Friday, October 16, 2009

Math methods

When I was in school, I was pretty consistently a math underachiever, always scoring in the top percentiles on standardized tests, but rarely succeeding in class. My mother blames this tendency on my second grade teacher, who liked to announce to the whole class when I made a mistake. Some of it may also be due to gender bias -- girls weren't supposed to be good at math. But whatever the reason, it was my own lack of confidence in math that kept me from achieving well. I second guessed myself all the time. Frequently I would look at a problem and know the answer, but without knowing exactly why I knew it. Then, in trying to prove it to myself, I'd make a mistake. It wasn't until I was in sixth grade, while at the American School in London, where my math issues were identified appropriately. I didn't need remedial math. I needed more challenge and confidence. So along with 3 or 4 other kids in my grade and the grade above, we were pulled out of our regular math class and put with Mrs. Heumann.

Mrs. Heumann was one of the very best teachers I ever had. She was tiny and wildly energetic, one of those people who seemed to inhabit her whole body and also several inches of the space beyond. I had thought I'd been thrown into remedial math, but Mrs. Heumann didn't seem to know that. She worked us hard. On the very first day, she took away our pencils and paper. "We're doing math in our heads. Because you need to know that you can." And I could. We all could. And we were good at it. I moved away before the end of that school year and I was very sad to say goodbye to Mrs. Heumann. But amazingly, some of her lessons stuck, especially the one about "you can do it." I still battered my head against the wall sometimes with math, but I kept at it. I was even on my junior high math team for a year. I couldn't believe it.

But after high school calculus, I never took math again. I went to a college without distribution requirements outside the major. The closest I ever came to math again was a microeconomics class that was so bad, I stopped going to class after the first month. The teacher was canned after a single semester and I got the only D on my college transcript. Pretty good, considering I only ever showed up on test day and rarely cracked a book.

But as I see AJ struggling in similar ways, I've been thinking about all this again. AJ has a brain that absorbs higher math concepts readily. He's had a good understanding of complicated issues since preschool. But those things that require memorization or tedious practice often give him enough time to talk himself out of the simple solution and into something more complex and erroneous.

One of the things that can, I think, help students like AJ and like me back then (and maybe me now) are some alternative ways of thinking about the problem. One of the great strengths of the Everyday Mathematics curriculum that AJ's school uses is its support of multiple solving methods. But as the curriculum is actually taught, there are not that many methods endorsed. I've been digging around for other possibilities to help. AJ is very visual and physical, so here are two that have interested us in particular.

1. Finger Math. At one point in my own math struggles, my mother came home from the library with this book, or one very much like it.

I was fascinated. Based on a system used in Korea, Finger Math takes counting on your fingers to a new level by assigning different values to your fingers. The fingers of the right hand are worth 1; the thumb is 5. The fingers of the left hand are worth 10; the thumb is worth 50. This allows you to count to 99 on your fingers. The book also explains how to use fingers for adding, subtracting, multiplying and dividing, although I no longer remember the methods. I need to reacquaint myself with it. Here is a website that explains the same system.

2. Chinese method. Earlier this week, Dedicated Elementary Teacher Overseas posted a video of a Chinese method of addition that fascinated AJ and I. It involves drawing lines to represent the columns of numbers and adding the points of intersection. AJ and I were both fascinated and need to play around with this a little. Here's a video explanation:

Do you have any alternative math methods or tricks you like to use? Fill us in!

Tuesday, October 6, 2009

Transfer students

I've been finding links to this story, about a home-schooled gifted boy who tries to go to public high school, in a lot of gifted forums over the last couple of days. I feel for this kid, I do. Schools can be really frustrating to work with, as the parents of this boy know -- they pulled him out of public schools when the school's couldn't adequately handle his needs. And no one should have to take the same classes over again if he's already passed them. But I also feel like this is not totally responsible journalism. This is a very one-sided article. The school cannot adequately respond, thanks to privacy laws. And no investigation into their point of view appears to have taken place.

I think the problem here is not so much the giftedness that the author focuses on as the transfer of home-schooled students into the public schools. Schools have strict guidelines they need to follow in order to ensure students have met state mandates. This may or may not be the right approach for any given kid's education, but it's the way public schools work. It does seem to me that community college classes should count for high school providing they meet the requirements of the equivalent class. But do they? The author doesn't tell us that.

Maybe this school really is the bad guy. But in my experience, many, if not most, schools can be convinced to do the right thing if you handle it in the right way. When I was about to start my junior year in high school, I moved to a large urban public high school in Indianapolis, IN, after spending my first two years of high school in Connecticut and France. My Connecticut schools were public too, but were smaller and much more like college prep. I arrived at my new school a year ahead in English and French, and I'd finished the Latin curriculum the new school offered but wanted to keep studying. I was behind in history because, after spending a number of years in Europe, I'd never studied American history. And as my previous school had reduced gym requirements, I had to take freshman gym and health in my senior year -- oh, the humiliation! The school could have told me to just take the courses they offered. It was a huge and very bureaucratic place. But they didn't. In junior English, when the class read Macbeth, which I'd studied the previous year, I worked on Hamlet as an independent study. At every juncture where I'd studied something previously, the teacher let me choose another relevant work instead. In French and Latin, I attended a regular class and got practice speaking, but the teachers assigned me my own work that I did on my own in the back of the room. For the rest of my courses, I was able to make adjustments on my own. By high school, I was my own best advocate. I didn't need my parents' help. And my teachers were just happy, I think, to have a student who wanted to work more instead of less.

As far as I can tell, the difference in my case is that I didn't ask for alternate classes, only alternate work. I wasn't trying to get out of high school early. I just wanted to be challenged. I didn't have to deal with the administration or school board. I worked with the teachers themselves. If there was any red tape to be handled, they handled it. I also wasn't trying to transfer in credit from community college or homeschool curriculums, which may be more difficult. But it seems to me that if the issue is keeping a child challenged, going through the bureaucracy of the school is not the only way to handle it, nor is it even necessarily the best way.

School District changes gifted ID matrix

In the last year, I've learned a lot of educational jargon like "cluster" and "matrix." If only "matrix" were as exciting as it sounds. It's actually just a fancy word for the cocktail of test scores, recommendations, and school work portfolio that results in a score that determines whether or not a given student is admitted into the gifted program.

As we discovered last year when AJ had a bad testing day, the matrix in our school district has included 2nd grade OLSAT scores, teacher and parent recommendations and a portfolio of work. This sounds good in theory, but the OLSAT scores were so heavily weighted that the other things didn't really make any difference. The district knew there was a problem, but hadn't been able to put through changes. Last year only one person in our school tested into the program the normal way. AJ got in because we had him privately tested. Several other children who should be in there were not. The school said they'd retest in January when the next testing cycle began, but most of us think that is far too late. Kids should not have to wait for appropriate material.

I knew something was up when we went to the gifted program orientation meeting a couple of weeks ago and they mentioned offhand that the district would not be using the OLSAT anymore.

Today I got a call from the mother of one of the kids who, like AJ, had been informally identified but hadn't met the OLSAT requirement. I've been helping her navigate the advocacy process for her son. She heard from the gifted teacher that instead of waiting until January, they'd be using the MAP scores and, where necessary, administering the ITBS (Iowa Test of Basic Skills) and it would be happening in the next week or two. The ITBS was what I had asked for for AJ last spring. I knew they could do it -- they administered it to all the kids who'd been identified (all two of them at AJ's school). There's no reason other than money that they couldn't do it for others. I even offered to pay for it, but was told it wasn't an option. I'm glad they've come to their senses. I'm not sure what changed to make this possible, but it's definitely a step in the right direction. So it sounds like AJ's challenge class will be getting a little bigger. I'm not sure how he'll feel about that, but I think this is a very good thing.

I know this is not all due to my work. I also know the work I've done in the last year -- in advocating for AJ and others, in taking the time to get to know the curriculum policy makers, in teaching others how to advocate for their kids -- would not have gotten this far this fast if the school hadn't recognized the problem and been willing to change. But nevertheless, it feels like a personal victory. The schools may still think of me as a pain in the ass, but at least I'm a pain in the ass who got something done.

Sunday, October 4, 2009

Another day, another test

AJ came home this week with scores from the NWEA MAP testing that all kids third grade and up take in the fall and spring. The MAP is a self-leveling achievement test. The students take the test on a computer and the computer adjusts the questions based on the students answers. As more and more answers are correct, the questions get harder. The tests are used for K-12, so there are a lot of levels. This is the first time AJ has had a chance to take what I'm learning is called an "off level" test, meaning there is less of a problem with hitting the test ceiling, as he did with the WISC-IV. The MAP, however, is a very different kind of test

AJ felt like the reading part of the test was hard, mainly because a lot of the questions dealt with vocabulary, which he either knew or didn't. The math he thought wasn't hard at all. On both parts of the test, he scored in the normal range for an 8th or 9th grader, or at least that's what the charts tell me. This seems wildly high to me, but when I looked at the breakdown of what subjects are covered, they seem like things he probably knows how to do. Am I overestimating what kids know? I'm not sure. I'm also not sure this really means that AJ is performing 5 or 6 grades ahead of his level. But maybe he could be. I'm not really sure.

AJ also came home last week with a brochure from the gifted coordinator about Northwestern University's Midwest Talent Search -- an opportunity for a true off-level test. For AJ's grade level, the youngest eligible grade, that means the EXPLORE test developed by ACT (for older kids, it means the SAT or ACT), which is designed to be administered to eighth graders and used as a high school entrance exam. AJ is really interested in taking it so, as he put it, "I can see what I"m up against," but I'm not so sure what the point is. There's been a lot of testing around here in the last five months. He doesn't need the scores for anything. He qualifies for every program he might need to qualify for with the scores he already has. But if he really wants to do it, should I let him?

This brings me back to my ambivalence about testing in general. I hate that I had to cave to it last year, because I feel like his test scores shouldn't matter if he's demonstrating in class that he needs extra material. But the system is so score reliant. I've been good at getting around a lot of things in the public school system, but not the reverence for test scores.

But even feeling as I do about testing, I can see how it's useful. I'm a teacher myself, and although I don't use standardized tests with my college students, I know how important some kind of systematic evaluation can be. But at what point do you cross the line into lab rat status? And does it make a difference that AJ himself is initiating this? I don't want him obsessing about scores. Am I crazy to worry about this stuff so much?