This chapter in the book I found very interesting and to say the least, certain facts left me speechless. The fact the the amount of material that was retained after just 6 months, by Amber Hill students, was a mere 9%, was astonishing! Yet, having said that, I have had many situations where I will be in class and ask the students to recall information that has been previously taught to them, and an astonishing number of students will respond with, "we never learned that before miss!", yet I know they have, since I was the one who apparently taught them.
What this chapter seemed to present in a very clear and concise matter was that Amber Hill students, who were instructed in a traditional mathematics classroom, were pressured and driven by the GCSE, responded to questions in a cue-behaviour manner, had poor problem solving skills and used little to no thought process in answer questions, all of which lead to poor GCSE results and more importantly, little understanding and retention of mathematics. Again and again Jo Boaler makes the comment that the Amber Hill students had learned appropriate mathematics methods, but did not have the ability or skill necessary to apply the correct methods. This is something that I can relate to. Too often my students know their "mathematics", but do not know how to apply the mathematics to a given complex problem or real life situation. And this, the application of mathematics, is the most important and relevant function of teaching mathematics. If a person cannot apply the knowledge that they have acquired, then the knowledge is out of reach and for the most part, unless!
The Phoenix Park students, on the other hand, seem to be much better problem solvers, and seem to have the ability to apply the knowledge that they have acquired to novel situations. Also, the teaching and learning fashion of Phoenix Park, was not driven by the GCSE's. This seem to result in the students being better test takers! As contradictory as this may seem, considering that Amber Hill students should be use to taking test and should thus be accustomed to such environments as the GCSE's, unlike Phoenix Park students, the Phoenix Park students did not seem to get as frustrated and stressed out as the Amber Hill students if they faced a challenging or novel question. This I strongly believe is largely do to the fact that the GCSE's were not focused on and were not a huge deal for the Phoenix Park students. Thus, the stakes did not seem that high. This is the complete opposite situation for Amber Hill students. The other major factor in this, is that Phoenix Park students were use to dealing with novel problems, working through the problems themselves and use to applying all their math skills to any given situation, which the Amber Hill students were not. The Amber Hill students were not exposed to the connection and network of mathematics topics.
A few question that arose in my mind while reading through this chapter was, if the Phoenix Park students were being taught in a fashion (open-ended, reform) that the school and mathematics department thought was the best method to develop mathematical students, then why would they revert back to the traditional method of teaching mathematics the last few weeks before the GCSE in an attempt to fully and finally prepare the students for the exams???
Finally, a closing thought; The purpose of the GCSE is "to acquire skills, that they [students] are going to be able to use and apply in the rest of their lives, rather than to get some kind of body of knowledge", which to me seems to be in direct opposition of what the GCSE is actually testing! ............. Just a thought!
-
Friday, October 30, 2009
Tuesday, October 27, 2009
Phoenix Park
After reading chapter 5 describing how Phoenix Park presented mathematics and the general nature of mathematics that the school (both teachers and especially students) held, I was struck by awe, as well as, concern and questions.
First of all, I am intrigued by the nature of mathematics that is held by Phoenix Park; the notion that math is about thinking, probing and problem solving, not the unfortunate side effect of traditional math classrooms that inevitably portray mathematics as a set of rules and regulations to following, and that any problem can be solved in a short amount of time, without thinking! This is the notion of mathematics that I would like to present to my students, and I am sure that I am not! Too often I find students who rush to get the math completed, who do not think about the problem they are faced with and end up with an solution that is completely non-sensible. This I feel is a major concern with the mathematics that is being taught in our school systems, students are not aware of whether or not their answers make sense, mostly because they do not think about the mathematics, they simply apply some rule that they think is appropriate and assume they are done.
Some of the concerns and questions that I had about the Phoenix Park approach to presenting mathematics, include:
- I wonder what the classroom in Phoenix Park looks like. What resources (textbooks, manipulatives, Internet/web resources) do the students have at their finger tips? I tend to think that if I were to implement this form of "teaching" in my classroom, right now, me class would not be physically arranged to accompany the students needs.
- secondly, I personally would have serious issues with the notion/idea that students who do not want to engage and do work, can simply avoid the math. The major issue that I have with this is that I feel that students who do not want to engage would be a major disruption to students who do want to engage. Also, I have a fear that most of my students would choose not to do anything......and class would be a waste. I guess that the reason of this is that I feel my students (most of them anyways) are not responsible enough to handle the responsibility that accompanies such a type of learning and teaching style.
- Finally, Jo Boaler say in chapter 5, "All three teachers seemed concerned to help and support students and, consequently,spent almost all of their time helping students who wanted help, leaving the others to their own devices." This approach seems to be in complete contradiction to the method that my school presents. I feel that I send almost all of my time in class is spent on "helping" students who are unmotivated and seem to not want my help. So I feel that this approach would not fly in my school. Having said that, I personally would rather spend my time helping those who want my help, engaging, pushing and challenging them!
First of all, I am intrigued by the nature of mathematics that is held by Phoenix Park; the notion that math is about thinking, probing and problem solving, not the unfortunate side effect of traditional math classrooms that inevitably portray mathematics as a set of rules and regulations to following, and that any problem can be solved in a short amount of time, without thinking! This is the notion of mathematics that I would like to present to my students, and I am sure that I am not! Too often I find students who rush to get the math completed, who do not think about the problem they are faced with and end up with an solution that is completely non-sensible. This I feel is a major concern with the mathematics that is being taught in our school systems, students are not aware of whether or not their answers make sense, mostly because they do not think about the mathematics, they simply apply some rule that they think is appropriate and assume they are done.
Some of the concerns and questions that I had about the Phoenix Park approach to presenting mathematics, include:
- I wonder what the classroom in Phoenix Park looks like. What resources (textbooks, manipulatives, Internet/web resources) do the students have at their finger tips? I tend to think that if I were to implement this form of "teaching" in my classroom, right now, me class would not be physically arranged to accompany the students needs.
- secondly, I personally would have serious issues with the notion/idea that students who do not want to engage and do work, can simply avoid the math. The major issue that I have with this is that I feel that students who do not want to engage would be a major disruption to students who do want to engage. Also, I have a fear that most of my students would choose not to do anything......and class would be a waste. I guess that the reason of this is that I feel my students (most of them anyways) are not responsible enough to handle the responsibility that accompanies such a type of learning and teaching style.
- Finally, Jo Boaler say in chapter 5, "All three teachers seemed concerned to help and support students and, consequently,spent almost all of their time helping students who wanted help, leaving the others to their own devices." This approach seems to be in complete contradiction to the method that my school presents. I feel that I send almost all of my time in class is spent on "helping" students who are unmotivated and seem to not want my help. So I feel that this approach would not fly in my school. Having said that, I personally would rather spend my time helping those who want my help, engaging, pushing and challenging them!
Wednesday, October 21, 2009
Amber Hill
After reading this chapter, I had the general thought that how these students were being taught is how I was taught, however, because of my learning style and personality (desire to succeed and persistent), I was successful.
I imagine that most classrooms still teach ion this fashion. We are beginning to move toward more exploration and explanation. For example, in my mathematics classes, one would regularly see students performing investigations (often with the aid of manipulatives) in an attempt to have students discover some mathematical concept. Also classroom discussions involve various students explaining how they arrived at an answer or concept in an attempt to have students realize that there is more than one way to arrive at an answer and also allowing students’ time to develop reasoning and communication skills.
Having said all of this, I still feel that if I were to ask my math students their views about the nature of mathematics, I am fairly certain that most of them would have the same basic beliefs as the students at Amber Hill:
- That math is about following rules
- That math is not about understanding and making sense
- That all math problems can be solved in a few short minutes
Also, to add to this, I have witnessed my students use cue-based behavior. They are not confident enough in themselves and in their understanding of mathematics. For example, when a student answered a question in class, I responded to the answer by simply saying “ok!” (I neither approved the answer nor disapproved the answer). The student immediately changed her answer, she was now unsure of the answer. The student was correct, however like most students, she fears being wrong and lacks confidence in math.
I think that these common beliefs in the nature of mathematics, that were evident in the Amber Hill students as well as my own students, are a result of the environment in which mathematics is taught and the way the mathematics is taught. Even with the minor changes that exist in some math classes today.
I imagine that most classrooms still teach ion this fashion. We are beginning to move toward more exploration and explanation. For example, in my mathematics classes, one would regularly see students performing investigations (often with the aid of manipulatives) in an attempt to have students discover some mathematical concept. Also classroom discussions involve various students explaining how they arrived at an answer or concept in an attempt to have students realize that there is more than one way to arrive at an answer and also allowing students’ time to develop reasoning and communication skills.
Having said all of this, I still feel that if I were to ask my math students their views about the nature of mathematics, I am fairly certain that most of them would have the same basic beliefs as the students at Amber Hill:
- That math is about following rules
- That math is not about understanding and making sense
- That all math problems can be solved in a few short minutes
Also, to add to this, I have witnessed my students use cue-based behavior. They are not confident enough in themselves and in their understanding of mathematics. For example, when a student answered a question in class, I responded to the answer by simply saying “ok!” (I neither approved the answer nor disapproved the answer). The student immediately changed her answer, she was now unsure of the answer. The student was correct, however like most students, she fears being wrong and lacks confidence in math.
I think that these common beliefs in the nature of mathematics, that were evident in the Amber Hill students as well as my own students, are a result of the environment in which mathematics is taught and the way the mathematics is taught. Even with the minor changes that exist in some math classes today.
Monday, September 28, 2009
A History of My Mathematics Life.....
When asked to describe my mathematics classes from kindergarten to grade 6, my mind for the most part goes blank! I have very little memories of school during that time of my life, and even less about mathematics in particular. I have no idea what my classroom may have looked like, if it contained any mathematics posters or displayed and of the students’ mathematical work (or even of I did any type of mathematical work that would have been of the type to post on the classroom wall). I cannot remember using any sort of manipulative or whether or not I worked independently or in a small group. The only thing that I remember of mathematics in primary and elementary school was that there seemed to be quite a bit of drill and practice (addition, subtraction, etc., in workbooks) that was completed as homework. Also, I remember having to learn my multiplication tables by way of memorization without any comprehension of what exactly 4 X 6 really meant. The few memories that I do have accessible to me, seem to put mathematics in a light that was a drill, practice, and memorization topic. Not one of understanding, applying, reasoning and/or communication of the subject.
Having very few (or almost no) memory of primary and elementary mathematics has a huge implication for me!.....one that I never stopped to consider before this time......... if my early years of mathematics has so little bearing on my memory, it must have had very little impact on my life! Considering my current love and appreciation for the subject now and my post secondary education status (mathematics minor), this concept of mathematics having little or no impact on early years of my life is amazing to say the least.
When I move into my junior and senior high school mathematics memories, they start to become more prevalent. I remember enjoying mathematics very much, actually my favorite subject, until chemistry in level II. A mathematics class would consist of a chalk and talk lesson, then practice problems from the textbook to work on. In terms of assessment, all that I have a memory of completing is assignments and tests. When I think back onto my math classes, they are so different from what I do and use in my classroom now, when I teach the subject. I guess part of the reason I enjoyed math so much in high school was because I was good at it. Math was a subject that I could sit in class and listen to, understand the issues, do and finish the work that was assigned in- class (which meant no homework!! Yahoo!), and never had to study at home for the tests, yet still get an A+ in the course!
When I move into post-secondary education, in terms of mathematics, I did a minor in mathematics, so I completed the required 8 courses. I have to admit, while I found mathematics in university much harder than in high school, I still thoroughly enjoyed. It again was a subject that I could work on and understand, and I got progressively better with my results in my mathematics courses the further into my degree I went.
I understand that all of the above memories, and I’m sure even more that I can’t quite remember now, have helped shape who I am today regarding my understanding and view of mathematics. I feel that mathematics is not so much a subject or topic to be simply studied, but is a part of life. I have concerns about the current lack of motivation and interest students and parents display when talking about or referring to mathematics. This is something that I hope to change, if only for the students that I teach. I hope to impact my students’ lives in such a way, as to leave them with more memories and fonder ones than I have of mathematical education in school, in a hope to boost the attitude toward mathematics in a more positive light!
Having very few (or almost no) memory of primary and elementary mathematics has a huge implication for me!.....one that I never stopped to consider before this time......... if my early years of mathematics has so little bearing on my memory, it must have had very little impact on my life! Considering my current love and appreciation for the subject now and my post secondary education status (mathematics minor), this concept of mathematics having little or no impact on early years of my life is amazing to say the least.
When I move into my junior and senior high school mathematics memories, they start to become more prevalent. I remember enjoying mathematics very much, actually my favorite subject, until chemistry in level II. A mathematics class would consist of a chalk and talk lesson, then practice problems from the textbook to work on. In terms of assessment, all that I have a memory of completing is assignments and tests. When I think back onto my math classes, they are so different from what I do and use in my classroom now, when I teach the subject. I guess part of the reason I enjoyed math so much in high school was because I was good at it. Math was a subject that I could sit in class and listen to, understand the issues, do and finish the work that was assigned in- class (which meant no homework!! Yahoo!), and never had to study at home for the tests, yet still get an A+ in the course!
When I move into post-secondary education, in terms of mathematics, I did a minor in mathematics, so I completed the required 8 courses. I have to admit, while I found mathematics in university much harder than in high school, I still thoroughly enjoyed. It again was a subject that I could work on and understand, and I got progressively better with my results in my mathematics courses the further into my degree I went.
I understand that all of the above memories, and I’m sure even more that I can’t quite remember now, have helped shape who I am today regarding my understanding and view of mathematics. I feel that mathematics is not so much a subject or topic to be simply studied, but is a part of life. I have concerns about the current lack of motivation and interest students and parents display when talking about or referring to mathematics. This is something that I hope to change, if only for the students that I teach. I hope to impact my students’ lives in such a way, as to leave them with more memories and fonder ones than I have of mathematical education in school, in a hope to boost the attitude toward mathematics in a more positive light!
Monday, September 21, 2009
Video - Sir Ken Robinson
After viewing the video of Sir Ken Robinson giving a speech at the TED Conference in 2006, a few issues stuck with me.
Sir Ken Robinson was trying to get across the concept that we are educating children out of creativity. This is something that I tend to agree with. With the structure of the education system, the theory of curriculum, does not allow for creativity. How is it possible to have a curriculum that is so highly structured, pre-specified and numerous, and yet allow for creativity. The very aspect of creativity and originality does not lend itself to being pre-specified before the teaching. That is to say, that not all the curriculum outcomes need to be predetermined, they can be developed based on the student, the setting of the class environment and then created by the teacher. As stated by the Elliott Eisner, teaching a child should be a work of art and that a students' product should be "a surprise to the teacher and the student".
Secondly, education is often viewed as a preparation of adulthood, and again I feel that this is another factor that leads to the mis-education of children (the education out of creativeness). Education is a preparation for adulthood just as much as it is a process of current living! Sir Ken Robinson makes note that without the willingness to be wrong, or the preparation of possibly being wrong, one will be less willing to take risks and chances and thus cannot hope to be creative. This means that part of education, a process of life, is to allow children to take risks, to be wrong, to learn for their mistakes and eventually be intelligent and creative - to be able to view problems in several ways and solve them in several/differing ways!
Sir Ken Robinson was trying to get across the concept that we are educating children out of creativity. This is something that I tend to agree with. With the structure of the education system, the theory of curriculum, does not allow for creativity. How is it possible to have a curriculum that is so highly structured, pre-specified and numerous, and yet allow for creativity. The very aspect of creativity and originality does not lend itself to being pre-specified before the teaching. That is to say, that not all the curriculum outcomes need to be predetermined, they can be developed based on the student, the setting of the class environment and then created by the teacher. As stated by the Elliott Eisner, teaching a child should be a work of art and that a students' product should be "a surprise to the teacher and the student".
Secondly, education is often viewed as a preparation of adulthood, and again I feel that this is another factor that leads to the mis-education of children (the education out of creativeness). Education is a preparation for adulthood just as much as it is a process of current living! Sir Ken Robinson makes note that without the willingness to be wrong, or the preparation of possibly being wrong, one will be less willing to take risks and chances and thus cannot hope to be creative. This means that part of education, a process of life, is to allow children to take risks, to be wrong, to learn for their mistakes and eventually be intelligent and creative - to be able to view problems in several ways and solve them in several/differing ways!
Subscribe to:
Posts (Atom)