a-time method of getting things done. It didn't work for me. With so much time, I could not make any decisions! You limit your amount of brainstorming, with the intention of getting started. Then you sit there trying to figure out how to really get started. It just seems like such a waste to just sit there and think.

Problem solving. Being able to make quick decisions comes with the highly valuable skill of problem solving. I think its funny that when people have problems, whether they are last minute or not, they go and start crying to someone else about how things aren't going as planned rather than making the modifications to just fix it. You got a problem? Then fix it yourself! Don't waste time whining to others. Procrastination forces you to do this.

Efficiency. I think it was my dad who once said, "The laziest people are the most efficient people." I admit that I am lazy (I think I admit way too many my own faults on this blog). But I will also say that often times, I can finish projects or quick tasks in a fraction of the time compared to most others. When procrastinating, you really have to be able to catch on fast, and work efficiently, or the quality of work will suffer. You create strategies and devise methods to make sure every working second is productive and efficient (I think I've used the word efficient enough times already, but efficiency really is key to procrastination!)

Brainstorming. In order to be an efficient procrastinator, you really must know what you're doing. While I'm procrastinating, no project is ever completely out of mind. I'm constantly brainstorming, and forming, and structuring, and exploring constantly in my head. Although efficiency is key, brainstorming provides the foundation of procrastination. With sufficient amount of brainstorming prior to working, you can get things done quickly. Fast. Like That.

I will continue with my Part II soon. My rules and tips on how to procrastinate, sort of.

Wordle

2009-01-13T23:01:00.000-08:00

Did this at wordle.net. I just thought it was interesting that the word "students" stood out so much.

Classroom Observations

2009-01-13T19:35:00.000-08:00

This is my third year teaching, but only my first year doing BTSA. Oh, the joy. Sarcastic much?

Anyhow, I completed my observation of a veteran teacher today--of my department chair, actually. It was a useful and somewhat enlightening experience, though not because I gained a lot of new strategies and ideas as one would hope.

I'm not saying that my department chair is a bad teacher. No, far from it. I really admire and look up to him as a model teacher and strong leader for the math department. However, observing him today helped me to realize that even the best teachers have to deal with real students.

Classroom Management. This year, I have really worked to earn the respect of the students and have been really successful in actually managing the classroom, compared to years past at least. While in the dept chair's class though, he also sometimes struggled to have students settle down, or grab complete attention.

"5-4-3-2-1..." Nope still talking. Actually, I used that technique last year. It didn't work for me. This year, I just silently raise my hand, and they tend to quiet themselves down. It works well for me.

Teaching Strategies. I think its funny how I feel like every day should be have an exciting activity or lesson that's completely innovative and different. As much as I would like that, it's just not possible. After some time, I just run out of ideas (or run out of ideas I've stolen). I don't like to do the same thing over and over, week after week, because then even my best strategies get old and boring for my students. On the other hand, if they do work, of course I do bring them back, regularly.

Today I observed a very straight-foward, direct-instruction lesson. Examples were already set up on the board, and he went through them one by one. A bit dry for my taste, but it works. I always tell myself, there's gotta be a way to change it up a bit, to encourage more critical thinking, or collaboration, or something! But when my mind fails, I always rely on--yup, whiteboards (if you read my last post).

There are always a variety of activities you can do with whiteboards, so if they seem to be getting bored, its very easy to modify the instruction. I don't think I'll ever be able to just do problems, then give a worksheet. I don't know why.

Technology. This teacher is very tech savvy. I was actually surprised that the only technology he used was a projector to show the daily bulletin, and the document camera to explain homework questions. I do the same.

Post Observation Thoughts. I think its funny when you are formally observed by an administrator, we are expected to pretty much put on a show. Not that the strategies I use during an observation I don't use on a regular basis, but I feel that administrators often forget what it's like to be in the classroom themselves.

Especially as a math teacher, I feel like some administrators don't really understand the idea that students say "I don't get it!" Or what happens in an every day classroom setting. I already have strategies planned out in my head for my formal observation with the Principal.

I realize she likes to see student collaboration, technology, and class control. Luckily I already do those on a regular basis, and I'm going to be sure I use either the Quick Draw for Points activity or Math Conversations activity. Though I want to do the math conversations, I'm leaning toward QD4P since it seems easier to implement when working with rational expressions.

Anyway, so how did this observation help me? First of all, it made me realize that all teachers have normal class days, and they don't always give amazing lessons that will blow everyone away. Learning about so many ideas and activities at conferences, workshops, school, and other teachers, I always feel like everyone is doing amazing things in their classrooms every day. I tend to forget that other teachers are real people and have real students.

I know it is not okay to show up to work with the same boring lesson and strategies every single day of the year. I will continue to strive to be the best teacher that I can, and that includes varying instructional strategies, engaging activities, and student collaboration. However, I understand that is normal to have the occasional "normal" lesson, as well. And now because of today, I'm okay with that.

A Routine Day

2009-01-12T17:52:00.000-08:00

I admit, I am not perfect.

My biggest flaw (which I would never mention in an interview, yet am quick to admit to the public) is also one of my strengths, sadly. And that is the art of procrastination.

When it comes to procrastination, I am the biggest culprit. I wait until the last minute to work on... well, everything. Some people are great at working on things in a timely manner, but I'm the type of person who will wake up at 4 a.m. on the day a project is due so that I can complete it by 9 a.m.

Is it stressful? Perhaps, at times. Does it affect the quality of my work? Well, that one is debatable. After all, I do consider procrastination an art.

I'll save my little "schpeel" on procrastination for another day, though.

Although I procrastinate, it is very rare that I walk into my classroom without anything prepared for the day; but it does happen. And today was one of those days.

It's interesting, though, that when you have a routine set for the classroom, the lessons do pretty much flow. I usually plan a variety of activities throughout the class period (ya' gotta if you teach in a block schedule), but there are those activities that always come up and that you can always fall back on. That was today.

When I have nothing else, I know I can always rely on [drumroll please...] MINI-WHITEBOARDS! No matter how often I use these things, the students never get tired of them!

Notes-->Examples-->Practice on whiteboards--> Rinse and repeat!

So today's lessons consisted of taking notes from PowerPoint slides I made in a couple minutes prior to class, example problems worked out using a combination of my wireless tablet and inquiry-based classroom discussion, then practice problems on the whiteboards.

With set routines, there's no guessing or struggling to get through the day, and the students leave the classroom happy that they didn't have to spend an entire class period of 95 minutes on a worksheet. In addition to that, I get immediate feedback on who does or does not understand it, and I can change the lessons or practice on the fly.

Now, I don't ever want to become one of those teachers who walk in their classroom every day, and do the same routine every day of the year, with hardly any planning. But I do want to make sure that on the days that I do come in not fully prepared, I still have lessons that are effective and engaging.

No teacher is perfect, and I know my flaws. But part of overcoming your flaws is knowing what to do when you screw up. I'm pretty good at that.

Building Leadership

2009-01-07T19:49:00.000-08:00

I decided to experiment today with my Algebra I students with a new activity. After handing back their Unit 5 test results, rather than going over the problems, I decided to try something a little more fun. I'm not sure it was as useful in reinforcing the mathematics, but the students really enjoyed the activity, and I was finally able to see some of the students step up to show their leadership skills.

The Activity

Students assemble a "Class Solution Manual" for the Unit 5 test.

The Fun

The students must organize themselves and work as a class to complete the project in a specified amount of time. The students are assigned roles and work together to create this manual.

The Roles

Two task leaders. They have the most difficult job. They must organize the entire class and act as the leaders to be sure that they complete their jobs. These two positions are elected.

Two builders/designers. The role of the designers is to design and compile the final product. They are the creative minds behind the book, and also must be fast workers and be able to identify and label the type of problems in the book.

Three writers. The job of the writers is to write the final solutions for each problem. Solutions to each problem are handed to them, and they must rewrite them so that they are neat, organized, and fully explained.

Three checkers. The job of the checkers is to check the accuracy of the solutions. These students should be students who scored high on the test. In addition to checking the solutions, they may assist students in solving problems, and explaining explanations to the writers, but they may not write anything.

Solvers. All the remaining students are solvers. Their job is to find the correct solutions to the test problems.

The Machine

Aside from the specific roles, I did not give very many directions to the students. I explained that once they start, the task leaders are in charge all directions come from them, and all questions should be directed toward them. From there, the book goes through the assembly line.

1. The solvers solve the problems.
2. The checkers assist them, and check for the correct solutions.
3. Completed solutions are handed off to the writers to rewrite in an organized and and fully explained way.
4. Fully written solutions are then handed to the builders to add to their book.

Observations

I was very curious how this activity would play out. I was actually very impressed with how the students handled themselves. I gave them less time than I had anticipated, but in the end, the students were able to put together a decent product (and I think there was only one mathematical error).

Four students wanted to be the leader, one was clearly elected, and there was a tie breaker election for the second task leader. Two great leaders were elected. We chose the rest of the roles and I let them get started with about 25 minutes to complete the book.

They got to work fast. The leaders quickly organized all the roles and gave clear directions, while their "employees" listened intently. It was great watching how motivated they were to get started on this project!

With any project, they did hit a couple bumps in the road. One problem that arose was that I forgot that there were two versions of the test. After the leaders discovered that the problems were in different orders, they quickly resolved the problem, and production promptly resumed as if nothing happened.

There was one issue where one girl was not working on the assigned problem, and the leaders, again, quickly defused the problem.

The students were fully engaged in the project and taking pride in each of their assigned roles. I was very excited to see the leadership skills shine even in the students that were not elected leaders.

Although the leaders were the only ones NOT required to do anything math related, they both ended up playing the role of checker, writer, and builder, to help out wherever they noticed a bottleneck in production. After 25 minutes, the students turned in their product, and I was pleased.

It was not the best constructed book, but is was very high quality for an entire book produced in only 25 minutes, and the students had a blast putting it together!

The Reflection

I've been wanting to do an activity where the students get to really lead themselves, but I've always had problems with this. In small groups, I always notice that the students don't show the same motivation to lead others, or to be the best. I always felt maybe the class just the skills to be more autonomous, but now I realize that it not their lack of ability, but rather lack of motivation.

There are a couple changes I would make in the future. First of all, I should some how make it required for the leaders to somehow keep everyone busy. Toward the end of the period, after all the solvers completed their assigned problems, all the work was left to the builders to complete the project.

This left the rest of the class doing nothing to do except for socialize. Although the teacher instincts in me wanted to give them something else to do, I decided to continue to let the leaders be in charge. All I did was remind the task leaders that they have plenty of free resources and that their goal is to get the product to me by the end of the period.

In the end, I feel this was a successful activity that can be modified to be even greater.

I have a headache, so this description may not make much sense, or even be complete, but I wanted to write it anyway. I may write a full lesson later to clarify all the prep, materials, and process later on, but I'll stick with this for now. Any questions, go ahead and ask me.

New Year's Resolutions...Kinda.

2009-01-05T21:28:00.000-08:00

With each new year we are given the chance to turn a new leaf--HA! What a load of crap!

I remember learning that phrase "turn a new leaf" in the third grade. My third grade teacher had the entire class write three new goals on a leaf cut out of green paper, and they were posted in the room.

Well, it seems that the elementary teachers did a great job teaching their students about making their new year's resolutions, because EVERYONE does it. But come December 31st, how many of us actually accomplished our goals? Wait, how many of us even REMEMBER what our resolutions were (that is if you didn't choose a generic resolution like lose weight, or save money)?

I don't know the actual numbers, but I am almost certain the answers to both questions are pretty abysmal.

I must give props to the teachers though, because they did an awesome job at teaching about the important skill of goal setting. Not only does almost everyone I know make resolutions, but they write them down and make them known.

So what's the problem? Well, obviously people don't follow through--at no fault of the teachers, of course.

Here's my other problem. Setting goals is not something that is done only once a year. Goal setting is an ongoing and dynamic process that requires constant evaluation and revision. Situations change, priorities change; life is not linear.

Revising a goal is not equivalent to failure. When a goal is no longer a priority, it makes no sense to continue to waste time and resources to reach that goal. At the same time, when your priorities no longer align with your goals, THEN you are setting yourself up for failure!

==========================

So one of my students asked me today, "What are your new year's resolutions?"

I'm pretty frank with my students, and I was a bit hesitant, but I told them my resolutions:

1. Get over my strange fear of the telephone (at least with friends and family).
2. Have a conversation in American Sign Language at least once per day.

Hypocrite? Yeah, you can say that. What can I say? My third grade teacher made an impression. Come December, will I remember it these goals? Probably not, but at least I have a blog post to remind me.

Happy New Year, everyone!

Starting the Year Off Right

2009-01-04T17:12:00.000-08:00

It's back to the classroom tomorrow! I had a wonderful vacation that went by much too fast; but that's every vacation (except sometimes summer when you're waiting and waiting for that next paycheck).

When I first started, all the teachers always warned, "If you lose control of the class when you return from break, then you've lost control for the rest of the year."

So here I am, planning for tomorrow's classes, trying to think of ways to ease the students back from vacation, yet intense and relevant enough to jumpstart the students' minds again and get them going for the year. I don't have exact lesson plans or full ideas yet--yes, I know I'm a MAJOR procrastinator--but here's my strategy, so far:

1. Give students time to "debrief"--The students will not be able to to focus coming from either an exciting or a boring vacation. They all want to talk about what they did (or how lame their break was), and get it all out their systems. We all act the same way; there's no stopping it, so planning for it is a must.

2. Review--Come on...two weeks off? Even I can't remember what we did last year without looking back at my calendar! Perhaps something in game form for my Algebra I students, but my Algebra II can handle a more focused activity.

3. Introduce a simple topic in an interactive way--Whether the students have an abundance of energy to spend, or have that glazed-over look from sleeping late every night, they are going to need an activity that will wake them up, or focus their energy on.

4. Simple practice--Something that the students can either work on individually or in small groups, just to get them back in the routine of performing mathematical computations.

Alright! Now that I've wasted more time, it's back to creating the actual plans. Though, since when has blogging about teaching ever been a waste of time?

Do Higher Scores = Better Understanding?

2009-01-03T10:48:00.001-08:00

Every year, my school cheers at the fact that our students continue to meet our AYP. My very small district has been the focus of studies to understand how our API scores have grown so dramatically, given our schools demographics. We are well on our way to reaching the golden score of 800.

I recently read an article out of NEA Today, the National Education Association's primary publication. It was titled "NCLB: Is it working?".

Here's a link to the online version of the article. http://www.nea.org/home/20755.htm

I actually started writing this blog post about a month ago, but it was one of those posts where you write something, then erase it. It remained a draft...only the title was saved. I finally brushed it off because high stakes testing has been an issue lingering in my head for quite a while, and this article got me going again.

It's a simple question. Do high scores really mean our students are understanding more?

Now I won't try to summarize the article. If you're reading this blog post, then you know how to read and can read the article yourself. So if you haven't yet, go ahead and click the link and read it now. Here it is again: http://www.nea.org/home/20755.htm.

================

Alright, so back to the question. In the words of George W. Bush, "Is our students learning?" I will give credit where it is due and say I believe that much of what my school and district is doing is improving the education of our students--but not everything.

Unfortunately, working in an education system is all about "playing the game". Administrators focus on ways to increase test scores because higher test scores is what is expected of them, by law. Teachers implement these strategies and adapt strategies to work in their own classrooms because that is what is expected of them by the administrators. In the end, we have teachers using great strategies, but not always used in the best ways.

Let's take our professional learning communities (PLC's--Don't you just love the buzz words?), for example. Being able to meet with colleagues twice a week to share best practices and develop new ideas I believe is a wonderful resource I have at my school. It's funny though because very little sharing actually takes place; I'd say about 5 minutes out of the entire meeting. What really happens? Reviewing and planning common assessments.

Okay, I'm not saying that common assessments are a bad thing. I think they are just fine and dandy. But when our meetings are used to plan more testing (which by the way the test questions are taken directly from a list of California Standardized Test questions), then you KNOW all the teachers are there so we can better teach to the test!

Uh-oh, is that Campbell's Law I hear? Am I saying that our students are doing better because they are learning how to answer these specific types of questions? I'm not not a researcher, so I won't straight out say yes. Let's just say probably.

I see it in my own classes. Last year, I made it a point NOT to teach to the test. Wow, did my students do horribly on those common assessments! Time to play the game, right? This year, my students are doing dramatically better. Am I a better teacher? Well, yes. But that's not the point. Many of the strategies I am using are the same!

So what am I doing different? You guessed it, teaching the students how to answer these specific types of questions. Their homework? All test questions (different numbers of course, but same concept and wording). Do I feel my students are understanding better? Not so much.

I still don't like the idea of teaching to a test, and of course I assess my students in a number of different ways. For example, my daily quizzes are usually worded in a way where I can measure their understanding, on different levels, and are very open-ended. They are required to give explanations rather than solve problems. From what I see, the students are better able to perform the math that they practice, but their understanding of the mathematics is still the same.

Some students get it, and some don't.

But at what point does it no longer matter if the students are getting it? I have a lower D-F ratio than last year, so more students are passing. My students are doing better on the common assessments. But the number of students that are really "getting it" is probably about the same as last year.

So am I going to continue teaching to the test? Probably, at least until I find something else I want to do. However, I'm also going to continue to use strategies that build student understanding, logical and problem solving skills, and mathematical thinking.

Those who get it, great! Those who don't? Well, is it so bad if I pass a student who worked hard to be able to answer these test-specific math questions? I mean, that is what is expected of them.

Blogging for Teachers

2008-12-31T12:07:00.000-08:00

I originally made this blog to share and record some math lessons and ideas for myself, and for people who happen to stumble upon (I feel weird saying that phrase now since StumbleUpon.com is such a common thing.) my blog. However, it seems that my posts have been less about that, and more about...other random things.

It's interesting though, because when I used to keep a personal blog (on LiveJournal), I used to write just to write, and primarily for myself. Whatever flowed from my fingers to my keyboard is what was posted online.

Now, I feel that I have actually made my blogging a much more useful tool for myself. Although I still write mainly for myself, I keep in mind the possibility of an audience, and one that may be a little more professional. This forces me to do real reflections, and also forces me to try to relate my thoughts to how others may perceive it.

Also, I always try to tie it in with teaching or math in some way; even if that connection is a far reach, it forces me to try to make it relevant. I'm able to put together thoughts that I've read from other blogs, and better understand ideas from other people and synthesize them with my own.

I recently read an old post about the benefits for teachers to create their own blog. However, one point that was mentioned, and what I feel is more important than writing your own blog, is just the act of participating in a blogging community.

Now, to me, "participating" does not necessarily mean you have to be a big blogging authority in your community, where all of your posts are relevant and you constantly contribute to the community through posts and comments on every related blog. Participating, to me, can be as easy as reading the posts of others on an occasional, yet consistent, time line.

At this point, I enjoy writing my own thoughts and ideas, as well as reading those of others. But for the most part, I hang out in the background as a silent participant. I rarely make comments, but do steal ideas from the posts and comments of others. This is my way of participating.

In the future, as I start to learn more, I may be more confident in being a more active contributor to the community. However, what is most important is that I am constantly looking for ways to improve my teaching, improve my mathematics, and improve myself, through the means of the ideas, experiences, and input of other people.

The teaching profession REQUIRES you to continually evaluate your own practice in the classroom. Even the most seasoned teachers should continue to evolve their teaching methods. Unfortunately most teachers don't realize that participating in the blogging community is one of the easiest most accessible ways of doing this. And its probably one of the most fun ways too!

Fast Forward

2008-12-31T11:27:00.000-08:00

As a teacher, and even more so as a math teacher, I am constantly trying to explain "things" and helping others make sense of the world around us. People sometimes describe mathematics as a universal langauge, or the universe's language. I'm not really sure if that is so, but it does bring up some questions that will never be explained by math.

What is the one question that everyone asks, but never finds an answer to? People search the world, the universe, themselves to understand this, but of course to no avail. From mathematics, to science, to religion, and maybe even to death, will anyone ever be able to answer the question--

"What is the meaning of life?"

The quick and easy answer--no.

I'll stop right there with that question, and bring up a different one. "Is there a meaning to life?" And I believe that there is a quick and easy answer to this one too--yes.

I recently watched the movie "Click" for the first time with Adam Sandler. Quick synopsis: It's about a man that is given a magic remote that allows him to fast forward through his life. Skip a sickness? Sure. Fast forward through boring parts? No problem. Want to chase down that next temporary high point in life? It could that too.

What does this have to do with teaching? Not too much. But let me reflect a bit on my own life. In the weeks preceding Winter Break, I found myself counting down for it to come.

Don't judge me, everyone does it.

Anyway, fast forward to today, my vacation is almost over, and I'm thinking back to those times when I was counting down for days like today, New Year's Eve, and I realize that what I just said is exactly what I did. I just fast forwarded my life to this "temporary high". I can't remember any details of what I did those days. In fact, I'm pretty sure I did nothing memorable during those times. It's as if I was put on auto-pilot to get through those days until I can finally "enjoy" my vacation.

It's pretty ironic, though. I keep "fast forwarding" through my life, not willing to wait for the exciting times (You know you've said the words "I can't wait!" before, too.), yet every year that goes by, I think, "Why is time going by so fast? I want to stay 22 forever!"

Now back to my question, "Is there a meaning to life?" I said the answer is yes. I don't know what it is, but I'm sure there is some sort of "meaning" in every moment of our lives. And though I'll never know what it is, I do know that when we fast forward through life, some of that meaning is lost. What was I supposed to learn, or feel, or understand during those times that just went by?

I can't say that I will never fast forward through my life again. I know I will...but at least now I'm aware, and I might just be able to slow myself down, turn off my auto-pilot, and enjoy even the boring and mundane moments in life.

Merry Christmas!

2008-12-25T11:58:00.000-08:00

Last Friday, I had on my PowerPoint slide "Happy Holidays!" and I was saying this to my students as they left on vacation. Then a student asked, "Is it illegal for you to say Merry Christmas?"

I really don't know the laws, but I'm pretty sure I won't get arrested or fired for saying "Merry Christmas" to my students. However, at the same time, I want to make sure I don't exclude any of my students, so I stuck with the politically-correct phrase of "Happy Holidays!" Now, I was reading someone else's blog about looking for holiday "violations" in the classroom, and it really made me think. Yes, Christmas is a religious holiday--but is it really a religious holiday anymore?

ProjectEuler.net and Problem Solving

2008-12-17T22:44:00.000-08:00

Thanks to Patrick for suggesting to use Python for my new project/hobby.

My code:
http://www.yuglook.com/projecteuler/

I downloaded it and actually solved Problem #3 rather quickly. It took a little bit longer to solve #4, and though I'm sure there is a better way to solve it, I decided to use the problem to learn more about programming with Python than thinking of the most efficient way of solving it. I may return to it to try finding a better way, but there are still many problems to solve!

As I said in the last post, I never really enjoyed programming while in college. I find it interesting that I am actually excited to be able to program again. A friend responded to one of my tweets about ProjectEuler claiming that it sounds difficult, especially since she does not know how to program. That really got me thinking. As much as I disliked being a computer science major, I now realize that programming has become one of the most useful and applicable skills that I learned while in college.

With so many computer applications available, many people claim to be "proficient" with the use of a computer, yet I find myself still having to explain little details which always seemed common sense at first (and I don't consider myself to be very knowledgeable about computers), but then I realized it made sense to me because I had a slight background in programming and thus, logical, programmable thinking.

For example, many people claim to know how to use Microsoft Excel (or some other spreadsheet program), yet I have seen so many spreadsheets that either do not make sense, or are not even used as a spreadsheet at all--I don't consider a spreadsheet that doesn't use formulas to calculate values a real spreadsheet. Yet people still feel that they know how to use the application.

On the other hand, I don't claim to be the best spreadsheet builder, but I do know how to find my way around numerous applications, even ones I have never used before. People sometimes ask me questions, and truthfully, I usually don't know the answer, but I find out for them. This is the skill of a programmer.

Another example, my dad. He's a programmer for Qtask. He's what you would call a serial problem solver. If he just overhears that someone is having a problem--it doesn't matter the situation--he will always try to help others come up with a solution. Does he have any knowledge or background on the situation? No. But for some reason, he's always able to help (whether you like it or not).

When it comes to his programming, he is also very successful. But like all programmers, he does not know every single programming language. In fact, I doubt he knows everything about even a single language. But he's an effective programmer because he's an effective problem solver.

Now onto my experience. I have a minor in computer science. I've had my share of programming courses, which though it won't help me land a job in a computer field (nor do I want such a position), the concepts learned can be applied in many ways. This new project is an example of that. Picking up and solving problem with a language that I have no experience in using. I'm not claiming to be an expert, or even a semi-skilled programmer, but the skills I have learned while programming have already shown to be useful on many occasions.

I would hope that more people choose to take a course in programming to build on these same skills. Similar to math, it challenges your critical thinking and problem solving skills, yet is more applicable to the real world. I challenge you to challenge yourself. But don't take a course just because I said to. Take it because you are ready and willing to learn.

ProjectEuler.net

2008-12-16T16:48:00.000-08:00

I was sitting in my classroom, trying to get some grading done (though not very successfully, since I was distracted by Twitter and going through my rss feeds on Google Reader), when Justin Duer tweets me to check out projecteuler.net when I got home. Always looking for more distractions, I didn't wait to get home, but jumped on the site right away.

What is ProjectEuler? It's a Web site that has a series of mathematical problems that may be solved using a computer and programming skills to solve. Basically, you write your own program to build your problem solving, math, and computer programming skills.

Now the fact that I had to do some programming made me a little weary. I did get a minor in Computer Science, but only because I decided to switch my major because I didn't enjoy it. But the idea of doing problem solving and learning and developing my math skills made me want to try it. Unfortunately, I don't have a compiler or anything installed on my school computer, but I was able to solve the first two problems really quickly by just using a spreadsheet. That good me hooked enough.

My next hobby/project is projecteuler.net. I think it would be great to get more like-minded friends helping each other and discussing strategies on this. I even thought it might be a great way to get students more interested in math and programming, but...maybe another time. If anyone wants to join me on my new math adventure, I'd love to have people I can discuss the problems with. I'm only on problem number 3, and haven't decided what language to use. I'm guessing I'll stick with C++ since that's what I'm most familiar with, but I'm up for learning new languages.

Copy This!

2008-12-11T18:56:00.000-08:00

Why do students have such difficulty with graphing linear functions? I can see how the concept of what a graph is can go right over their heads; representing the solutions of an equation can be pretty abstract for young, concrete minds. But when you simplify it to something as simple as counting up and down, left and right, shouldn't the students be able to at least get the graph onto the paper?

In a book called Made to Stick, authors Dan and Chip Heath discussed the game of "tappers" and "listeners". The goal of the tappers is to choose a song from a list of well-known songs (like "The Star Spangled Banner" or "Twinkle Twinkle Little Star") and tap the song to the listeners in hopes that the listeners will be able to guess the song. What usually happens is the tappers become frustrated and surprised when the listeners are not able to determine the tune that the tapper is trying to tap. The problem is the tapper has the song playing in their head as they tap the song, but they don't realize that they can actually hear the tune. However, the tune is not playing in the heads of the listeners, while the tapper assumes that they can hear it.

I'm sure you can already see the analogous relationship with this game and the classroom--or am I assuming too much in this blog, as well? Anyway, while reading another teacher's math blog, I stole--yes stole. (That's what teachers do. They steal ideas, worksheets, materials, left and right)--I stole the idea of the PowerPoint slide posted at the top of this post, to have students take the slide and copy it onto their own coordinate plane. Now, I didn't implement it the same way the other teacher did due to lack of time, but I did try to keep a general count of how many students were able to do it. First time around--only about five students out of a class of about 20 students graphed it correctly.

Wow that was an eye opener for me. How can I expect them to graph a line using numbers when they couldn't even DIRECTLY COPY a line using no numbers or anything?

This was a "song" that I realize was only playing in my head, and this small piece of information has really helped me to understand how my students think. This will definitely impact the way I teach graphing next time.

If only it were easier to realize when you're tapping to a tune that only you can hear, life would be much easier.

(Edit) Note: Made to Stick is an awesome read if you're looking for some new material. It isn't strictly focused on helping teachers, though there are several references to how the strategies are used in the classroom. I recommend this book to anyone who wants their message to be remembered by others.

Coffee Stains

2008-12-07T17:58:00.000-08:00

@Starbucks on Twitter posted this link to this amusing article with awesome illustrations. http://is.gd/ae1o. I know how important coffee is to teachers, so I believe this post is appropriate.

My experience with coffee is very different from the writer of that blog post. Sitting here grading tests made me realize how much coffee is a part of my life. I don't have the awesome storyline and pictures to express my connection to coffee, but I do have just a few points I wanted to make before continuing with my teacher duties.

I was introduced to coffee at a young age. I can't exactly remember my first taste, but I do remember that my parents drank it on an almost daily basis. Of course coffee was the "grownup" drink, and that made it all the more desirable. My parents didn't really allow me to drink it, but I was happy when they would give me a cup filled with about a half-inch of coffee in it. At that point, I have always been a black coffee drinker. Some people think it's gross that I don't add anything to it, but that's the taste I grew to love.

Now I am definitely NOT a coffee connoisseur. Can I taste the differences in different coffees. Well, yes. Can I tell you where it's from, how its grown, and describe every flavor down to its finest detail? Not even close. What I can tell you is one of two things: (1) I like it, and (2) I do not like it. And if it falls into category one, I will drink it and enjoy it. However, if it falls into category two, I will still drink it and enjoy it.

Coffee to me is not a matter of taste (though I still love the hazelnut coffee at Panera Bread), but rather a matter of feelings, motivation, and memories. Why do so many people go back to Starbucks every morning? I'll tell you right now, it is not because of their good taste. In fact, many people describe Starbucks to be bitter, which I can actually agree with (not all blends/roasts). The people who return to Starbucks are people like me.

When I think coffee, I automatically think Starbucks--and not because they are on every corner (or at least they used to be). Let's think about it.

Feelings - Christmas, happiness, crisp cold weather, success, achievement, friendships. I know, those aren't emotions, but it's pretty difficult to describe how I feel when I think Starbucks. I used to be a barista for Starbucks, but aside from the great people I worked with back then, Starbucks has offered me a place to succeed in school, to catch up with friends, or just to sit and enjoy a warm cup of coffee in the beautifully cold weather.

Motivation - I am currently sitting in Starbucks "working". Starbucks is equivalent with getting work done...usually.

Memories - I have so many memories of Starbucks, not only the ones that I frequent in the area, but all across the United States. From Alaska and geocaching, to grabbing a quick cup while driving around the night streets of Atlanta. Unfortunately for The Coffee Bean, I can't think of a single memory related to it.

Now that's just Starbucks. If you ask me about my favorite coffee places, here they are: Starbucks, Panera, Denny's. From the coffee stains on my homework in college, the coffee stains on my students' homework assignments today, coffee is and always will be a part of my life. There is so much more to coffee than the coffee stains I shown today. Interested? Come join me. As for me, it is time to return to my grading.

Nerd Shirts

2008-12-05T17:20:00.001-08:00

I would describe myself as a nerd; I’m a nerd only to a certain degree though. Do I care about how I look? Not too much. Do I have “nerdy” interests? Well, do you know anyone else that enjoys writing about math related topics? Do I like nerdy shirts? Yes!

The name of this blog was taken from a t-shirt that I purchased at a math conference in 2007. In bold letters, the shirt reads “Kiss My Asymptotes”, then shows a graph of the function y = 1/x. There were so many other t-shirts that I wanted to buy, but the costs were a bit too high. I couldn’t resist that one though.

I was recently reading a friend’s blog on the Google Reader that I now use, and he had an old post for another math t-shirt that I loved. It made me decide to look back at some of the other t-shirts that I found amusing and would buy for myself if I they were lower in price.

Yes, my favorites now:

Pac-Math
Imaginary Friend
I won't explain this one...
Hexadecimal... get it???
i over 8 (My absolute favorite, because it fits me so well)

My [Teacher's] Guide to Happiness

2008-12-03T01:27:00.000-08:00

This post is actually a continuation of my previous post about keeping a positive attitude. It actually started as part of the post, but I realized that my guide turned from "Keeping a Positive Attitude in Class" to a "Guide to Happiness". So I decided to just write a separate entry for this.

So what are my ways of staying happy and keeping a positive attitude toward life?

1. Simple--Tell yourself you are having a great day! I heard this one from a friend, but I realize it was something I had already been doing and had internalized into daily routine. Whether you verbalize it or write it down, this act of believing its a great day really does brighten your day. I often like to use Twitter (www.twitter.com) to express my positive feelings, but sometimes I just talk to myself out loud, reminding myself how awesome I feel.

You have to want to be happy.

2. Smile :) I'm not sure why this works, but it reminds me of advice that people would give to people in customer service. Even when on the phone, if you smile while talking to the person, your tone seems that much more personable and helpful.

3. Appreciate the small things. This goes along with number one. Sometimes it doesn't make sense to just say, "Wow, I'm having a great day!" What is actually making the day great? Lots of things! Some days when I ride my bike to work, I smile and sometimes hold back my own laughter to myself just enjoying the cool, brisk air. Now maybe this sounds corny, but the small things that make me smile genuinely make me that happy. Enjoy the sun. Enjoy the rain. Enjoy the smell of chimneys burning still in the morning. Stop and smell the roses. Okay, maybe I don't actually do that since I don't really care for the smell of plants (allergies anyone?), but you get my point.

I can still remember a cool December evening during my time at Cal State Fullerton. I was walking and looked up and watched the palm trees dance in the light wind as I stuffed my hands in my pockets to warm myself in the cool weather. Then I thought to myself, I will never see these palm trees move in this exact form ever again in my life. At that moment, that short insignificant moment in time greatly appreciated in value.

4. Appreciate the people around you. This is one I need to work on more. I have always been an introvert. Quiet, shy, and at times even a loner. When people are around, I'm often spaced out. But more and more, I am finding myself enjoying the company of others, the connections with others and drawing positive energy from others. A few times I have tweeted to my friends, "Wow these students are soo annoying." Those are my off days. And as I said, those days are okay, and I strange as it sounds, I appreciate being able to experience frustration sometimes (but not daily). However, one thing that I find works is instead of feeding off the negative energy of others, bring about positive energy.

An example: Coming back from Thanksgiving Break, we had plenty of work to do in class, but of course no one's mind (including my own) were completely functioning. Does this lead to frustration? Well, yes it could. But instead of showing frustration, I change the tone of the class. "Did anyone see the moon and the two planets align in the sky last night?" That question just shattered the negative mood that had built up as students are eager to share what they saw or heard, or become curious about what we were talking about. However, I didn't ask the question to lighten their moods. I asked the question to lighten my own--remember the teacher's attitude dictates the class tone. Did I waste time in the class? Well, some might say I did. But in the end, the students get back to work with a more positive attitude, and me? I'm happy, and maybe this may sound bad, but I put my happiness before the learning of the students.

No job is worth sacrificing your happiness.

5. Lastly, hold on to memories and look forward to making more. Am I one of those people keep items that have some sentimental value to me? No...in fact, far from it. I'll toss anything away, really.

When I say hold on to memories, I mean the ones that are actually in your memory. People always say "don't live in the past" but really, without your past, who are you then? I used to keep an online journal (which I really should start again) where I logged some of my memories. I occassionally go back to reread some of them just to think about where I've been, but I don't need the journal to remind me of the past. Sometimes I enjoy taking the time just to think back about any memory that pops into my head (maybe that's why I'm a bit spacey sometimes), whether sad, happy, exciting, or even humiliating. Yes, it makes me happy.

Now, to finish off number 5 and the short list of things I do to stay positive and happy, you must be ready and willing to make new memories. Do something exciting. If an opportunity comes your way, sure take it. You never know what it will lead to.

Keep a Positive Attitude

2008-12-02T23:20:00.000-08:00

There's one math teacher that I work with that whenever someone asks him "How are you?" he responds with, "Ask anyone, I'm just spectacular!"

Now this piece of advice applies to teaching, but even more so, it applies to life.

Keep a Positive Attitude!

In the classroom, the teacher's attitude, the teacher's demeanor, and the teacher's expectations set the tone for the entire class, whether negative or positive, demeaning or encouraging.

Now I admit that I do not show up every day with a smile on my face or excitement in my voice. Nope--just like everyone else, I sometimes wake up on the wrong side of the bed and gripe about having "one of those days". And that's OKAY to have those days, but I do realize that it is my choice and my attitude that not only affects my day, but also the attitudes of my students while they are in my class.

On my bad days, the students seem to do worse. Their learning capabilities diminish as they feed off of my negative energy, which in turn causes them to put less effort, creating more frustration. I used to think it was the attitudes of individuals in the classroom that brought a class down, but through a little non-scientific experimentation and observation, I realized that it is not the attitude of the individuals, but the attitude of the teacher reacting to the individuals that bring down the class tone.

Now, I know it is tougher to keep a positive attitude than it sounds in writing, but I believe it is definitely worth the effort.

Geocaching!

2008-11-30T07:35:00.001-08:00

If you love the idea of a high-tech treasure hunting game, you would probably love geocaching! You can do it all over the world, and it is tons of fun. Perhaps this post isn't very math related, but using GPS units to reach specific coordinates down to the minutes and seconds is someone mathy, if not downright nerdy. People hide "geocaches" and give the coordinates to the players, who then go out and try to find it. Some are very easy and quick to find, but be careful, because some are extremely tricky and though they may be in plain sight, they are VERY well camoflauged where you may be touching it without even knowing!

I put a geocache counter on my side bar to track how many caches I have found today. I'm only at 34 caches at the time of writing this point, so I am nowhere near being a veteran, but am finally understanding the ropes and starting to find caches faster, even some of the trickier ones. If you want to join in on the fun, just visit http://www.geocaching.com/ You can add me as a friend too, my name on there is Yuglook.

[Edit 11/30/08]

I did have to add one additional math nerd news. This was given in the title of one of the caches I found yesterday: V=pi r² h. BIG math hint that helped us find it. Guess the shape of that cache!

Math Appreciation

2008-11-22T16:19:00.001-08:00

Last night, I went around wearing my shirt that I bought from a math conference last year. It says "Kiss my asymptotes" and has a picture of the graph for y=1/x. I never wear this to school because I feel it might not be deemed appropriate. However, it is one of my favorite shirts.

Last night, walking around with that shirt on really boosted my spirits--not because I feel like a math nerd for sporting that kind of shirt, but because it helped me to realize that everyday non-math people also have an appreciation for mathematics. I received several compliments on how awesome my shirt was, and it proves the point that I make to my students that you don't need to be a mathematician or some nerd to appreciate mathematics.

Flash Memory Reader- Andy Naughton

2008-11-17T21:18:00.000-08:00

I posted this to my students and to my friends on Twitter:

http://tr.im/15ag First person to explain how this works MATHEMATICALLY gets ex. credit :) Just simple algebra and close observation.

I first saw this at the Palm Springs CMC-South Math Conference that I blogged about a few days ago. One of the presenters used it as an opener to her session. I caught on pretty quick, and saw the pattern on first time doing it. I was amazed, though, how few MATH TEACHERS were able to spot the trick by the third or fourth try.

Now, granted some of the teachers in the room were elementary school and middle school teachers; and I can imagine the elementary school teachers struggling to be able to explain how this works since their main focus is not mathematics. But to have middle school teachers, who may be required to teach Algebra in 8th grade in California if Congress still chooses, not able to explain it or fully understand place value was pretty saddening. Even worse were the high school math teachers leaning over to peak at my answer. Um, hello? Even if you weren't a math major, all it takes is close observation and a little algebra.

How can we expect our students to learn to be more curious about mathematics, and build better problem solving skills when our teachers are struggling themselves?

I must admit, though--Andy Naughton is pretty slick in trying to hide the trick by constantly switching the symbols to deter you from seeing the pattern.

Mathvids.com

2008-11-17T20:48:00.000-08:00

I tried finding some Tweeple (Twitter People, that is) that are discussing things that were math-related. Unfortunately, doing a Twitter search for "math" or "algebra" or anything mathy, there really wasn't anything interesting. Most posts were about people complaining about their math homework; and in fact, my random math posts showed up several times on the search.

However, one person I am now following is @mathvids. Interesting enough, I added @mathvids when they had no posts, followers, or even following anyone, but they did end up posting a link to their site, mathvids.com. Now, it seems the site is still growing, but I did enjoy the idea behind their web site, where professors, teachers, and people can share their math lessons through video. Share ideas, methods, strategies, etc.

I actually started watching a few calculus videos to refresh myself on some of those topics (it has been so long since I last did any calculus). It was interesting enough for me to sign up for their free membership, and I'll keep watching to see if it grows to something bigger.

CMC - South Math Conference, Palm Springs, CA

2008-11-11T01:56:00.000-08:00

It has been a while since I updated this blog. I actually have drafts for four different posts saved right now, but none even close to being complete. However, I do feel compelled to finish a blog discussing a few of best ideas I learned from the Math Conference hosted by CMC that I attended this past weekend in Palm Springs, CA.

This was my second year attending and WOW did I have a blast. Staying in the sleek Hotel Zoso, enjoying the nightlife in Palm Springs, and even dabbed at a little geocaching, it was definitely a weekend to remember. At the same time the workshops I attended were all wonderful. Two in particular, I will be discussing: "Algebra as Representation: From Arithmetic to Algebra" presented by Andy Clark from Portland, and "A Different Way to Differentiate Instruction" presented by Lois Moseley from NUMBERS Mathematics Professional.

Algebra as Representation: From Arithmetic to Algebra

Every math teacher complains the same problem every year. The students have not mastered any of the skills that they should have learned in middle school! Of course, the middle school teachers complain that the students have not mastered any of the skills that they should have learned in elementary school! Now, this workshop went into many aspects of developing student thinking to transition from arithmetic to algebra--concrete thinking to abstract concepts. However, what really caught my attention was a strategy that I definitely want to start using within my own Algebra I classes.

One of the biggest skills students lack is number sense, especially when it applies to fractions, decimals, and percents. Unfortunately, in early math education, we tend to use spiraling methods to prepare a student for tests rather than teach for mastery. We touch on a topic rather quickly, then move on to the next concept, often with little or no means of having the student continue to use and build on the idea except for a few review problems along the way. Repetition is one of the keys to master, but on the other hand, we do not want to bombard the student with worksheets of the same type of problem to be solved over and over again. Instead, important concepts should be revisited and explored every day to encourage the students to develop higher levels of understanding rather than just learn one method and repeat without understanding.

To remedy this problem, Clark presented one strategy he called ... actuallyI forget what he called it, but I want to call them "dailies" because it reminds me of my daily quests I used to do when I used to play video games. At a set time in every class (beginning mostly, but whenever you choose) the students perform their daily task of filling in a percent circle that has one hundred dots all the way around. On the first day, they fill in the first circle, which represents 1/100, or 1%, or .01. One student puts it on the board, and everyone else logs it in their notebook. The next day, another student fills in the next circle, leaving two circles filled in, representing 2/100=1/50, or 2%, or .02. And so on, and so on.

However, when you reach important milestones, such as 25%, you do a bit more exploration, to encourage more understanding along with the repetition. For example, 25% = 1/4 = .25. Then we can ask, "What is half of 25%?" Students can look at their diagram that they are drawing, and see that it would be 1/8, or take 25 divided by two to get 12.5%. At 75% We can ask, "What is 75% of 2 meters?" and "What is 75% of an hour?", or have students draw a picture to solve the following problem: "A number plus 75% of that number equals 35. What we are building is the students' abilities to create a mental image of this circle, and apply the conversions to percents, fractions, and decimals in their mind and to the math.

If it is done for 100 classes in a row, the repetition would have a significant impact on the student's retention, and the continual exploration will improve understanding and fluency of the conversions and when one form might be more appropriate than another. Now I just have to figure out a way to post this circle in the classroom, where both of my Algebra I classes can utilize it.

A Different Way to Differentiate Instruction

Mosely showed a different way of integrating instruction with informal assessment in order to promote thinking in all students, while differentiating both the instruction and assessment making the math accessible to all students. Her process involved differentiating through parallel instruction, language elements, and questioning. Within each part, she gave great strategies that allows access to all students, promotes thinking of all levels, and gives students the ability to build on their understanding at their own pace while covering the same content standards and giving the teacher accurate methods of assessing their progress.

In order to fully explain, I am waiting for Lois Mosely to post her PowerPoint slides for me to download. Once I get that, I will continue to update this and discuss this post more. However, I will touch on each element lightly.

Parallel Instruction

In most math classes, the teacher completes and example and the students are so busy copying the problem that they miss the most important part--the thinking behind each step. In her example of parallel instruction, she suggests presented the common steps for each problem first, then posting two problems: one teacher, and one student. The students do not copy the teacher problem, but rather use it as a guide in order to complete the student problem on their worksheet. As the teacher completes one step, the students complete the same step, but on their own problem. The problems may in fact, not even math perfectly step by step, but would still follow the same guidelines on how to solve it. This allows the students the support of how to do each step, yet requires them to think about the reasoning on each step too, resulting in less students saying, "I understand it when you do it, but I have problems when I have to do it myself!"

Language Elements

Students do no realize that to learn mathematics is to learn another language. However, in mathematics, there are three different elements to it. First we have the academic language. This is language that is used in the classroom, but may in fact be used cross-discipline, in other classrooms. Words like "compare" or "describe" are words the student must understand in order to understand the content. That brings us to the next part, content language. Mathematics introduces a number of vocabulary words and concepts that the student must be able to define and USE in order to be successful. If a student is asked to find the perimeter of a shape, it would be difficult to complete the task if the student has no idea what a perimeter is. Lastly, the most difficult part of the math language is understanding the symbolic language and being able to create connections between the symbolic language and verbal meanings seen in the content and academic language elements. For example, an algebra student must understand that the equation 2x + 1 > 5 can be explain as, "two times the value of x, plus one is greater than five." In this translation between the different language elements, we see where much of a student's understanding of the mathematics breaks down.

One strategy implemented by Mosely was the use of read-alouds. This can be used to assess as a class and find individual areas where they lose fluency in the mathematics. For example, if you post x^2 and have students read it aloud, student may often say, "x two," warning the teacher that the student may not understand the meaning of "x squared". This can be applied to all symbolic statements. Model to the students how it should be read, then have students read it aloud and listen carefully for the students that do not read it correctly. Then, fix any errors immediately. In addition to read-alouds, just focusing on the content language will greatly improve student understanding. Addressing words such that have multiple meanings (inside and outside of math, such as the term "degree") is important to having students fully comprehend the language aspect of mathematics.

Questioning

Probably the most important aspect of the presentation was the use of questioning as a method to assess student understanding and build on the knowledge of each student, yet allowing the teacher to differentiate instruction and allow students to develop at their own pace without eliminating any rigor from the instruction. However, this form of questioning is different than usual. Rather than asking the students the question, the teacher would create a visual prompt and have the student develop their own questions. Based on the questions, the teacher can see what level of thinking the students are at, and their own understanding of the concepts presented based on the content of the questions. For example, imagine a rectangle with two sides labeled a and b. Students who understand the concept of perimeter well may ask, "Write an expression that gives the perimeter of the rectangle." An excellent application of the term perimeter. A low level student may ask, "Which is longer, a or b?" A student who can create even higher level questions where they can synthesize and include previous concepts has a high understanding of the current concept. For example, "Give the area of the rectange is 12, and a = 4, find the perimeter or the rectangle."

When students first begin this process of forming questions, it is imperative that the teacher accept ALL questions and does not rank any about the rest. Students must be encouraged to develop their own questions, which allows for the differentiation of instruction while having all student ideas being acknowledge, appreciated, and accepted. Further, students are not asked to solve the questions nor rank them, but must consider each of them. All levels of thinking are required to learn mathematics, and you cannot build the higher levels without understanding the lower level reasoning first.

What to do with these questions is also important. Creating an environment of questions and encouraging students to continue exploring is vital to helping students learn. Posting the questions on sentence strips on the the Math Wall will encourage this.

***

Many other strategies were learned, and activities were presented, but I wanted to focus on those two workshops and those specific strategies. I feel these alone will improve my teaching in the classroom and hopefully improve understanding deeper than a students ability to "do the problem." I look forward to seeing how students will react to them, and how other teachers will use it and continue to modify instruction to support all students.

...More to come on this in the future.

Building Relationships

2008-10-16T20:25:00.000-07:00

Building relationships with students is probably one of the most difficult, yet worthwhile things that a high school teacher can do. Unfortunately, how many teachers actually attempt to make those connections?

The teacher must be willing to invest time and energy into their students. With over 130 students, I've already found that it is impossible to build personal connections with each and every student. In fact, it's already mid-October and I still find myself struggling with a few of the names (although I must admit that I'm horrible with recalling names of people that I have known for years). However, just because I feel it is an impossible task, it does not mean I must give up completely; the relationships I have developed this year are already making a difference, especially in one particular class.

In one of my Algebra 1 classes, I have two students failing. They came into my classroom with very low math skills, unprepared and unwilling to work. Both have disabilities that affect their confidence and inhibit their ability to fully function in the classroom. Even with modifications in my lessons, and constant monitoring, I still struggled to get them to participate in every aspect of learning. However, I made it a point to be sure that I provide these students with the best education possible and I wanted them to know that their success is important to me. I would not let them fail.

The Typical Teacher. Both of these students came into my class after school had been in session for about two weeks. Now in my third year, I can see how the attitudes of other teachers can rub off onto less seasoned teachers like myself. Adhering to strict consequences and attempting to "control" the class was something I started doing more. (Now I must admit that my classroom management is much more effective this year, but not because I made stricter policies, but because I am being more consistent with my policies.) I tried to be like the other typical teachers that slave to have more "discipline" in their classroom.

Where did this bring me? The first unsuccessful student comes into my room and puts his skateboard down by the wall. With his long shaggy hair and glazed-over look, I wondered what kind of student he was going to be--mistake number one. A few minutes into the class, I notice the student was not paying attention at all. His head was down, and he showed no interest at all in what we were learning. I walked over to his desk and quietly asked him to keep his head up and pay attention--mistake number two. He continued to look down at his desk, showing complete disinterest. I called on him by name and asked him to look up at the board--mistake number three. Walking around the class, the student calls me over and asks if he can talk to me after class. At that point, I began to realize that I probably screwed up with my attempt to keep the student "engaged". After class he told me that he had vision problems--severe vision problems where he can't even read something directly in front of him. Realizing my mistake, I quickly apologized for calling him out in class. I felt terrible and acknowledged that maybe the typical teacher approach was not the best way to deal with students. Each one is so unique with their needs that a one-size fits all plan is completely ridiculous.

Less than a week later, I noticed the student sitting in Viewpoint. I guess another teacher didn't come to the same realization that I had.

The Teacher Who Won't Give Up. Unsuccessful student number two comes in with an attitude. Much of the time I come to his desk, he has nothing written down, no notes and no work. Teachers would normally dole out consequences and send home negative feedback to the parents. I decided to try a different route. Each time I came by, I stepped him through the problems step by step, sometimes even telling him exactly what to write and how to write it. I showed to him that I would not give up and that I would not continue to let him feel lost and confused in the classroom. Slowly, I began doing less and less and letting him do more of the thinking, and relying on asking him more questions to direct his learning. Does he still sit there and do nothing at times? Of course, but I still have not given up.

Now, over a month into the school year, both of these students are still the only students earning an 'F' in my class. Am I failing them? Am I failing at making a difference in their lives? Although their marks in my class do not reflect it, I am proud to say that they are FAR from failing. One student comes in every tutorial into my classroom looking for something to do. The other continues to participate and thanks me by shaking my hand for everything I do to accommodate him in my class. But that's not how I measure success. I'm measuring it by what they are learning. Are they performing to the Algebra I standards? No, but they are making great progress.

Both have agreed to meet with me at least once a week after school. This past Wednesday was the last time we met. The first thing I gave to them was a worksheet with 45 addition and subtraction problems. It was amazing to watch them actually ENJOY doing the math problems. They struggled and I helped them realize their mistakes, They even had a little friendly competition going on. Then I asked them to take out their homework so we can work on some of the current concepts that we were learning in class.

I told them that we were going to skip practicing solving equations so that I don't hold them too long and I can let them go. To my surprise, they both replied that they WANTED to stay and keep working! Wow.

The changes I have seen in these students are not any that I have seen in any of my students before. The one with the attitude now walks into my classroom with a smile, and I always greet him. How has this affected my classroom? Sure, I still struggle to get work done in class, but I understand they struggle with the math and need more attention. Fortunately enough, they are able to get the attention that they need, the right kind of attention. Because of this, discipline problems in this class are virtually non-existent, and I must say that out of my three years, I am actually really enjoying teaching this year.

The Human Calculator

2008-10-12T19:05:00.001-07:00

After writing my post about using a calculator, I realized that I wish I were faster at doing simple calculations in my head. I tend to get distracted easily and forget numbers, but I'm trying to learn new ways multiplying numbers faster.

I find it interesting that our standard algorithm for multiplication starts from right to left, yet it is best to perform multiplication mentally from left to right.

Here's a trick when multiplying two double-digit numbers, when the numbers are between 11-19:

Take the larger number, then add the last digit of the smaller number. This is the first two numbers of your product(unless you need to carry). Then multiply the last two numbers and that becomes your last number.

Example1: 11 times 17. 17+1 = 18, so think 18_. 1*7 = 7, so the answer is 187.
Example2: 14 times 19. 19+4 = 23, so think 23_. 9*4 = 36, so instead of 23_-->236, you add that three to get the answer 266.

When multiplying two double digit numbers where the first digits multiply to less than 10, we can use a similar strategy.
Example: 24 times 36. Again, I start on the left. 2*3 = 6, which means 600, but I just remember the 6. Then I cross over, 4*3=12, so I think 72. Then I cross the other way, 6*2=12,so I think 72+12=84. Then I do the last two, 4*6=24, which becomes 840+24, which is 864. The trick for me is eliminating the numbers I don't need to remember, and remembering just one number at a time, rather than several numbers that I would add at the end, like in the standard algorithm. Starting from the left allows me to do this. I remember the number 6, then 72 (I can forget the 6 at this point), then 84, then 864 is my answer.

It's interesting that I never thought of this before until I actually decided that I want to learn to do more mental math. But what I am doing is nothing new. In fact, many people multiply like this I'm sure, and if not, all I'm doing is using the well known distributive property.

Let me explain...
24 * 36 = (20 + 4) * (30 + 6). Remember FOIL? First- 20*30 = 600 (but I think 2*3), Outside 20*6=120 (I think 2*6), Inside 4*30=120 (I think 4*3), and Last 4*6=24. Add them up,600+120+120+24, you get 864. Fun stuff, huh. Just takes more practice not to doing it quicker and quicker.

Now I need to find this video where this guy does these crazy "magic" math problems, but there's no trick to it. He really just does it. I don't plan to ever be as good as him, but I'm making it a new goal to be a much faster human calculator.

The UC Syndrome

2008-10-10T23:52:00.000-07:00

"We need to fix those counselors at your school!"

Well, maybe that wasn't really a quote, but more of an attempt to quote someone who was attempting to quote someone else. In any case, it may just be true.

The UC Syndrome. The belief that a student is not successful unless they attend a UC (that is a campus in the University of California system, for those of you who are not from California) or some expensive private university.

It seems like our counselors all suffer from the UC Syndrome. I'll take it further; most of the staff at my school suffers from the UC Syndrome. No, there are too many students, families, staff, and random people in this state that suffer from the UC Syndrome.

The school you decide to attend does not equate with one's success. Yet, why do the counselors push students to attend a UC just to make themselves look good. Do they care if their students become successful in life? Or do they only care to make themselves look successful by boasting the number of students who they sent to a UC each year (not even bothering to find out if they even actually graduated)?

I know many people who have attended various UC's and private schools, only to drop out a couple years later for various reasons. Does that bother the counselors or other school officials who pushed them to attend those schools? Not at all, because they don't even know! If they don't know, then that suggests they did not really care to begin with. To them, they did a GREAT job by sending the student to a UC to fail.

Of course, dropping out of school is not the end of the world. In fact, in many cases, it's the real beginning of life where real learning takes place and real success is realized. However, because of the UC Syndrome, many would-be successful students are put at a disadvantage. On the other hand, students who persevere through community college and earn their degrees from a Cal State are looked down upon in high school, yet emerge as leaders and often with much more cash in their pockets.

Some examples...

A bright and articulate young woman was offered the President's Scholarship at Cal State Fullerton, a full-ride scholarship for four years, among other benefits. Because of her counselor, she opted to attend a UC because she was told it was a better school for her major in the sciences. She ended up changing majors a few times before finally taking a break from school all together. Now, almost nine years after graduating from high school, she has yet to obtain her bachelor's degree.

Another intelligent young man was pushed toward attending an expensive Southern California private university only to drop out two years later with over $60k in student loans. He dropped a large sum of money into a partial education that will yield him no return. Last I heard, he was attending a local community college.

A quiet, yet intelligent and passionate young woman had the opportunity to attend a four-year university, yet decided to attend a community college first. She spent three years at the community college, then three more years at a Cal State before obtaining her degree in business. Although it took her longer than expected to obtain her degree, she proved to be a successful leader, serving as President of the nation's largest student business organization, FBLA-PBL. Further, even with six years of college, she graduated with no student loans, and virtually no debt.

I will say it again. Attending a UC does not equal success. Even those who do graduate assume considerably higher debt compared to a student to started at a community college. Of course, I'm not saying a UC is a mistake, but it may not always be the best decision, especially for those who have more difficult financing their higher education. For some, attending a UC or private university may be the right decision, but students should not be pushed to attend a UC or brainwashed to believe that UC's are better schools. And we must definitely stop counselors from making decisions for the students that are not in the students' best interest.

As I attempted to quote the attempted quote,

"We need to fix those counselors at your school."

Tutorial Time

2008-10-09T21:44:00.000-07:00

Tutorials built into the school bell schedule is a great tool for teachers. Students can make up or retake tests. It allows time for all of the intervention programs on campus to monitor the progress of unsuccessful students. But best of all, it allows struggling students additional time to work with the teacher on a one-on-one basis--or does it?

The additional tutoring and study time, in my opinion, was to be able to offer students additional time to get extra help on concepts that they did not understand. However, I find I do not have nearly enough time to provide support to the students who need it.

It's strange that there are some teachers who strategize how they can get students to show up to tutorials, and some even make it mandatory. That is definitely NOT my problem. I have the issue of managing the high number of students who attend my tutorial, each one with a completely different need. If I could dedicate even half of a tutorial session to one student, or even a small group of students with the same needs, tutorials would be very effective. However, trying to help students in two-minute intervals is definitely not providing the students with the support that they need. In fact, it is just a big waste of time for some students who I start them off on a problem, yet can't return to check their progress until ten minutes later. In between, I'm answering several other questions, signing tutorial cards, and filling out grade cards.

I'm supposed to develop a plan for BTSA (ugh, extra work with no additional pay) to start a system to "better utilize" tutorials to support my D/F students. Now when I say "better utilize", I really mean make a mandatory tutorial policy for my students. I started to think about it though, and if I dedicate ten minutes per D/F student each week, with over twenty unsuccessful students among my five classes, then that's over 200 minutes I need to dedicate just toward helping these students. With tutorials, I can only spend about 80 minutes tutoring my D/F students, leaving over two hours of my personal time each week that I would have to spend in order to complete this task. At the same time, I'm ignoring my 'C' and 'B' students who are already coming in to get extra help during tutorials and after class, which may in turn create a larger D/F ratio.

Ten minutes per student each week. That is definitely not enough time to turn a failing student into a successful one, especially if they do not put in the additional time on their own to practice their math skills.

It was suggested by my BTSA mentor to offer community service credit or extra credit to my advanced students to tutor others during tutorial in order to unload some of the burden of providing help. Although this is a valid suggestion, I still find there are some inherent problems with my students tutoring math. First of all, I do not teach honors classes, so although I do have a few bright students, they are not always quick to understand the content. Further, the students do not have any training in tutoring or teaching mathematics, and often just "show" students how to complete the problem, while the student copies the work onto the homework and claims to understand the concept.

Other issues I find making note of is the extra credit. The only students I would trust to become tutors are students that already have A's in the class and do not need the extra credit. At the same time, giving an A-student extra credit allows them to slack off in class (unless it's an honors class, where in that case, you have a few overachievers who like to have 105% in the class).

As for community service, I do have a few AVID students who do need community service credit, but at the same time, coordinating volunteers and hoping they actually show up is a project on its own. When students are volunteering, they are not reliable on always being there, especially since many of them have many other commitments, as well.

Now, I do not want to make it seem like I do not want to put in the extra time to help my unsuccessful students. In fact, that is far from true. I have already convinced two students to see me weekly after school until they are earning a C in my class. Further, I am offering online tutoring sessions with me if they cannot make it into tutorials. I also understand the school's policy of directed intervention rather than intervention by invitation. However, the tutorial policy in its current implementation is not working for me, and I can't think of any way of maximizing student support while keeping sane.

I do have one suggestion for changing the school schedule to better accommodate student needs and teacher needs. I believe it would be an amazing idea to extend the school day by another hour and make it mandatory for every student to participate in at least one extra-curricular activity. Struggling students can then also be pulled out of this extra-curricular "class" weekly for 15-30 minutes to work with the teacher of the class he or she is failing if the teacher so chooses. Further, studies show that students that get involved in at least one activity are more likely to succeed in high school. The difference between this and tutorials is that everyone is taking advantage of the extra hour by getting involved, AND the class meets every day, creating more time for the teacher to meet with struggling students. Of course, with the extra hour added into the schedule, teachers would need to have a small pay raise.

It's a win-win situation for everyone! However, that day will never happen.

Math Conversations

2008-10-06T17:57:00.000-07:00

The only way to learn another language is to actually use it.

Math Conversations
Materials:
Individual whiteboards and markers, PowerPoint w/ projector, paper

Grouping:
Partners

Time:
Depending on the length of each problem, 15-30 minutes.

Directions:
The teacher posts a problem and several key TARGET WORDS.
Partner B copies the TARGET WORDS onto a piece of paper.
Partner A completes the posted problem on the whiteboard while explaining to Partner B each step. Partner A must try to use the TARGET WORDS as many times as possible within the explanation.
Partner B checks the work of Partner A as he completes it, and creates a tally count of each time Partner A uses one of the TARGET WORDS.
Partner A must use each TARGET WORD at least once, but if possible, use the TARGET WORDS multiple times.
At the end, Partner B copies the work off of the whiteboard onto the paper.
The teacher posts a new problem and TARGET WORDS, and Partner A and B switch roles.

***Be sure to do an example first with the entire class to be sure the directions are clear. The teacher should perform the part of Partner A, and the teacher can select a student to play the role of Partner B, who will tally all the times the teacher uses a TARGET WORD. Make it clear that the goal is to use the TARGET WORDS, and set the example by going out of your way to use the words in your explanation.

Here's a link to a portion of the PowerPoint presentation I used today in my class:
http://vyew.com/room#/104280/math_conversations

**********************************

I've told my students several times, learning math is like learning another language. In order to really excel in mathematics, you must be able to read, write, and speak it. Too many students are focused on mimicking the steps performed by the teacher or by other students, only to fail to understand the true meaning of what they are doing.

Now, I must admit, that I felt that I was inundated with English language learner strategies while completing my credential program, but at the same time, I realized the importance of providing equal education to students of all backgrounds and abilities. However, now I have also learned the importance of using many of these strategies for ALL of my students because they are, in essence, developing their math language skills.

"Math Conversations" is one of the most effective strategies that I have adapted for use in my math classroom. Building on the idea that students must be able to speak "Math" in order to learn it, this activity actively engages students to use the key terms that students need to practice and comprehend. Not only that, but my students actually enjoyed them too. I asked my fifth period, "Raise your hand if you felt this activity helped you to better understand graphing systems of linear inequalities." Every student raised their hand, and about half of them raised them enthusiastically. One student exclaimed, "We should do this for everything we learn!" Now, I don't want the activity to get old fast, so I politely said no, but did acknowledge that we will continue to use the activity throughout the year.

New Math! Math on YouTube...

2008-10-06T02:18:00.000-07:00

I thought this was funny...

New Math!

At the same time though, Whooosh...It would go right over the heads of my students. Now, I admit, I don't think I learned about the octal numeral system until I started building Web sites and ended up looking it up when I learned about hexadecimal systems to create my color schemes, but I really do not know which of my students understand place value, or even what they are doing.

Now, I guess it says that the video was made in response to this video.

Math Education: An Inconvenient Truth

I have mixed feelings about this video. Referring back to my calculator post, I believe that students must learn their basic multiplication facts. Similarly, I agree with this lady that the students should know the algorithm that we all learned in elementary school. Now as she said, the methods demonstrated could be used as useful tools for teaching place value and logical thinking, but the students in the end must learn the quick and sure-fire way of multiplying.

However, the video makes reform mathematics seem like a complete failure. I believe that our education needs to find a balance between exploration and learning algorithms. I was looking up other videos, as well, and I found this interesting mental math shortcut to multiplying.

Multiplying Shortcut

Now, I was taught the standard algorithm of multiplication, but you don't need to be a mathematician to understand how the shortcut works. In fact, if I was given the chance, and perhaps more time to explore, this may have been a method I could have been using since elementary school! Yet, I had become so ingrained in the single method taught to me, that I never bothered to make multiplying even easier!

In the end, I must still side with Miss I-Hate-Reform-Math. You can think of these algorithms like another tool (like a calculator). The students must build the skills to use these tools while in elementary school so that they have it at their disposal when they reach higher level mathematics.

Technology OUTSIDE the classroom!

2008-10-05T23:30:00.000-07:00

One of my goals this year was to lower my D/F ratio in all of my classes. However, I realized that the only way I can do this is by offering additional support to my students outside of the classroom. Now, I do teach in a lower income neighborhood, so access to technology is limited for many of my students. However, that does not mean I should restrict myself from using technology.

I am going to try something new with my students where I can offer online tutoring outside of school. I took some time tonight to try out several sites that can facilitate that goal, and found one that stood out above the rest.

http://www.vyew.com

Tomorrow, I'm going to take a poll of my students to see how many of them have access to the Internet at home or somewhere else. Hopefully there will be at least a few who can take advantage of new technology to improve on their math skills. I'll write more once I get the chance to really test it out with my students and get their feedback, but I think it will be something that will be very useful to some of my students, especially for help with their homework.

But first, here are a few thoughts about each of the sites I did review.

vyew.com

Pros: Easy to use interface. Pages saved in an organized manner. Quick access, with no downloads. Shared desktop ability. Control over user access in meeting. Free conference call number. Math add-ons! Works with Google Chrome brower. Completely free!

Cons: Supposedly there are banner ads, but I didn't see any. Shared desktop application is still a bit buggy. No recording of voice to create recorded lessons. Limited number of "books" and uploads.

dimdim.com

Pros: Easy to use interface. Free! Awesome recording ability (which is great for creating online lessons that students can review even AFTER the meeting is over). No downloads.

Cons: No math features to help with math equations. No way of limited a user's access to the whiteboard during a meeting.

E-lecta.com

Pros: Many features!

Cons: Cluttered space. Download that makes my virus scanner go crazy (@#$!#!??), Gave me some error on the Vista platform. NOT Free, and pretty pricey at that.

wiziq.com

Pros: Can sell your tutoring services. Simple, easy to use interface. Can offer teaching services to all types of people.

Cons: Not as many features. More difficult to invite students into your virtual classroom. Have to pay to get some of the features offered by other sites for free.

Overall, they were all great sites, but I have decided that vyew.com is my favorite that balances ease of use for me and my students, variety of features, and best of all FREE TO USE! I did like dimdim.com very much, too. I will probably be using that to create online lessons available for download for students, or it may be my second choice if vyew.com does not work out for me. Now, it's time to test it out. Wish me luck!

Calculators and Algebra

2008-10-05T17:59:00.000-07:00

Students should use calculators in their high school math classes.

Don't get me wrong, I think all students should have their multiplication facts memorized. It pains me when I ask a student to multiply 4 times 6, and they sit there silent for over ten seconds, only to answer "Ummm...28?". Division is even worse.

At the same time, I don't rush for a paper and pencil when asked to calculate 78% of 216, or to divide 8,983,123 by 37--and no, I don't attempt to do these calculations in my head either. You can expect me to reach into my pocket and bust out my calculator (on my phone, I'm not that big of a nerd that I carry a calculator with me...usually). I'm good at math, but I'm lazy too. I take that back; I don't like the word lazy.

I like to be efficient.

Okay, let's go back to my classroom. The students don't know their multiplication facts, and they are supposed to learn the abstract concepts of Algebra. Let's think about that again--they don't know basic mathematics, but they are expected to dive right into solving equations, graphing functions, solve algebraic word problems, etc., and according to the state of California, they have over 30 standards and sub-standards that they should know by the end of the year in Algebra 1. Do you see something wrong with this picture?

Now let's take calculators out of the picture. The students start learning about Algebra, they understand what the teacher says, then they try it for themselves. They struggle with the addition, subtraction, multiplication, and division, and end up with the wrong answers. They fail; they get frustrated; they give up. I don't have time to teach them arithmetic, and now they aren't learning the algebra either.

Now let's put calculators into the hands of struggling students. The students start learning about Algebra, and they understand what the teacher is saying. They apply what they learned and use a calculator to quickly get the answer. They succeed in getting the correct answer, increasing their confidence, and increasing their ability to continue on in Algebra. Further, their calculator just told them that 28/7 = 4, reinforcing their multiplication facts.

Why are we depriving students of a very useful tool to learning mathematics? If they have not learned their multiplication facts by now, they will NOT learn it while in an Algebra. We don't deprive English students of spell check; in fact, we encourage it! My job is to teach the students Algebra, and critical thinking skills, and a calculator is a tool we all use in our every day lives.

If all students had a calculator at their disposal, Algebra classes could be performing at much higher levels, and would not be working on problems that have been "dumbed-down" so that the students are able to perform the mathematics without a calculator. Mathematics could be applied to real world problems, where we know we do not always get nice round whole numbers. Algebra students may use calculators to do some real thinking rather than worrying about multiplying incorrectly, or their brain shutting down because they saw the ever so dreaded FRACTION! Mathematics would once again be useful in life.

I have so much more to say about this, and this just scratches the tip of the iceberg on this topic. Calculators in high school mathematics should be added to the high school curriculum. In elementary school, not so much. Keep doing those speed multiplication tests I used to do in the third grade. Maybe then, I won't get students who look at me confused when I ask them to divide 28 by 7.

Teacher Blog

2008-10-05T17:44:00.000-07:00

This is only my third year as a math teacher, but my philosophy on math education has already made some major changes since the start of my career. From technology to testing, there are so many different perspectives and arguments on how math should be taught and how students and teachers should be held accountable.

So what is this blog about? Well, based on the title, it may not always be the most professional blog. I bought a shirt that has "Kiss my Asymptotes" from a math conference, and it's one of my favorite, but I never get to wear it to work, but it's not necessarily just for fun either. People have told me to make a blog about my experiences as a teacher, but that's not why I did this either. Sometimes, I just have things to say about teaching math, and this is my place to say it.

These are just my thoughts and opinions, and random math/teacher related "stuff" that I find. Who is going to read this? I have no clue, and most likely no one. No one "normal" is interested in this stuff, and if you do, then I'm sorry :(

Are any of these thoughts going to based on research? Perhaps, but most likely not. But enjoy them anyway!

JT