Saturday, October 24, 2009
Michelle 's Presentation
I just realized that in my blog on chapter 5 I hadn't extended congratulations to Michelle on a job well done! Your presentation was wonderful, it was clear and concise it helped us track and make sense of what was said in the chapter. Good on you... as the British would say! ... or is that Australian? , never mind, still applies. Sorry for being tardy with comments!
Sunday, October 18, 2009
Phoenix Park
Standard 1 of NCTM's 'Professional Standards',(1991)is entitled "Worthwhile Mathematics Tasks"
The teacher of mathematics should pose tasks that are based on-sound and significant mathematics:
-knowledge of students' understandings, interests, and experiences;
-knowledge of the range of ways that diverse students learn mathematics
and that:
-engage students' intellect;
-develop students' mathematical understandings and skills;
-stimulate students to make connections and develop a coherent framework for
mathematical ideas;
-call for problem formulation, problem solving, and mathematical reasoning;
- promote communication about mathematics;
- represent mathematics as an ongoing human activity;
-display sensitivity to, and draw on, students' diverse background experiences
and dispositions;
and
-promote the development of all students' dispositions to do mathematics.
Phoenix Park's mathematics program certainly met this standard. The curriculum at Phoenix Park was teacher designed, it required the teachers to "know a lot about the students - what they knew what would be most helpful for them to work on" in this they meet the descriptors from the NCTM standards. In fact the mathematics tasks that the students of Phoenix Park were given to work on allowed for openness and creativity. The teachers supported this creativity by making "deliberate efforts not to structure the work for students", they did not give closed answers to student questions instead they would reform the question in a way that invited the students to explain what they knew and to identify what they needed to find out, something I am currently working on in my own instructional style. The students were guided to make connections and to reason and communicate their thinking and in doing so developed a mathematics disposition that was based on the belief that it was more important to think in mathematics than to remember rules. I was very impressed with the learning opportunities for students at Phoenix Park.
It was very surprising to me that time on task for both Amber Hill and Phoenix Park was about equal. I would say that I had a very strong reaction to the descriptions of students being permitted to wander at will and to be noticeably off task for long periods. There was no attempt by the teacher to refocus or encourage them to return to the work at hand and I found this disturbing. I couldn't help but think that a little structure in this area would have benefited the students. I can only suppose that the teachers felt it more important to create an atmosphere in the classroom where students were unafraid of being wrong and willing to explore mathematics concepts then it was to impose any useful level of discipline. I'm not 100% sure that they aren't right in this but I'm a long way from this in my teaching.
The teacher of mathematics should pose tasks that are based on-sound and significant mathematics:
-knowledge of students' understandings, interests, and experiences;
-knowledge of the range of ways that diverse students learn mathematics
and that:
-engage students' intellect;
-develop students' mathematical understandings and skills;
-stimulate students to make connections and develop a coherent framework for
mathematical ideas;
-call for problem formulation, problem solving, and mathematical reasoning;
- promote communication about mathematics;
- represent mathematics as an ongoing human activity;
-display sensitivity to, and draw on, students' diverse background experiences
and dispositions;
and
-promote the development of all students' dispositions to do mathematics.
Phoenix Park's mathematics program certainly met this standard. The curriculum at Phoenix Park was teacher designed, it required the teachers to "know a lot about the students - what they knew what would be most helpful for them to work on" in this they meet the descriptors from the NCTM standards. In fact the mathematics tasks that the students of Phoenix Park were given to work on allowed for openness and creativity. The teachers supported this creativity by making "deliberate efforts not to structure the work for students", they did not give closed answers to student questions instead they would reform the question in a way that invited the students to explain what they knew and to identify what they needed to find out, something I am currently working on in my own instructional style. The students were guided to make connections and to reason and communicate their thinking and in doing so developed a mathematics disposition that was based on the belief that it was more important to think in mathematics than to remember rules. I was very impressed with the learning opportunities for students at Phoenix Park.
It was very surprising to me that time on task for both Amber Hill and Phoenix Park was about equal. I would say that I had a very strong reaction to the descriptions of students being permitted to wander at will and to be noticeably off task for long periods. There was no attempt by the teacher to refocus or encourage them to return to the work at hand and I found this disturbing. I couldn't help but think that a little structure in this area would have benefited the students. I can only suppose that the teachers felt it more important to create an atmosphere in the classroom where students were unafraid of being wrong and willing to explore mathematics concepts then it was to impose any useful level of discipline. I'm not 100% sure that they aren't right in this but I'm a long way from this in my teaching.
Wednesday, October 14, 2009
Chapter 4 follow up
As I read through chapter 5, my thoughts returned time and again to Chapter 4. I felt like I had a little more to say I guess and wanted to make this post before we discuss the next chapter. The more I read the more I realize how much there is to do to make a classroom an inviting, exciting arena for mathematical learning/understanding. The teachers at Amber Hill, however good intentioned they may be, were not being effective, shouldn't they have been able to see that? I turn the mirror on myself and ask if I have not also been guilty of this very thing. I pay much closer attention now to the what and why when planning and get a great sense of satisfaction from knowing that the small changes I've made can be built upon and its all good for the students!
As long as I'm looking in that mirror I must admit that I have been guilty of 'excessive prompting' in the past. Allowing students to think, that break between question/problem and answer is excruciating. I have noted that the students have noticed the changes too, at times they have such quizzical looks on their faces as in " When is Miss going to step in?" It is a bit of a tight-rope walk and a lot of getting rid of bad habits to know when is the right time to step in. I struggle on! What has inspired me to be aware is the idea that Boaler presented from her observations at Amber Hill " The teachers thought that students would not or could not think" this " learned helplessness" is something I do not want to be a part of continuing. I know there will be times when I will 'fall of the wagon' so to speak but it has become an important issue for me.
Finally, when I think about all that I read and learned in chapter 4, differences between teacher beliefs and actions, the development of negative student attitudes toward mathematics, the lack of true mathematical understanding have all been eye opening for me. However, it is the idea that the students from Amber Hill were considered to have inadequacies based on the social group they were identified as having come from, that bothered me the most. The studies Anyon, ( 1981) cites that find that schools in lower socio-economic areas "discouraged personal assertiveness and intellectual inquisitiveness in students and assigned work that most often involved substantial amounts of rote activity" is perhaps, shameful! ( maybe that's too strong a word? Hmm?) As I comb through research for this course I have come across the following quote, "All students regardless of their personal characteristics, backgrounds, or physical characteristics must have the opportunity to study - and support to learn - mathematics (NCTM, 2000, p.12) hallelujah brother, say it again! Equity is certainly one of the critical issues facing mathematics education today, Amber Hill certainly demonstrates that.
As long as I'm looking in that mirror I must admit that I have been guilty of 'excessive prompting' in the past. Allowing students to think, that break between question/problem and answer is excruciating. I have noted that the students have noticed the changes too, at times they have such quizzical looks on their faces as in " When is Miss going to step in?" It is a bit of a tight-rope walk and a lot of getting rid of bad habits to know when is the right time to step in. I struggle on! What has inspired me to be aware is the idea that Boaler presented from her observations at Amber Hill " The teachers thought that students would not or could not think" this " learned helplessness" is something I do not want to be a part of continuing. I know there will be times when I will 'fall of the wagon' so to speak but it has become an important issue for me.
Finally, when I think about all that I read and learned in chapter 4, differences between teacher beliefs and actions, the development of negative student attitudes toward mathematics, the lack of true mathematical understanding have all been eye opening for me. However, it is the idea that the students from Amber Hill were considered to have inadequacies based on the social group they were identified as having come from, that bothered me the most. The studies Anyon, ( 1981) cites that find that schools in lower socio-economic areas "discouraged personal assertiveness and intellectual inquisitiveness in students and assigned work that most often involved substantial amounts of rote activity" is perhaps, shameful! ( maybe that's too strong a word? Hmm?) As I comb through research for this course I have come across the following quote, "All students regardless of their personal characteristics, backgrounds, or physical characteristics must have the opportunity to study - and support to learn - mathematics (NCTM, 2000, p.12) hallelujah brother, say it again! Equity is certainly one of the critical issues facing mathematics education today, Amber Hill certainly demonstrates that.
Saturday, October 10, 2009
What's Current, What's useful, What's useable?
Inquiry project research has led me down some very different ( and interesting) roads, I'm not the most adept researcher. Just lately I've been considering changing my topic, but haven't reached a decision. One of the reasons is the difficulty I'm having finding information on original topic but mainly its because I've become interested in a couple of other ideas that have cropped up.
New idea maybe: Self -regulated Mathematics Learning??
This area of thought is intriguing to me and seems destined to be connected to differentiated instruction ( althought i've yet to find the connection). Perhaps choosing this will allow me to 'kill two birds with one stone' as I am on the starting end of the learning curve about DI. Mainly I'm interested in any concept or approach that can help inquiry-based learning of mathematics. Students who are good 'problem-solvers' need, I believe, a strong background in mathematics knowledge ( facts,symbols, definitions, algorithms etc) but it is not necessary for this 'knowledge' to be received only through direct-instruction. I truly believe that if we make teachers aware of the 'how to' and not just the 'why' of teaching using an inquiry-based approach we will see it used more and more as an instructional approach. Perhaps my 'inquiry' for this course will lead me to a place that will be helpful in this regard.
I am never sure when an idea, that seems new to me, is actually still current in the field of mathematics. Is self-regulated learning a viable topic or have we moved on .... I guess that's a good question for Thursday!
New idea maybe: Self -regulated Mathematics Learning??
This area of thought is intriguing to me and seems destined to be connected to differentiated instruction ( althought i've yet to find the connection). Perhaps choosing this will allow me to 'kill two birds with one stone' as I am on the starting end of the learning curve about DI. Mainly I'm interested in any concept or approach that can help inquiry-based learning of mathematics. Students who are good 'problem-solvers' need, I believe, a strong background in mathematics knowledge ( facts,symbols, definitions, algorithms etc) but it is not necessary for this 'knowledge' to be received only through direct-instruction. I truly believe that if we make teachers aware of the 'how to' and not just the 'why' of teaching using an inquiry-based approach we will see it used more and more as an instructional approach. Perhaps my 'inquiry' for this course will lead me to a place that will be helpful in this regard.
I am never sure when an idea, that seems new to me, is actually still current in the field of mathematics. Is self-regulated learning a viable topic or have we moved on .... I guess that's a good question for Thursday!
Thursday, October 8, 2009
Critical Reflections - Chapter 4 and My Presentation
I would like to begin by thanking everyone for participating in the discussion surrounding the issues I found in chapter 4, what a relief!
Amber Hill is a school with some critical issues in mathematics that need resolving. The teachers are caring, more than competent, "All the mathematics teachers were well qualified mathematics specialists", and efficient. Their effectiveness, however, is an entirely different matter. I do believe it would be wrong to say that 'no' mathematics learning took place at all ( and Boaler doesn't) but it must also be said that very little true mathematical knowledge or understanding happened.
To read about these classrooms is to recognize the forms of instruction, the ways students felt, the motivations behind teachers' actions. The old adage " people in glass houses shouldn't throw stones" comes to mind. It was heartening to read that "students did not blame their boredom on the intrinsic nature of mathematics" Still we sure have a long way to go folks! See you next Thursday!
Amber Hill is a school with some critical issues in mathematics that need resolving. The teachers are caring, more than competent, "All the mathematics teachers were well qualified mathematics specialists", and efficient. Their effectiveness, however, is an entirely different matter. I do believe it would be wrong to say that 'no' mathematics learning took place at all ( and Boaler doesn't) but it must also be said that very little true mathematical knowledge or understanding happened.
To read about these classrooms is to recognize the forms of instruction, the ways students felt, the motivations behind teachers' actions. The old adage " people in glass houses shouldn't throw stones" comes to mind. It was heartening to read that "students did not blame their boredom on the intrinsic nature of mathematics" Still we sure have a long way to go folks! See you next Thursday!
Critical Reflections - chapters 1-3
I guess I was caught up in preparing for my presentation, I've just realized I hadn't posted a reflection on Chapters 1-3, mea culpa Luckily I'd made a few notes, here they are:
After reading Schoenfeld's introduction, it did in fact "induce me to read on",( of course the fact its required reading played a part too!) This being my first graduate level course I am unfamiliar with the rigors of research and what makes a reliable study, suffice it to say I was suitably impressed by Boaler's explanation of her study and have no doubts that her findings are accurate and founded in truth. I was struck but the inclusion (in both Schoenfeld's and Boaler's introductions) of gender as an issue. I must have been living with my head in the sand, I so thought that had been dealt with ( this was an issue yea those many years ago when I did my Bachelor's degree) . Upon reflection I wonder if it wasn't because I didn't see gender in math. In other words I don't expect the boys to do better than the girls, I just expect ( and find) that there are always a mixture of abilities in any classroom.
I was also struck by the idea of reality versus facade in education. When Boaler described Amber Hill, its Principal, its reception area, classroom/hallway behaviour, I started to get a picture of the school, as was her intention. This was then contrasted with what was happening at Amber Hill,( type of instruction, level of learning etc) and one quickly realized that 'you have bite into the chocolate to find out what flavor is on the inside'. I'm sure as we progress through the book Amber Hill will reveal itself to have some redeeming qualities. I look forward to the journey!
Postscript: Now that I've looked so closely at chapter 4 I realize that as Boaler states (p.47) "the portrayal of mathematics at Amber Hill is quite bleak" More about that in my next entry!
After reading Schoenfeld's introduction, it did in fact "induce me to read on",( of course the fact its required reading played a part too!) This being my first graduate level course I am unfamiliar with the rigors of research and what makes a reliable study, suffice it to say I was suitably impressed by Boaler's explanation of her study and have no doubts that her findings are accurate and founded in truth. I was struck but the inclusion (in both Schoenfeld's and Boaler's introductions) of gender as an issue. I must have been living with my head in the sand, I so thought that had been dealt with ( this was an issue yea those many years ago when I did my Bachelor's degree) . Upon reflection I wonder if it wasn't because I didn't see gender in math. In other words I don't expect the boys to do better than the girls, I just expect ( and find) that there are always a mixture of abilities in any classroom.
I was also struck by the idea of reality versus facade in education. When Boaler described Amber Hill, its Principal, its reception area, classroom/hallway behaviour, I started to get a picture of the school, as was her intention. This was then contrasted with what was happening at Amber Hill,( type of instruction, level of learning etc) and one quickly realized that 'you have bite into the chocolate to find out what flavor is on the inside'. I'm sure as we progress through the book Amber Hill will reveal itself to have some redeeming qualities. I look forward to the journey!
Postscript: Now that I've looked so closely at chapter 4 I realize that as Boaler states (p.47) "the portrayal of mathematics at Amber Hill is quite bleak" More about that in my next entry!
Sunday, September 27, 2009
Sir Ken Robinson
What a difference 15 minutes can make to a persons views on learning. I watched Sir Ken Robinson make a case for creating and supporting the need for creativity in education. I couldn't help but see the correlation between what Sir Ken calls "educating people out of creativity",(2005) and the difficulty students have with making connections among and between math concepts and processes . I have watched students struggle to communicate their mathematical reasoning. I have seen that many are unable to apply learned concepts in new or different circumstances. I have long questioned if the difficulties students were demonstrating were due to the fact that children may not have the cognitive maturity to isolate their thought processes as is needed in the latest approach to mathematics . Otherwise, as my thinking went, wouldn't the reform in the approach to instruction of mathematics that has been in practice for more than 10 years, have mediated this weakness and produced children who could explain their thinking?
Now it occurs to me that the root of the problems we are seeing in the learning of mathematics may be due to the fact that we have an educational system that has, as Sir Ken says, " educated people out of creativity" (2005). Sir Ken makes the argument that creativity is as important as literacy and that our education system is failing to cultivate this, (In a later speech at the Apple Educational Leadership Summit (2008) he added that creativity is as important as literacy and numeracy.) If creativity is not valued, if students learn early that mistakes are the worse things you can make how can we expect them to truly understand the underlying concepts in mathematics. Without creativity, without being willing to try new ideas and be wrong, students quickly turn to the teacher to show them the 'right' way to do math. In other words, if creativity was valued as much as literacy and numeracy then perhaps students ability to create understanding and learning in any area through investigation would be a natural process and as such more successful.
In our school district we have the following 'specialist' positions, Instruction and School Leadership , Student Support Services, Math/ Technology, Science/Technology,Primary/Elementary Math, Primary/Elementary literacy but no where is there mention of creativity. It is mind boggling to realize that the system we have invested so much in was founded on a model designed, according to Sir Ken, to meet the needs of the industrial revolution! It is ironic that the shift in thinking and instruction of math that teachers have been asked to make is based on teaching children to see 'the big ideas' in math. Seeing the big ideas means being able to think outside the box,make the connections, understand the underlying processes are all necessary in mathematics. However, the fact that even futurists are unable to predict what the world will look like in 5 years begs the question just who needs to look at the bigger picture? Sir Ken makes a very good case for changing our education system to one that nurtures creativity, not just for mathematics, but to better prepare students to have 'live lives of purpose and meaning"(Robinson, 2008). Isn't this the point of what we do after all?
Now it occurs to me that the root of the problems we are seeing in the learning of mathematics may be due to the fact that we have an educational system that has, as Sir Ken says, " educated people out of creativity" (2005). Sir Ken makes the argument that creativity is as important as literacy and that our education system is failing to cultivate this, (In a later speech at the Apple Educational Leadership Summit (2008) he added that creativity is as important as literacy and numeracy.) If creativity is not valued, if students learn early that mistakes are the worse things you can make how can we expect them to truly understand the underlying concepts in mathematics. Without creativity, without being willing to try new ideas and be wrong, students quickly turn to the teacher to show them the 'right' way to do math. In other words, if creativity was valued as much as literacy and numeracy then perhaps students ability to create understanding and learning in any area through investigation would be a natural process and as such more successful.
In our school district we have the following 'specialist' positions, Instruction and School Leadership , Student Support Services, Math/ Technology, Science/Technology,Primary/Elementary Math, Primary/Elementary literacy but no where is there mention of creativity. It is mind boggling to realize that the system we have invested so much in was founded on a model designed, according to Sir Ken, to meet the needs of the industrial revolution! It is ironic that the shift in thinking and instruction of math that teachers have been asked to make is based on teaching children to see 'the big ideas' in math. Seeing the big ideas means being able to think outside the box,make the connections, understand the underlying processes are all necessary in mathematics. However, the fact that even futurists are unable to predict what the world will look like in 5 years begs the question just who needs to look at the bigger picture? Sir Ken makes a very good case for changing our education system to one that nurtures creativity, not just for mathematics, but to better prepare students to have 'live lives of purpose and meaning"(Robinson, 2008). Isn't this the point of what we do after all?
Subscribe to:
Posts (Atom)
