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updates for 05.01.2012

6 new posts today


More Problem Solving (NCTM Takeaway 3)

By popular demand (and because I need somewhere to organize this for myself), I’m going to put up a series of posts about what I learned at the NCTM conference. If you’re a math teacher, I hope this is as valuable for you as it is for me! (If you’re not a math teacher, I promise I’ll include “NCTM Takeaway” in all the titles so you’re warned in advance. These are posts you definitely don’t have to be reading. I also promise I’ll return to regular posts soon enough.)   I left all my notes at school, so today you get more problem solving puzzles, from a Logic session by Diana Cheng. I carry these around with me because I'm actually really enjoying working through them myself. The first three would work well for middle school kids, but the "Numerical Pattern Puzzles 2" are much more challenging. I think I've figured out #1-6, but #4 took me so long that I'm only now getting to the last two problems. If you get an answer to anything in the Puzzles 2 section, I'd love to see it so I can check my own work. (Or if you were really quick on #4, I'd love to hear how you did that too!) You could leave it in the comments, or save people the spoiler and email me at mathinaz@ymail.com.   Numerical Puzzles 1 1) A printer uses 207 digits to number the pages of a book. How many pages are numbered in the book?   2) In a video game, capturing a large jewel gives you 7 points. Capturing a small jewel is worth 3 points. What is the largest score that is impossible?   3) A jar is full of jellybeans If you count them by either 2s, 3s, or 5s, there is always one jellybean left over. If you count the jellybeans by 7s, there will be none left. How many jellybeans are there in the jar? Numerical Puzzles 2 4) A man goes to the bank and cashes a check. The teller read the numbers on his check wrong, and gives the man cents for dollars and dollars for cents. The man then sees a friend of his who owes him $10.00. After his friend pays him back, the man buys a soda for 66 cents. The man counts the money he has now and discovers that he has twice as much money as the face value of the original check. What was the face value of the original check.   5) A large purse is full of coins. If you count them by 13s, 23s, or 31s, there will be one left over. If you count them by 73s there will be none left over. How many coins are there in the purse?   6) License plates are issued sequentially; in a state where license plates consist of three letters followed by three numbers, the following sequence could be issued: ABC998, ABC999, ABD000, ABD001,... The last license plate issued in this state was AZY987. No letters or numbers in this license plate are repeated. How many license plates must be issued after this one before another plate will also have no repeated letters or numbers?   7) One morning, the parson tells his sexton: "I met three people on the way here today. The product of their ages is equal to 2450. The sum of their ages is the double of yours. What are their ages?" In the afternoon the sexton told the parson that he could not answer the question as asked. The parson added: "I can only say that one of the three is older than me." How old is the parson?   8 ) In the country of Nacirema, there are only two types of coins, worth 13 cents and 17 cents. Can you buy a 20 cent newspaper in Nacirema and receive exact change? How?   Seriously - if you do these problems (especially 4-8) it would be a big favor to me if you'd share solutions so I can check mine. Thank you :-)        




Examining NYC DOE's Only Egg Basket

When the leaders of the largest school district in the country decide to put all of their proverbial eggs in one basket, that basket had better be strong.  In the case of New York City, this basket is the June 2010 'research' report by MDRC entitled 'Transforming the High School Experience:  How New York City’s New Small Schools Are Boosting Student Achievement and Graduation Rates' and the January 2012 follow up report 'Sustained Positive Effects on Graduation Rates Produced by New York City’s Small Public High Schools of Choice.' This is the paper that is always cited by Bloomberg, Walcott, and Suransky when they proclaim that the ends justify the means when it comes to shutting down schools.  In his recent New York Daily News editorial, 'Close bad schools, save their students' Walcott wrote

A study by the independent education research group MDRC confirmed how well our new schools are working. Among other things, the study found that they “markedly improved graduation rates for a large population of low-income, disadvantaged students of color."
When these reports were released, many of the flaws in the conclusions were analyzed.  But since the DOE had no other evidence that their reforms were working, they continued to cite this study every chance they could.  Since the other excellent efforts to demonstrate the flaws in these reports have not caught on enough, I've decided to reinforce by analyzing the papers myself using the most recent data about the schools involved in the study. The study attempts to measure the effect of shutting down 23 large high schools and opening 216 small high schools.  As the big high schools were closed, their students were scattered around the district.  The new small schools got new crops of ninth graders so it seems difficult to compare the new schools to the old schools since they have different kids.  For this study, they came up with an interesting approach.  Since students apply to the different schools, and many of the schools require a lottery to see who gets in, they set out to compare the achievement and graduation rates of the students who entered the lottery and were admitted to 105 of the small schools to the students who entered the lottery but 'lost' and went to regular schools. The big finding was that the graduation rate for the students who won the lottery was 6.8% higher that for students who had entered the lottery but didn't get into one of those 105 schools. As an isolated statistic, this sounds moderately successful.  Certainly for the 6.8% who graduated and might not have otherwise, it is significant.  As these small schools serve about 400 students each, they have a combined enrollment of 40,000, so 6.8% is over 2,700 students.  But as I examined these two papers carefully I've determined that there are many additional factors that call the success of this program into question.  In this post, I'll highlight the most significant ones. 1.  Who wrote the paper? The paper was written by MDRC, which is "a nonprofit, nonpartisan research organization" according to the Jan 2012 update.  It was funded by Gates, which is interesting, but not surprising.  Gates funds a lot of research and much of it contradicts the corporate reform theories. What I learned, though, and what I haven't seen reported elsewhere is that while three authors wrote the June 2010 paper, Howard S. Bloom, Saskia Levy Thompson, and Rebecca Unterman, only two of them wrote the Jan 2012 update.  Missing from the update is Saskia Levy Thompson.  Why the omission?  Well, she couldn't work on that because two months after the first paper, in August 2010, she was hired as a top DOE executive making $174,410.  And, no, I'm not implying that she created skewed research to land a job, but it is still something 'interesting' considering that this paper remains the only piece of 'proof' that closing down schools is an effective reform strategy. 2.  Do the 105 schools serve the 'same kids' as the schools they replaced? The schools that had been shut down, according to the report, had graduation rates around 45%.  The new schools had a 68.7% graduation rate.  If it were the 'same kids' this would be quite an accomplishment.  Well, they don't try to claim that it is the same kids which is why they don't boast a 20% increase, but just a 6.8% one.  This is because the 'control group' which are the students who lost the lottery and had to go to a regular school had a graduation rate of 61.9%.  In other words, the kids who entered the lottery were 'better' than kids who didn't. This is revealed completely in table 2.3 on page 31 of the June 2010 paper.

The most dramatic line is the one about special education.  While 14% of NYC 9th graders are Special Education students, the percent of students who entered the lottery was actually 15.5%.  But somehow only 6.7% went to the 105 small schools.  How can this be?  Statistically, it is nearly impossible that only 6.7% would win the lottery if the pool had 15.5%.  Well, the reason was not that only that number happened to win the lottery.  But most of of the Special Education students who 'won' the lottery were not able to attend those schools since those schools, being small schools, could not offer the accommodations that they were entitled to.  This statistic, alone, should invalidate any conclusions made in the study.  Of course when you have much fewer Special Education students, you also have fewer sever behavior issues which tend to take a lot of time and energy to address. In several other categories we see that the 8th grade lottery winners were 'better' than the lottery losers. The net result of all this manipulation of the entering students could surely account for the 6.8% increase in graduation rate. 3.  What is the 'expected' graduation rate increase based on peer effects? The fact that the graduation rate of the students who went to these 105 schools was 6.8% higher than the graduation rate of the students who lost the lottery and went to regular schools can easily be explained by peer effects.  If you separate the more motivated students, they will do a little better than if you mix those students in with less motivated students.  This is something that everyone already knows.  It is not, though, something that can be the basis of a policy change.  If they really wanted to take this experiment to an extreme, they would separate all the more motivated students out and have schools just for them.  The other schools would get much worse since they would not have enough motivated students to set examples for the others.  I would have expected the graduation rate to increase by more than 6.8% so I don't see this experiment as much of a success. 4.  What about some of the other results, not often quoted? On page 53 of the June 2010 report, they have this table comparing different levels of graduation rate and also achievement results on certain tests.

Notice that the control group (students who lost the lottery) actually had a higher percent of Advanced Regents diplomas and also had a higher percent of students getting over a 75 on the Math A Regents.  Looking at this table, it is safe to say that the results of this experiment are, at best, mixed. 5.  What level of achievement have these small schools actually accomplished? Looking over the 2010-2011 Comprehensive Information Reports (CIR) for these schools, I was struck by how poor their achievement was.  In a school that is producing many 'college ready' students, we should see a good number of students taking some of the more advanced Regents.  These would include Chemistry, Physics, and higher math.  There are three different math regents, Integrated Algebra, Geometry, and Algebra 2 / Trigonometry.  Advanced 8th graders often take the Integrated Algebra Regents, even in a low performing middle school.  'Average' 9th graders and 10th graders who are behind could take that test too.  I took a random school from the list, Validus Preparatory Academy, to see what sorts of Regents they took.  Only 42% of 190 students passed Integrated Algebra.  This is a test, I know from grading it, that only requires getting about 30% correct to get scaled to a passing 65%.  Only 45 students took Geometry, of which only 16% passed.  Only 5 students took Algebra 2 / Trigonometry, of which just 1 student passed.  One student took Chemistry, though there was not a score for that student, and zero students took Physics.  The combined SAT average for this school was 1062 out of 2400.  This is only a little better than you get for writing your name on the paper. As Validus Preparatory Academy was just chosen since it was the last school on the list alphabetically, I decided to look at the 'best' school, according to the 2010-2011 city progress report.  The 'It Takes A Village' school scored at the 99.4th percentile on the city progress report.  In a school that high, you should expect a lot of kids taking Algebra 2 since that is really an 11th grade course while 12th graders would be taking precalculus, or even calculus.  We should also see many students passing Chemistry and Physics. It Takes A Village had 23 students take Algebra 2 (19 passed), 31 for Chemistry (19 passed), and 40 for Physics (25 passed) The fourth 'best' school, The Urban Assembly School for Media Studies had 9 students take Algebra 2 (5 passed), no Chemistry, and no Physics. Some other schools had higher percentages than these, but, in general the academic achievement and rigor at these schools was very thin.  For their five best schools, the average SAT scores were 1135, which was below the city average of 1222.  For AP exams, they had an average of 17% passing vs. 30% for the city.  And since the demographics of these schools gave them a 'peer index' of 2.27 which is above the city average of 2.25, they can't even use their demographics as an 'excuse.'   6.  Have any of these 105 schools been, since, shut down? As of the most recent school closure announcements, seven of the 105 schools have been closed.  This 7% is not that different than the percent of schools throughout the 1,100 schools that have been shut down. The seven schools are International Arts Business School, Gateway School for Environmental Research and Tech, Manhattan Theater Lab High School, Global Enterprise High School, Performance Conservatory High School, Urban Assembly Academy for History and Citizenship, and The School for Community Research and Learning. Conclusion Shutting down schools and reopening new ones is likely to create an illusory bump in some statistics -- in this case the 6.8% improvement in graduation rate.  A brand new school with all first time freshmen will be free of the distraction of the repeater freshmen.  In that way, I'm not surprised that there were minor increases.  But these increases are just a result of this dynamic and not from getting a crop of better teachers.  In time these schools will likely begin to suffer the same problems that brought down the schools they replaced. This is not a scalable solution and it seems to be doing much more harm than it is good. As always, I really encourage professional journalists to dig deeper into this than I am able to do in my limited spare time.  There is certainly a Pulitzer Prize in journalism waiting for the reporter who takes down the corrupt corporate reform movement.    



Laughter and stickiness

Two stories, both from my M-4 block today:

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First, a story of laughter. During today's intro to new material, R (the same R about whom I wrote a month ago) volunteered to read a word problem. The final sentence of the problem was, "Who was driving at a higher average speed?" Inexplicably, R read this as, "Who speeding highest drive?" The class and I were in uproar for a solid five minutes. Every time I tried to get back to the problem, someone (or I) would start giggling, and we'd be back to square one. I don't know what we found so funny, but it was nice to share to share some genuine and extended laughter with my kids. (Before I find myself criticized for being a terribly insensitive teacher to R, please note that (1) he was laughing along with us; (2) he is not an ELL and normally reads perfectly well; (3) I have an extremely close relationship with him and we joke around with each other all the time.)

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Second, a story of stickiness. My M-4 block is probably my most advanced class, in terms of both maturity and academic rigor. This consistently allows us to finish lessons early and either work on extension activities or, more often, engage in interesting and deep discussions about anything and everything. Today was a prime example of the latter. With twenty minutes to spare after a lesson about rates and proportions, I decided to take a risk and start gushing about how incredible it is that the Earth is traveling at a speed of about 30,000 m/s around the Sun, which in turn is traveling at a speed of about 250,000 m/s around the center of the Milky Way, which in turn is traveling at a speed of about 300,000 m/s through the universe—and perhaps more importantly, that we can measure all of these things using math and science. My kids ate it up. They were literally on the edges of their seats as the conversation moved from outer space to rocket propulsion technology, to the Drake equation, to Noetic theory, to quantum mechanics, and finally to modern theoretical physics research. In the end, it was neither a lack of topics nor the end-of-school bell that brought the discussion to a close, but pure mental exhaustion from learning and teaching so many new things. And it occurred to me after the kids shuffled out of my classroom that even if they don't remember exactly what they learned about calculating rates and proportions, at least some of them will remember that there was a day in my class when they learned how rockets work, or that there's an astronomical equation that estimates how many alien civilizations exist in the Milky Way, or that electrons behave reeeeally weirdly when you shoot them through little slits. I think that's genuinely sticky learning, and I'm so grateful for days like today, when I feel like my kids get a rare but tantalizing taste of the true value of math and science.



Patience.

Teachers need to be patient. Really patient. SO INCREDIBLY PATIENT. Because here’s the thing. Some kids will get stuff the first time. And then there are some kids who will kind of get it the first time, but then they will really get it the second time. And then there are some kids who need to see something 3, 4, 5 times before they get it. All of that takes patience. But then there are the kids who still don’t get it after six billion examples, three billion leading questions, nineteen thousand either/or choices, and 392 erasures. For these kids, teachers need the patience of a…searching for a good metaphor…they just need to be really patient. Like a saint or something. I am not a saint. Just ask my parents. So sometimes I get frustrated with making the same mistake over and over and still not knowing it, and then I let that frustration show on my face, and then the kid can tell I’m frustrated, and since their fragile self-confidence was halfway hanging on the fact that I believed they could do it, they crumple. And then I’m the worst person in the world, because what kind of awful jerkface gets upset with a kid because they don’t understand? BUT IT IS SO FRUSTRATING! I have a student who cannot multiply. It’s bizarre, because sometimes she can miraculously do it, but we have been working on things like 53 x 12 since literally November, me reteaching her multiplication every time it comes up (which, as you might imagine, is often). We worked together, one on one, half an hour a day for three months. I still have to reteach every time it comes up so that we don’t get things like 7 x 14 = 38. (For extra bonus points, can you see the mistake she always makes? Sometimes she gets 92, which is a different mistake. Write it up and down and it might jump out at you…) And it doesn’t help that this particular kid has such language issues, she just doesn’t understand what I’m saying half the time. So then we get situations where she does one problem wrong three times, we work like heck and she knows she’s getting it wrong and she knows I just explained how to do it right, but she can’t for the life of her understand what I’m saying. She’s upset because I’m using this awful excessively patient tone, which exacerbates the language issue because she’s flustered and desperate to do it right, and she still can’t do the problem. Sometimes she cries. And then I feel like crap. I have another student who cannot remember pretty much anything, especially multiplication facts. Here’s a recap of our conversation with flash cards today: Me: “What’s 7 x 7?” Her: “Uh….” (Ten seconds later.) Me: “It’s 49. What’s 7 x 7?” Her: “49.” Me: “Great! What’s 8 x 8?” Her: “Uh…” Me: “8 x 8 fell on the floor, picked itself up it was…” Her: “64!” Me: “Awesome! What’s 7 x 7 again?” Her: “Uh…” &*(&#@!&$!!!!!! Blach! It’s so incredibly frustrating. For her and for me. Anyone got ideas for memorizing multiplication facts for kids who can’t remember things reliably? I’m thinking taping facts to her desk until she memorizes one, then switching it out. Or starting everything I say to her with a math fact, the same one all day. I’m hoping desperately that one billion more repetitions will do the trick, because I’m kind of at a loss as to what else to do. I’m tired of feeling like a jerk when they don’t get it but although my patience is less than saintly my determination is terrier-like, and I’m not ready to give up yet. Until then, I guess I take some deep breaths.




Oh Praxis, What Have You Done to Me?

I learned about my acceptance to TFA two weeks before the April Praxis.  Silly me decided to give it a go.  How hard could it be?!  I’ve spent 7 years studying Biology, I’ve got this! HAHAHA.  Silly, Rabbit, Praxis is for the studious!  Don’t get me wrong – I’m sure I could have aced the test if I had taken it when I got out of undergrad.  But I haven’t stared at a plant in 8 years!  Animals?  We’re mammals, right?  Other than that, I don’t know!  And ecology?  Something with plants and animals?  I hate Animal Planet.  My knowledge of ecology ends with my ability to spell it! Minus the fact I overanalyzed every questions, was way behind schedule and almost didn’t finish, I would like to say I did complete the test.  Won’t know my score for several weeks and on the practice tests I was right at the passing line.  I studied but I’m not positive how well I did with two weeks to study.  I am going to register for June just in case I didn’t pass, but my fingers are crossed. I love tutoring with all of my heart but I wish I didn’t have so much going on right now.  I’m working 60-80 hours a week and trying to prep for TFA.  I can’t wait until the school year is over and my tutoring commitments are done.  Not because I don’t enjoy spending time with my students, but because I want to come home and collapse without worrying about the next night’s lessons.   Ironically, I am sure this is a small taste of teaching! So current status?  I’ve been smacked down by Praxis and now I’m running around like a chicken trying to get ready for June.  Ready or not, here we go!




Angels and miracles.

This morning I woke up after four hours of sleep, awake. I'm rarely awake when I wake up, but I was practically laughing. Five am, I'm clicking away, putting in grades, thinking about my lacking lesson plans. Antsy from the weekend, I emailed my sisters about my anxiety then hopped into my running shoes. 5k at six am, anyone? Haven't done that in a while, but good God was it what I needed. Hip hop Pandora station, I didn't even touch my lesson plans, just got my Do Nows and homeworks together, then ran across Dumas in the hazy dawn. The kind of run that pulls you forward. Not that it wasn't work, but my brain was so full the only way I could make space for my day was by pounding some of it into the pavement: past the post office, around the girls' house, in some lop-sided figure-eight. It was the anxiety, propelling me, flying me through the gray. Somehow I felt like my life had ceased being my own. I can't remember the last time I spent a weekend night in Dumas, can't remember the last time I sat and really concretely planned out my week, can't remember my last commitment that really held me accountable. Instead I've been swimming in a social life (not even kidding! it IS possible!), wondering how to re-immerse myself in being a twenty-something. It was the anxiety, too, that made me put on this necklace. I used to wear a bee every day, one that sister gave me, that calmed and protected me, that everyone loved. My students know it's from my sister, that it helps me feel calm about my mother's absence, that it means everything to me. I lost it. So today, digging through what jewelry I have here, I found the guardian angel necklace my dad gave me for Christmas. I'll be straight with you: I hated it when I got it. It looks like something a conservative grandmother might wear on a broach, and it's totes not my style. Today, though, anxiety and fear reigning, I giggled as I looped it around my neck. Remembered my aunt telling me the protection that comes from circles: rings, bracelets, necklaces. The sixth grade talent show is Friday, with a dress rehearsal Wednesday, both during school. I've been freaked out that I'm not doing enough, that my kids are messes, that no one understands "stage presence" or "rehearsal" or "showing up to something you committed to". Also been freaked out that our stage wouldn't show up, that we would have no PA or mics for the singers, that the lighting would be weird and my kids would, frankly, embarrass me. School, 8:00am. Students are walking in. Lisa comes up to me with a giant poster board flopping around. "Where can I put this?" "What is that?" "A talent show poster!" My students spent their weekend making more advertisements for the show. Posters had cut and glued construction paper all over. The performers names and acts written in marker across bright colors. All of this! School, 8:10am. My students have just left for block and I'm setting up my smartboard with the day's lesson. In walks Mr. W, a man I am in awe of. He coaches my girls' basketball teams, sings in the church I visited for friends & family day two weeks ago, subs in our schools, and if rumors are true is an ex-military man. As our talent show meeting started up last Thursday, he suddenly arrived in my room and stayed until 5pm, helping me coach and control all the kids. As I'm flitting about my room, too much coffee already ingested, he says, "You still need a drum set?" My heart explodes on the spot. "A drum kit? You can get us one?" He's good at dramatic effect, just stares at me for a minute with a half-smile. "Yeah, we're seeing what we can do." We being his church. "You know it will mean so much to Austin if he can play on a whole set. You are so amazing! Thank you so much!" I'm spilling over with gratitude. He nods slightly at me, pauses. "...you all have a PA or anything?" MY HEART EXPLODES AGAIN. I have been emailing and calling the junior high music teacher, desperate to get my hands on her PA for the past two weeks, to no avail. In fact, I've been downright terrified about the lack of a PA. What if no one can hear my singers? What if my dancers have no music to dance to? "You're kidding. Are you my miracle today or what? Your church can help us with that, too?" "Well, we'll see. I just thought you might need it." I gush for another five minutes, Mr. W leaves, hopefully with full understanding that I AM DYING OF GRATITUDE. School, 8:30am. My kids come back from block in ten minutes. The secretary comes into my room, "Mr. C called, he wants to know where you want the stage. He's on his way." "ON HIS WAY? WITH THE STAGE?" Mr. C promised me the stage two weeks ago, but I wasn't sure about logistics. Five minutes later, literally, two of my students' parents and a third man I've never met were unloading a three-piece 9' x 12' stage with stairs into our gym. I thought I was going to die. School, 3:10. After a stressful day, a talent show rehearsal is the absolute last thing I want to do. I tell my kids I need a five minute break and escape to the teachers' lounge for a honey bun. My vice principal offers to get his speakers from home for us to use. Gets them, brings them back. I rally the kids and take them to the gym. There unfolds our first with-stage rehearsal. I am floored, absolutely floored. When I was in drama in high school I always new I'd want to be a director, that I love doing that kind of thing-- staging and blocking, making logistics decisions, organizing. This is the closest I'll get, but I love it. My kids are hysterical, talented, and confident. They're down for anything, follow directions, and stayed until 6:30, only leaving after their repeated begs of "Can we please do it just one more time?" are turned down. Parents have started commenting that I'm stealing their kids away. All I can think with each step of this is how much better it will be next year... And it goes without saying this necklace ain't coming off for a long while.




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