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!
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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.
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