Summarizing book notes
Jun. 1st, 2009 06:15 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
velvetpageI've discovered that Twitter is actually a good tool for summarizing notes, because it forces me to be very succinct; however it's not a good tool for storing those notes, even with tags attached, so I'm transferring them here starting now. The book isMathematics Education at Highly Effective Schools that Serve the Poor: Strategies for Change, by a team of people led by Richard S. Kitchen. It starts by setting out three themes, which are very familiar to me because they're exactly like the themes for improvement in literacy instruction. In order, they are: high expectations paired with high support; challenging mathematics content paired with excellence in instructional practice; and the importance of relationships, particularly as it regards access to immediate help and feedback. All of these are pretty much straight out of the literature surrounding reform in any academic discipline, and they're reiterated over and over again in the vision our school developed for its literacy improvement. They feel like old friends at this point.
For the naysayers who claim that new teaching methods are watering down the curriculum and failing to teach kids basic skills, there's a little paragraph about teachers seeking a balance between skills and conceptual knowledge, such that kids develop both. I have a feeling (based on the literacy research mentioned above) that the book is going to make the point that skills are best acheived using the vehicle of problem-solving, where the kids decide for themselves that they need certain skills to answer the big mathemtatics questions they're asking/being asked, and so develop the skills right along with the conceptual knowledge, in the end learning both better than they could learn either separately.
A. Thompson (1992) (if anyone wants the full reference, let me know and I'll get it for you; ditto any other cryptic reference in these summaries) identifies three main possible views of the nature of an academic discipline. The first is instrumentalist, where a discipline is seen as an isolated body of discrete skills. This is the view that gives us explicit grammar instruction - there's only one way to do it right - as well as memorization of times tables and the algorithmic method of learning basic computation. (The algorithmic method is almost certainly what you, the reader, were taught in school; it's the one that has you lining up the digits, adding the ones, carrying the tens to the tens column, adding the tens, carrying the hundreds, etc.) The second is Platonist, which regards a discipline as a body of connected and unified knowledge but still values the teacher as the sage on the stage - that is, the teacher's job is to show the students how everything fits together. I often accidentally find myself in this role though it isn't what I'm aiming for. The third is problem-solving, in which the students are given a big question, preferably one with more than one answer, and then are encouraged to find their own way to solve it. This involves the students figuring out for themselves how to compute what they need to compute, without being given an algorithm for it. Unsurprisingly, this last is the one teachers should be striving for.
It's interesting to note, though, that the authors often talk as though the Platonist and problem-solving viewpoints are complementary rather than mutually exclusive. I'll be looking to see how they see the two approaches blending; I'm guessing it's about stepping in when the kids get frustrated and pointing them in the right direction, or pointing them towards ideas that are still too advanced but which can broaden their understanding of the current topic. Recent example: my kids are not ready to explore the depths of Pascal's Triangle, but they are quite ready to model the first few lines of it with coin flipping and to figure out the pattern to extend it into the sixth and seventh and eighth rows. Now when they see it again expressed as (x + y) to various powers, they'll recognize the pattern and have an easier time with the algebra.
QOTD: Students who are provided support to develop their own mathematical strategies to solve computational problems perform significantly better than those who are taught to memorize algorithms to solve similar problems. (p12)
I'm also looking forward to seeing the role they suggest for ability groupings. Sorting students by ability is both accepted as a way to target students' specific weaknesses and ameliorate them, and maligned for creating a climate where those seen as "less-able" are given a less-challenging curriculum through the groups in which they're placed. In literacy, the solution is flexible groupings based on a wide variety of criteria of which ability in a specific area (rather than overall) is just one. I'm still struggling to implement this in math, though I've got a pretty good grasp of it in language.
For the naysayers who claim that new teaching methods are watering down the curriculum and failing to teach kids basic skills, there's a little paragraph about teachers seeking a balance between skills and conceptual knowledge, such that kids develop both. I have a feeling (based on the literacy research mentioned above) that the book is going to make the point that skills are best acheived using the vehicle of problem-solving, where the kids decide for themselves that they need certain skills to answer the big mathemtatics questions they're asking/being asked, and so develop the skills right along with the conceptual knowledge, in the end learning both better than they could learn either separately.
A. Thompson (1992) (if anyone wants the full reference, let me know and I'll get it for you; ditto any other cryptic reference in these summaries) identifies three main possible views of the nature of an academic discipline. The first is instrumentalist, where a discipline is seen as an isolated body of discrete skills. This is the view that gives us explicit grammar instruction - there's only one way to do it right - as well as memorization of times tables and the algorithmic method of learning basic computation. (The algorithmic method is almost certainly what you, the reader, were taught in school; it's the one that has you lining up the digits, adding the ones, carrying the tens to the tens column, adding the tens, carrying the hundreds, etc.) The second is Platonist, which regards a discipline as a body of connected and unified knowledge but still values the teacher as the sage on the stage - that is, the teacher's job is to show the students how everything fits together. I often accidentally find myself in this role though it isn't what I'm aiming for. The third is problem-solving, in which the students are given a big question, preferably one with more than one answer, and then are encouraged to find their own way to solve it. This involves the students figuring out for themselves how to compute what they need to compute, without being given an algorithm for it. Unsurprisingly, this last is the one teachers should be striving for.
It's interesting to note, though, that the authors often talk as though the Platonist and problem-solving viewpoints are complementary rather than mutually exclusive. I'll be looking to see how they see the two approaches blending; I'm guessing it's about stepping in when the kids get frustrated and pointing them in the right direction, or pointing them towards ideas that are still too advanced but which can broaden their understanding of the current topic. Recent example: my kids are not ready to explore the depths of Pascal's Triangle, but they are quite ready to model the first few lines of it with coin flipping and to figure out the pattern to extend it into the sixth and seventh and eighth rows. Now when they see it again expressed as (x + y) to various powers, they'll recognize the pattern and have an easier time with the algebra.
QOTD: Students who are provided support to develop their own mathematical strategies to solve computational problems perform significantly better than those who are taught to memorize algorithms to solve similar problems. (p12)
I'm also looking forward to seeing the role they suggest for ability groupings. Sorting students by ability is both accepted as a way to target students' specific weaknesses and ameliorate them, and maligned for creating a climate where those seen as "less-able" are given a less-challenging curriculum through the groups in which they're placed. In literacy, the solution is flexible groupings based on a wide variety of criteria of which ability in a specific area (rather than overall) is just one. I'm still struggling to implement this in math, though I've got a pretty good grasp of it in language.
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(no subject)
Date: 2009-06-01 11:03 pm (UTC)Any copies of any of this relating to literacy that you would be willing to provide (or originals I could borrow and copy at my school) would be very, very welcome. I'm looking at teaching myself all of this over the summer so that I can design a literacy intervention strategy for our school. You know, because God forbid the Board should actually provide us with help. Sigh.
(no subject)
Date: 2009-06-01 11:10 pm (UTC)This is one of the areas where two separate unions works against common good; there's so much knowledge out there right now in primary/junior, but even if we're technically qualified for intermediate/senior, transferring unions to accept high school jobs in literacy is a PITA and probably grievable by you guys, so you get to muddle through the old-fashioned way.
(no subject)
Date: 2009-06-01 11:14 pm (UTC)Book you lent me....Reading Power, by Adrienne Gear? Completely, totally forgot about it. Just found it on my bookshelf at home. Now it shall have to wait until July, anyway - my life is about to get crazy-insane until about June 24.
(no subject)
Date: 2009-06-01 11:17 pm (UTC)I can get you a couple of elementary phone numbers to call - the principal of the LIPTs for a start - and see if you can work out a deal to get some support from the literacy team at the elementary level. It's in the Board's best interests to get that exchange of information happening ASAP, after all.
(no subject)
Date: 2009-06-01 11:20 pm (UTC)Yes please re: phone numbers! That would be great. I'd really like to know what's happening with our feeder schools, too, so I'll hit up our Student Success team members to find some contacts there. It's such a crappy time of year to ask anyone for help, though. Not to mention I can't really do much in terms of program development right now, due to the aforementioned impending craziness!
Off to Curves.
(no subject)
Date: 2009-06-01 11:34 pm (UTC)(no subject)
Date: 2009-06-01 11:45 pm (UTC)(no subject)
Date: 2009-06-01 11:42 pm (UTC)Your best bet is to call the principal in charge of the Literacy Improvement Project, Deb Chebo (I'm not at all sure I spelled that last name correctly) and get yourself on her agenda for support in September. I'd also consider placing a call to your superintendent and seeing if you can get their go-ahead to form a multi-level capacity building task force; the middle school teachers mostly aren't much further ahead than the secondary teachers and some sharing of resources across the divisions is in order.