Homework Success

I am trying a new homework system and so far it's working like a charm. I let kids choose which problems they want to do from the textbook -- they can literally choose ANY problems, as long as they bring me a certain number of problems each week. If they miss one week, they know that they need to do extra the next week. Their job is to pick problems of appropriate difficulty levels, show all work, and check answers against back of the book. In other words, I am more interested in them building good study habits over time than I am interested in seeing immediate results, because I find that the consistent at-home study habits are direly lacked in my high-schoolers, and the time to fix that is in the middle school while they are still young and gullible malleable.

What value does this have for them? Each week, I collect and provide feedback on all assignments. I randomly grade some problems to see if they are doing them accurately, and I comment on: the difficulty of the problems chosen, whether they seem to have already mastered this topic and ought to move on to another, if they are not checking answers against the back of the book, or if they demonstrate repeated procedural issues and need more work on this topic. Over the course of 2 or 3 weeks, I saw kids go from completely not doing any problem correctly to getting close to 100% correctness. WOW! I even had one kid write me a grateful note at the bottom of the paper, for helping her understand the concept. The truth is, I have not changed anything I am doing -- I had always been there at lunch time to answer questions, but it is the kids who have changed their behavior significantly. They now realize when they are doing something wrong, versus when they are doing it correctly every time, so their questions have become a lot more purposeful.

Amazing, eh? And I am up to about 90% homework receipt rate in most of the classes. Even my one remedial class is doing this with enthusiasm. (In that class, I took a giant leap of faith and let them choose what amount of problems to bring me, and the class agreed on 20. I was shocked, because 20 problems a week is a LOT for kids who normally don't even do 5 problems a week on their own time! But, they didn't want to lose face considering that the younger kids are bringing me 15.... And so far, they've been good on their word.) Some kids are even bringing me extra problems and turning work in when I forget to remind them the week before. It has indeed changed the dynamic of my classes, simply by offering kids a voice in setting their own goals in homework and making homework a continuous dialogue of their learning. (And, grading different problems on homework from different kids keeps me from wanting to stab my own eye in boredom.)

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This is not new, but I took my 9th-graders outside for 60 minutes of out-of-the-classroom trigonometry today, armed with their inclinometers, calculators, and measuring tape. It was so lovely, and they now have a really concrete idea of situations involving both the angle of elevation and the angle of depression. YEAH!

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I worked with my students on a systems of equations word problem today involving a mystery 2-digit number. "A mystery 2-digit number has a sum of digits equal to 7. When you reverse its digits, the value of this number increases by 27. What is the original number?"

It was such a lovely problem because I got to work with kids one on one and discuss base-10 number system at length. We worked through 639 = 600 + 30 + 9 = 6(100) + 3(10) + 9 and I asked them what a two-digit number "ab" will have as its value. Kids were all able to come up with a(10) + b, and then come up with the equation a(10) + b + 27 = b(10) + a more or less all on their own!

It was awesome. I love it when I remember to facilitate students using the concrete -> abstract continuum and I can see the mind spark that it generates. I had a professor in grad school who used the same continuum whenever introducing new abstract ideas, and he is one of the clearest lecturers I've ever had. Note to self: Never start a discussion with algebra...

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Lastly, I am really excited to get into the nitty-gritties of mathematical modeling with my 8th-graders. We are finishing up the second round of lab writeups this year, and this time they even incorporated graphing calculator regression results and discussed the R^2 values. I think that during the rest of the year, I will guide them through a series of optional MYP pattern-investigation tasks as enrichment to our regular curriculum, and they will need to choose one task at some point to complete a full writeup for. This way, before they even go into the high school, they would have already had some experience with the two types of portfolio tasks in the IB program and understand mathematical processes at a high level.

(For example, right now I am looking at a task that ties nicely into our systems unit. They need to generate multiple systems with consecutive odd coefficients and constants, such as 5x + 7y = 9 and 23x + 25y = 27, to recognize the pattern in their solutions, to test their generalization, and then to prove their generalization using algebra. How brilliant and challenging.)

For this and other reasons, work is INSANELY busy. The weather is starting to be beautiful in Berlin, but I have yet had any time to enjoy it!

MYP Grades

I know this seems obvious, but I am a big proponent of giving very realistic grades and very specific feedback. In the MYP, final class grades are given on a scale of 7. To me, this is how I view different levels:

MYP levels	How I see the student
level 7	A student has demonstrated both conceptual and technical fluency in all topic areas. They can approach new situations with independence and confidence. For a student in level 7, I pinpoint areas where they can still create further goals for themselves, so that they understand that a grade of 7 is not an end-all.
level 6	A student has demonstrated technical fluency in all skills learned during the semester, but sometimes cannot see the bigger picture and therefore misapplies skills. The difference between a level-6 and a level-7 student can also be their level of independence in approaching new situations.
level 5	A student demonstrates a "normal" achievement in their grade, with an ability to independently perform maybe 75% to 80% of all of the skills and a reasonable ability to articulate the big ideas.
level 4	A student has working knowledge of a vast majority of the topics but needs frequent help to get through the nitty gritty algebra of those problems. A level 4 student demonstrates procedural issues mostly, coupled with small conceptual issues.
level 3	A student has serious gaps/misconceptions in one third or one half of the key areas. Typically, a level 3 student has not taken the responsibility to seek help outside of class to address those major areas of weakness.
level 2	A student only demonstrate some small pockets of effort, very inconsistently, throughout the semester, and has also poor mastery across the board with the content topics.
level 1	A student basically sat around and did practically nothing (even after various conversations with students and parents), did not turn in most assignments, and has a poor understanding across the board with all topics.

For me, thinking about grades like this has been very liberating. I don't feel the need to nickel and dime kids on particular assignments, although I still record and look at all of their grades when making this determination.

In this sense, the grading encompasses both their learning habits and their academic performance, which I believe go hand-in-hand to indicate a child's success. In the MYP, by the way, this breaks down further into 4 different grading criteria: Knowledge and Understanding (for example, quizzes and test grades); Communication in Mathematics (for example, clarity of explanations in writing, and appropriate use of symbols and sufficiency of work shown); Modeling in Mathematics (for example, labs and patterns investigations that take a student from data to equation to predictions/generalization to explanations); and Reflections in Mathematics (for example, does the student complete test corrections regularly to reflect on and learn from their mistakes? After a lab, do they provide a complete error analysis to reflect on sources of inaccuracies in their data?). Those are criteria we look at when we determine whether a student is a 1 or a 7, but in general, their final grades still need to reflect where they stand, both academically and as a student who is still learning to learn.

It is important that you do not inflate grades in the middle school, because if you do (which unfortunately happens sometimes, because some teachers want to keep middle school chummy-feely like elementary school), you end up sending home the wrong signal that the student is doing "OK", and they end up in high school with both sub-par skills and study habits. Yikes. I find that when I have a clear framework of what different MYP grades mean to me (as I outlined above), I can more confidently assign grades and not have to feel bad one way or another for possibly inflating/deflating.

I also think that it is very important in an MYP program to have the same teacher for two-year rotations, because the goal of giving holistic grades is to provide opportunities for improvement. If you look at my impressions of the grade boundaries above, it is quite "easy" for the kids to move from one boundary to the next with some motivation and work. Transitioning students from teacher to teacher every year can be very disruptive in that process, and confusing in their attempt to grow as learners. Following a two-year rotation, it is my personal belief that going to a different teacher becomes beneficial, as the student learns to not rely too heavily on a single teacher's teaching style, and instead becomes more self-reliant.

Grade 7 Buttons Sale Project

I am very excited and NERVOUS about our Grade 7 buttons sale. It's an idea I got from a former colleague/supervisor, but I've modified it to have the kids actually design buttons and sell them.

So far, here's the deal:

* I investigated and found a German website that makes custom-made buttons (aka. badges or pins). They cost 1.14 Euros each if you order 50 buttons at once, or they cost 1.02 Euros each if you order 100 buttons at once. Each order goes with one design (so if you want multiple designs, you submit an order for each).

* The kids start by sketching out some button designs. They then take their 3 favorite designs to conduct an informal market research. Questions to ask: Would you buy this design (and which design out of the 3 would you most likely buy)? How much would you pay for this, knowing that the proceeds are going to support charity? The kids are encouraged to ask at least 20 people, some within our class and some outside, so that they can get a realistic read on the market and also support the business plan they will write, with actual data.

* We sit down and start creating one table / graph / equation altogether to compare buttons sold and profit made. For simplicity's sake, we assume first that we will order 50 buttons and we will sell at 2 Euros. The kids answer some questions about how much profit we'd make if we sell zero buttons (pure losses) or all 50 buttons. They also analyze the break-even point. They do this all on their own with little help from me, but I do go around and check their answers, and we discuss the analysis as a class after they have completed all questions on their own.

* Then, the most exciting thing happens! They continue on to part 2 of the project, in which they have to choose 3 different price points to sell the buttons at. They make the same analysis as before, assuming still that they order in bulk of 50 buttons (with unit cost 1.14 Euros). And after that, they create another table for analyzing what would happen if they ordered 100 buttons at once (with unit cost 1.02 Euros), again comparing numbers of buttons sold (up to 100) and the net profit.

* As they finished the tables, I went around and showed them how to check their table values by writing the profit equation, putting it into the graphing calculator under [Y=], and pulling up the table of values for that function. A little bit of technology and math for my Grade 7's! Woohoo!

Today, all the kids more or less finished this last part above. They were so excited about the whole thing that they wanted to keep working on it, even though I gave them the option of stopping and playing a group game halfway through the period (it was Friday afternoon).

This means that next week, they will only need to: finish making their graphs for these new functions, analyze their equations, break-even points, potential for sale (based on informal market research), and then they will be writing the business proposal to submit to me and the principal! yay.

I have already gotten permission to choose two best business plans, to split the class into two groups, and to actually order the buttons / carry out the sales. All proceeds will go to a charity of their choice.

Lovely! I'm nervous we'll lose money in the end, but it's the uncertainty that makes this business project great!

Assorted Updates

Howdy, world!

Things have been busy since I got back from Belize, but I wanted to jot down some updates before I forget:

* I am very thankful that over the holidays I had a chance to co-chaperone our school's Senior Math Competition Team to go to the Hague to attend the ISMTF competition. The kids were absolutely wonderful, and two of them placed at the competition -- a really amazing accomplishment out of about 200 contestants, considering that many of the problems were quite tricky even for their math coaches, and the individual competition consisted of 10-minute lightning rounds in which you had to correctly complete as many questions out of 5 as possible (during 10 minutes). But, the thing that I loved the most about this experience is meeting some amazingly dedicated math teachers from the IB world -- many of them are international teachers who have taught and coached math teams at the same schools for nearly 30 years. They have known each other since they were freshly married and have become lifelong friends and colleagues, who look forward to the annual meetup and visit each other on holidays. They were so inspiring (because these were definitely NOT stale old teachers) and they made me think about where I will be in 30 years. My colleague, who has been going to these competitions for more than 20 years, is a mini-celebrity at these events and has organized a few of them herself. (That is no small feat, considering that it involves -- amongst other things -- finding enough local parents to host 200 kids for free and to provide them with dinners and rides!) The orchestration of the competition was like Swiss clockwork. I was immensely impressed, and the kids had so much fun bonding with each other, with me (whom they didn't know before the trip), and even with kids from other schools!

This experience has made me want to become a second math coach for the Senior Team, so that I can make sure I get a chance to go to these competitions annually. (And because I was frankly embarrassed by how long I took doing those problems this time. I need to train!) But, we'll see if I can actually commit to weekly Thursday math sessions after school...

* I am also thankful for my colleagues. For reasons I wish not to discuss publicly, I found myself returning to school in a fairly difficult situation. To my surprise, colleagues who happened to come across the news of the situation have come to me to offer their support/recognition of my teaching and my dedication to kids. My supervisors have also basically offered their faith in my work without questions. It has made me very thankful, despite it being a difficult situation that has yet to be resolved.

* I have been thinking about blogging about the awesome method the British use to teach young children to read. Did you know that in many places in England, they do not teach kids the names of alphabetical letters until the kids have learned to read phonetically? For example, instead of teaching a kid that the letter D is called "dee", they teach the kids from the get-go that it's called "duh" and that "G" is called "guh". Today on the bus, I heard a little girl say, "Duh, oh, guh... that is dog! Eh, guh, guh... that is egg! Huh, aaa, tuh.. that is hat!" It was clear that she is just learning to read, and she was easily piecing together the phonetics that she already knows. That makes so much more sense than how we teach kids the names of the letters first!!

* I recently watched a middle-school production of Romeo and Juliet. I had thought that I would hate how they would switch out the entire cast every 15 minutes to allow more kids to go on stage (imagine 10 Romeos and 10 Juliets in the span of 2 hours), but in the end I just found it irresistibly charming that there is actually a theater production that involves the ENTIRE 8th grade, with no exceptions. What a truly lovely idea -- and the kids were so excited about the whole thing before, during, and afterwards! I heard kids say, "My parents are here, and they don't even speak English!!" Awww. They even did the infamous Cha-Cha line dance during the scene where Romeo sneaks into Juliet's house during a party and meets her for the first time. Truly, it was the cutest thing ever and was worth getting back home at 11pm after a late-night bus ride.

* I am thinking about going on a backpacking trip through Asia this summer. I think I can swing 4 weeks, and maybe I can meet up with friends who already live there (Andrea, who's in Seoul; Helen, Aaron, Howard, Skye, who are in Taiwan; friends from college who live in Singapore; Stephanie, who lives in Hanoi...) I am very excited! The flights cost about $1000 roundtrip, which I think is reasonable, and then I can just take trains from place to place. Do you have recommendations? I've never done something like this before, and definitely not solo! To be perfectly honest, I'm quite nervous, but I think this could be my last summer in a long time (possibly ever) to be able to do this... And Geoff, my better half, has already done this a long time ago, so it's unlikely that we'd ever do this together. So, it's definitely on my mind.

That is it. Peace out, world.

Destination Wedding Planning

Geoff and I have started working on the logistics of our wedding, and I am actually genuinely surprised by how complicated even the details can be!

Originally, we were going to have a summer wedding, since as a teacher that seems to make the most sense for me to get married during a long vacation (and Geoff's schedule is flexible). But, as it turns out, we decided that we wanted a destination wedding -- both to trim down the overall wedding costs for us and to allow us to spend some quality time with our guests who do decide to come -- and that changed everything. We picked out Belize as our desired destination, because we had both loved the island of San Pedro when we visited it a couple of years back. We checked airfare briefly and it costs about $500 to $600 to fly roundtrip from the States, so it's not entirely out of the realm of possibility for our friends who may wish to come, but at the same time would help to keep the wedding small and intimate. Plus, having the wedding in Belize opens up the slim possibility that our Salvadoran friends (who don't make American wages) might be able to fly/bus in as well to come to our wedding.

But, the decision to have a destination wedding in Belize changed everything because we cannot get married during the summer months (June - August) in Belize. That's the rainy season, so now we have to get married either during my February break (1 week) or my Easter break (2 weeks). We have not totally made up our minds yet as to which time frame is better in 2013 (since February is too hectic for us in terms of traveling from and back to Europe, and April is possibly more expensive for our guests because Holy Week is a popular Latin American holiday), but Geoff and I contacted a wedding planner and took a trip to Belize this past week (during my very short February break) to look at some potential venues and to meet our destination wedding planner.

Whew. I've never been one to dream of a perfect wedding (I think the most romantic part is to marry someone you have already been with for a number of years...), so to me the wedding-day logistics actually aren't so important as making the schedule and the cost feasible for our guests. Geoff and I looked at a variety of venues and resorts, some very posh and some that are more casual. (Geoff likes the posh resorts, because he thinks that people who are paying to fly to Belize will expect a certain level of luxury, but I prefer the more casual locations that have a more authentic island feel.) Even though many of our guests might opt to stay at hostels -- and San Pedro has some truly lovely ocean-view hotels/hostels that are reasonably priced and centrally located -- we wanted to give our friends an option of staying in our close vicinity, at the same resort, if that's what they choose to do. After visiting places with our wedding planner, we still have not decided anything -- not a date nor a venue, because we are waiting to hear back about group room rates and also whether we can block entire sections for our wedding guests. But we are very excited! During our short second trip to Belize, we had such a great and relaxing time in this tropical paradise that it absolutely affirmed our decision to get married there. Everything just felt perfect this second time back; we think that our guests will have a blast with all of the natural loveliness that Belize has to offer.

So, consider this a teaser! I am nervous that it's not all going to work out, but we're super excited that it could be completely amazing. :)

PS. Here is the link to our wedding planner's blog. She has some amazing photos of past weddings, that give you a feel of the raw beauty of San Pedro!

Three-Variable Charts

In the context of preparing my students for their IB portfolios, I realized that it is absurd/funny that in secondary math we don't often deal with three-variable relationships, for example when both volume and temperature will affect pressure. In science, I am pretty sure that at the secondary schooling level you'd discuss things like when you change only one variable to see its effects, and afterwards you hold that one as constant and change another variable, and in the end you try to aggregate their overall impact on the outcome. In secondary math, we (ironically?) shield the kids from this. So, for much of their schooling, kids only know how to make and analyze two-column t-charts involving two variables.

In IB, the curriculum certainly expects a bit more, at least in its portfolio investigations. The IB portfolio tasks go straight into the investigation of the individual and aggregate effects of two variables on a third variable. This notion is unfamiliar to the students, so I was thinking about how to introduce them to this idea of observing and representing three-variable data.

In thinking about how to broach this, I was reminded of the sizing charts I often see on the back of the commercial packaging of tights/stockings. If you have never bought a pair of tights before from a certain brand, you often need to read the sizing chart to check the correct size to purchase. And what are the TWO factors that determine your size of tights? --Height and weight, you say. (Or, at least I hope you do. One of my girls immediately replied today, "Height and color!" sigh. Is it too much to hope that they like math over fashion?)



The boys in my class giggled when I brought this up as an "everyday" example of visualizing the relationship between three variables. (One of the boys said, "These IB tasks are sexist.") Two variables go on the outside of the table (ie. weight across and height vertically down), and the contents of the cells -- ie. the size in this case -- would represent the third variable. In mathematical terms, when you organize something in a table of this form, you can more easily find the formula f(a, b), where the "key" or input to function f is a tuple of two variables, rather than just a single variable.

Again, it's funny to think that this type of relationship must be very common in "the real world", and yet we discuss so little of it in school. Can you think of other everyday examples (ones that won't make my high-school boys giggle)?

My First Screen-Capture Vodcast!

Since I was not able to find a video introducing the kids to Type I tasks for the IB, I thought that I should try to make my own.

Here it is. I had to record it a few times because:

1. The screen capture program kept canceling out because Escape is one of the hot keys for canceling and I hadn't realized. So every time I hit Escape from the Prezi full screen, my screen capture video would disappear without an error message. I had thought for a while that I was maxing out the recording time limit, but eventually I figured out what was happening.

2. When I finally successfully taped one, I found myself "huhing" and "umming" too much. It was annoying, so I had to re-do it.

In the end, it's not perfect, but it's alright. I cannot tell if it's just me, but the audio and the video got a bit out of sync towards the end, but I think it's still something I'll save for the future, because it's always better to give the kids something they can watch at home in case they have questions while completing the project. And I am pretty amazed by how easy it was to do! I used "Free Screen Recorder" and the built-in microphone to my laptop, if you're curious. The program is free and the AVI pops up automatically after you save the file.

Addendum February 8, 2012: My students thought it was very helpful to look at the video side-by-side with looking at an actual project sample from the past. I walked them through the infinite surds task in order to illustrate the different stages of the mathematical investigation.

Intro to IB Type 1 Task

I pulled together a Prezi for introducing to my students the necessary elements of the IB internal assessment Type 1 task. In the IB program, the kids have to do two portfolio assignments, each of a very different nature. I personally enjoy looking over the tasks, because they involve doing very rich mathematics. What I don't enjoy is that the kids have to do these difficult tasks alone at home and that similar tasks are not built into the rest of the IB Math curriculum.

Anyway, different from Type 2 tasks (which involve modeling a real-world set of data with different function types, choosing the most appropriate function based on end behavior, and justifying the choice based on the context of the data), Type 1 tasks involve looking for and generalizing patterns. Last time I was able to find some great resources (vodcasts) for introducing the kids to Type 2 tasks, but this time I did not find parallel resources for Type 1 tasks. So, I pulled together a Prezi and when I have time over the summer, I'll flesh out another presentation in similar format, going through one specific example task.

Here is the Prezi, if you are an IB teacher and are interested in possibly using it in your class. To walk myself through the steps of the IB Task 1, I have looked at 4 different recent tasks: the stellar numbers, the infinite surds, logarithm bases (if log(X)/log(a) = c, log(X)/log(b) = d, what is log(X)/log(ab) in terms of c and d?), and a problem involving matrices. All four are drastically different in terms of the mathematical content they use, but I think they are all excellent applications of IB topics, just at a fairly sophisticated level. I have to really think about how to incorporate pieces of them better into my classroom in order to enrich student learning consistently and to reinforce their algebra skills!

Project Pictures

For me, January is the best time to do projects, because it's a fun/nice way for us to ease into the second part of the year. :) So, here are some project photos!

Here is the best 3-D project of this year! They call it a pencil rocket. It's made up of an octagonal prism, topped by an octagonal pyramid, with four right triangular-prism fins and a rectangular concavity. (They are going to put a picture of their friend inside the rocket concavity.) The kids calculated the volume and surface area of this thing they had designed, and made 2-D nets. The other projects are still rolling in slowly, but if any of them turn out to be amazingly cool, I'll post more pics!



And a few beautiful systems of equations project posters from my 8th-graders!



Heart.

The project madness goes on, however. I'm still manning hands-on projects in Grade 7 (a bunch of uber-cool patterns activities I got from my old Department Chair from NYC), culminating in a Buttons Sale. The kids will design their own buttons and write a business plan, and the principal and I will pick two plans, provide the seed money, divide the class into two groups, and see if they can actually make the profit they intended to make.

In Grade 8, we're doing the bungee jump project... which is always my favorite, except this year there is a bit of twist. The rubber bands I got from the school secretary for free are of low quality, so every time they do a new trial, they have to make a brand new rope with all new rubber bands to ensure the rope hasn't already been stretched out!!! I guess it's not too bad, considering they'll only be trying up to about 8 or 9 rubber bands before they do the regression/prediction and build the "for real" rope. But still! Definitely a twist I had not not anticipated from the past years' experiences of doing this project.

In Grade 11, I assigned as a semi out-of-class project for the students to work on the wonderful trig project from Kristen. (To be nice to them, I didn't mention that last year I had given the same trig project to my honors 9th-graders. Oh, how I miss those amazing 9th-graders!!) I've only given the kids one full day (80 minutes) to work on the problems in class, during which the class maintained that eerie silence for a while as they had to think hard about how to approach the problems. We'll see what final questions they will have tomorrow, and whether they can come up with all the correct numbers by next week!