First, kudos to Michelle for leading a terrific discussion on this chapter. I thoroughly enjoyed the class.
The more I read through this book and reflect on Boaler's research the more I become angered when I walk into the math classrooms I find myself in. Everywhere I turn students are disinterested, disruptive, unwilling to engage, and excude hopelessness. We are the Amber Hill's of the world and after realizing the implications of such an identity we still remain resistent ot change. I recall my first two years of "teaching" - if I can call it that - junior and senior high. Overwhelmed with the business of the job and feeling disillusioned most of the time I did notice some interesting facets of how a math class can work better. Throughout Boaler's discussion regarding "Time On Task" my mind goes back to those two years. I began to notice that class management - the behavior and flow of the class was so much better when the students saw more of the front of me and less of the back. Besides being able to span the classroom and spot those off focus, the students in general felt more engaged, more a part of the math learning that was taken place. Whether I taught from a projection unit or from my laptop through power points and graphs the class was quieter, questions of interest from the students were more frequent, and the sense of enjoying the math rose so much higher. Today, I realize even this method of teaching is not the ideal practice, it sure was a huge improvement from the times when I basically taught "chalk and talk".
As I move about from school to school this fall I see the excitement in student's when the smart board becomes a tool for learning in class. They want to use it, experiment with it, and have it a part of the routine in math class. I wonder if we as teacher's have the same enthuasism? A lot of us don't have the training, confidence, time - whatever reason (or excuse) we'll use to impliment many of the new technologies available for teaching and learning. We are working against the grain in so many aspects of the education system. We have to basically fight tooth and nail for resources, plead for PD to be able to adequately implement these new sources into the classroom. However, we must find a way to make sure this change happens. We need to collaborate and unit like teachers of Phoenix Park and develop pilot projects on a small scale at first to test the water, to fell the security if that's what's necessary to essentially catch up with a generation that is moving beyond the ways and means we remain stuck in. With respect to open-natured teacing methods at Phoenix Park, Boaler noted that "what for some students meant freedom and opportunity, for others meant insecurity and hard work." I think the same could be true for many of us teachers. For some, we can finally tear ourselves away from the textbooks and test-driven nature we've been mandated with. For others, such a teaching style would open up vunerabilities and insecurities - which can be rememdied and which can be changed.
We've been complaining about the textbooks in our high schools particularly since they were brough in during 2002. As the years went by more issues were brought to light about the inappropriateness and inadequacy of these for student learning. Not enough practice! Not enough examples! No answer keys! Those chants echoed in every corridor around the province by students, teachers, and parents alike. To remedy the situation, some of us locked up the textbooks and replaced them with plasters of worksheets, binders of teacher notes and workbooks that some parents, some students, and even some teachers began buying hand over fist - all in an attempt to "fix the math". However, the problems still remain. Scores have not increased. MPT success is dropping. Frustrations are growing. Pockets are emptying. And, the reputation of mathematics continues to crumble. Why aren't the voices calling on a new approach to teaching math being listened to? Are our parents misinformed on how their children are learning? Are we, as educators ignorant to the implications our teaching acts are having on many of our young people? Yes, it's definitely challenging and scary times in our math classrooms.
Thursday, October 29, 2009
Saturday, October 17, 2009
Chapter 4 - Amber Hill Experiences & Reflections
First, congratulations to Sharon for leading and delivering a very organized and interesting discussion on Chapter 4. The class led to some particular issues that I wanted to bring forth here in my blog.
Our discussion and Boaler's research provided to really reflect on how much "learned helplessness" we are disabling our students with. I pictured myself there as Tim in the math class, embarassed that I too perhaps acted out very much like he did some of the time. I knew students in my class were distracted, they weren't listening. I waled around my classroom as students worked from their textbooks adn instead of asking them to really think hard about the problem I would end up helping many of the weaker students out by providing a receipe - a step by step set of instructions to get them through the problem successfully. Did I do that out of pity for the students who I though just couldn't get it? Was it just to satisfy my own frustrations with the students who couldn't learn from my teaching? (What is wrong with them, they couldn't learn from me - I taught it clearly, didn't I???) In the end my leading questions, my coaxing, my ignoring of wrong answers, and my endless lists of rules and algorithms did nothing for those who never really got it the first time around. My way of teaching was not working for those who needed it to work, who depended on it to work. I was in such a panic to in getting through the work, in meeting the deadlines that I rarely afforded my students time to really think and grapple with the problems I had given them to consider. I look back now and shamefully realize how many things I was doing wrong in my class, that was really to their detriment. Why didn't I see it then? Why did I do the things I did? We are addicted to teaching the way we are. It has become so ingrained within us that change seems almost incomprehensible.
Hilary's teaching of trigonometry also send me back to the past, questioning if my teachign was as ineffecitve as hers, if I ended up confusing my students more with enless rules to remeber and unclear explainations all in an attempt to give my students a procedure to learn . Now ina ll honesty, my students probably did not develop a clear sense of what the rules meant, where they came from, or how they related to different situations they encountered. Three years later, and after many mistakes, Boaler and our discussions made me realize that I, like Amber Hill teachers, are "driven by a desire to compartmentalize and provide models and structures that make sense for teachers but often do not for students" (p. 32). We are driven by the race against the clock, against ourselves - trying to pass a test that we are set up to fail. Given the structure we have in place, all of us as teachers, really are set up for failure. We will not cover all the curriculumt he way we want to, we will not meet all our students needs the way we know they need us. Then, we blame ourselves and the system. Every year it's the same routine. But really, do we try to change it? Sure we do, we go faster, assign less questions, further falsely exemplying the myth that mathematics is all about speed. We, too, end up lowering our expectations.
During the discussion in class I raised the notion if we as educators do expect less of ourselves and our students if we are teaching in a socio-economically deprived school versus an urban setting where parents are generally more educated and achievenments are often higher? Is the bar lower in the working class, rural schools? Are we satisfied with minimum successes in our math classes if we know we won't be held as accountable? One thing is for sure though, the students often meet us where we hold the bar.
Hearing the students voices through the quotatiosn Boaler presents here really gives us a wake up call that students do want change. The only ones standing in the way of this change, is us. We hear from our students on a regular basis, the brighter ones too, that the work is boring, monotonous, yet we continue to stuff it to them, we continue to stay the course - all int he name of perceived success in testing. I knew my most intelligent students were extremely bored within my grade 9 class. It was not until late in my second year of teaching that I really realized students apperciate and develop cognitive thinking at a higher level when their work is made enoyable. We dubbed the day long math workshop for our students "Math Fun Day" and in groups scattered about our gym they were givena series of small projects from the four main topic they studied in the previous months. I finally seen so many of my students happy, but also engaged, inquisitive, and relaxed. They remakred to be after that the stress of assessments had entirely left them. They were learning the concepts I tried beating into their heads with boards and books simply by using their hands with tangible products. They still made mistakes but they laughed them off and reflected on why their project results didn't turn out as they had hypothesized. Then I knew assignments and tests handed back with red ink all over them really didn't result in students reflecting on why they went wrong, really didn't correct the mistakes students made, really didn't improve their interest or their learning.
With the images and thoughts resurfacing from that math fun day Boaler brought back to life many ideas that I questioned back then too. How useful are time-on-tasks as an everyday lesson plan for mathematical learning? To what extent does our obsession with keeping students quiet and orderly play in inhibiting real learning from taking place? Like Keith (p.41), as soon as many of our students enter the classroom and open their textbooks they are switched off. The rule following can't be helping either. The cue-based teachign we transmit is doing more long-term damage than we even realize or will acknowledge. However, we hold on to the conventional pedagogical practices in mathematics but still scratch our heads and wonder why so many of our students stop working.
Our discussion and Boaler's research provided to really reflect on how much "learned helplessness" we are disabling our students with. I pictured myself there as Tim in the math class, embarassed that I too perhaps acted out very much like he did some of the time. I knew students in my class were distracted, they weren't listening. I waled around my classroom as students worked from their textbooks adn instead of asking them to really think hard about the problem I would end up helping many of the weaker students out by providing a receipe - a step by step set of instructions to get them through the problem successfully. Did I do that out of pity for the students who I though just couldn't get it? Was it just to satisfy my own frustrations with the students who couldn't learn from my teaching? (What is wrong with them, they couldn't learn from me - I taught it clearly, didn't I???) In the end my leading questions, my coaxing, my ignoring of wrong answers, and my endless lists of rules and algorithms did nothing for those who never really got it the first time around. My way of teaching was not working for those who needed it to work, who depended on it to work. I was in such a panic to in getting through the work, in meeting the deadlines that I rarely afforded my students time to really think and grapple with the problems I had given them to consider. I look back now and shamefully realize how many things I was doing wrong in my class, that was really to their detriment. Why didn't I see it then? Why did I do the things I did? We are addicted to teaching the way we are. It has become so ingrained within us that change seems almost incomprehensible.
Hilary's teaching of trigonometry also send me back to the past, questioning if my teachign was as ineffecitve as hers, if I ended up confusing my students more with enless rules to remeber and unclear explainations all in an attempt to give my students a procedure to learn . Now ina ll honesty, my students probably did not develop a clear sense of what the rules meant, where they came from, or how they related to different situations they encountered. Three years later, and after many mistakes, Boaler and our discussions made me realize that I, like Amber Hill teachers, are "driven by a desire to compartmentalize and provide models and structures that make sense for teachers but often do not for students" (p. 32). We are driven by the race against the clock, against ourselves - trying to pass a test that we are set up to fail. Given the structure we have in place, all of us as teachers, really are set up for failure. We will not cover all the curriculumt he way we want to, we will not meet all our students needs the way we know they need us. Then, we blame ourselves and the system. Every year it's the same routine. But really, do we try to change it? Sure we do, we go faster, assign less questions, further falsely exemplying the myth that mathematics is all about speed. We, too, end up lowering our expectations.
During the discussion in class I raised the notion if we as educators do expect less of ourselves and our students if we are teaching in a socio-economically deprived school versus an urban setting where parents are generally more educated and achievenments are often higher? Is the bar lower in the working class, rural schools? Are we satisfied with minimum successes in our math classes if we know we won't be held as accountable? One thing is for sure though, the students often meet us where we hold the bar.
Hearing the students voices through the quotatiosn Boaler presents here really gives us a wake up call that students do want change. The only ones standing in the way of this change, is us. We hear from our students on a regular basis, the brighter ones too, that the work is boring, monotonous, yet we continue to stuff it to them, we continue to stay the course - all int he name of perceived success in testing. I knew my most intelligent students were extremely bored within my grade 9 class. It was not until late in my second year of teaching that I really realized students apperciate and develop cognitive thinking at a higher level when their work is made enoyable. We dubbed the day long math workshop for our students "Math Fun Day" and in groups scattered about our gym they were givena series of small projects from the four main topic they studied in the previous months. I finally seen so many of my students happy, but also engaged, inquisitive, and relaxed. They remakred to be after that the stress of assessments had entirely left them. They were learning the concepts I tried beating into their heads with boards and books simply by using their hands with tangible products. They still made mistakes but they laughed them off and reflected on why their project results didn't turn out as they had hypothesized. Then I knew assignments and tests handed back with red ink all over them really didn't result in students reflecting on why they went wrong, really didn't correct the mistakes students made, really didn't improve their interest or their learning.
With the images and thoughts resurfacing from that math fun day Boaler brought back to life many ideas that I questioned back then too. How useful are time-on-tasks as an everyday lesson plan for mathematical learning? To what extent does our obsession with keeping students quiet and orderly play in inhibiting real learning from taking place? Like Keith (p.41), as soon as many of our students enter the classroom and open their textbooks they are switched off. The rule following can't be helping either. The cue-based teachign we transmit is doing more long-term damage than we even realize or will acknowledge. However, we hold on to the conventional pedagogical practices in mathematics but still scratch our heads and wonder why so many of our students stop working.
Experiencing School Mathematics - Ch 3
Structured, disciplinded, and controlled. In a nut shell that basically summarizes the illusion many teachers, administrators, and district personelle have when they picture the ideal classroom and school. We have become exceedingly great at molding the clients into beings that learn, listen, and respond in a unision of our choosing. We bend over backwards in our institutions to induce obedience and conformitiy to the nth degree. We tell students to "just be quiet", to "put their heads down" , to "just sit there" if there's not willing to participate - all in the name so that we can cover the curriculum, so that we can get our end of the job done. The fallout is huge, but we plead innocent, helplessness. The mess of a system we have helped to create has polarized our students and staff alike. Teachers pin themselves against each other to hoard materials, to secure funding for their department. Our staff rooms are no different than the student's cafeteria - we immediately congegate ourselves into "strong subject loyalties" as the students hoard into their familiar peer pockets. What Boaler describes in Amber Hill is very much what we find, but more sadly, what we want to find in the school we teach at. It's less stressful on us, right? Our parents will give us less grief if we follow the status quo. We perceive these schools as being safe, secure, stable. Us teachers like that. A lot.
One idea that was raised in our class continues to stay with me. We talked about the teacher who come June 1 claps the chalk off their hands and says "I'm done." We've imparted the necessary knowledge from the curriculum unto our students. We've got all our mandatory tests in, all review sheets practiced and corrected, and heaven forbid all the "good questions" from the textbook assigned. Why do we continue to think this way? How come we don't want to raise the bar, to dig further, to take the extra time and investigate mathematical modelling situations with our students? Why are we stuck? Some say it's the time pressures, the work load, the fact that come May and June we are worn so thin we just want to survive. I say it's because that's what our school systems, our departments of education have expected of us, because that's what we believe our jobs are. As Edward Losely was quoted as saying "you've got the national curriculum basically and if you cover the national curriculum you're doing your job." However, the jobs we're doing are failing children, are dismantling many of their inherent abilities. Oh sorry, I forgot, those abilities aren't wanted in our classrooms. Leave them at the door. Sir Ken, come save us!
As I read the second half of this chapter and came to realize the drastic differences between Amber Hill and Phoenix Park I realized that hmmm, just maybe there is a better way. I knew instantly that I could buy into such a system of "progessive education, placing particular emphasis on self-reliance and independence." (p. 18). I have been in very few school's where the ambiance was one of peacefulness instead of screaming and chaos. My curiosities increased with bewilderment firstly over the fact their mathematical teaching virtually eliminated the use of textbooks. Secondly, the notion that teachers allowed students to work on their own, unsupervised, while still expecting them to be responsible for their learning was truly fascinating. Tell me, please tell me where I can find a staff room where I won't suffocate from listening to endless complaints form my colleagues, where people are actually relaxed and unintimated by their administrations. What is the directions to Phonnix Park again?
"Jim treated the students as if they were adults; he rarely reprimanded them, and when students misbehaved he had conversations with them about the inconsiderateness of their behavior" (p. 20).
Jim's demenaour with his students is one we really need to start incorportating more into our relationships with our students. I've seen white board in the general office completely full with dentention lists more backlogged than the surgury appointments at the Health Sciences Centre. I admit I was one of those who assigned students to a complete hour of silence, without sound, without movement. After the hour they'd dash for the door, only to find themselves back there again the following Tuesday. However, after supervising the dentention session once I vowed unto myself never to subject my students to such a waste of time again. I was working against years of a tradition at this school - this is how it is. I admit too I never spoke with my misbehaved students enough either to really understand the reasons for their actions but I tried to change despite what was going on around me. I began to model myself after another teacher on our staff, one who had the respect of all students, but more interestingly, the respect of the lower-achievers, the ones who "caused all the trouble in the school." I remember asking Paul how he did it and his message was simple: make them feel important, that they matter, that you care about their futures more than you care about the material you're given to cover. They just needed attention, recognition, validation, conversation. Rising above the politics of the school and the traditions they peached I followed Paul's advice and witnessed noticeable differences in the demeanour of many students. Finally, it started to become a pleasure to teach them. Who knew which just a few simple changes in me, the teacher, could reuslt in such monumental changes for them, my students. Today, I see Paul's philosophy resonating once again here across Boaler's pages as I uncover Phoenix Park's raison d'etre.
One idea that was raised in our class continues to stay with me. We talked about the teacher who come June 1 claps the chalk off their hands and says "I'm done." We've imparted the necessary knowledge from the curriculum unto our students. We've got all our mandatory tests in, all review sheets practiced and corrected, and heaven forbid all the "good questions" from the textbook assigned. Why do we continue to think this way? How come we don't want to raise the bar, to dig further, to take the extra time and investigate mathematical modelling situations with our students? Why are we stuck? Some say it's the time pressures, the work load, the fact that come May and June we are worn so thin we just want to survive. I say it's because that's what our school systems, our departments of education have expected of us, because that's what we believe our jobs are. As Edward Losely was quoted as saying "you've got the national curriculum basically and if you cover the national curriculum you're doing your job." However, the jobs we're doing are failing children, are dismantling many of their inherent abilities. Oh sorry, I forgot, those abilities aren't wanted in our classrooms. Leave them at the door. Sir Ken, come save us!
As I read the second half of this chapter and came to realize the drastic differences between Amber Hill and Phoenix Park I realized that hmmm, just maybe there is a better way. I knew instantly that I could buy into such a system of "progessive education, placing particular emphasis on self-reliance and independence." (p. 18). I have been in very few school's where the ambiance was one of peacefulness instead of screaming and chaos. My curiosities increased with bewilderment firstly over the fact their mathematical teaching virtually eliminated the use of textbooks. Secondly, the notion that teachers allowed students to work on their own, unsupervised, while still expecting them to be responsible for their learning was truly fascinating. Tell me, please tell me where I can find a staff room where I won't suffocate from listening to endless complaints form my colleagues, where people are actually relaxed and unintimated by their administrations. What is the directions to Phonnix Park again?
"Jim treated the students as if they were adults; he rarely reprimanded them, and when students misbehaved he had conversations with them about the inconsiderateness of their behavior" (p. 20).
Jim's demenaour with his students is one we really need to start incorportating more into our relationships with our students. I've seen white board in the general office completely full with dentention lists more backlogged than the surgury appointments at the Health Sciences Centre. I admit I was one of those who assigned students to a complete hour of silence, without sound, without movement. After the hour they'd dash for the door, only to find themselves back there again the following Tuesday. However, after supervising the dentention session once I vowed unto myself never to subject my students to such a waste of time again. I was working against years of a tradition at this school - this is how it is. I admit too I never spoke with my misbehaved students enough either to really understand the reasons for their actions but I tried to change despite what was going on around me. I began to model myself after another teacher on our staff, one who had the respect of all students, but more interestingly, the respect of the lower-achievers, the ones who "caused all the trouble in the school." I remember asking Paul how he did it and his message was simple: make them feel important, that they matter, that you care about their futures more than you care about the material you're given to cover. They just needed attention, recognition, validation, conversation. Rising above the politics of the school and the traditions they peached I followed Paul's advice and witnessed noticeable differences in the demeanour of many students. Finally, it started to become a pleasure to teach them. Who knew which just a few simple changes in me, the teacher, could reuslt in such monumental changes for them, my students. Today, I see Paul's philosophy resonating once again here across Boaler's pages as I uncover Phoenix Park's raison d'etre.
Monday, October 12, 2009
Experiecing School Mathematics - Ch 2
Two aspects discussed in chapter 2 raised enough curiousity within me that warranted an entry here on my blog: test design in standardized testing and mixed vs. ability grouping. In Newfoundland CRT tests at the junior high level are designed with 62% of the test closed constructed repsonses, exclusively multiple choice items. The items cover all three main stands of procedural, conceptual, and problem solving. The problem we've found in the past is that stem of a lot of these questions are so long in text and worded so poorly that many students cannot even understand what it is there're asked to find. In many instances too a lot of these questions required more workings, more thought, more understanding of mathematics that some open-ended questions would (which were worth three times the multiple choice item). A lot of weaker students would end up getting most of these questions wrong because a) they couldn't process all the reading of the question and b) most students have the impression that multiple choice questions should not require a lot of time and work to find the correct answer. Here's a questions from the CRT test in 2005.
Josie noticed a rainwater barrel read 18 L at 2:00pm. At 3:00pm it read 14 L and was leaking water at a constant rate. Josie got back at 3:30pm with a 5 L bucket to catch the water until she could fix the leak. There was 12 L left in the barrel then. How long, in minutes, will Josie have to fix the leak if she works until her bucket fills up?
(A) 30
(B) 60
(C) 75
(D) 125
Some will argue it is a perfectly fine question and perhaps it is. But for one mark in a test I think is perhaps a stretch. I remember looking at this quesiton in particular the following year in my first year of teaching. I gave it to my class on a chapter quiz to see how they would handle it. I recall there being a lot of questions from students not understanding the premise of the question. Perhaps it's a language problem, perhaps it's a lack of ability on the student's part to think critically. That's just one example, perhaps there's a lot more out there. My point in all of this is that if the standardized tests are to reamin then their design styles need to become more open response in nature. Students will only put down their workings on the page in a coherent manner if they know there's a chance they can earn marks from it. Of course it's about the money - it's a lot cheaper to put a response form through a solution feeder to spit out the results than itis to hire hundreds of teachers to mark the papers. But, really how can we discover the falsehoods students have in their mathematical thinking if an evaluator will never see their work on the question. It would be interesting to have a pilot CRT with exclusively open response items and then have follow-up commentary and research done on how much better or worse the students would perform, in addition to antedotal evidence on their views about writing such a test. We definitely need to rethink how we assess our own students' thinking. I've already been a fan of oral defenses, mathemtical modelling presentations, and other alternate forms of assessment to provide my students with the opportunity to show how much and what they understand about mathematics through alternate means from pencil and paper.
The other idea raised by Boaler here that I've often debated with myself is how our math classes are organized. Amber Hill used a system of teaching their students in ability grouping, or sets, whereby the different sets were taught similar content, but the higher sets were generally taught at a faster pace and covered more difficult material. At Phoenix Park the students were taught in mixed abilit classes through all three years less three weeks before the national exams when they were place in target groups for the test preparation. Here in Newfoundland we have mixed ability grouping for the first ten of thirtenn years of the students schooling. During times in my practice I wished for ability grouping because I seen so many of my brighter students bored and dragged down by the pace of our classes. I seen so many weaker students frustrated by the seemingly fast pace I was "covering the curriculum" Yes I too was one of those obsessed with covering the curriculum, teaching with the text. Perhaps, there in lies my and my classes problems! But in any regard I felt I could not provide the help the weaker needed and coul not meet the expectations of my enriched students. The job of teaching to the "middle, normal" students is frivilous. I was frustrated with what was happening in my math classes, feeling helpless in an attempt to save the class and save myself. If only I could have them all separated accoridng to ability I though so many times. Unfortunately I never gave enough attention to what would happen to those int he bottom "barrels" Boaler says "the set in which students are placed has significant implication for their attainment some years later." Powerful statement. And so from that I asked, "Should I really be deciding which opportunities a student should have access to later int heiur life right now when they are merely 13 or 14 years old." If we decided to initiate such a program whereby a student was put in the lowest set in grade 7 and as a result could not apply to any university or college program because they would not have the pre-requisites met further in their secondary schooling. I seriously found myself begininng to realize that we need to stop the practice of cutting the legs off from under our children in their early teenage years. We're basically throwing those who don't fit the norm, who don't comply, who don't understand the way we teach, into courses that bring them to a dead end, that close more doors in their lives than are opened.
If only we would lay down our texts and answer keys, then maybe we could develop a system that allows the weakest of the weak and the strongest of the strong to co-exist in the same classroom. The teachers at Phoenix Park did and it worked. Why can't we?
Josie noticed a rainwater barrel read 18 L at 2:00pm. At 3:00pm it read 14 L and was leaking water at a constant rate. Josie got back at 3:30pm with a 5 L bucket to catch the water until she could fix the leak. There was 12 L left in the barrel then. How long, in minutes, will Josie have to fix the leak if she works until her bucket fills up?
(A) 30
(B) 60
(C) 75
(D) 125
Some will argue it is a perfectly fine question and perhaps it is. But for one mark in a test I think is perhaps a stretch. I remember looking at this quesiton in particular the following year in my first year of teaching. I gave it to my class on a chapter quiz to see how they would handle it. I recall there being a lot of questions from students not understanding the premise of the question. Perhaps it's a language problem, perhaps it's a lack of ability on the student's part to think critically. That's just one example, perhaps there's a lot more out there. My point in all of this is that if the standardized tests are to reamin then their design styles need to become more open response in nature. Students will only put down their workings on the page in a coherent manner if they know there's a chance they can earn marks from it. Of course it's about the money - it's a lot cheaper to put a response form through a solution feeder to spit out the results than itis to hire hundreds of teachers to mark the papers. But, really how can we discover the falsehoods students have in their mathematical thinking if an evaluator will never see their work on the question. It would be interesting to have a pilot CRT with exclusively open response items and then have follow-up commentary and research done on how much better or worse the students would perform, in addition to antedotal evidence on their views about writing such a test. We definitely need to rethink how we assess our own students' thinking. I've already been a fan of oral defenses, mathemtical modelling presentations, and other alternate forms of assessment to provide my students with the opportunity to show how much and what they understand about mathematics through alternate means from pencil and paper.
The other idea raised by Boaler here that I've often debated with myself is how our math classes are organized. Amber Hill used a system of teaching their students in ability grouping, or sets, whereby the different sets were taught similar content, but the higher sets were generally taught at a faster pace and covered more difficult material. At Phoenix Park the students were taught in mixed abilit classes through all three years less three weeks before the national exams when they were place in target groups for the test preparation. Here in Newfoundland we have mixed ability grouping for the first ten of thirtenn years of the students schooling. During times in my practice I wished for ability grouping because I seen so many of my brighter students bored and dragged down by the pace of our classes. I seen so many weaker students frustrated by the seemingly fast pace I was "covering the curriculum" Yes I too was one of those obsessed with covering the curriculum, teaching with the text. Perhaps, there in lies my and my classes problems! But in any regard I felt I could not provide the help the weaker needed and coul not meet the expectations of my enriched students. The job of teaching to the "middle, normal" students is frivilous. I was frustrated with what was happening in my math classes, feeling helpless in an attempt to save the class and save myself. If only I could have them all separated accoridng to ability I though so many times. Unfortunately I never gave enough attention to what would happen to those int he bottom "barrels" Boaler says "the set in which students are placed has significant implication for their attainment some years later." Powerful statement. And so from that I asked, "Should I really be deciding which opportunities a student should have access to later int heiur life right now when they are merely 13 or 14 years old." If we decided to initiate such a program whereby a student was put in the lowest set in grade 7 and as a result could not apply to any university or college program because they would not have the pre-requisites met further in their secondary schooling. I seriously found myself begininng to realize that we need to stop the practice of cutting the legs off from under our children in their early teenage years. We're basically throwing those who don't fit the norm, who don't comply, who don't understand the way we teach, into courses that bring them to a dead end, that close more doors in their lives than are opened.
If only we would lay down our texts and answer keys, then maybe we could develop a system that allows the weakest of the weak and the strongest of the strong to co-exist in the same classroom. The teachers at Phoenix Park did and it worked. Why can't we?
Wednesday, October 7, 2009
Experiencing School Mathematics - Ch 1
"The question of which approach we should use to teach mathematics in schools is one that has perplexed parents, teachers, mathematicians, and others for decades (Benezet, 1935)." Boaler cited this work from more than 70 years ago, but she wouldn't have to change one word arguably to make it a researched fact from 2009. Amazing isn't it. What is wrong with us mortals that we cannot seem to find a reasonable, efficient, effective methology of teaching mathematics that works for all parties involved? We've complained our ways through decades upon decades of teaching this subject yet very little changes from each "new math" curriculum to the next. It's not the curriculum as such that the problem is about, but moreso how we teach the curriculum, we it's delivered - that is how it's taught and learned. She notes that "there is an established concern that many people are unable to use the mathematics they learn in school in situations outside the classroom" (p.1). Then, the first question which comes to my mind is if the students are actually learning the maths. The inability to transform the knowledge and skills one acquires in the classroom should be transferable into real life situation, in mathematical modelling that makes sense to the person. If not, we, as teachers are not doing a good enough job of teaching. Period. Jo Boaler's impressive research here is truly fascinating to me in that we are finally seeing careful research being done on how different approaches to mathematics effects teaching and learning.
Relatively new to the study of research but still knowledgeable enough given my prior graduate courses and B.Ed. program, the fact that she took on a 3 year longitudinal study with such a high number of participants is truly commendable and more than impressive. In addition, the fact that she not oinly monitored th effectiveness of Amber Hill and Phoenix Park's approaches to teaching math, but also analyzed the means through which these approaches influenced the the students actions, teacher decisions, curriculum perceptions, and student-teacher relations. In our day to day grind as educators we seldom have the chance to delve into the core of why our math system seems to be failing so many, why our basic classes are overflowing and our advanced classes are cancelled because of low registration. I could tell from the first chapter this book will finally give me the insight I have been looking for. It is intriguing to know that there is a system, tried and true out there (and not too far away either) that is better than ours, that is working, that has the results to back up their rationale for why they do what they do. How come we're not following? How come we're not even making an attempt to follow? In fact, it seems we're going even further in other direction. Moreover, our parents, our students, and yes, many of our teachers are preferring a system that reverts back to the past, that essentially ignores the results of this research. It is embarassing that we as teachers are in the dark about the issues Boaler is about to raise. Are we really equipped to not just teach but to teach well? I fear we're not. Are we aware of the issues surrounding gender and learning styles for example? I fear we're not. Are we making far too many generalizations during our time in the classroom? This time, I fear we are.
And so I put my faith and trust in Boaler to show us the way to better teaching to engage our minds and finally give us reason to pause, and perhaps, just maybe speak out and seek out to find the change we so desperately need.
SAW.
Relatively new to the study of research but still knowledgeable enough given my prior graduate courses and B.Ed. program, the fact that she took on a 3 year longitudinal study with such a high number of participants is truly commendable and more than impressive. In addition, the fact that she not oinly monitored th effectiveness of Amber Hill and Phoenix Park's approaches to teaching math, but also analyzed the means through which these approaches influenced the the students actions, teacher decisions, curriculum perceptions, and student-teacher relations. In our day to day grind as educators we seldom have the chance to delve into the core of why our math system seems to be failing so many, why our basic classes are overflowing and our advanced classes are cancelled because of low registration. I could tell from the first chapter this book will finally give me the insight I have been looking for. It is intriguing to know that there is a system, tried and true out there (and not too far away either) that is better than ours, that is working, that has the results to back up their rationale for why they do what they do. How come we're not following? How come we're not even making an attempt to follow? In fact, it seems we're going even further in other direction. Moreover, our parents, our students, and yes, many of our teachers are preferring a system that reverts back to the past, that essentially ignores the results of this research. It is embarassing that we as teachers are in the dark about the issues Boaler is about to raise. Are we really equipped to not just teach but to teach well? I fear we're not. Are we aware of the issues surrounding gender and learning styles for example? I fear we're not. Are we making far too many generalizations during our time in the classroom? This time, I fear we are.
And so I put my faith and trust in Boaler to show us the way to better teaching to engage our minds and finally give us reason to pause, and perhaps, just maybe speak out and seek out to find the change we so desperately need.
SAW.
Thursday, October 1, 2009
Experiencing School Mathematics - Forward
As I made myself comfortable in the silent reading area of the QEII I opened Jo Boaler's book expecting to finally find something of interest (knowing of course that Mary surely would put an intriguing selection on the syllabus) to us as math teachers - something practical for us to ponder and reflect on, a story that will enlighten us as to how we do things ourselves, and yes, an opportunity for reflection of our own system and of ourselves. I didn't need to go beyond Schoenfeld's brillant forward to realize that this would be exactly what I'd find. Even though I'm relatively new to the profession I was aware through my practice and studies it is veru difficult to find longitudinal studies of this nature in a multifaceted manner. Alas a study of not just the students but also the teachers. His forward grabbed me and ignited an interest insdie me to read further, to become informed on the nature of the issues, the results she found, and hopefully answers to "What Can We Do About It Now?"
His praise for her scholarly work ix z terrific stepping stone to keep the reader engaged in discovering what it is she has to say. As a teacher I put myself right there, aware of which school it is I was a part of, more certain of which school I wanted to be a part of. His forward was very informative in introducing my ignorant self to a different way of mathematical instruction, through sets, with many options in a decentralized type of education system. Familiar with preparation for standardized testing I knew instantly "this book is for me." We, as teachers here in NL are slaves to the system, robots pushing through a curriculum to cover it before the June plague hits our students and ourselves. This forward held fo rme the promise that finally, substantial, reasonable, unequivocal evidence exists that "students who receive project-based instruction that does not focus on skills learn more mathematics than students receiving traditional skills-based instruction." He brought up the old-age issues of gender vs. math performance which I look forward to reading about.
By including verbatim quotes from Boaler's book, Schoenfeld gives us a glimse into the brillant research and conclusions she has made over the three year period. He executes justification for reading the book (to the American audience) beautifully by explicitly stating the universality of the themes. We know these schools could exist in anytown. We know our children could be the victims and product of such a system. As our eyes go down the page we realize that her findings are relevant, are real to ongoing educational debates that are forever purging our classrooms of children, our moral as educators, and our system as a whole.
Alan Schoenfel, I will definitely read on!
SAW
His praise for her scholarly work ix z terrific stepping stone to keep the reader engaged in discovering what it is she has to say. As a teacher I put myself right there, aware of which school it is I was a part of, more certain of which school I wanted to be a part of. His forward was very informative in introducing my ignorant self to a different way of mathematical instruction, through sets, with many options in a decentralized type of education system. Familiar with preparation for standardized testing I knew instantly "this book is for me." We, as teachers here in NL are slaves to the system, robots pushing through a curriculum to cover it before the June plague hits our students and ourselves. This forward held fo rme the promise that finally, substantial, reasonable, unequivocal evidence exists that "students who receive project-based instruction that does not focus on skills learn more mathematics than students receiving traditional skills-based instruction." He brought up the old-age issues of gender vs. math performance which I look forward to reading about.
By including verbatim quotes from Boaler's book, Schoenfeld gives us a glimse into the brillant research and conclusions she has made over the three year period. He executes justification for reading the book (to the American audience) beautifully by explicitly stating the universality of the themes. We know these schools could exist in anytown. We know our children could be the victims and product of such a system. As our eyes go down the page we realize that her findings are relevant, are real to ongoing educational debates that are forever purging our classrooms of children, our moral as educators, and our system as a whole.
Alan Schoenfel, I will definitely read on!
SAW
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