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
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