Monday, June 25, 2012

My First German Post: Traveling

Ich werde sehr bald weg gehen! Ich bringe mit mir Kleidung und Geld fur einer Monat. Ich bringe auch meiner Kindle, weil ich werde auf dieser Urlaub alleine sein. Ich fliege nach Singapur, dann im Zug fahre ich nach Malaysia, dann nach Thailand und dann endlich nach Vietnam. In Singapur habe ich zwei Freundinnen, und ich werde mit einem bleiben. Ich freue mich schon darauf! Tschuss, und bis bald! xoxo.

Mini-reflection on my progress with my German tutor: I am pretty happy so far with the bits of German I've been managing to pick up, and most recently I was able to converse simply for about 90 minutes straight with my tutor, mostly in German with only bits of English when I got stuck in the middle of a story. I feel that compared with people who have been sitting in a traditional Volkshochschule setting for the same amount of time (in terms of months committed), I am at least on par in my ability to express myself, even though on average I put in less than half of the hours they're putting in, per week. But, the drawback of studying with a private tutor is certainly that it's very adhoc, and less social. My listening isn't as strong as it would be if I were in a group setting, because my German teacher is relatively introverted and I typically have to keep the conversation going on my end. It's great because I get a lot of speaking practice, but my listening (always a weakness anyway, in any language) is lagging behind. My grammar is also weak, because we learn grammar in a pretty adhoc way instead of systematically as we would in a traditional class, so what I can say is based on my natural feel for languages instead of based on learned rules.

I am considering switching it up and enrolling in a Volkshochschule class in the fall, but I am not so sure yet about the 6 hours/week time commitment or the commute. (It'd be a significant step up from 90 minutes/week, at a cafe 3 blocks away from home.) I am still thinking about it, because I don't want to wait too long (ie. another 6 months or a year) and get to a point where my immersed fluency becomes much better than my grammar and I would have to enroll in a class that is really boring for me most of the time, just to fill in all the missed grammatical bits... Eventually, in the long run, I want to finish proper B-level classes and then take on a tandem conversation partner so that I can gain real German fluency, but these goals conflict naturally with the additional responsibilities I wish to take on at work next year. So, I am still thinking about it.

But, I am in a good place. I feel that when you acquire a new language, the first real break-through is when you can start to understand the gist of most conversations-with-strangers directed at you. Because, after that point, you can start picking up more vocabulary and grammar purely by context. That's where I am at, and I find that finally the words on a page are no longer words on a page, but linked to real auditory interactions as well. So, I am in a good place! Happy about getting here by the end of our first year in Germany, even though I cannot remember where we were with our Spanish by the end of the first year.

Sunday, June 24, 2012

The Mathematics of Scheduling Classes

After a chat with my colleague from the math department who does the scheduling for the entire MS and HS of our school, I have become very intrigued by the mathematics of scheduling. His background is in Discrete Mathematics, and the professor under whom he had studied way back when has recently been awarded the equivalent of the Nobel Prize in mathematics. So, this colleague is a semi-expert in tackling problems such as this. He took over the task of programming for our school's MS and HS schedules a few years back because of his personal interest in the complexities involved. He told me it's like a big Sudoku puzzle that you don't know whether there is a solution for. Even though he uses software to help, much of it is too complex for the software and he has to manually do a lot of it. Often, when the software gets "stuck" from all the rules that have been inputted, he has to go back to the drawing board, try asking departments to change their teaching assignments on particular teachers, in order to enter in new rules, in new orders, in hopes of getting the software "un-stuck" and to progress further. Tough task! And, as it turns out, it is most mathematical.

Here are some basic things that make scheduling for our MS/HS school tricky and difficult:
  • We share facilities (such as art pavillion, cafeteria, and gym) with the elementary school. So, all of those classes are blocked out during certain days and certain times. 
  • We are an IB school, which means that kids get to choose in Grade 11 and Grade 12 (and to a lesser extent, in Grades 9 and 10 as well) any combination of high-level and standard-level classes from our offerings based on their interest. Because we truly believe in kid's choice, we don't limit the types of combinations they can have, but it also means that we need to weave together the classes to allow for a variety of combinations.
    • Imagine kid 1: English-High, Math-Standard, Chemistry-Standard, History-High, Economics-High, Music-Standard.
    • Imagine kid 2: English-High, Math-High, Biology-High, History-Standard, Economics-Standard, Spanish-Standard.
    • Imagine kid 3: English-Standard, Math-Standard, Physics-High, Economics-High, Music-High, Art-Standard.
    • All of these combinations of schedules (and all other possible combinations) need to be supported, which comes into conflict with our next constraint....
  • Because we are a relatively small school (only about 60 kids per grade), that limits the number of classes that can be offered. So, for example, there is only 1 section of High-level mathematics in Grade 11. All 10 or so kids who are interested in taking that class will need to be able to fit that one class into their schedules. We cannot afford to open up an additional section of High-level math in Grade 11, when there are only about 10 kids total who are capable of taking math at that level. Same with kids in High-level classes of most other subjects, probably.
    • FYI: High-level IB math is really intense. It goes into differential equations and stuff, well beyond Calculus AB of the A.P. system.
    • In the IB, each kid is required to choose 3 High-level classes to take. Again, this means we need to have a master schedule that supports the variety of possible combinations of High-level classes that kids might wish for. A TOTAL MATH PROBLEM!!!!
  • Because we want to allow the flexibility of students changing their choices of high- and standard- level classes during the year (typically in Grade 11), we need to piece together department schedules in a way that allows a student to change options without too many problems during the year. Hopefully as well, this means that they will incur minimal changes in teachers of their other classes.
As a result, one of the consequences of these cross-constraints is that all Grade 11 math classes, regardless of levels, must be taught at the same time. Same with all Grade 12 math classes. (It's not obvious perhaps why that is, but it's a natural fallout of reasons #2 through #4 above.) Another indirect consequence is that all teachers must teach a lot of different "preps", so it is common for a teacher like me to teach 5 different grades during the week, because at the same time that I am teaching, my colleagues are teaching other sections of the same age group.

So very interesting, eh? Have you worked with scheduling before? Can you chime in to say something about the mathematical nature of this problem? Notice that we're not even talking about physical space constraints above. This is mathematical problem-solving at its richest!

Wednesday, June 20, 2012

Math Pop-Up Book Samples!

Here are some results from my Grade 7 and Grade 9 math pop-up books! They are really fantastic. Up side: The kids were really excited about the project and doing good math all the way through the last week of the year, even though it was not graded. One kid even said she wishes she had been able to finish the book before her family packed all their stuff for their move. (No worries though; I'll make sure I mail it to her.) The down side: tomorrow's the last full school day and I'm still not done giving last-minute feedback on all these Grade 7 books. I plan on getting to school early tomorrow to finish mistake-searching on all of them, and then give the kids 40 minutes in class to help each other fix them before they take them home for good -- but, fixing on our last day!! What a rush job. :( But, they've already done a terrific job and most of them have only very small fixes still to make tomorrow. I think it's doable. Crazy ambitious of me though! I hope next year, if I repeat the same project, I'll have to be smarter about pacing it as to avoid all this end-of-year stress.

PS. This post is a follow up to this post where I had conceived the idea and written a bit to include the project descriptions. If I were to do this again though, I'd re-work the project description to include the phases of the project:
Phase 1. Gather at least 4 problems per topic, of appropriate difficulty. Need to sufficiently address all listed sub-topics with these problems. (2 to 3 days)
Phase 2. Write rough-draft explanations and get them reviewed by the teacher. (3 to 4 days)
Phase 3. Start to build the book. Get the first pages checked to make sure format of "pop-up" is actually useful and interactive. (3 days)
Phase 4. Peer review, followed by teacher review, for mistakes in arithmetic or algebra. (1 day)
Phase 5. Fix the parts of the book as necessary. (1 day)

Math Movie Dub

Hilarious video from my students in re-enacting famous movie scenes and putting math-speak in there. We also had a successful math scavenger hunt, 4 creative board games, a math tutorial DVD, a math pop-up book, and a trebuchet project all from the same class. I will definitely miss my awesome Grade 8s next year!

Tuesday, June 19, 2012

Letter to New Teachers

(In response to Bowman's idea of letter to new teachers...)

Dear Brave New Teacher,

Welcome to the amazing world of teaching. I hope you are prepared for the emotional journey. Here are some things that might help you along during your first year (or maybe first few years):

1. Be emotionally prepared that your first year (and maybe two years) is/are going to be tough. One of the things that frustrated me the most about pre-teacher training was that they had mentioned all of these issues you were supposed to be thinking about, without telling you precisely how to solve those problems. It took me a long time to figure out that it was because our learning theories are so new that we don't yet have all the answers. That fumbling in the dark is also what makes teaching so exciting, in the long run. Everyday, you are going to be forced to problem-solve, to be creative and resourceful, and to forge your own road. Don't be afraid to try new strategies, as long as you realize that it will take close to a month for any new "thing" to show its effect on a student.

2. Teaching is a craft. Therefore, reflecting on your teaching practice is extremely important. You can do it in writing, in meetings with another teacher, or in your head, but you need to think deeply and critically and continuously about how your class is going, and what the experience is like for each individual student in your class. The more you think about each student's experience individually, the more issues you will see with your own lessons, and the faster you will change your strategies and grow.

3. Your attitude is what will make or break you. If you are positive and you keep at it, you will get through the rough patches and IT WILL GET BETTER. During my first year, for at least the first semester, I thought everyday about quitting. Now I love my job and I cannot imagine doing anything else.

4. If you are teaching at an inner-city school, here are some things you need to consider: Why kids put their heads down, why they wear hats and chew gum in the classroom, why they take out their phones or iPods, how often a kid goes to the bathroom during your class, why a kid leaves trash at their desk, why a kid comes late chronically, and --most importantly-- why they don't do those things in other teachers' classrooms. How do other teachers address misbehavior? What is considered misbehavior at your school? During your first year, nothing can be overlooked as a "detail." Teaching is as much a behavioral science as it is an intellectual science. You should find a mentor, or multiple mentors, to whom you can turn to for disciplinary advice. And you should do it as much as you can during your first year. At some point, my first-year mentor was coming into my room literally everyday to watch how my students were going nuts. With his keen observations and concrete suggestions, things got slowly better.

5. You need to find a senior teacher in your department to mentor you, unofficially. Show them your lessons and your worksheets. Do not be afraid. If they are a good teacher, they will be glad to help you. It is my 6th year of teaching this year, but I still sought out a senior teacher to be my unofficial mentor when I arrived at my new school to teach an unfamiliar math curriculum. You will be immensely glad of the little and big things that person can help you with, and you will also build a tremendous working relationship with that person for the long haul. Having an insider to mentor you will also help you navigate the school system and to tip you off on whom to ask when you need something.

5. Always be nice to the secretaries. Extra, extra nice. You will need their help some day -- and anyhow, they're usually pretty awesome people!

6. Always remember that you are handling someone's child. That is the greatest trust someone can place in you.

7. Lastly, you need to work for people who share your values and your vision of a school. Do not compromise your values for the sake of a job. Remember that you need to be happy (both personally and professionally) in order to succeed as a teacher!

Best of luck in your new awesome career,

Wednesday, June 13, 2012

Course Survey via Google Forms

I can't believe this had never occured to me before, but I am experimenting with collecting course survey results via Google Forms this year. So far, I like it!

Here is an example of the 8th-grade survey results coming in (but they have the rest of the week to finish them at home, since some of them were finishing up their projects today):

Advantages: I can keep it for posterity without creating extra work for myself. I can easily share the results with my colleagues and my students. I can still view in each row what one individual's experience was like in my class.

Disadvantages: Still not completely anonymous. If I wanted to, I could trace who wrote the responses, based on submission timestamps and how quickly each student had finished their survey during class. If your connection isn't great or if the laptop isn't well charged, the kid could lose their work before/during submission.

But, overall, I think it's better than a paper survey! The kids are more likely to provide you with thoughtful answers, if they are typing rather than writing.

Addendum June 14, 2012: I decided to extend the use of Google Forms to grading our entrance placement exams! As an international school, we get a fair amount of applicants throughout the year, and today I was given 5 exams to grade on top of what I already am trying to finish up before the week is over. So, instead of just grading those exams, I decided to create Google Forms for all the questions and to enter in the ANSWER KEY as the first submission, so that future prospective students can be asked to submit their answers via the Google Form, to be compared by a math teacher quickly with the answer-key row in the same spreadsheet. This will make the grading process much easier, and we can still go back to skim through their paper exam if we need to drill down further into the process they took or to see how far along they got in the solution before they made a mistake. It will trim the grading process for each of those entrance exams down to 5 minutes, and thereby ease the load on all the teachers and also improve the turnaround time for the admissions people. I think it could be a win-win.

The only drawback I see is that if we allow kids to do this, it means that they will have access to the web while taking the exam, so in order not to skew their results, I think the admissions people will need to either be present in the same room as the kid while they're entering their final answers (after having completed the exam on paper), or give them a strict time limit for the computer-entry part (again, assuming that they have already completed the exam on paper). Because it's not machine-graded, if they are inexperienced in entering the expressions, such as if they put x2 instead of x^2, it should not matter to the teacher who is looking quickly through their answers. I am excited about this potential for seriously streamlining this grading process!

Saturday, June 9, 2012

Introducing Calculus in the IB

In light of my recent reflections on my students' weakness in connecting application problems to algebra concepts (see this post), I started my new Calculus unit a different way than I did the last time. This is only the second time I have taught Calculus (in the IB, it's one of the topics and not an entire course), but the first time I did it I had started with the video that introduced the idea of instantaneous rates and worked my way through the idea of limits, then worked through the various traditional differentiation techniques, before we arrived finally at the applications. That was pretty ineffective, I found. The kids, by the time they got to the applications, struggled with putting them together with the algebra skills, and they found the entire topic to be very challenging and were daunted by the complexity and variety of problems/situations presented on different IB exams.

This year, I did something entirely different.

Day 1, I gave the kids a polynomial function and asked them to use the graphing calculator to find the dy/dx derivative values at specified places on the graph. They sketched the graph, wrote down the derivative values next to the appropriate parts of the graph, and then as a class we hypothesized what the derivative values meant. This was good for two reasons: 1. They're expected on the IB to know how to find derivative values on a graph using a GCD, 2. they got to go from concrete numerical examples to a more abstract definition / generalization of the meaning of a derivative, which helped me reach those concrete thinkers. Then, I gave them another sine equation, and they had to find all the places on the graph (within the standard viewing window) where the derivative was zero. Again, we discussed how they did this, and why that made sense based on their previously generated definition of the derivative.

Day 1 was very successful because by the end, the kids had conceptualized the meaning of a derivative value and were looking at me with these "duh! this is so easy!" looks. They learned the notations dy/dx and f'(x), and we went over how to find the derivative function of a polynomial function (justifying it by showing how, graphically, a cubic function "flattens" to a quadratic if you roughly sketch out its derivative values on the same graph).

Day 2 was also very successful. Instead of introducing more derivative rules, I introduced the idea of f"(x), and we linked f(x), f'(x), and f"(x) to physics. I told briefly the legend of Newton inventing Calculus to support physics, and together they figured out that if f(x) tells you the position at time x, then f'(x), its rate function, must be called the speed function, and f"(x) must be called the acceleration function. Great! With this itty-bitty bit of Calculus that they now "know", I threw them headlong into two 15-point application questions from old IB exams on differential Calculus. They struggled, of course. Two word problems took them about 60 minutes, including discussions as a class. But, it was very productive struggle, and in the end it had fully reinforced their understanding of the meaning of f(x), f'(x), and f"(x). Many of them figured out by themselves that if you need to find out the time that an object comes to a stop, you would set f'(x) = 0 and then get x, and then with that x value and the original f(x) formula, you can find the stopping position of the object.

It was lovely, because instead of the traditional approach of stuffing all the differential Calculus algebra skills down their throats at once, we slowed down enough for them to first digest the meaning, and zoomed out of the algebra skills just enough for them to see the bigger point of it before continuing with more detailed derivative rules.

On Day 3, we learned about the derivatives of sine, cosine, and also about the Chain Rule. It was pretty smooth. I had introduced the derivative of sine by asking them to sketch a sine wave, and from that, asked them to determine/sketch the shape of the derivative function graphically by first sketching the places where f'(x) = 0 and then thinking about what happens between those points. This was challenging, but some of them were able to figure it out. We referred back to the IB formula sheet afterwards to confirm our graphical intuition that f(x) = sin(x) --> f'(x) = cos(x), and we did some examples of the Chain Rule together before I threw them into another 3 old IB problems that required some resourcefulness and that involved the new rules learned on this day.

I am going to keep trying this approach in IB, breaking a big algebra concept into smaller and smaller chunks and integrating the end-to-end process very early, to see where the kids are getting stuck and to adjust instruction accordingly. I'll keep you posted on how effective this is, but my gut feeling is that it will increase their overall confidence with trying new problems on their own, because essentially they will be already doing this all the time with me as part of regular instruction.

Friday, June 8, 2012

Motivating People

I just finished reading an amazing book. I had picked up Developing the Leader Within You by John Maxwell expecting it to offer up some tips and strategies on how to get people to work with you. The book was that and also completely something else. I would say that more than 80% of the book focused on how you need to first work on yourself as a person, in order to effectively lead others. Makes sense, doesn't it? It just wasn't what I had expected.

Maxwell is incredibly blunt and concrete in his examples, discussions, and points. He makes bullet points on things you need to have, need to consider, need to be. His theory is that first you need to work on yourself as a person to embody all the necessary qualities, and then you can work on your people relationships, and then you can consider introducing changes. In that order.

Some memorable quotes (they tie in nicely as well to education, character ed, and a lot of other things that have been on and off my mind):

"The dictionary defines integrity as 'the state of being complete, unified.' When I have integrity, my words and my deeds match up. I am who I am, no matter where I am or who I am with. [...] Integrity is not what we do so much as who we are. And who we are, in turn, determines what we do. [...] We are all faced with conflicting desires. No one [...] can avoid this battle. Integrity is the factor that determines which one will prevail. We struggle daily with situations that demand decisions between what we want to do and what we ought to do. Integrity establishes the ground rules for resolving those tensions. It determines who we are and how we will respond before the conflict even appears. [...] It is the pivotal point between a happy person and a divided spirit. It frees us to be whole persons no matter what comes our way."

"Note the difference: In the beginning the skills of a leader are essential. No change will ever occur if the psychological needs are unmet. Once change has begun, the skills of a manager are needed to maintain needed change. [...] A change can make sense logically, but still lead to anxiety in the psychological dimension. [...] So before introducing change, we have to consider the psychological dimension."

"Leadership leaks should be planned and positive, preparing the people for the meeting where the change will be formally presented." --> KSI'ers, this totally parallels what Pearl Kane said about talking to all the key people before a meeting to get their support on a new plan. By the time the meeting rolls around, you should have already garnered support from all the key players or "influencers", as Maxwell calls them.

"Notice I did not say our attitudes determine how we feel. There is a great difference between how we feel and how we handle our feelings. Everyone has times when they feel bad. Our attitudes cannot stop our feelings, but they can keep our feelings from stopping us."

"My father [...] is a leader's leader. One of his strengths is his positive attitude. [...] As he opened his briefcase, I noticed a couple of motivational attitude books. I said, 'Dad, you're seventy years old. You've always had a great attitude. Are you still reading that stuff?' He looked me in the eye and said, 'Son, I have to keep working on my thought life. I am responsible to have a great attitude and to maintain it. My attitude does not run on automatic.'"

"[...] When we tell one of our children, 'Change your attitude,' the message is too general and the change we want is unclear. A more effective approach is explaining behaviors that signify bad attitudes. If we help them change their behaviors, the attitude will change on their own. Instead of saying to our kids, 'Get a grateful attitude,' we ask them to give one compliment to every member of the family each day. As this becomes a habit in their lives, the attitude of gratitude follows."

"People don't care how much you see until they see how much you care. I emphasize again: people buy into the leader before they buy into that leader's vision. Cultivate trust. Be transparent and patient. Start where they are by seeing through their eyes. Seek to find their hopes and dreams. [...] Go for the win-win. Remember, when you help people get what they want, they will help you get what you want."

"You don't have to make every decision, but you should always be accessible. If your people are smart, they will keep you informed, and if you're informed, you're a part of the decision. With that in place, it's easy for you to back your people and that eliminates second guessing."

Love Maxwell! I hope you find his words inspiring as I do. If you have time to pick up this book, I highly recommend it. It reads a bit like a sermon, because he uses anecdotes on every page and his background is religious. But, he definitely cuts through all the fluff and offers great and very detailed advice. Great stuff.

Monday, June 4, 2012

Leadership in the Classroom

I've picked up some books on leadership, because I will need all the people skills I can get in order to motivate my department colleagues to work together, on things they don't necessarily already believe in. You can laugh secretly if you will, but I think leadership can be taught and learned, and I think next year I will appreciate every piece of advice I have gathered on this topic.

One thing that has surprised me is how closely aligned the leadership principles are to my vision of an effective teacher in their role as a classroom manager. The first book I finished on the topic, unbeknownst to me at the start of the book, was written by a pastor who worked for years as a religious leader. (His name is John Maxwell.) Here are some examples of things he mentioned that I think apply very well inside a classroom:

"Thomas Aquinas [...] once said that when you want to convert someone to your view, you go over to where he is standing, take him by the hand (mentally speaking), and guide him. You don't stand across the room and shout at him; you don't call him a dummy; you don't order him to come over to where you are. You start where he is, and work from that position. That's the only way to get him to budge."

"Always deal with the problem issues up front. This establishes a base of trust, which is necessary in any relationship. Failure to recognize and handle problems allows them to color the issues and create barriers and negative feelings. [...] Count on having to deal with problems at some point. Better it be at the start."

"The boss drives people; the leader coaches them. The boss depends upon authority; the leader, on good will. The boss says 'I'; the leader, 'We.' The boss fixes the blame for the breakdown; the leader fixes the breakdown. The boss knows how it is done; the leader shows how. The boss says 'Go!'; the leader, 'Let's go.'"

"In the workforce, successful managers have learned the tremendous value of encouragement. It's the greatest management principle. Why? Because you get the kind of behavior you reward. You don't get what you hope for, ask for, wish for, or beg for. You get what you reward."

And, I can't find one of the quotes that I liked, but something else that touched me toward the end of the book was about how you can make a lasting impact on a person (a sign of successful leadership) by encouraging them that they are capable of doing something, and then helping them to achieve success while under your leadership. This will give them tools and confidence to be successful long after you are gone. This parallels what I have been thinking about the most important gift we can give our students -- the confidence that they can work at something and actually get better at it.

The book had other gems, more specific to leading a group of people at work; I really like how he's a straight-shooter, even though some of his principles are too closely affiliated with running a church for me to immediately see how it applies outside of the religious field. But these quotes above I think are excellent reminders for building relationships with our students, and I am already on my second Maxwell book (and feeling pretty excited about it)!