Goodbye, Expat Life; Hello, Repat Life?

As I type, I am sitting in Geoff's hometown in NJ. We're en route from Berlin to Seattle, stopping over just long enough on the East Coast to attend a wedding. It has been my first real break since January. The first time that I have had real time off, not thinking about wedding or work or looking for work or moving logistics. And the sun is beaming beautifully outside; even the sweltering tri-state humidity cannot begin to bother me when I am sleeping 12 hours a day. I am spending most of my time just hanging out with the in-laws in Jersey, but am also idly looking up friends in NYC during the week. During the coming weekend, Geoff and I will be visiting the Museum of Math, as well as catching the "new" musical Once. Although I love New York, I cannot help but feel relieved that we don't live there anymore. The city is a total wallet-zapper!

On a more personal note, things have been pretty rough at home, since my mom has been in the hospital for a couple of weeks now, and Geoff's parents have had health scares of their own recently. I think this is the start of an era -- the years when we feel lucky whenever our parents get over a scary episode of something without it becoming life-threatening; it's no longer the norm that our parents get sick and they would get better. It's scary, and we're still waiting for biopsy results to see whether my mom will get lucky this time. I really hope so, but as my mom has already said, if it's not this and not this time (that becomes life-threatening), then it will be something else at another time. That realization has hit me very hard lately, and I don't know how to navigate through my web of feelings about it. I think grief is a very selfish thing, because as soon as you start to dwell on your own grief, you're already prioritizing your own fears and needs over the tremendous needs of the person who is actually ill. So I have tried to keep everything latent, because I don't know when my mom will need that extra boost of positivity from me. The wait for diagnosis has been agonizing, but I keep reminding myself that it is 10 times more difficult for my mom than it is for the rest of us. It helps to keep other things in perspective.

So, it was with a heavy heart that I had said goodbye to Berlin. Amidst all the furniture-selling, packing, cleaning, painting, paperwork logistics, and long-distance phone calls to Shanghai, the time simply flew. There are many things that I could say about Berlin, but most of all, I will remember the wonderful friends that we've made there. Although it was quite random that Geoff and I ended up there, we were fortunate to experience the city on its way to becoming -- truly -- one of the greatest cities in the world. When I think back about my two years there, I will always remember how charming the neighborhoods were, with their parks, biergartens, craft and flea markets, and slowly savored Sunday brunches. The city can throw a helluva open-air party, or two or three. And I've never been in any other city where the train is habitually still packed to standing-room at 5am, with a diversity of languages to rival that of NYC.

So long, Berlin! Thanks for all the wonderful memories. I wish that there was more time, and that the goodbye wasn't quite so hasty and so distracted, but I am sure that we will visit again soon.

PS. Next year, I will be teaching Algebra 2, Precalculus, and Calculus. To keep myself from being overly lazy all summer, I plan to do some Calculus planning starting in late July or early August. Any resources that you can point me at would be awesome!

PPS. On a different note, if you visit Germany at any point as a tourist, I highly recommend talking to the locals and going to a traditional German sauna to try their Aufguss experience. It's not to be missed! The experience is so exclusively German that you can hardly find any English info about it on the web, and the descriptions that you do find do not adequately describe it...

New Things to Try This Year

I decided this year that I should really put some effort into maintaining my portal page so that I can live by example to show that it can be a useful tool for our department. The initial tinkering was really hairy, because our school uses a free portal software that is quite user-unfriendly, but after a bit of emails back and forth with THE portal lady, I've managed to get all five of my classes up and running with a basic title, an announcements section, and a document section. YAY!

I plan to use this extensively this year, especially because of the printing quota situation. (My friend who used to give me her extra printing quota, is no longer working at our school this year, and anyway I feel that it's too early in the year for me to be begging for copies.) I think it would also provide transparency for parents whose children have special learning needs. So, here we go. All lessons go up on the portal upon finishing the planning, and homework will be posted as well, along with additional resources such as mixed IB practice sets, which I will no longer print out for my whole class. I am still offering lunch-time review sessions this year for my Grade 12 IB students, but I will expect those in attendance to have already printed out and completed the packets on their own prior to coming to see me at lunch, so that I can really focus on helping to address their remaining issues instead of just waiting around for them to try problems.

From a department head's perspective (I am just rambling now), the hierarchical organization of the portal pages is important as well, and our department should align with the other departments' organization of their pages, for example. Fortunately, my colleague had already done some planning with regards to this. Right now, my goal is to just focus on my own pages, and once I get mine really up and running, I will be able to do a demo for my colleagues and to serve as their in-house technical go-to person, should they need some help with customizing their pages. (As it is not always so easy to get in touch with portal people at a moment's notice, with them being in the basement of a different building and us being on the top floor of ours.)

Another thing I am trying with my new "low" Grade 9 group this year is a system of modeling how to take notes. I will, for once, produce my own hand-written notes in advance, word for word, so that I know exactly what they should write down. The notes will be in a two-column format and they will cut a thin incision in the piece of paper and fold half of it back, so that they can use it as a flashcard / non-fancy foldable down the road. I am asking all kids in that class to maintain a binder for me, and the notes I ask them to take will have both bulleted key points (for the verbal learners) and diagrams (for the visual learners), along with the foldable portion (for the more drill-focused learners) and of course worksheets to help solidify and apply the concepts. This will not replace my typical scaffolded worksheets and projects, but it is a way of concretely reinforcing base building blocks for the kids who need that extra help with organizing information. If I am introducing a new concept, for example, we can do all the normal exploratory stuff and then come back to the notes as a whole-class wrap-up discussion. In the long run, I think it will be a superb addition to my overall teaching, but I am starting with this class just to try it out. Anyway, I met my group for the first time today and they were great! I gave them a little chat about our hopes for them to catch up on all the algebra concepts (by lessening the amount of "traditional" geometry I will teach to them this year and replacing it with more focused algebra reinforcement), to assuage their anxiety about being in the "low" class. We will see how it goes this year. I know that, as always, it will probably be challenging (as a starting point, many of these Grade 9's cannot plot given coordinates (x, y) after the summer, as I had feared might be the case...), but I hope that this year will go even better than last year's group, and that I will manage to get more of them caught up by the end of the year!!

Also, it looks like I will be teaching integer operations this year. Any good ideas?? I've never done this before, but I want to start with elevator word problems and then work our way to simple addition / subtraction statements. For multiplication and division, should I use a number line model to explain why there are "rules" like (-)(-) = (+)?? Anything you can send me would be super, and if I change parts of it, I'll re-post to give back to the community. :) xoxx

PS. In a recent middle-school PD, I realized that I am an impulsive do-er as a teacher (and more or less in life in general). These little changes I am trying are not very well-thought out, but I tend to go with the first potential thing I am excited about, and then later learn from my mistakes. Are you like this, too??

China!

I just got back from an amazing school trip to China. We went to Beijing, toured around for about 3.5 days, and then headed over to Shanghai for about 6 days. The kids had a very authentic experience -- in Beijing we were greeted by a partner school that did all kinds of performances as part of their welcome ceremony, and they also took us to one of their students' houses to show the kids how to make traditional northern dumplings. We ate a feast in that three-generation family's courtyard and the kids and the adults from the school sang spontaneously to entertain us, showing true Chinese hospitality in a way that you could not have explained to the kids in words beforehand. In Shanghai, our students stayed in host families -- an even more authentic experience. During the day, they went to classes with their host students in the morning (at a public middle school in Shanghai, with 60 kids and one teacher per class), and in the afternoons there were special activities planned for them, such as calligraphy class and traditional seal-cutting class. It was really neat; they really had a hard time picking out a favorite memory afterwards, because everything was so different. The teachers were wined and dined by the school as well, and even at the end, we enjoyed a spectacular performance of traditional instruments at our send-off party by this Shanghai school. The Shanghai school also had a plethora of extracurricular activities, such as Chinese orchestra (of traditional instruments), traditional Chinese opera (taught by a professional opera singer), and an English(!) drama class for 6th-graders, taught by an American! We got to see all of this in action, and our kids even got to participate in their Cinderella play-reading along with the Chinese students. Needless to say, it was a really unique and interesting experience!

For me, even though I had been to both Beijing and Shanghai before, this trip was a special experience. In Beijing, we had a fabulous guide who knew all the histories of the dynasties and leading up to the fairly recent introduction of communism in China. He was fabulous and truly an amazing character -- the kids wanted to take him with us to Shanghai! If you or your friends/family go to Shanghai, I would highly recommend looking this guide up well in advance (he books up quickly, sometimes months in advance); his name is Xiao Wei and you can reach him at weiyilun123 AT 126 DOT com.

In Shanghai, because I was there with 3 colleagues who were great fun, we went out one night and had a great time in the city. We had dinner on the Huangpu river, and then we went up to the top of one of the super posh hotels (costing around 1000 Euros a night) and had a drink at the top while overlooking the entire city. At 10pm, the city shuts down its lights to save energy, and we were there at the top while the blackout happened. It was really spectacular and special!

I also met up with my parents a few times during my stay in Shanghai, which was really awesome. They took me out to eat at one of the "famous" soup dumpling places that they had learned about from watching food programs on TV; for 35 very delicious soup dumplings and a bowl of noodles, we only paid a total of 38RMB for the three of us! (That is about 5 Euros total.) Amazing!

Another thing that made the trip special was to go to China with colleagues who had grown up in East Germany. A lot of the nuances which would have gone unnoticed by me (such as how certain people have power in the schools because they have shown loyalty to the party), did not go undetected by them. For example, did you know that in every school in China there is a special "Party Secretary" whose job is to ensure that the school does not speak or act in a way that is out of line with party politics? To hear the other teachers point out certain things and to also hear them speak of their own experiences back before the Berlin Wall came down, was fascinating for me and a great learning experience.

On the students' side, everything was pretty fabulous. In the beginning, we had some minor issues of lack of sensitivity towards the host culture, but by the end, the kids had seen and experienced so much kindness that they themselves were extremely grateful and gracious towards their host families. It was truly a cultural lesson you could not have brought to your school or taught in a vacuum.

And now, counting down till the end of school!

PS. I would have loooved to post some more photos from the trip, but I need to abide by school policy to not post student photos! Bummer... We even took some neat videos.

Thoughts About Cultural Sensitivity

A recent incident has stirred up some feelings for me regarding cultural sensitivity in schools. As a teacher, generally I feel responsible for the character education of all of my students, so whenever an occasion arises -- in class or otherwise -- where I see that someone is being offensive or hurtful to others (for whatever reason), I address it firmly and make sure I send out a message that that type of behavior is absolutely unacceptable.

As a person of proud Asian descent, I am particularly bothered on a personal level when I see actions around the school setting, that stereotype and/or demean Asian people. But, countering this is not always so easy, especially because in many cultures besides in America (surely in German as well as Salvadoran cultures), there is much less cultural sensitivity in general. I have heard a colleague say things to me that would be considered highly offensive if said in the States, even in private, much less in a professional environment. As a teacher in El Salvador, you live with the reality that one boy out of at least each class is nicknamed "(el) Chino" because they have slanted or small eyes. One "Chino" from my Precalculus class was a blond boy; the nickname was not meant to be hurtful or disparaging. Other culturally "acceptable" nicknames are "(el) Gordo" (the fat one), "(el) Chele" (the pale one), etc. Totally unacceptable in the States but totally common-place in Latin America.

So, the line becomes gray in other cultures. --Or does it?

That is what I have been thinking about the last few days, since I had to deal with a kid who repeatedly put offensive images about Chinese people on a slideshow that he was trying to put together about China. As it turns out, neither the boy's mom nor the other colleague involved in the incident thought the pictures were so bad. (The images made fun of how Chinese people eat cats and dogs, and also had bad English phrases on them like "Sum Ting Wong?") The pictures were so offensive to me that I had to delete them off of my desktop immediately after sending them along to another adult, so that I could get rid of the negative feeling that the images caused me. When my colleague saw the pictures, their first reaction -- in my presence -- was to laugh. Is it my job to educate them? Where does my role as an outsider fit in, in terms of pushing back on these cultural sensitivity issues?

On a semi-related note, recently, an acquaintance mentioned on Facebook that she received a letter from her bank with a Chinese card tucked inside. She was offended, because she's actually Vietnamese. From an outsider's perspective, maybe you would think she overreacted, but unless you are from a country that constantly gets lumped into another country's ethnic group, you cannot begin to understand how she feels. (Her last name is Nguyen, by the way. That is the most common Vietnamese last name. The person at her bank who made this Asian publicity stunt needs to feel bad; that is like addressing a Kenny or O'Connor and saying they are Swiss.)

So, this is what I know: Racism is real, and it is hurtful. Whether or not a person is actually racist, their behavior and choices speak volumes for them. If we do not educate our children about what is acceptable and culturally sensitive, then they will grow up to be adults who help to propogate harmful racial stereotypes.

So, again, my question is: What is my role as an educator to help to stop this? Does my role change in an international setting? If you have thoughts, please feel free to add them. Otherwise, this is something I guess I'll have to figure out for myself, because it is important and worth thinking about.

An Epic Week

This week has been epic. It was a week when I tried to do something for everyone. It was my last week with my Grade 12 IB students (since the next two weeks will be Spring Break, and after that I'll be absent from school for a week to chaperone a trip to China, and after that they go on a week of "study leave" before the IB exams); my last week teaching material to Grade 11 students before their semester exams; and the week that my MS principal and I looked through and picked two Grade 7 buttons business plans to invest money into. All of my 7th-, 8th- and 9th- graders had to come to a conceptual stopping point before vacation AND they had to be sufficiently solid in the new concepts that they could do independent practice/review without me, during my week-long absence after the break. It was a week when I promised to draft up 3 different semester exams so that I could help my colleagues agree on final exam content and dates for three different grades, so that I could send my own students off on their Spring Break with all of the necessary studying information. This week, as a Grade 12 team, we had to send in audited samples of graded student portfolios to the IB Organization, and internally, we had to submit estimated IB grades for the 12th-graders. This week, I finished babysitting/monitoring the enrichment research projects for the kids who are going to China with us, and they successfully presented their projects to their parents at the last trip meeting during Monday evening.

In the end, the week was smooth, without a hitch. It has wound down beautifully, and even though I am running on 5 hours of sleep today (went dancing yesterday), I feel very satisfied with what I was able to accomplish during this week.

And, oh boy, am I ready for Spring Break! I am looking forward to being in the States for a week, followed by being in Beijing and Shanghai (while chaperoning students) for 10 days and SEEING MY PARENTS!!! and eating some yummy soup dumplings. And when I come back, it'll only be a short sprint (punctured by another whole-school field-trip week and various holidays) until the end of the school year!!

Responding to Student Needs

I've been slowly reading Lost at School as part of a professional book club at work. Honestly, I don't think much of the book is ground-breaking stuff, but it's a nice common-sense teaching book to spark some common-sense teaching discussions. It provides a good focal point at work for discussions about what is important to all of us, rather than discussions about our individual concerns.

Here is a quote that I liked that helps me view my current experience through a different lens:

Good teaching means being responsive to the hand you've been dealt.

It goes without saying that each group of kids is different. The task with each group is to get a handle on its collective strengths and limitations and work toward building a community where each member feels safe, respected, and valued. But that takes time and concentrated effort. It doesn't happen by itself. And it looks different every year. That's what it means to be responsive.

It also goes without saying that every individual in a classroom is different. [...] The ultimate challenge is to be responsive in both ways -- to the group and to the individuals in it -- simultaneously.

I think this really nicely outlines all of the things that are on my mind constantly, as I struggle to grow into being a "good" teacher for my kids.

* My Grade 7's have a few lagging performers who haven't yet figured out that math is important and they need to come see me outside of class for help, so (in response) I weave all of their review of past topics that they're still weak with into our normal class. Every test is cumulative and hits every past topic, and we review accordingly beforehand. I also send daily emails home to let parents know when their kids miss an assignment. And, once every few weeks we play a game that reviews an old skill that I want them to fully master.

* My Grade 8's are a bimodal group, so I need to balance between keeping the really advanced kids challenged and giving the strugglers time to work on their factoring skills when the leading coefficient isn't 1. I do so by introducing every factoring tool possible (looking at graphs & using quadratic formula), and also giving the top-top kids extra graphing calculator assignments to work on independently.

* My Grade 9's are the lowest group in the grade, so there are kids in the group with serious language issues, others with no mathematical memory past the current day, and a few kids who are working very hard to bridge the gap of their learning. I need to provide tasks that are accessible to all kids and allow them to work at their individual paces, and I give them free reign to correcting/re-doing all old assignments as many times as they want. Frequent assessment with clear skills expectations is key to making sure all kids are given regular feedback, and I've met half of their parents already to discuss my concerns about the kids.

* My Grade 11's are a mixture of returning kids and new kids to the school. The returning kids are much more experienced with the first topics of the year, but to ensure that all kids have a fair shot at the IB exam, I'm teaching them all from scratch to make sure the new kids get proper training. Again, it's a balance act of approaching the topic from many angles to ensure that the returning kids are challenged and enriched and pushing the new kids along with some urgency to make sure they do a bit of extra homework to keep moving at the same pace as the others. In the longer run, I've worked out with a colleague that she can transfer the kids who need a bit more nurturing into my group, in exchange for moving kids who wouldn't mind/could handle moving at a much faster pace into hers. We're both happy with that arrangement and think it will maximize the benefit to all kids.

* My Grade 12's have a lot of gaps in their knowledge. They basically don't know/remember anything they are supposed to know from Year 11, and so I've been interleaving as much of old material as possible into current topics to help them review. I know that in the spring, I will have to do some very heavy-duty concept-mapping and explicit learning strategies like algorithm flashcards to get them familiar with the basic concepts of each topic, before we can start doing integrated review and test prep. I am prepared to make that happen and I have a plan for how to help them be successful. (It'll involve topic-based worksheets / individual tests when they're ready / moving on to individually review the next topic when both they and I agree they've mastered the basic ones, or repeating the cycle until they do improve.)

It's stretching me professionally to consider the various academic and emotional needs of my many groups and to attempt to address individual needs within each group. But, I am loving the challenge! :)

(...Now, if only someone could tell me if it's having any actual effect on the kids...)

Integrity Brain Dump

I've been reflecting extensively about integrity, because this year I am really trying to do a better job with the character education program I am teaching as part of the Grade 8 homeroom. Already I've talked to the homeroom kids about: appreciation as a tool to smoothing over difficult confrontations; manners and cultures; why we come to school (and why that's a privilege); the idea that our intelligence is not fixed, and that our knowledge can improve our brain's processes and in effect we can "get smarter" over time; setting goals and brainstorming study skills. I have found that by opening my own life experiences up to the kids, I am making the textbook lessons more meaningful for me (and thereby, hopefully for them as well). Every week, I try to tie the lesson to something a little bit deeper, and the kids have reciprocated by opening up with their own thoughts and experiences as well, allowing me a sneak peek at their thoughtful and insightful side, which I don't always see in the context of a math class.

Something that has been on my mind (although not necessarily in the Grade 8 character-development curriculum) has been the issue of integrity. The more I think about it, the more integrity seems to weave itself into everything that we do, which means both that it's necessary for me to talk about integrity issues with the kids, and also that it is very difficult to get a clear, convincing, effective message across in a single discussion. I am going to do a brain dump over here; feel free to add your own thoughts.

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When we think about integrity, we mostly think of not lying and not cheating. In school, we only talk about integrity as a reactionary mechanism -- usually after something bad has already occurred, such as group cheating or plagiarism. What we need to do is to actively address integrity issues as a school as a prevention mechanism -- and that can be done in our individual curricula (ie. history and English, where morality is explored in the context of literature), or in our character-education classes.

The first stumbling block I have is how to talk to kids in a convincing way about the importance of integrity. Why should they bother not doing certain things, if they know that they cannot or probably will not be caught?? I think we are dissuaded from negative behavior for any number of these reasons below (depending on our own morality developmental stage):

* Being worried about consequences (ie. punishment) that may occur to us personally
* Upholding our reputation (another form of personal consequence)
* Being afraid to hurt or damage others who trust us
* Believing that our individual needs should come after our commitment or obligation to a group/policy/community (Relativistic morals?)
* Believing that the action is wrong on an absolute scale

As you probably agree, our aim to talk to kids about integrity is roughly equivalent to moving them along the spectrum of reasons towards the intrinsic motivators rather than the extrinsic motivators. But, doing so is difficult. The best that I can come up with is talking to kids about my own view of my own personal integrity, in order to shed light on what it means to me, personally. (I grew up in a family that raised us on stories that carried inherent values, but I'm not sure if my kids have the same relationship with their parents.)

So, here are some examples I've come up with for where I think I exhibit a personal integrity, in a way that is perhaps subtler than not cheating and not lying:

My integrity is reflected in the way I work at my jobs. When I was 17, I had my first job evaluation by my Starbucks store manager. I was nervous, and I had asked my friend if he was nervous as well. This is what he said: "I always do my best on a job, whether or not someone is watching me. And in the end, that's all I can do. There is no reason to worry." I still carry that work ethic with me today. I don't ever compare myself with other teachers in my department; I need to do my best within my own frame of possibilities. Over time, that frame will expand. So, it doesn't matter if someone is years more experienced than me or if they choose to leave at 3pm; what matters to me is that I do my very best every single day for every kid in my class, within my own realm of possibilities. Furthermore, I don't ever worry about whether I've earned my place at work, because I've never lied or cheated on any test, project, resume, or interview to get there.

My personal integrity also means to me that if there is a legitimate way to get something done, that's what I'll do even if that means my life will probably be made a bit harder. I remembered today an incident where I went to a supervisor asking for a day off after months of not taking a single day off -- there had been days when I was so sick that I could not stand up, and still I had shown up to work. The supervisor told me no, that I couldn't have this day off to go to my friend's wedding, even though I was requesting it far in advance. I was really upset, but even then I refused to call in sick that day. My personal integrity means that I need to represent what is true, even if that truth would inconvenience me.

When we put ourselves in the shoes of a hiring manager, it's clear why integrity is important. Whom would you rather hire -- a conniving employee who might lie about their results, or an employee who would own up to their mistakes and reflect upon them with others? For the same reasons, we prefer our politicians to have integrity, because so much goes on behind closed doors in politics that we have to be able to trust them (at least a little). When the situation is gray legally but not ethically so, we can only hope collectively that those in charge (such as the bankers giving out mortagages) are doing their part to ensure that the interest of the larger community is protected. Integrity, therefore, is clearly something that we value as a community.

When does a kid encounter integrity issues? All the time, I bet. Inside and outside of school, I bet. Imagine a kid whose parents want him to go home early, while the temptation is to hang out late with his friends. He can either: 1. stay out and then make up an excuse afterwards, 2. go home and then sneak out, 3. try to reason with his parents to get a later curfew, but going home at the promised time, even if it's early. Which is the least pleasant but the most honest option for a kid? Probably #3. In situations big and small, whether or not they even give it a second thought, they are constantly being confronted with choices and reinforcing their own integrity, or the lack thereof.

So far, these are all just my thoughts. I am giving an anonymous survey next week in my homeroom and I'll be tallying the opinions to get a feel for what kids consider to be cheating behavior, whether that definition is tied to the outcome (ie. if they successfully cheated or not), and what they think are the most important factors that discourage them from certain types of behavior. From those surveyed results I'll plan some discussion points and go about it, leaving much of it open-ended to hear what the kids have to say about the issue.

The point is that I want to open the door for more proactive conversation about integrity and less reactive conversation. Thoughts? Ideas??

Addendum 10/14/2011: In case you are interested, here is the survey I am going to pass out.

Day 2!

This year has been very interesting so far, and today was only Day 2. Teaching 5 grades at once is a wild experience; in the first 1.5 days I've simultaneously:

* Taught matrix multiplication through application to weighted class averages (Grade 12)

* Reviewed fraction models, comparison of fractions/decimals, and what types of things can be modeled with fractions through stations work (Grade 7)

* Run a paired "blind drawing" activity to teach basic geometry vocabulary -- points, lines, planes, parallel, intersect, collinear, coplanar, etc -- and to practice visualization from words. (Grade 9)

* Started a "Savings Race" algebra task involving comparing/relating multiple representations (Grade 9)

* Used a border-of-square-pool rich task to introduce patterns, generalization through algebra, and re-arrangement of equations (Grade 8)

* Umm, and I haven't even seen my 11th-graders yet!! Tomorrow'll be the first day. On the agenda is looking at a rich patterns task and moving them through it to generate linear functions and to start to look at how to generate quadratic functions from a table of values.

(What's been the most challenging about this is that most of this was material I had to create from scratch without previous lesson plans to fall back onto, and I think that's going to be the norm for this year.)

As it turns out, I have two kids who don't speak ANY English, and that's going to be a real challenge/interesting experience this year, I think. I'm going to need to do drastic modification for them, like asking them to bring bilingual dictionaries to class, keeping a vocabulary journal, and I will be pumping all the assignments through a Google translator for them to have two copies, one in English and one in (crappy translation of) their native language. It helps that I will have a push-in language assistant, so I'm going to do everything I can to make sure we work together to help these kids.

Craziness. I'm a bit stressed, you know, as might be expected with the big change. But it's good. Today I had a really productive day with every group, and it felt great. Let's hope tomorrow's a good day! :)

...Did I mention that our school does not have bells? We expect kids to get to class on time based on a culture of respect for the schedule and the class. They've been doing this for about 7 or so years now. It's still early in the year for me, but I think it actually works! Amazing.

Changes for the New Year!

One of the reasons why I love being a teacher is that each school year offers a fresh start -- a chance to do it better. Over the summer, I had an opportunity to listen to a lot of great speakers and to figure out for myself what changes I would like to introduce this year. Some of the things they said were not new; I had heard it all once in grad school, and had even read some of the same articles before. But, back then, I was in my first or second year of teaching and everything was about survival. I did not have the luxury of thinking about how giving a 5-second wait time can make a world of difference in my class. I needed to put out fires and to make sure that kids were doing thoughtful assignments and that the unit was cohesive and that kids were learning good habits from me and that the problems are scaffolded appropriately.

I think that as a slightly less newbie teacher now (I still feel very green, now going into my 6th year), I am at a different place in my career and my PD. I am fortunate to have had some great mentors along the way and some great resources for working on developing lessons that have worked out OK for me and the kids. Now I need to focus on my classroom craft, on how I ask questions, on building a better relationship with kids, on making sure that every kid is thinking hard every moment of the class, not only about the content but about themselves as people and as learners. Those are the bigger things I want to try to address this year -- hopefully by implementing "small" changes with big impacts.

So, I have in mind some things I want to do (they're not all such small changes, but I think they're manageable!):

* I am going to ask my new math colleagues to observe my teaching, and I am going to ask them right at the beginning of the year, before I have an opportunity to chicken out. I am going to schedule a teacher once every week in the beginning, and to ask them to observe me on a specific classroom goal I am trying to work on. For example, one of my classroom goals this year is to increase wait time and to facilitate effective whole-class discussions. I am going to ask my colleague to give me feedback specific to that, and also general feedback on the class and the lesson. Then, a couple of weeks later, I will ask a different colleague to come in, observe me on my wait time, and also to observe me on whether I am asking open-ended, exploratory questions and letting kids come to their own conclusions without me being The Authority. Then, a few weeks later, I'll ask a third colleague to come in and observe me on open-ended questioning and also how my kids are doing with meta-cognition. Eventually (ie. Semester 2??), I'll work my way to the bigger evaluation criteria, like the ones outlined in our rubric for mathematical practices.

Why am I doing this? It's two folds: 1. Obviously, as I have said, I want to get better at my classroom craft, and I know that having someone else in the room will help remind me that I'm supposed to be working on that actively. 2. I feel that it would be a great way to bond with my new colleagues and to show them by example that I value their input. Hopefully this will also open doors to talking about what we are doing in our classrooms, and hopefully if my colleagues see that I am comfortable asking for their direct feedback on my teaching, then they would feel comfortable down the road letting me observe their teaching as well.

* I am going to start a 4-people Critical Friends Group. At Klingenstein we rehearsed a protocol for reviewing lessons and/or a unit that you are struggling with. What I liked most about the protocol was that it removed subjectivity as much as possible and helped the person who is receiving feedback feel protected and not judged (well, if you stick faithfully to the protocol, that is). It also fosters cross-curricular feedback and collaboration, since these CFGs are typically made up of people from different departments (another way this protocol ensures you remain the "expert" of your domain and your colleagues are minimally judgmental and mostly supportive). I have already gotten an OK from one of the administrators to put out an announcement to all the staffers at the start of the year, to find 3 volunteers who are willing to be guinea pigs with me for a cycle of 4 rounds during Q1. Each of us would bring in something to share with the group -- something that we are genuinely struggling with and would like support/feedback on. If at the end of Q1 they all hate it, I'll ask for new volunteers and start a different group. If they like it, I'll break it into more groups and have them each facilitate a new group to help the idea grow at the school.

Why am I doing this? It's a way of taking PD into my own hands and to make sure (like this blog and general blog-reading does) that I am having quality reflections on teaching throughout the year.

* I am starting a new system for homework. It's a balance between letting kids have optional homework assignments but still using homework effectively as assessment tools. For each homework assignment, I am going to assign problems in all the following categories:

A: Self-assessment (You are expected to do this and make sure you can get the correct answer as provided. Show all work!)
B: Optional practice (If A was not completely straight forward, you should do these and check answers against those provided.)
C: Extension (Here's what's coming soon... TRY IT and let me see how far you get. Show all work!)
D: Teacher assessment (I want to see how many of you can get this correct. We're shooting for 100% on this! We'll review answers tomorrow in class.)

Why am I doing this? I agree with the SBG folks that kids should not be forced to do "busy" homework if they already get something, but I disagree that kids always know when they need that extra practice. I am going to make it explicit for them by providing homework solutions for all the problems (except the Extension and Teacher Assessment problems), and they can stop when they feel like they really get it with ease. The extension problems get kids to be used to working with/examining problems just beyond their reach. Teacher assessment is something I can have kids quickly write down numeric answers to on a sheet of paper (or hold up a whiteboard) at the start of class for me to assess where the class stands. This keeps homework meaningful for all of us.

* I am going to do weekly student feedback cards so that I can get ongoing, "formative" feedback as well.

* Allot time for meta-cognition. I want to do this early and frequently, so that it becomes part of the kids' routine during class. I wrote a separate blog post about some strategies for implementing this back in July, but obviously it could be less sexy methods, too, like building it into a worksheet.

* Once or twice each unit, I am going to build in "hinge points" into a lesson. We learned about this at PCMI this year, and it's something I am really missing in my classes. I am not going to go crazy with this, but a couple of times each unit I do want to create a lesson that can "hinge" one way or another depending on my on-the-spot assessment of where the kids stand. This way, lessons are not always so linear from A to Z, without taking into account kids' reactions in real time.

* I want to be more patient. One of the most powerful lessons I learned at KSI was that kids are learning from you every second in your presence. Am I being the adult that I want them to grow up to be, every minute of everyday? That's such a powerful question and one that I am afraid to answer, because the responsibility of it all seems daunting. I am going to try harder than ever to be that model adult every moment, every day.

Over the course of the summer, I've thought a lot about this list of changes and I believe it's a good, manageable one. It's ambitious, but most of it (except CFG) are small things that I can implement without changing EVERYTHING I am already doing, which is important to me. Wish me luck!

End-of-Year Mini Reflection

To be frank, I did not enjoy the end of this school year. For some reason, towards the end of May a bunch of stuff happened that left a sour taste in my mouth. Like, plagiarism type of stuff. It made me feel sick in my stomach to know that cheating is so rampant at the school -- at all levels, honors and regular, and relatively few kids seem immune to it. It seems like lots of kids care overly much about their grades and think it's harmless to cheat occasionally, and lots of other kids who do value the actual learning still think that it's harmless to help their friends cheat once in a while.

This realization turned the year around for me, in a negative way. Instead of looking forward to my classes everyday, I walked in daily and felt like I was in the middle of strangers whom I couldn't trust, and I was just counting the days until it was over. Not a good feeling to end the year on, especially because I had felt all along that we were doing great projects and the kids were putting in a lot of effort. It just seemed like something had happened during the last two weeks of the school year, because all of a sudden my high-effort kids just dropped off and stopped studying, around the same time as the series of distressing and disappointing plagiarism incidents.

Thinking back, last year (2009-2010) at around the same time in late May, my bottom kids were staying with me once a week for extra help, and the rest of the class envied them as their test grades jumped up 20% from the beginning of the quarter to the end -- a reflection of their improved understanding, as a direct result of their efforts and perseverance. I remember feeling euphoric, like I knew the kids were ready to be sophomores and to take on additional responsibilities and challenges. This year? I am not so sure. What an awful feeling to end the year on.

...So, there I was, ready to go into the summer wondering about my own worth as a teacher. ("Maybe if I were a better teacher, my kids would not have ended the year with these negative choices. Clearly I messed up big somewhere to cause this..." type of thinking.) And yet, all of a sudden, kids started trickling in to thank me for having taught them and to say goodbye before I leave for Germany. Some of the kids I have not taught in a year. One girl whom I have taught now for two years wrote me a thank-you card that said, in short, that I have changed her relationship with math.

Then I was busy with packing and cleaning and closing accounts, so I did not have time to sort through my feelings about all of this. Until today.

Today was our last faculty meeting. During the meeting, the principal wanted us to go around and share what were the key uplifting moments for us this year. Mired still in my (I guess you could call it) anger and hurt about the plagiarism incidents, I had trouble recalling the highlights that made my year. And then two things came into mind. One of them was when my juniors in Precalculus started showing up to see me after school for help, sometime in Q3. Some weeks they would come once in a big group; other weeks they'd come one or two at a time, everyday. And how, a couple of months later, when the intercom announced that it was Teacher Appreciation Week, this class burst into spontaneous cheering and applause. For me! When I was not even looking at them. (I was writing something on the board at the time to take advantage of the morning announcement.) The other outstanding memory was the thank-you card that I had described above. I can't do it justice, so I took a picture of it to share with you why a single card had such an emotional impact on me.



Thinking -- I mean, really thinking and letting my emotions sink in -- about these two particular incidents during the meeting finally brought me out of the semi-depressed rut that I had been in for the past few weeks. I still have so much to learn and I want to be SO much of a better teacher in Germany than I was here, but maybe, in the end, this year itself wasn't all bad.

So, Prost! to a new beginning! This is the true blessing of a teacher: each year, we each get a fresh chance at getting it right. Or, at least, getting closer to getting it right.

Choices

This is the part of the year when I start to emphasize to students that every day, they're making choices towards their learning. During Quarter 1, I pretty much hand-held the freshmen through all quiz corrections. Every time a kid did poorly on a quiz, I emailed home and convinced their parents to talk them into staying after school for some remediation. Last year, there was a change sometime during the latter part of Q3 where kids started to be proactive on their own about their learning. I want that to happen sooner this year. Like this time, I told kids specifically if I thought they needed extra review time with me after school before the test. Most came, although a couple of the kids didn't come because of sports commitments or other things. I told those kids sternly that they're making a choice, and they have to understand that consequences follow their every choice. That way, if they don't end up doing too hot on the exam, it'll be a learning experience for them about making positive choices.

My First Presentation!

I did my first presentation ever! It was for my math department, and I ran it workshop-style, about the resources on the internet I use to help me plan my lessons. I split the time between letting the teachers experience some of the lesson ideas I've found and liked, and letting them dig through the links on Sam Shah's Virtual Filing Cabinet to find things of particular interest to their classes.

I think it went very well! I received some very positive feedback from the other teachers, and some of them said that they are ready to start using the material next week! :)

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In other news, Q1 is coming to a close. (There are just 2 more days -- just enough for me to do review and test in all classes.) I can't believe it, but at the same time, I am very happy with the way Q1 went this year in Geometry. (In Precalc, I am still learning the ropes, so I think Q1 went just OK.) I've begun to survey the kids about how the class is going, and their responses have been very positive, as well! Q2 promises to bring some neat material in both classes, so I am definitely looking forward to this next chunk of the year! :)

How I do Assessments

It's Week #4, and I am finally ready to tackle writing about how I do pacing and assessments. I'm no expert at this, but I've got a system that I think works pretty well for me.

I did a lot of blog reading this summer about other people's ideas of math teaching. I'd say that a majority of them are keenly interested in writing about their venture into what's called the Standard-Based Grading, which is basically re-testing/remediating the hell out of every kid until they get every concept right -- even if that means you've already tested that same kid 10 times on the same topic. Also, it seems like SBG believers don't count homework into the student grades, furthering the strength in their belief that they assess only knowledge, not effort.

Personally, I decided that this would not be the right time for me to implement SBG. Knowing myself, I fear that it would take my focus away from my own planning for content and focus my energy on the logistics of assessments. Likewise, I am not sure my freshmen have the responsibility it takes to only have optional homework assignments. Maybe some day SBG will happen in my classes, but in the meanwhile, I decided that it would still be feasible for me to incorporate some nice features of SBG into my weekly planning.

Here are the things I already implemented throughout last school year (2009-2010):

• I consistently give the kids time in class to work on practice quizzes and practice tests, at least one day before the real assessment. This serves two purposes: it helps kids who have trouble decoding instructions to see them once, the day before an exam; it also helps all kids to focus in on the topics and skills I think are the most important; it also helps me do last-minute troubleshooting of conceptual issues before the actual graded assessment.


• I consistently give kids opportunities to make up points from the quizzes, by doing corrections the day after. I typically allot 10 to 15 minutes at the beginning of class to allow kids to do corrections on a couple of questions (and I cap the number of points/questions they can make up, in the interest of precious class time). I circulate during this time and kids can ask me or each other for help.


• Every quarter, before the end of the quarter, we spend a full day in class making corrections for the tests we've taken that quarter. This way, kids can make up some more points and they also spiral back to some material they didn't get along the way.

Changes I've made this year (some are inspired by SBG):

• Every week, the kids will have either a quiz, a test, or a project due. So, every week, I am formally assessing them in some way. Some weeks, like this current one, they have multiple things due.


• We are still consistently doing practice quizzes even with the near-weekly quizzes. I only see the kids 4 times each week because of a hybrid block schedule that we have, so that means that we're spending about 30 minutes one day reviewing for a quiz, and 20 to 30 minutes another day taking the quiz. That sounds like a lot of time spent on assessments alone, but the truth is that I get to walk around and give them feedback during the "practice quiz" time, so I see it just as any other regular mixed-review work time, except with more focus on the exam topics (and therefore, more urgency from the kids).


• I no longer spend time in class doing quiz corrections. Instead, the quiz correction option is always available to all kids to complete on their own time, and I make kids who fail a quiz stay with me during that week to make up the quiz points after school. This concentrates my efforts on the kids who really need the remediation on those particular topics, and ensures that the remediation happens more-or-less right away for those kids.


• Instead of doing quiz corrections as a class, each quiz (and corresponding practice quiz) I include one problem from the materials of the previous quiz. I only re-test the one type of problem that I feel that as a class, the kids struggled with the most. In reviewing for the new quiz, I can highlight again that old skill, and they have a new opportunity to show me that they now understand this topic.


• We're not that far into the year yet, but I plan on re-testing most commonly missed problem types on subsequent tests as well.

A brief note about why I make these choices: I feel that assessment needs to come in many forms, and be constantly happening. Part of the reason I don't make homework optional is because when I go around and check kids off for homework each day (during their Do-Now), I am actually looking at their work and giving on-the-spot feedback on major conceptual errors. I agree that we should re-test kids on certain topics so that kids feel like they are responsible for old material, but I don't think there is a point in re-testing something to the whole class if 85% of the class got it right the first time. (Example: Well more than 80% of my kids got both algebraic problems completely correct for Segment Addition Postulate vs. Bisected Segments on the last quiz. It's not an efficient use of our class time for me to put it again on the next quiz for everybody.)

I also think remediation is important, but I struggle with spending too much class time remediating all the time. Pacing-wise, my preferance is to have the quiz a few days after I've finished teaching that chunk of material, to allow kids time to ask me questions after class or during lunch, if they still need help. So, pacing-wise, this looks like I will teach something until Friday, give a short practice quiz in class on Monday, and give the actual quiz on Wednesday. Meanwhile, I'm teaching new material the rest of Monday, all of Tuesday, and the rest of Wednesday and Friday. (Remember I only see each kid 4 times a week.) This leaves me in a pretty good situation to quiz again the following week. Projects don't conflict with that schedule either, because I give kids plenty of in-class time to work on projects, and for the most part, they shouldn't need to see me outside of class for help on projects. So, my own outside-of-class time is carved out to help only those kids whom I've identified as needing remediation on the most recent quiz.

I like a lot of things about the SBG, but I don't get how SBG teachers can convince their kids that remediation needs to happen immediately, if they allow their kids the option of re-testing all the way through a quarter. Also, I don't get how they manage to keep their own sanity in place near the end of a quarter, with all the student requests for re-testing. So, until I can answer those questions for myself (in a satisfactory manner), I'm going to work on continuously revising my own assessment system so that it adopts more of the good things I see in SBG...

Slopey Linear Goodness

It's the end of Full Week #3, and I am in the midst of linear functions with my Precalc class. I decided to try something a little different with graphing lines this year. I'm tired of teaching every kid to re-arrange terms into y=mx+b form only to have them then not remember how to graph a line of that form. This year, I've been telling kids to just come up with TWO points that fit an equation, and then to connect them. This allows them to find the slope immediately via looking at the graph, and then if they want to, they can either extend the line (if it's a simple case) or plug in a point to find the y-intercept, as per usual. I like this "graphical" approach for two reasons: 1. It re-inforces, at every step, the idea that a line is the locus of solutions to that equation. 2. Most kids with a decent number sense can look at a linear equation (of any form) and think up in their heads at least one (x, y) ordered pair that satisfies that equation. If a kid can't think of the ordered pairs intuitively, then at least the idea of plugging in an x and solving for its related y value makes SENSE to the kids. As opposed to the whole re-arranging terms thing, which they only half-understand, at best.

So, for example, today we saw in the textbook a problem that said, "Find the equation of the line through (2, 3) and parallel to 3x - 2y = 5." The way we approached it was we first took a look at the line 3x - 2y = 5. Some kids figured out that (3, 2) and (1, -1) were two points on that line. We graphed and connected the two points to graphically find the slope of that line = rise/run = 3/2. Then, for its parallel line that we're looking for, we graphed (2, 3) then moved towards the y-axis via the same rise/run until we graphically found its y-intercept, which happens to be zero. So the equation we're looking for is y = 3x/2 + 0.

Obviously, out of habit, some kids want to immediately re-arrange the given equations into y=mx+b form and to do the whole problem via algebraic manipulation, which is all good with me (as long as they can do it correctly). At this point in their junior year, I feel like I want to just try different strategies to fill in the holes of their understanding. Maybe some kids are already good at the traditional methods, and that's great. For the rest, I want to offer them a little bit of a different strategy that might make more sense to them.

Sprinkled into this week was Sweeney's Slope Rida sing-along (yes, I sang with my kids to the instrumental version... I also showed them Sweeney's rapping video, even though I couldn't do the rap myself... and I even got another teacher's econ class to come in, be their audience, and to sing along!!), as well as his trick for remembering the difference between zero and undefined slopes and the first of the graphing stories from Dan. (I plan on doing a graphing story per week. Keeping it light, maybe on Fridays!)

Overall, it has been a good week. :) There's a lot of stuff I'm throwing at my kids this week, so I won't really know until next week how well they are doing, exactly. But, I think it'll be OK!

Lovely Week!

I am having an amazing teaching week. :) Highlights:

• I started doing MATH origami with my Honors Geometry kids! It's fantastic!! The whole idea is that I would give them diagrammed instructions (with no words on there whatsoever), and they would have to try to figure out how to make the end product by reading the diagrams. On Day 1 of trying this (ie. today), I gave them something that I had thought would be really easy (I had tried it myself and it was relatively easy for me to figure out), and both honors classes were completely stumped (and incredibly engaged)! Yessss. This module is going to be great.
  
  This first one was supposed to show them how to fold / cut out a regular pentagon out of a square sheet of paper. In the end, after their struggling with it for 15 - 20 minutes and having had varied levels of success / frustration, the bell rang and I announced that we'd have to re-do this particular exercise next week (ie. making pentagons again). The difference is, next time, I'll guide them through reading the diagrams step-by-step (paying careful attention to where the creases are supposed to be and which points should meet up), and we will work on precision as a class. My hopes are that their regular pentagons from next week will be precise enough to allow us to introduce some good geometric vocabulary, and to measure congruent interior angles. :) After that, I have plans for them to make a regular hexagon, followed by a tetrahedron that requires no glue!! (Even other teachers are loving the tetrahedron. I went around Open House yesterday to show off my new origami toy in between parents talking to me, and all the teachers wanted to run off with it! haha. That's how you know it's kid-ready, I guess!)
  
  By the way, all this good stuff came from 3-D Geometric Origami, which is a super fun booklet of foldable geometric shapes (2-D and 3-D). In doing these constructions, we can introduce naturally a slew of geometric terms about faces, edges, angles, etc. I have plans to get the Honors kids stronger at independently building stuff throughout the first quarter, so that when we move on to heavy-duty compass/ruler constructions of polyhedron nets in the 2nd and 3rd quarters, they'll be kinesthetically (and emotionally) ready.
  
  (The regular Geometry kids will benefit from the origami lessons as well, but because they will need more time getting through the regular curriculum, I'm not going to give them the serious polyhedron net construction projects later in the year. They'll still do some good compass constructions though, because I plan on doing some simple line designs with all my Geometry classes, and those require the construction of regular polygons.) :)



• In other news, all of my Geometry kids have been working on setting up algebraic equations with info embedded in geometric diagrams. They seem to be doing better this year with distinguishing the different scenarios for setting up different types of equations. I'm not sure if it's just because it's my 2nd time teaching these exact topics, or what, because I don't feel like my approach has changed drastically from last year, and the kids are having significantly less trouble. There's only been micro-changes, like this year I have emphasized the idea, "Do we have enough info to set up an equation? Do we now? Do we now??" as I put up algebraic lengths piecewise on the board. Does that really make a huge difference in their comprehension??



• Precalc has been smooth-sailing as well. This week (thus far), we did some good graph-reading, reviewed what a function is, and introduced how to identify its domain and range given a graph. I have a lovely activity for introducing functions, which I didn't come up with but I feel like has been smoothed out over the years every time I present it. Now, it's gotten down to me preparing (in advance) a series of ordered pairs representing a function, and putting them on post-its. (Input goes on one post-it, output goes on another. You stick the two post-its together, front and back.) I draw a "function magic" box on the board with an arrow going in and one coming out, and I start to reveal ordered pairs as I stick the input post-its in and return with the output value on the other side. The reason why I use post-its is simple: as I reveal the ordered pairs, I stick them onto the board in function diagrams (the ones that look like two big ovals, one for domain and one for range), and kids copy them down from the board, one ordered pair at a time. For this intro demo, I always choose some numbers with patterns, so that kids can get excited about making predictions -- and I also use a function that has shapes/symbols as inputs and where the output is consistent, ie. always 5. This way, I can show them that even when one output is shared by different inputs, the function still behaves "predictably" (ie. if it returns 5 always, that's pretty damn predictable) and is still a function. And it also shows them that functions are not limited to numeric domains and ranges.
  
  After this, I have the kids pair up and I give each pair a set of flash cards, showing functions and non-functions in graphs, tables, diagrams, and word descriptions (ie. "a function that maps age to height"). The pairs of kids have to separate them into two piles, one for function and one for non-function. It's not fancy, but it works really well to quickly go through MANY examples and the kids are really actively engaged. In the end, we quickly go over the answers as a class.
  
  As for teaching about domain/range of graphs, I totally stole Sam Shah's idea of domain / range meters, and the kids thought it was funny (and probably thought I was "not cool"), but it worked like a charm!! I was thrilled. Kids were beeping (umm, quietly... these kids are waaaay docile...) when they were doing their own classwork problems. heehee

I love teaching! I love the world. Off to Day 2 of Open House (this time, with freshmen parents)!! :) :)

GeoGebra... times 3!

I made a GeoGebra spirals applet -- for use in my Precalc class! Yay. I'll be introducing geometric and arithmetic sequences sometime during the next week, and even though we'll spend most of that period working on finding numeric trends embedded in composite patterns and such, I think that at the end of class, I am going to use the applet to help them appreciate the connection between nature and geometric sequences. :)

Anyway, that's enough preamble; check it out for yourself! You can make a spiral outwards (if geometricRatio > 1) or inwards (if geometricRatio < 1), and I'll ask the kids to make predictions about what they will see with those ratios before we toggle the numbers. You can also turn on Trace for point B in order to see the actual spirally points.

Amazingly, that's three times in one week that I'll be using GeoGebra. (First time I'll be showing my Geometry kids briefly what Mr. H created per my request, so that they can better visualize why 3 points will define a plane in space. The second time, I'll be taking my Geometry kids down to the computer lab to do a full period of GeoGebra exploration in pairs about Segment Addition Postulate and the midpoint of a segment. See worksheet below if you are interested in seeing just how explicitly I structure an activity like this for 9th-graders who've never seen any geometry software before. If you want the actual file, drop me a note. I did all the way up through step #15 with my 9th-graders from last year and they had all loved it, so I am interested to see if the more challenging parts I tagged on this year will end up "breaking" it. --I guess we will see!)






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Also this week, I'm pulling out an old middle-school activity that I liked a lot, in introducing angles and the estimation of angles. I found out on Friday (during the beginning of our tangrams project) that a handful of my kids didn't know how to recognize right angles in a diagram. Some of the same kids also didn't know that when one angle is 90 degrees (at what looks like a perpendicular intersection), its adjacent angles would also be 90 degrees. ...I have to say, that's pretty alarming. So, umm, we're starting from the basics.

The activity is one that I've done with middle-schoolers many times. You give kids each a piece of patty paper, and you get them to fold it several times and to cut an arc so that when they open it back up, they have a circle that has creases across every 22.5 degrees. Then you just start calling out angles that are multiples of 22.5 degrees, and kids have to figure out (without a protractor) how to use their patty paper to show 90 degrees, 45 degrees, 180 degrees, 135 degrees (at which point, they would have to put it together with someone else's angle), 67.5 degrees, etc. Essentially, the kids learn to estimate angle sizes by comparing them against benchmark angles and thinking about fractions of 90 degrees. (You could also use this manipulative to discuss why when you compare two angles, the sizes of their rays don't matter.)

Let's go, Full Week #2! :)

Process Goals and Fun with Graphs!

It is timely that I came across this nice post today about goals, because I had been thinking yesterday about listing out some goals on my wall that are not topic-specific, so that I can refer to them throughout the year as I work with my kids on different assignments intended to address one of those life (or processing) skills.

Examples for Geometry:

• Visualization of parts vs. whole (Isolating info from one part of a diagram; combining info across multiple layers / perspectives.)


• Mechanical precision (Measuring and constructing lengths within 1 mm error and angles within 1 degree error; building solid models that won't fall apart.)


• Comprehension of diagrammed instructions (ie. for building anything)


• Attention to details in written instructions


• Judgment of reasonableness (of any physical or visual quantity)


• Effective written and oral communication


• Perseverence and resourcefulness


• Team work

Examples for Precalculus:

• Interpretation of data (Understanding trends / real-world significance / impact.)


• Fluidity with technology (Using graphing calcs fluently and flexibly.)


• Flexibility / creativity of problem-solving approaches


• Risk-taking and reasoning about the unfamiliar


• Precision and clear step-by-step organization of thought process / math work


• Increased self-management of progress, frustration level


• Effective written and oral communication


• Perseverence and resourcefulness


• Team work

Maybe it's just me being cheesy, but I think both the students and I might benefit from my posting these goals on the wall -- especially if I do actually highlight different skills throughout the year, as is appropriate to a given lesson, so that the kids would feel like they're not just learning content for content's sake and we are working towards a bigger picture.

My lists of goals are pretty generic (not really even math-specific, for the most part... Most are just good habits of mind...), but they are reminders of what is most important to me. Naturally, between the freshmen (Geometry) and the juniors (Precalculus), there is quite a bit of a "life experiences" gap. So, my goals for the two groups are pretty different as well. My juniors don't need as much for me to hold their hands on following directions, but they might need a nudge to be more creative and/or persevering. Versus the freshmen, whose first task of this year is to learn to consistently read and follow instructions. :) They each are at a different developmental stage with their meta-learning.

We have an opportunity each day to impact kids, mathemagically or otherwise.

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By the way, I found some nice graphs for my graph-reading lesson that is coming up. They're neat, even though they are not terribly complex in a mathematical sense. (The textbook's got a couple of nice complex graphs to use for rigorous classwork exercises, so I feel like I could afford to spend the rest of the period looking at interesting -- albeit simpler -- graphs with the kids.) They have to do with the mobile market, digital textbooks, and digital music. I plan to have fairly open-ended discussions about trends in those graphs, who might be interested in reading them, and what their implications might be for those people. And then maybe end with why these kids should finish college.* It could end up being a total flop of a lesson hook, but I am curious to see what these juniors can bring to the table.

If I have time, I am also thinking about adopting a middle-school post-it bar graph activity to composite bar graphs and scatter plots. I would give every boy a yellow post-it and every girl a pink post-it, and we would start a bar graph template on the board -- for example, models or brands of cell phones. They would go put their post-its on the board, in the appropriate column, and we would re-arrange the post-its to stack the pink post-its on top of the yellow post-its, in order to create a composite bar graph showing how many boys, girls, and total # of students have each type of phone. You can also do this exercise with scatterplots (for example, height vs. foot length) and see at a glance 1. what the overall trend is within the class, and 2. what the gender-specific trend is within the class. Using only colored post-its! And requiring maybe only about 10 minutes, discussion included. ...I'll try to squeeze it into my Precalc lessons this week and tell you lurkers how it goes.

*From what I hear, many Salvadorean private-school kids end up dropping out of college in the States, because they either lack the academic skills or -- more commonly -- can't deal with the fact that they no longer have a live-in maid and a designated chauffeur. This waste of an opportunity is terribly sad, considering that their parents can afford them to obtain a U.S. college education, while the majority of people in this country are living in poverty and many are starving. :(

But, can you really blame the kids for this injustice?? They are a product of the system (of huge disparity in wealth). sigh.

Vectors and Wait Time

I've been working with my (regular) Precalculus kids for a full week on vectors. Since I didn't want to teach them just rote algebra procedures, I made them do everything graphically. Adding and subtracting vectors graphically, scaling graphically, etc. As predicted, some kids figured out for themselves that <a, b> + <c, d> = <a + c, b + d>, and I told them that it's all good to use this algebraic method to double-check their graphing work. But, I'm pretty pleased that...

1. Kids were able to answer this question using only graphical addition: List 5 vectors whose sum is <-3, 4>.


2. When I wanted to introduce the graphical subtraction of vectors, I first gave the kids some diagrams of pairs of vectors to look at and I asked them to choose a pair that represented a vector and its "negative." Almost every kid got it right! They figured out for themselves that vectors of equal magnitudes and pointing in opposite directions represent "negatives" of one another. And we discussed how V + (-V) = <0, 0>, just like how 5 + (-5) = 0. That was pretty neat, because it was a tiny reference to set theory. (Or some such goodness in higher math.)

And I am truly amazed by how great these juniors have been in class. We spent a good chunk of class today working on using protractors and rulers to carefully duplicate vectors, and I was fully expecting them to throw frustration tantrums because of the precision I required. But, they were super! I am not holding my breath that this will remain the case, but I'm certainly doing my best to keep the class extremely smooth-running to avoid the 3-week-in rebellion. (I won't lie; it also helps to have a handful of kids from my honors class last year now in regular Precalc with me. I still think it's extremely silly of them to drop out of honors, but given that they're taking many other honors classes, I guess I can sympathize. MAYBE.)

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On the Geometry side, I had a really great experience with the shapes puzzle I had posted a link to. Kids were talking to each other using geometric vocabulary; they wanted more time on the assignment before discussing solutions as a class... I actually felt bad when I cut them off at 15-20 minutes of individual efforts struggling with the puzzle, because I could tell that the kids were really trying to figure it out on their own.

It was awesome. It made me think again about the issue of wait time. Giving kids just 5 more minutes on a thoughtful assignment sometimes makes such a huge difference.*

*Note: I think the issue of wait time is intrinsically tied with the timing and type of hints you give. For example, my first regular Geometry period felt significantly more frustrated on the assignment, because I gave them no hints while working. My second period (also regular Geometry), started to make visible breakthrough when I said after a good 15 minutes of individual efforts: "By the way, here is a hint: everytime you tag on a triangle to a shape you have already found, you end up changing the number of sides in that polygon."

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Geoff comes back this weekend. :) I'm so excited!!!

Teaching Estimation!

I had decided sometime last year that as one of my focuses (foci?) for Geometry, I would push their estimation abilities this year. We would estimate before measuring everything.

Today was Content Day 1 of Geometry, and I gave them a list of questions to answer as the Do-Now. Kids had NO IDEA how to answer some of these questions, which was my intention. We ended up with a really great discussion about how you would go about estimating some of these. (We ran out of time today, but I plan on returning to these very quantities on Monday and have them actively measure some of these, to check their own accuracies in estimation. Estimate-measure-estimate-measure-estimate-measure!)

• What is the height of this classroom in centimeters? In meters?


• What is the length of your foot in centimeters? In millimeters?


• What is the length of your hair in meters?


• What is the distance of your house from the school in kilometers? In meters?


• How many hours are you in school a week? How many minutes?


• How many kilograms does your textbook weigh? How many grams?


• How fast can you run in m/s?

It was great! (And funny that even when they know how big a meter is, they still can't estimate how fast they can run in m/s.) Some kids said really awesome things like, "I am about 160cm tall, and the classroom is about twice my height," or "Our new principal* is about 200 centimeters, and he is about a meter away from the ceiling." I followed this Do-Now/discussion by teaching them the mnemonic device for remembering how to convert between metric units. (Kangaroos Hopping Down Stairs Drinking Chocolate Milk).

The big concept (often overlooked) that I always try to teach for unit conversions is that when the unit gets larger in size, the number needs to get smaller. ie. 1 kg = 1000 grams. Otherwise the right-hand side of the equation either shrinks too much (if both the unit and number are getting smaller) or expands too large (if both the unit and number are getting larger) to remain equal to your original quantity! I say this even during metrics conversion, because if the kids get this concept down, it's a lot easier for them to figure out that 78 cm = ______ inches should have an answer that is smaller than 78, even though the numbers are messier.)

We used the Kangaroo Stairs to figure out how many decimals you move. (ie. Number of steps you take on the stairs = number of places you move the decimal.) Again, once the kids can reason through whether the number needs to get bigger or smaller, they can usually figure out the rest with a small bit of practice. Moving the decimal isn't the hard part; knowing which way to move it is the crux of those problems.

It was lovely.

*Yes, our new principal is a giant. :)

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My Precalculus class was also awesome today! We had to teach vectors as part of the support for their Physics classes, so I adopted Kate's activity of pushing desks around to show how vectors add differently when they point in same/different/perpendicular directions, and I also drew arrows (vectors) on transparencies and moved them around a large projected grid, to demonstrate how you would add vectors graphically. The kids figured out quickly as a class that you can find the magnitude of a vector with simple Pythagorean Theorem. Yesss!

It was really cool. I think I've got some difficult kids in there (or so I hear), but my plan is to kill them with kindness for now, so that three weeks in, they'll feel bad to act up in my class. So far, so good.

First Day Details

A small but neat trick that I picked up from another teacher last year is that you can write the kids' names on post-its, and then put the post-its on their desks before they walk in on Day 1. That way, they will already be quietly looking for their assigned seats on their way in, you can take roll easily on Day 1 (by seeing if there are post-its that remain unoccupied), and they can also hand you back the post-it with their names corrected if they prefer to be called something else.

I really liked that idea. Especially because last year, the school was scrambling their schedules until the very last minute, we didn't receive the updated rosters until the morning of Day 1, and I especially wanted the semblance of order in my classroom to set the tone for the rest of the year.

This year, I am taking that idea a bit further and adding on a layer of getting-to-know-you. I'll write their names on a survey beforehand and stick the named surveys on their assigned desks. (...Yes, I do realize it's quite a bit more work this way than having them fill out their own names, but for some reason I like it better than posting a seating chart on the wall!) That would give them a semi-thoughtful do-now in addition to filing in quietly. Afterwards, I'll have a short chat with them about my expectations. (I have re-written my syllabus as a letter to the students this year, to emphasize the idea that we are building an important relationship right from the start.)

None of this is original, but as with all disciplinary measures at the beginning of a year, the devil's in the details.

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I am heading into my fifth year, and generally I am feeling really upbeat about it. I'm up to two-and-a-half preps this year. (To make it a bit more manageable, I am going to try to keep my honors and regular Geometry classes paced similarly, except going into greater depths and throwing in extra projects that are sequence-independent for the honors classes.) After a bit of paperwork chaos, it looks like I'll also be teaching Precalculus as I was hoping for. Yay!

I've pretty much got the whole year outlined, in both Geometry and Precalculus. Since it's the first time I'll be doing Precalculus, I can't yet gauge how ambitious those units are, so I'll reveal them piecewise as I figure it out. I'm feeling pretty great about Geometry, because I have revamped my entire curriculum from last year (keeping bits here and there that I liked, but re-doing the whole sequence and adding a whole bunch of new activities), and my two Geometry partners for this year seem to be on board with the plan.

Onwards! I think it's gonna be a very busy, but good, year. :)