As Sharon so effectively talked about in her blog, I too am becoming increasingly frustrated with the procedures I find myself and my students stuck in. As I read through Boaler and continue my substituting the feelings of ineffectiveness in how we're teaching and how students are learning are growing. I long now to have a full time position where I can begin to impliment some of these ideas we're discovered through Phoenix Park's approach. And like Sharon, I'm being to realize that I can't wait. Each day that goes by without bringing about change runs the risk of perhaps losing another student, turning them further away from mathematics learning, entrenching them with fictious ideas about the relevance of math in their own lives. We need to start today.
Terri-Lynn raised a very important question during her presentation: How often do you see students handing in answers in which they have no concept of whether or not they are even logical, let alone the correct response? We see it all too often in our classes where students do not (for many reasons) thinking about, analyze, and interpret the answers they have arrived at. I think our methods of extreme pencil and paper tasks without enough investigative work and explorations have often led students to a point in their learning where they haven't been taught the fundamentals of checking the reasonableness of an answer. We overhwlm them with so much classwork assigned from textbooks and extra assignment practice outside of class that it would be too time consuming to go back and check all their answers. Another thought of mine just came up here and it is this: I think we are perhaps assigning too much work for our students to complete. I think that often times our teaching strategies are too time consuming, especially when it comes to having students write off notes from the board, and as a result the majority of the practice, the time when students need to talk math between each other, is often lost in the classroom. That means the majority of the work is then left to be done in isolation usually away from class. The math is then perceived as labouors, monotonous, and routine, instead of something that should be interacitve, interesting, and fun inside class. We really can do more with less.
As we read through this book we realzie the importance of incorporating project work into our math classes. Geeno and MMAP (1998) reported that in this type of work students "develop abilities of collaborative inquiry and of using the concepts and methods of a discipline to solve problems." Given this highly significant piece of research it is quite evident that the inquiry and cleverness we expect from our students is not going ot happen by osmosis, or by us standing in front of them asking them to dictate onto their exercises what we say. We have trained our math student not to be disciplined, but rather dependent on us. While substituting for a math teacher a few weeks ago one of hte classes I had to supervise a junior high test. He had written in the notes that it was ok to provide help to the students during the test, give them hints, etc. A year ago I probably wouldn't have blinked at such a request. That day I couldn't stop blinking. We weren't five minutes into the test and hands were going up all around me. The test was constructed well and had a good range of quesitoning for the class so I didn't perceive there would be much trouble. However, the students sat there like drowning rats desperate for a push, a start in a question. Everything from what the word "prime" means to "how do I draw a numberline to show + 3 multipled by -2 was asked. It was so disappointing to see so many students suffereing through this. I wondered to myself what are we really doing to our students? Why are they failing in their learning so badly? How did they get to the point where independence was non-existent in their math? Is it too late to change the tide? I hope not.
Wednesday, November 18, 2009
Tuesday, November 17, 2009
Exploring The Differences
As I continue to work through this fall semester both in my graduate studies and in my substituting experiences in a variety of classrooms and subjects, now more than ever I feel I'm both exploring and experience the differences of our schools and students. I feel the frustrations of my students when they're subjected to note taking and textbook drill. What once fell deaf to my ears is now being hear loud and clear - our students want to be challenged, they are bored with the daily routines of pencils and paper practice. The idleness I see all around me resonates so much more now, for I am finally feeling, through our class discussions and Boaler's words, the effects of such a stagnant method of teaching and learning smothering our schools. If we really listened to our students we'd find many of the solutions to classroom management, to a lack of student engagement, and to the stress we put on all our students in over testing. By incorporating their voices, their thoughts, we can put into practice a way of doing, a means of learning as Phoenix Park has accomplished.
"The Amber Hill students believed the mathematics they encountered in school and the mathematics they met in the real world to be completely and inherently different" (p. 111). What are we doing in our classrooms to bridge this gap? Are our practices and teaching styles making the learning relevant outside our class and into the everyday lives these students live? How sad it is that our education system demands are not being linked by our students in similarities to the real world. The math is not "totally different". The methods used can be the same! Our math classrooms can be social! And most important, our classrooms should provide opportunities for students to work it out for themselves, instead of relying solely on textbooks to provide algorithm after algorithm in how to "solve" the problems. There is a need on us now, like never before, as teachers to ensure perceptions of the environments created by the real world and the mathematics classroom are no longer inherently different, but rather, the same.
Although there are many, a particular idea Boaler raises from Lave (1996a) is that "notions of knowing should be replaced with notions of doing, arguing that the only indication that someone has knowledge is that they can use it" (p.117). This relational view is the essence of what Phoenix Park's approach to learning and teaching mathematics is all about. Like Paul and others at PP, our students too will support this logic and will fulfill it. Transmitting knowledge has been tried. It hasn't work. Why don't we try something different? That is, why don't we try holsitic means of thinking and doing with our students. Let's desconstuct the boundaries around school mathematics that currently exist, that currently cripple so many of our youth. It can be done.
One small step for math, one giant step for math minds.
"The Amber Hill students believed the mathematics they encountered in school and the mathematics they met in the real world to be completely and inherently different" (p. 111). What are we doing in our classrooms to bridge this gap? Are our practices and teaching styles making the learning relevant outside our class and into the everyday lives these students live? How sad it is that our education system demands are not being linked by our students in similarities to the real world. The math is not "totally different". The methods used can be the same! Our math classrooms can be social! And most important, our classrooms should provide opportunities for students to work it out for themselves, instead of relying solely on textbooks to provide algorithm after algorithm in how to "solve" the problems. There is a need on us now, like never before, as teachers to ensure perceptions of the environments created by the real world and the mathematics classroom are no longer inherently different, but rather, the same.
Although there are many, a particular idea Boaler raises from Lave (1996a) is that "notions of knowing should be replaced with notions of doing, arguing that the only indication that someone has knowledge is that they can use it" (p.117). This relational view is the essence of what Phoenix Park's approach to learning and teaching mathematics is all about. Like Paul and others at PP, our students too will support this logic and will fulfill it. Transmitting knowledge has been tried. It hasn't work. Why don't we try something different? That is, why don't we try holsitic means of thinking and doing with our students. Let's desconstuct the boundaries around school mathematics that currently exist, that currently cripple so many of our youth. It can be done.
One small step for math, one giant step for math minds.
Wednesday, November 4, 2009
Chapter 6 - What Could They Do?
I wanted to return back to the questions I asked during my lead discussion in class on Chapter 6 here within my blog. These questions were a reuslt of stunning quantitiative data Boaler presented to us in her study.
Firstly, she stated that 94% of AH and PP students correctly answered questions on the test concerning angle calculations whereas only 63% of those same students in AH and 83% of PP students correctly estimated the roof's angle in the activity. Also, the AH students in the highest sets (1 and 2) did worse that the students of AH ins ets 3 and 4. Are our teaching styles prompting inappropriate learning cues by our students? In AH and in many of our classrooms the answer is sadly yes. We are caught up in a system so focused on testing that we teach students to find clues within a question that would turn them to a particualr recipe for answering teh question correctly. Often times these cues mean the student has to do so little thinking the work becomes mechanical, thoughtless, robotic, useless. Are we truly aware of the implications such hints whether verbal or written are having on the independence of student thought and learning. We've become so good at this cueing that our students sometimes cannot succeed without it. They too have become conditioned to needing these explicit instructions in order to correclty answer many of their questions. In so many of our classes students arrive at nonsensical answers, unaware of the obvious errors in their answers. Many times it's because they take a word in the question out of context and do not have a full mastery of the outcome beng tested.
Students at both schools reported enjoying the activities immensely, particularly the AH students, many of whom asked if they could do more work of a similar nature. Are we doing a good enough job to make math class enjoyable for our students? Again, I must revert back to the system we as teachers have innocently and blindly taken as the "way" things must be done. We use the timelines from governement, the pressures from districts for improved marks, and the established doctrine of teaching to the test as all crutches for why we've taken so much of the poential fun and enjoyment out of math class. Replacing the investigations and modelling sessions we give them endless practice sheets to prepare for the summative evaluations months away. When times gets short something enjoyable is always the first to be cut because we think it's not as important as "time on task" routines of pencil and paper work. Again, it's not intentional, and some will say we don't know any better. However, Boaler is telling us better, she is now ensuring we do know better. She found only 3% of AH students added any creativity in their flat designs compared to 33% of PP students. We can create demanding cognitive takss while still having students adhere to certain rules within the class. So, let's listen to her. Let's try her approach.
Success on the GCSE exams was important for students at PP but their teachers were cavalier about exam preparation. PP provided no calculators to students needing them and the school was void of any real motivation or "gearing up" for exams. Are we giving our students enough responsibility? In many ways we, as teachers, are making our students more responsible and ready to learn. We ask them to show up to class on time, bring their supplies, complete the assigned work both in and out of class, hand in projects on time. I could go on. However, we bend ever so quickly, extend wilingly on times, and believe it or not become more stresses out over students responsibilites than they do themselves. Many of us bring the wiriting tools, the calculators, often the paper itself for our students to complete their work. Especially at test time we scurry around to bum calculators and scrap up things our students should have brought but didn't. Yes, we all forget things sometimes and there's nothing wrong in helping at times like this. However, we go to the extreme many a time. I think many of us in a desperate plea for improved scores in exams will cater to our students. I personally try to be as nice as I can when moments of "oops" come from my students. I have loaned loaned my own calculator and I have turned students away too to fend for themselves. It's a tough act to adhere to and one that we must practice every opportunity we get.
A question that raised a lot of interest in class was: How often and to what extent do we talk and stress CRT, public exams to our students, making it the focus and purpose of the course? It would be very interesting to do such a study in our classrooms, making note of the number of times we defer to "tests" as a reason for learning a concept, as a reason for paying attention, as the reson for doing well in the course. I have a fear that student hear more references to testing in their classes than any other feature of their education. From day 1 in the syllabus we highlight public exams 10 months down the road, instilling perhaps fear withint he class that everyone is here for one reason only: to be ready for that test. Again, I say our language is often deferred to test preparation because that is the system of education created and followed year after year. The top-down, hierarchial system demands a concentration on testing, on these results as a way to justify funding or lack there of, to declare success of a program or its failure. However, we as teachers are the adult, often the only adult in the classroom. We are the voice the students hear and from us they hear too much about testing, too much about getting ready for tests. Instead of putting emphais on learning for its own sake and relating it to the world around our students, we exhaust them with test prep and success. Next time, let's try to catch ourselves before we use the test as the focus of our conversations with our students. No doubt, it will be tough.
Of all the results revealed in this chapter the one that stood out to me the most was that only 9% of the AH top set of students retained the material they learned just a few months after it was assessed. PP students retained four times the amount that some AH students had.Therefore, are our tests giving a realistic picture of what our students are learning? These results show the damage, real damage that the current teaching and learning styles are having on our students long term retention and understanding. Tests really aren't all they're cracked up to be, yet we still use them to draw a line in the sand, separating those who know from those who don't. These tests determine really who succeeds, who make it, and who gets left behind. It's time to revisit the value of these test papers and their role in shaping our student's education and their futures.
Scott
Firstly, she stated that 94% of AH and PP students correctly answered questions on the test concerning angle calculations whereas only 63% of those same students in AH and 83% of PP students correctly estimated the roof's angle in the activity. Also, the AH students in the highest sets (1 and 2) did worse that the students of AH ins ets 3 and 4. Are our teaching styles prompting inappropriate learning cues by our students? In AH and in many of our classrooms the answer is sadly yes. We are caught up in a system so focused on testing that we teach students to find clues within a question that would turn them to a particualr recipe for answering teh question correctly. Often times these cues mean the student has to do so little thinking the work becomes mechanical, thoughtless, robotic, useless. Are we truly aware of the implications such hints whether verbal or written are having on the independence of student thought and learning. We've become so good at this cueing that our students sometimes cannot succeed without it. They too have become conditioned to needing these explicit instructions in order to correclty answer many of their questions. In so many of our classes students arrive at nonsensical answers, unaware of the obvious errors in their answers. Many times it's because they take a word in the question out of context and do not have a full mastery of the outcome beng tested.
Students at both schools reported enjoying the activities immensely, particularly the AH students, many of whom asked if they could do more work of a similar nature. Are we doing a good enough job to make math class enjoyable for our students? Again, I must revert back to the system we as teachers have innocently and blindly taken as the "way" things must be done. We use the timelines from governement, the pressures from districts for improved marks, and the established doctrine of teaching to the test as all crutches for why we've taken so much of the poential fun and enjoyment out of math class. Replacing the investigations and modelling sessions we give them endless practice sheets to prepare for the summative evaluations months away. When times gets short something enjoyable is always the first to be cut because we think it's not as important as "time on task" routines of pencil and paper work. Again, it's not intentional, and some will say we don't know any better. However, Boaler is telling us better, she is now ensuring we do know better. She found only 3% of AH students added any creativity in their flat designs compared to 33% of PP students. We can create demanding cognitive takss while still having students adhere to certain rules within the class. So, let's listen to her. Let's try her approach.
Success on the GCSE exams was important for students at PP but their teachers were cavalier about exam preparation. PP provided no calculators to students needing them and the school was void of any real motivation or "gearing up" for exams. Are we giving our students enough responsibility? In many ways we, as teachers, are making our students more responsible and ready to learn. We ask them to show up to class on time, bring their supplies, complete the assigned work both in and out of class, hand in projects on time. I could go on. However, we bend ever so quickly, extend wilingly on times, and believe it or not become more stresses out over students responsibilites than they do themselves. Many of us bring the wiriting tools, the calculators, often the paper itself for our students to complete their work. Especially at test time we scurry around to bum calculators and scrap up things our students should have brought but didn't. Yes, we all forget things sometimes and there's nothing wrong in helping at times like this. However, we go to the extreme many a time. I think many of us in a desperate plea for improved scores in exams will cater to our students. I personally try to be as nice as I can when moments of "oops" come from my students. I have loaned loaned my own calculator and I have turned students away too to fend for themselves. It's a tough act to adhere to and one that we must practice every opportunity we get.
A question that raised a lot of interest in class was: How often and to what extent do we talk and stress CRT, public exams to our students, making it the focus and purpose of the course? It would be very interesting to do such a study in our classrooms, making note of the number of times we defer to "tests" as a reason for learning a concept, as a reason for paying attention, as the reson for doing well in the course. I have a fear that student hear more references to testing in their classes than any other feature of their education. From day 1 in the syllabus we highlight public exams 10 months down the road, instilling perhaps fear withint he class that everyone is here for one reason only: to be ready for that test. Again, I say our language is often deferred to test preparation because that is the system of education created and followed year after year. The top-down, hierarchial system demands a concentration on testing, on these results as a way to justify funding or lack there of, to declare success of a program or its failure. However, we as teachers are the adult, often the only adult in the classroom. We are the voice the students hear and from us they hear too much about testing, too much about getting ready for tests. Instead of putting emphais on learning for its own sake and relating it to the world around our students, we exhaust them with test prep and success. Next time, let's try to catch ourselves before we use the test as the focus of our conversations with our students. No doubt, it will be tough.
Of all the results revealed in this chapter the one that stood out to me the most was that only 9% of the AH top set of students retained the material they learned just a few months after it was assessed. PP students retained four times the amount that some AH students had.Therefore, are our tests giving a realistic picture of what our students are learning? These results show the damage, real damage that the current teaching and learning styles are having on our students long term retention and understanding. Tests really aren't all they're cracked up to be, yet we still use them to draw a line in the sand, separating those who know from those who don't. These tests determine really who succeeds, who make it, and who gets left behind. It's time to revisit the value of these test papers and their role in shaping our student's education and their futures.
Scott
Thursday, October 29, 2009
Chapter 5 - PP Experiences and Reflections
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.
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.
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?
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