Deriving the Quadratic Formula

There are definitely moments when I look at myself and say, "wow, I am a dorky math teacher!" I like it, don't get me wrong, it's funny sometimes though.

Yesterday was one of those days. I was teaching my 10A students about completing the square to solve a quadratic function. The next thing we needed to learn was the quadratic formula; we all know it by the dorky song but I didn't really want to teach them that.

So I figured I'd take a more analytical approach. I figured it was a good group to do it with since they are all very quiet (I wouldn't get a lot of singing participation out of them to say the least) and very good at math.

So we started by completing the square on the general quadratic function: 0 = ax² + bx + c. Now I won't bore you with the process, but by completing the square (if some of you are curious about what I'm talking about, brush up on your math skills a bit!) with this general function, we derived the quadratic formula. That's right, instead of just making my students remember the quadratic formula, they now know where it comes from and why it exists! If that's not cool, I just don't know what is...ok, dorky math teacher again! Again, if your inner-dork is crying out for more math, this is a write-up of what was on my board yesterday and now in my students notes...so cool, I know :) Enjoy!

We Have New Furniture!

If you ready my last blog post, you know there was going to be a change in our apartment. It came last night at around 7 p.m. in the form of a big, ugly, very awkward Taiwanese version of a futon! Yay!

As much as I hate the fact that we got a random piece of furniture that in no way shape or form goes with the other couch and has a ver bizarre design, I love not having a broken couch in our apartment anymore. It may not be the perfect piece of furniture, but hey, it's new! And we went to Carefore last night right after it was delivered to get some pillows for it to make it more usable. All in all, I would call this a success for the apartment and even a mild victory for future house guests: it may not be super comfy, but it was described to us as a "sleeper couch." Again, more of a crappy futon type thing, but it will work. Yay, new couch!

A Taiwan Repairman

It is pretty standard in Taiwan that if something breaks, they can and will fix it instead of automatically replacing it. Scooters that would have been discarded years ago in other countries are still alive and, for the most part, running here. Chairs that are so broken they make odd popping and screeching noises when sat upon, are glued up and screwed back together to last another few months. It is impressive in a "reduce, reuses, recycle" sort of way, but very frustrating when you just want things to work sometimes.

Our couch at our apartment is a classic example of this. It started breaking at the beginning of the year and got progressively worse with each dinner party (people don't look where they are sitting when they have a full plate of enchiladas apparently) and finally got to a point where we couldn't use it anymore. I was pretty sure that it was ready for the dump, but when we called our landlord (our apartment is furnished by her) she told us she would send over a repairman. Fine, just fix it then; we just wanted a useable couch.

Little did we know how funny and productive it would be to have a Taiwanese repairman come to our apartment! I was home alone at the scheduled time and he managed to call our apartment phone which has NEVER rang before. I answered it with the classic Taiwan phone greeting "Wei" (pronounced "way") and a man on the other end started speaking in Chinese. I thought it was maybe the front door guard asking if I had a repairman coming, needing him checked in, so I just said "yes" in Chinese, but he kept speaking. I didn't know what to do at this point, so I just kept saying "what?" in Chinese. Eventually, I realized he couldn't get up the elevator because we need to scan our cards every time we go up or down for security purposes. So I went down and met him at the door. I had no idea what Asian man it would be, but I was pretty easy to spot being the only white woman in the lobby so he jumped right out at me and pointed to his hammer and other tools. Those were good enough credentials for me, so we went back up to the 10th floor.

After about 30 minutes of taking a hammer to our couch (it was really broken), I could tell he had given up hope. Total shocker! I thought he would have whipped out the tape and staple gun and sort of patch it back together before giving up like that, but sure enough he called our landlord and told her we needed a new one. What?! A new couch?! How could this be?!?! Then he kept saying something to us about 7, but we couldn't understand what he meant by that.

To our total shock, we got a knock on our door at 7 p.m. sharp. It wasn't a new couch, but it was the son-in-law of our landlady there to take the measurements for a new couch. This is going to be awesome! He said it is going to be delivered on maybe Wednesday of this week and we will have a new couch in our apartment! It will be like we're back in the States again- something breaks and you just get a new one. I don't think we'll know what to do with ourselves when it is delivered... a new couch, a new couch. Wow. This is going to be cool: I'll post a picture when it comes!

Forcing Students to Do Good

For any of you familiar with my school or at all familiar with the stories I tell, you know that the school I teach at is a very expensive private school here in Taiwan. It is the second most expensive school in the country and we generally teach students whose fathers own the factories that made the shoes you are wearing right now. Needless to say, our students generally lead very privileged lives.

So once a year, we like to force them to give back to the community just to prove a point I guess. We call it Common Good Day and it turns into a pseudo house competition. The basic idea is that each house (we have 8 "houses" in our school, just like Harry Potter) choses a charity or act of community service to do on the specific Saturday we set for this forced philanthropic work. Last year my house, Archimedes House, picked up garbage on the side of a mountain. I cannot even begin to explain to you how hot and totally pointless that was.

This year we decided we wanted to actually do something cool for Common Good Day. As a house we decided to put on a Coin Wars competition in the week leading up to the big Saturday. We set the rules a little differently than what I've done in the States but the same basic concept. Each house competes for the most points and you get points by collecting coins in your house jar and you can give negative points to other houses by adding paper money to theirs. Then to raise even more money, we decided to have a scooter and car wash for the teachers and other faculty at the school (see adorable pictures below).

To our complete amazement, both ideas were huge successes. In total, we raised almost $1400 in U.S. currency. We were so proud of our kids because they had everything to do with it: they were excited about it (completely different than last year), they took ownership in the activities (again, so polar opposite of last year) and had good attitudes on the actual day. I had no idea that they could wash a car so well! It was really great to see them work hard for something that was not directly benefiting them.

I think the best part about the day however, was deciding what to do with the money at the end. We went though a website called kiva.org that gives out micro-loans to people around the world that wouldn't otherwise qualify for them to help improve their lives. The cool thing about the website is that you can scroll through the people and chose who you want to donate to. All of our students in Archimedes House intently clicked through countless profiles for the better part of an hour decided exactly who they wanted to help. When they made their decisions they had reasons as to why they wanted to help the particular people that they chose and were really into it. It made me really proud of them- it's how community service is how to feel.

Stop Sitting in Your Desk, Get up and Draw It!

No one, myself included, has ever labeled me as a conventional teacher. I try as hard as possible to do things differently in my math classroom because I hate math lectures as much as any of my students do. Now of course sometimes they are necessary- it is statistically very unlikely that my students would be able to derive the quadratic formula without me simply lecturing on it. That said, with geometry you can do a lot of hands-on activities if you just think creatively.

I think that's the reason why I love teaching geometry so much because it is an entirely visual math. Not only do you look at pictures and diagrams with every problem, but you can really dive into visual aspects of real life with almost every chapter. Today was one of those days in geometry- it was so fun!

We just started chapter 6 which is all about similar polygons. Similarity is something that we see everyday in our lives (think blue prints, maps, etc.) but don't really notice all the time. So instead of speeding through the beginning of the chapter which just introduces the concepts, I decided to take an extra day to do some scale drawings in my class. Why continue to have my students sit in their desks when they could grab a tape measure and start drawing them to scale?

I watched all my students crawling on the floor and measuring all of the nooks and crannies of their terribly small Taiwanese desks. It was awesome to see students who normally sleep through first hour actively arguing with the student next to them as to whether the top of the desk was 41 cm. wide or 42 cm. I'm also a big fan of having them figure it out for themselves so I generally stay out of arguments like that: they finally settled on 41.5 cm. which I thought was an excellent compromise.

It's exciting as a teacher to see students use the math that we learn in class right in front of your eyes. It is also my firm belief that speeding through the book just to get to the end is a terrible way to teach students- what will they remember from that? It is my hope that even if my students remember almost none of the formulas I teach them this year, they will at least remember how to draw something to scale. I think that's more practical anyway.

Shrimp Fishing in Taiwan

There is a Taiwanese phenomenon where people gather around swimming pools stocked with shrimp and "fish" for them. You see these shrimp fishing places all over in Taiwan, and some people are crazy about it. In reality, I think it's just a good excuse to drink and hang out with your buddies while catching delicious crustaceans. Because in the end, you get to cook whatever you catch right there- score!

A lot of my coworkers and I have been very curious about shrimping (what we call the process of fishing for shrimp in these confined indoor pools) for a while now. So we enlisted the help of two of our amazing office secretaries to help us experience this truly Taiwanese tradition.

I cannot even describe to you how bizarre it is! We went to one that was pretty small so you sit around this swimming pool basically with a line in the water and wait for the shrimp at the bottom of the pool to nibble. Then you yank them out! True to form we did drink some beers and had some great conversations, so I would label it a success. We also managed to bring in quite the haul of shrimp to eat at the end of the night- I caught two myself! And most importantly, we got to spend some time with our lovely secretaries outside of school which was possibly the most fun part of it all.

I have obviously fished for actual fish before, but never a shrimp. I didn't really know if they would respond to my normal techniques!

Our secretaries/shrimp-fishing-guides for the night- Sindy and Elysa.

We worked hard for these shrimp, we deserved to roll them in salt and cook them on the spot!

The whole (motley) crew

Rainy Commute

There are clear advantages to living off-campus, I have written an extensive blog post on it even. However, when your only means of transportation is a scooter, things get a little hairy on rainy days...or I guess I should say wet.

I love my scooter, I do, but it lacks a roof and windows. My helmet is quite large and has a visor, but on days when it is really raining you get wet. I walk into my classroom and sort of shake like a dog on those days.

This week has been rainy every single day thus far. Monday, Tuesday, Wednesday, Thursday. I am keeping my fingers crossed for Friday as of right now, but listening to the constant pitter patter of rain outside at 5 p.m. on Thursday evening, I am not hopeful.

The only good thing about this is that I live in Taiwan and everyone has to deal with this issue. So the Taiwanese have come up with a brilliant solution: full body rain slickers that can cover a king sized bed if necessary. Now the picture you see is clearly not me, and unfortunately I don't have quite the Cadillac of rain covers like that, but it looks similar. Mine is big and baggy like that and goes down to my knees. I wear my backpack underneath so I look like a hunch back when I'm driving. It is really funny looking but I am never alone on the road wearing one!

Jolly Rancher Mania

It is no lie that candy in America is much higher in sugar than most of the rest of the world. Whenever I get any sort of candy made in Taiwan or other part of Asia, I can tell the difference right away. After living here for over a year now, I sort of like the less intense sweet taste- especially since eating some candy from the U.S. feels like it's melting your teeth as you consume it.

It is also a universal truth that all children love sugar. So all of our students are of course, no exception. They grew up eating the Asian candy that has a much lower sugar content (and probably lower levels of artificial dyes and sweeteners as well), so when they have American candy they sort of freak out a little bit.

I tend to have an almost constant supply of Jolly Ranchers in my classroom so I can win the teacher popularity test (thanks Mom for sending them in packages always!). There isn't actually a contest like that, but it is fun to bribe the kids with candy sometimes. And the students treat them like they are pure crack cocaine. It is funny but somewhat alarming at times.

Take today, for example. I accidentally mentioned to one 8th grade student that I would give her a Jolly Rancher if she visited me in my classroom and told me her favorite prime number. Before I knew it, there was a pack of children in my room yelling out numbers, not always prime, and just a constant demand of "We want candy!"

It was hilarious for the first five minutes and then I had to start getting brutal. Some of the older students couldn't simply tell me their favorite prime number for the goods, I made one of them tell me the four congruence theorems for triangles because I taught him geometry last year. I made another student solve an SAT math problem to get the sugary treat and simply made another say that math was their favorite subject. It was pretty fun even if it was sort of a loud headache for about ten minutes.

Although it gives me a good chuckle to watch them freak out over the candy, it does concern me somewhat. What are American candy companies putting into their products to make them so addictive and desirable? Can we get some of that for learning math?

New Tea and New Words

At lunch everyday, I try to spark up conversation that will involve all of my advisees. I have five kids and they all have their own interests and hobbies. So I tend to talk about myself and let them make comments/judgements- it works great!

Yesterday at lunch we were discussing tea. I was explaining my love of bubble tea and jasmine milk tea and really any other type of tea. Then they were telling me to try all of these other types of tea I should try. They suggested I try a chocolate milk tea with oatmeal in it. I thought it sounded strange and really gross, but I was curious, so I asked them how to say it in Chinese.

That was the moment I learned the coolest name in Chinese: Ke Ke Pow Pow! The best part about the name of this tea is that the "pow pow" at the end is said in the fourth tone which is down. You basically say "pow pow" like you're angry or perhaps shooting a toy gun. It is so fun! I went around school for the rest of the day asking kids if they likes that tea and for the most part, they just laughed at me.

To make things better, Vivi and ReRe, my two advisees in support of me trying Ke Ke Pow Pow, decided it was time for me to taste it. So last night when they were making a tea order for themselves and some other girls on campus, they ordered me one too. While sitting in the library on duty, I got to sip on some Ke Ke Pow Pow from 7-9 last night. I can't say that it is my favorite tea to drink, but I think it is my new favorite to say!

Oh No, I Didn't Mean to Offend!

There are times when I think to myself, "I am so cultured and sensitive to the feelings of other people!" and then there are times when I think "Wow, I sound like a racist right now!" Even living and working in Asia for over a year now, I still have quite a few of the second type of thoughts on a daily basis. I think that's sort of human nature, especially when you live in a culture so completely unlike your own. It is fairly normal to observe the differences you see and sometimes you react to things without thinking. Guilty as charged.

Yesterday I went to get a pedicure at a new place that I've never been to before. I had stopped in the day before to ask about price and appointment availability and talked to the owner/only employee (it was a super small place). She was really nice and even spoke quite a bit of English which always makes things easier.

When I walked in yesterday, I saw an Asian woman standing there so I dove right into this rant:

"Hi! I stopped in yesterday, you said you would maybe have time at 4 today? Is that still ok? I just need a pedicure..."

She sort of blankly looked at me, which of course made me nervous, so I kept going with more exaggerated arm flapping and pantomiming my words:

"It's ok if you don't have time, I live right around the corner so it's no big deal. Tomorrow? Some other time this week? Whenever, I can make it work..."

She must have realized what was going on at this point because she responded to my crazy ramblings in perfect English:

"Oh, ya I don't work here, I'm just another customer. Do you want me to call her? I think she's in the back."

I had no idea it was not the woman I had talked to the previous day! They were the same age approximately, same length hair, and I even thought their faces were very similar. I had made the classic "all Asians look the same" stereotype mistake in person and the woman (who didn't work at the nail place) looked mildly offended. There was literally nothing I could do to make the situation better. I felt really bad.

My nail salon racist moment is actually pretty funny because I am awesome at telling all of our students apart. I listen to some of the new teachers confusedly try to separate them in their minds and I silently mock them- how could they get Sam and Benson confused? They so clearly look different! And Angel and Tina? Really? They don't even look like they could be cousins!

Now I just have to eat my words. I guess a valuable lesson was learned: perhaps survey a room a little better before opening your mouth. Or maybe ask simple questions first, like "Are you the lady I talked to yesterday?" Oh, next time. Next time I'll try to make less of a fool of myself.