Thanks to all who participated in Thursday night's discussions. For those of you who couldn't make it, I can email a copy of the handout if you wish. It was a great semester with lots of thought provoking discussions. Thanks Mary for introducing open-ended approach to teaching. I am looking forward to implementing this method in my next teaching position (which hopefully is not... you know where)
To my fellow classmates, thanks for lending an ear, and offering your advice/experiences. I wish you all the best of luck in all of your future endeavors!
Merry Christmas all!!!
Jennifer
Sunday, December 6, 2009
Ability Grouping, Equity & Survival of the Quickest
As was suggested by Melanie in class, a more appropriate title for this chapter may have been “DISability grouping. The ability grouping experienced by students at Amber Hill greatly disadvantaged and discouraged students on a number of different levels. The differing opinions of student and teacher needs with respect to ability grouping was strongly evident in this chapter. Boaler identified four aspects of ability grouping which she believed had the most impact on students: working at a fast pace; pressure and anxiety; restricted opportunities; and setting decisions.
Teachers at Amber Hill believed strongly in a “one size fits all” approach to teaching and learning mathematics. As was indicated by Melanie, the primary reason for introducing ability grouping was due to the fact that teachers would have the opportunity to deliver the same content to the entire group. However, as was evident from the study, students were very dissatisfied with the structure of the lessons. Students were on opposite ends of the continuum- some felt lessons were too slow (and hence lessons are boring and students are not engaged) while other students felt lessons were much too fast (as a result students became confused and “lost”).
With respect to pressure and anxiety, many of the students at Amber Hill reported a feeling of judgement from peers within their particular set, which in turn created anxiety among students. This contrasts with teachers beliefs. They assumed that ability grouping would create a competitive environment for students, which in turn would increase student achievement. What the teachers didn’t anticipate was the negative effect ability grouping would have on students. In a number of instances students indicated they didn’t perform well on assessments due to a lack of encouragement to do well. They knew that no matter how hard they tried, they would only attain the grade associated with the particular set within which they were placed.
According to students at Amber Hill, ability grouping restricted many opportunities. The same group of students report feeling “cheated” by the system, as they would only attain the grade associated with the particular set within which they were placed. How frustrating this must have been! Even if a student had the ability and mathematical know-how to achieve an A grade, because they were in G set, then this was the highest mark they would receive.
Another characteristic which restricted the opportunities for ability grouped students as indicated by the students at Amber Hill was the fact that social class was a large determinant for student placement in a particular set. Very often, students from lower social classes were placed in lower sets, regardless of student ability. The same was true of students who were flagged as having behaviour problems. It was quite evident that decisions regarding sets was not always an accurate reflection of student ability.
I was alarmed and concerned to discover that set decisions were hidden from students and decided upon at an early age (as early as grade 4). This does not account for student growth, development and maturity. Just as one student can show much improvement with respect to ability, a student’s ability can decline as the student matures. Yet, this model allows for no change.
Through class discussions, we alluded to the fact that in Newfoundland and Labrador, students are not paced in particular sets as such. However, once students reach junior and senior high, there is a division based on academic ability. Students have the opportunity to take basic, academic, or advanced courses. As is the case in England, once a student chooses the basic course route, there is no change for that student- he/she has to remain in the basic stream regardless if student ability increases. That being said, student grades are not determined based on the course route they choose, each individual still has the ability to achieve a grade ranging from 0 – 100. As a math teacher I always encourage students to stick with the academic stream; I offer extra help and tutorials, and whatever else I can do to ensure the student experiences success. As well, for those who choose the basic route, I ensure all implications/restrictions of choosing such a route are made clear to both the individual and the parent. Unlike England, students in Newfoundland and Labrador have a choice as to which group they are placed in. A teacher can make recommendations, but ultimately the final decision lies on the shoulders of the student.
Teachers at Amber Hill believed strongly in a “one size fits all” approach to teaching and learning mathematics. As was indicated by Melanie, the primary reason for introducing ability grouping was due to the fact that teachers would have the opportunity to deliver the same content to the entire group. However, as was evident from the study, students were very dissatisfied with the structure of the lessons. Students were on opposite ends of the continuum- some felt lessons were too slow (and hence lessons are boring and students are not engaged) while other students felt lessons were much too fast (as a result students became confused and “lost”).
With respect to pressure and anxiety, many of the students at Amber Hill reported a feeling of judgement from peers within their particular set, which in turn created anxiety among students. This contrasts with teachers beliefs. They assumed that ability grouping would create a competitive environment for students, which in turn would increase student achievement. What the teachers didn’t anticipate was the negative effect ability grouping would have on students. In a number of instances students indicated they didn’t perform well on assessments due to a lack of encouragement to do well. They knew that no matter how hard they tried, they would only attain the grade associated with the particular set within which they were placed.
According to students at Amber Hill, ability grouping restricted many opportunities. The same group of students report feeling “cheated” by the system, as they would only attain the grade associated with the particular set within which they were placed. How frustrating this must have been! Even if a student had the ability and mathematical know-how to achieve an A grade, because they were in G set, then this was the highest mark they would receive.
Another characteristic which restricted the opportunities for ability grouped students as indicated by the students at Amber Hill was the fact that social class was a large determinant for student placement in a particular set. Very often, students from lower social classes were placed in lower sets, regardless of student ability. The same was true of students who were flagged as having behaviour problems. It was quite evident that decisions regarding sets was not always an accurate reflection of student ability.
I was alarmed and concerned to discover that set decisions were hidden from students and decided upon at an early age (as early as grade 4). This does not account for student growth, development and maturity. Just as one student can show much improvement with respect to ability, a student’s ability can decline as the student matures. Yet, this model allows for no change.
Through class discussions, we alluded to the fact that in Newfoundland and Labrador, students are not paced in particular sets as such. However, once students reach junior and senior high, there is a division based on academic ability. Students have the opportunity to take basic, academic, or advanced courses. As is the case in England, once a student chooses the basic course route, there is no change for that student- he/she has to remain in the basic stream regardless if student ability increases. That being said, student grades are not determined based on the course route they choose, each individual still has the ability to achieve a grade ranging from 0 – 100. As a math teacher I always encourage students to stick with the academic stream; I offer extra help and tutorials, and whatever else I can do to ensure the student experiences success. As well, for those who choose the basic route, I ensure all implications/restrictions of choosing such a route are made clear to both the individual and the parent. Unlike England, students in Newfoundland and Labrador have a choice as to which group they are placed in. A teacher can make recommendations, but ultimately the final decision lies on the shoulders of the student.
Girls, Boys, and Learning Styles
In chapter nine, Boaler delves into yet another contentious issue- one that is predominantly present at Amber Hill and yet another contributing factor to their low scores on GCSE’s. Boaler notes that while females in England now attain the same proportion of the top grades on the GCSE examinations as boys, important differences still occur among the top 5% of students in England, United States and other countries.
Until recently, I was ignorant to the idea that gender issues are still present in our classrooms. In fact, I was under the impression that the tables had turned and females were beginning to dominate the areas of Mathematics and Science. When I reflect back on my own high school experiences, it was females who dominated in the mathematics classroom. Because of my school`s small size, advanced math was offered through CDLI. All through grade 10, 11 and 12 I was the only female in my school to complete this course. At the district level, the majority of the class was comprised of females. After high school, I studied Mathematics at Sir Wilfred Grenfell College. Here, the mathematics classroom mimicked my high school math class- the majority of students were females.
At Amber Hill, it wasn’t because the boys had a better understanding of the material, they were simply better at playing the mathematical game and the fact that they had set different goals for themselves. For the boys, speed and attainment of correct answers was more important that the understanding of the material they were “learning”. It was all about rote memorization and reiteration of material for the teacher. In comparison, the girls were not into playing the math game- they had a desire and need to understand. They wanted to know “why” and “how”. It was very disheartening to discover that the reasons for females low performance on GCSE’s was largely attributed to the pedagogical practices employed in their classroom. Had the teachers taken the time to explain the mathematics, females at Amber Hill would have been much more successful.
Boaler introduces the idea of attribution theory and the notion that many females attribute their lack of success in mathematics to themselves. It was evident that the girls at Amber Hill did not blame their lack of understanding on themselves. Numerous times throughout the chapter, in interviews, questionnaires, etc., Amber Hill girls indicated their dissatisfaction with mathematics stemmed from the way in which it was taught, and that it had nothing to do with their own inadequacies. It is very unfortunate that although the girls expressed concern for the way and speed with which the math was taught, the teachers at Amber Hill did nothing to alleviate the problem.
Being a female, it was frustrating to read that the girls at Amber Hill had to make sacrifices to their understanding because the boys (and evidently the teachers) liked to quickly progress through lessons. I wonder how the accomplishments of the same set of girls would have changed had the pedagogical practices employed in the classroom changed? Would they had been successful had they been students at Phoenix Park where students had freedom to develop their own style of working, and who were openly encouraged to think for themselves to develop concepts and theories.
Until recently, I was ignorant to the idea that gender issues are still present in our classrooms. In fact, I was under the impression that the tables had turned and females were beginning to dominate the areas of Mathematics and Science. When I reflect back on my own high school experiences, it was females who dominated in the mathematics classroom. Because of my school`s small size, advanced math was offered through CDLI. All through grade 10, 11 and 12 I was the only female in my school to complete this course. At the district level, the majority of the class was comprised of females. After high school, I studied Mathematics at Sir Wilfred Grenfell College. Here, the mathematics classroom mimicked my high school math class- the majority of students were females.
At Amber Hill, it wasn’t because the boys had a better understanding of the material, they were simply better at playing the mathematical game and the fact that they had set different goals for themselves. For the boys, speed and attainment of correct answers was more important that the understanding of the material they were “learning”. It was all about rote memorization and reiteration of material for the teacher. In comparison, the girls were not into playing the math game- they had a desire and need to understand. They wanted to know “why” and “how”. It was very disheartening to discover that the reasons for females low performance on GCSE’s was largely attributed to the pedagogical practices employed in their classroom. Had the teachers taken the time to explain the mathematics, females at Amber Hill would have been much more successful.
Boaler introduces the idea of attribution theory and the notion that many females attribute their lack of success in mathematics to themselves. It was evident that the girls at Amber Hill did not blame their lack of understanding on themselves. Numerous times throughout the chapter, in interviews, questionnaires, etc., Amber Hill girls indicated their dissatisfaction with mathematics stemmed from the way in which it was taught, and that it had nothing to do with their own inadequacies. It is very unfortunate that although the girls expressed concern for the way and speed with which the math was taught, the teachers at Amber Hill did nothing to alleviate the problem.
Being a female, it was frustrating to read that the girls at Amber Hill had to make sacrifices to their understanding because the boys (and evidently the teachers) liked to quickly progress through lessons. I wonder how the accomplishments of the same set of girls would have changed had the pedagogical practices employed in the classroom changed? Would they had been successful had they been students at Phoenix Park where students had freedom to develop their own style of working, and who were openly encouraged to think for themselves to develop concepts and theories.
Friday, November 20, 2009
Knowledge, Beliefs & Mathematical Identities
The information presented in this chapter was, to some degree, not surprising. It was evident from preceding chapters that the experiences and development of mathematical knowledge at Amber Hill was very different from those experiences of Phoenix Park students. From preceding chapters it was apparent where the real learning took place- Phoenix Park. This occurred despite the efforts put forth by the teachers at Amber Hill- methodologies which they perceived would ensure student success, particularly on GCSE’s.
Amber Hill’s traditional methods and Phoenix Park’s open-ended approaches were not on “separate ends of the spectrum,” rather they fostered a different development of mathematical knowledge. The two schools differed in many aspects:
· Amber Hill students lacked confidence in their mathematical abilities and relied heavily on teacher support and cueing. In comparison, students at Phoenix Park were considerably more confident in their mathematical abilities.
· Amber Hill students made no connection of maths taught in the classroom to “real world” situations. Students at Phoenix Park were continually applying the math they learned in school to out-of-school situations.
· The students at Amber Hill were perceived as what Belencky, Clinchy, Goldberger and Tarule refer to as received knowers- expecting to accept knowledge from authoritative sources without contributing to knowledge or making connections across areas. In comparison, students at Phoenix Park were very mathematically empowered- they possessed the power to develop and use mathematical knowledge in the school setting.
· Unlike their Phoenix Park counterparts, the teachers at Amber Hill were continually motivating students and enforcing the importance of the upcoming GCSE’s. The students at Phoenix Park were largely self motivated, and the importance of the GCSE’s was rarely discussed (with exception to the couple of weeks leading up to the GCSE’s).
· Students at Amber Hill viewed mathematics as isolated and fragmented concepts. Their lack of success on applied assessment can be attributed to this notion that mathematical concepts are isolated.
It is evident that both sets of teachers believed they were using methodologies that worked best for the students. However, there was no mention of teachers taking the time to reflect and determine student areas of both strength and weakness. I, as do many teachers, often get wrapped up in the notion that “I know what work’s best” for my students. However, as is apparent in Boaler’s study, this is not always true. It is important to reflect, determine what “works” for students and what approaches to teaching are not as successful as others. That being said, it is very important to remember that what students find helpful one year may not be applicable the next. Although I have always considered myself to be aware of what methodologies are successful for students, I am continually exploring approaches that may work better. I am both anxious and excited to make use of Phoenix Park teaching strategies when I return to teaching in the upcoming year.
Amber Hill’s traditional methods and Phoenix Park’s open-ended approaches were not on “separate ends of the spectrum,” rather they fostered a different development of mathematical knowledge. The two schools differed in many aspects:
· Amber Hill students lacked confidence in their mathematical abilities and relied heavily on teacher support and cueing. In comparison, students at Phoenix Park were considerably more confident in their mathematical abilities.
· Amber Hill students made no connection of maths taught in the classroom to “real world” situations. Students at Phoenix Park were continually applying the math they learned in school to out-of-school situations.
· The students at Amber Hill were perceived as what Belencky, Clinchy, Goldberger and Tarule refer to as received knowers- expecting to accept knowledge from authoritative sources without contributing to knowledge or making connections across areas. In comparison, students at Phoenix Park were very mathematically empowered- they possessed the power to develop and use mathematical knowledge in the school setting.
· Unlike their Phoenix Park counterparts, the teachers at Amber Hill were continually motivating students and enforcing the importance of the upcoming GCSE’s. The students at Phoenix Park were largely self motivated, and the importance of the GCSE’s was rarely discussed (with exception to the couple of weeks leading up to the GCSE’s).
· Students at Amber Hill viewed mathematics as isolated and fragmented concepts. Their lack of success on applied assessment can be attributed to this notion that mathematical concepts are isolated.
It is evident that both sets of teachers believed they were using methodologies that worked best for the students. However, there was no mention of teachers taking the time to reflect and determine student areas of both strength and weakness. I, as do many teachers, often get wrapped up in the notion that “I know what work’s best” for my students. However, as is apparent in Boaler’s study, this is not always true. It is important to reflect, determine what “works” for students and what approaches to teaching are not as successful as others. That being said, it is very important to remember that what students find helpful one year may not be applicable the next. Although I have always considered myself to be aware of what methodologies are successful for students, I am continually exploring approaches that may work better. I am both anxious and excited to make use of Phoenix Park teaching strategies when I return to teaching in the upcoming year.
Friday, November 6, 2009
Exploring The Differences
Chapter 7 takes a close examination of the differences which existed between the two groupings of students, of which there were many. These differences can largely be attributed to the environment in which the two groups of students “learned” math. As mentioned previously, the learning environment at Amber Hill was very traditional in that the teacher introduced a particular topic at the beginning of the lesson followed by the completion of text book exercises which reinforced the concept just “taught” by the teacher. It was alarming to discover the huge sense of false understanding this created for the students. Alan, a year 10 student at Amber Hill, stresses this point in his statement “It’s stupid really cause when you’re in the lesson, when you’re doing work-even when it’s hard- you get the odd one or two wrong, but most of them you get right and you think well when I go into the exam I’m gonna get most of them right, cause you got all your chapters right. But you don’t.”
I wonder how many of us are victims of creating/having this false sense of knowledge in our teaching and learning experiences. It is no wonder that the children thought they could do the math, why would they think any otherwise when each class was conducted in exactly the same manner as the last- the teacher spends the better part of an hour introducing an isolated concept and the steps that have to be followed when presented with this particular type of problem. The students are then drilled to the point where every question is the exact same as the previous (which is the exact same as the examples given by the instructor), with the exception of the numbers present. When students did stumble upon a “problem” which they did not understand, students immediately looked to the teacher for help rather than thinking about the question. Assessment situations were no different from that of the classroom. Examinations were comprised of questions that were replicas of those found in the textbooks. The fact that students experienced success on the examinations may be attributed to the examinations comprised of isolated concepts which the students had just learned. Once the assessment was written, the mathematical concepts “learned” were forgotten.
Chapter 7 in Boaler’s study stresses, yet again, the importance of moving away from the more traditional methods of teaching as they simply aren’t working for all students. In order for students to experience success with mathematics we (educators) need to encourage them to delve deep, or to a depth that’s of comfort to them, into the subject and creating an understanding and thus knowledge of the subject.
I wonder how many of us are victims of creating/having this false sense of knowledge in our teaching and learning experiences. It is no wonder that the children thought they could do the math, why would they think any otherwise when each class was conducted in exactly the same manner as the last- the teacher spends the better part of an hour introducing an isolated concept and the steps that have to be followed when presented with this particular type of problem. The students are then drilled to the point where every question is the exact same as the previous (which is the exact same as the examples given by the instructor), with the exception of the numbers present. When students did stumble upon a “problem” which they did not understand, students immediately looked to the teacher for help rather than thinking about the question. Assessment situations were no different from that of the classroom. Examinations were comprised of questions that were replicas of those found in the textbooks. The fact that students experienced success on the examinations may be attributed to the examinations comprised of isolated concepts which the students had just learned. Once the assessment was written, the mathematical concepts “learned” were forgotten.
Chapter 7 in Boaler’s study stresses, yet again, the importance of moving away from the more traditional methods of teaching as they simply aren’t working for all students. In order for students to experience success with mathematics we (educators) need to encourage them to delve deep, or to a depth that’s of comfort to them, into the subject and creating an understanding and thus knowledge of the subject.
Saturday, October 31, 2009
Finding out what they could do.... or Couldn't!
To no surprise, the students at Amber Hill were outperformed by the students at Phoenix Park on both assessments administered by Boaler, and the state-wide assessments (the GCSE’s). The issue is not which method of teaching is better than the other, rather how do we ensure students develop the appropriated mathematical knowledge required. The students at Amber Hill were of the opinion that math was fragmented and consisted largely of rote memorization of formulas and algorithms. A technique which essentially, failed them when they needed it. In contrast, the students at Phoenix Park developed and discovered the concepts for themselves through a series of open-ended questions. They had the ability to take this developed knowledge and apply it to multiple situations. This self-developed knowledge led to a better understanding of the material and proved to be beneficial in not only test situations but also in situations outside the math class which required mathematics.
It was alarming to discover the poor retention rates of the students (only 9% of Amber Hill students had the ability to retain mathematical information for any extended period of time). Students at Amber Hill felt increased pressure and anxiety to remember formulas not knowing where they came from, or even when to use them. As we all know from personal experiences, understanding and developing formulas and theorems, as the students at Phoenix Park did, results in an increased ability to retain the learned information. In one of the previous sections a student from Amber Hill made the comment “as soon as you walk out the class.... you don’t really know anything, cause you’ve already switched off... as soon as you’ve walked out, you’ve forgotten about that lesson”. Thus providing some insight as to why the students did not retain information.
It was interesting to note that the students at Amber Hill did not “think” about the math. They simply looked for cue words as indicators of which formula to use. If, for some reason, the cues were absent, they were unaware of which approach or method to apply. As a teacher, I am guilty of telling my students to look for “key” words as indicators of how to go about solving a particular problem. As discussed in class, many common exams and public exams have questions appear in the order in which they were taught in class. For example on the 2009 Math 3204 public exam, students knew that the first series of multiple choice questions were going to deal with quadratics, as this is the first unit taught in 3204. Therefore, students knew how to accurately select the correct answer based on this.
I reflect back on my own learning experiences, which were very much traditional and very similar to those experienced by the students at Amber Hill. I remember just trying to get through yet another lesson, devising songs, poems, acrostics, doing just about anything to aid in the memorization of the “math”. It worked, for the most part, but only for the duration of that particular unit. As soon as the test was finished, I would push those math concepts to the back of my mind, only to make use of them when mid-year and final examinations came around. I only wish I were given the opportunity to delve into mathematics as the students at Phoenix Park were.
It was alarming to discover the poor retention rates of the students (only 9% of Amber Hill students had the ability to retain mathematical information for any extended period of time). Students at Amber Hill felt increased pressure and anxiety to remember formulas not knowing where they came from, or even when to use them. As we all know from personal experiences, understanding and developing formulas and theorems, as the students at Phoenix Park did, results in an increased ability to retain the learned information. In one of the previous sections a student from Amber Hill made the comment “as soon as you walk out the class.... you don’t really know anything, cause you’ve already switched off... as soon as you’ve walked out, you’ve forgotten about that lesson”. Thus providing some insight as to why the students did not retain information.
It was interesting to note that the students at Amber Hill did not “think” about the math. They simply looked for cue words as indicators of which formula to use. If, for some reason, the cues were absent, they were unaware of which approach or method to apply. As a teacher, I am guilty of telling my students to look for “key” words as indicators of how to go about solving a particular problem. As discussed in class, many common exams and public exams have questions appear in the order in which they were taught in class. For example on the 2009 Math 3204 public exam, students knew that the first series of multiple choice questions were going to deal with quadratics, as this is the first unit taught in 3204. Therefore, students knew how to accurately select the correct answer based on this.
I reflect back on my own learning experiences, which were very much traditional and very similar to those experienced by the students at Amber Hill. I remember just trying to get through yet another lesson, devising songs, poems, acrostics, doing just about anything to aid in the memorization of the “math”. It worked, for the most part, but only for the duration of that particular unit. As soon as the test was finished, I would push those math concepts to the back of my mind, only to make use of them when mid-year and final examinations came around. I only wish I were given the opportunity to delve into mathematics as the students at Phoenix Park were.
Tuesday, October 20, 2009
Teaching & Learning at Phoenix Park
I would like to begin by congratulating Michelle on a job well done. The presentation of material was clear and very concise. There were many discussions which elaborated on the issues presented by the teaching at Phoenix Park, which in turn increased my understanding of the teaching methods employed at Phoenix Park. I would also like to thank Scott for the wonderful spread of food, it was delicious!
I, like many of my classmates, would have loved to have had the opportunity to experience a learning environment similar to that encountered by the students at Phoenix Park. Instead, my learning consisted of traditional methods in which teachers introduced a particular topic, leaving little or no room for student self exploration. In comparison, students at Phoenix Park were introduced to a topic via open ended questions, which gave them opportunity to be as creative and in depth as desired. Students were responsible for their own learning, which in turn provided them with a sense of pride and accomplishment, which is sometimes lacking in the more traditional learning environment. This sense of pride and accomplishment led students to be more successful in mathematics, simply because they understood the mathematics. Boaler emphasizes this success in her following statement “The Phoenix Park students did not seem to have this shallow view of mathematics; they were aware of the depth of the subject-the different layers that may be encountered. The student also demonstrated an unusual awareness of the diversity and breadth of mathematics. They did not regard mathematics as a vast collection of sums; they seems to have a richer and more balanced view of the subject.” (Boaler, pg. 77)
As an educator, I questioned whether or not the techniques employed at Phoenix Park would be applicable to classrooms throughout Newfoundland and Labrador. My initial response was absolutely NOT, however, after much thought and discussion I am confident this open-ended approach to teaching would definitely work in our classrooms. That being said, in order for this approach to learning to work, a great amount of support from students, parents, administrators and board officials would be required. It would be a very time consuming process, and one which requires the teacher to be well organized and to have an extensive understanding of the subject material. As Sharon mentioned, it is not necessary that we do a complete program overhaul in one year, rather we could implement this particular technique at a rate comfortable to us. As well, a transition period for students is necessary as they move away from the more traditional methods of “drill and practice” and “practice makes perfect” towards an open-ended learning experience in which they are responsible for their own learning.
An area of concern for myself, as well as one pointed out by Boaler, is that of disruptive students. This particular type of student is present in all classes, across all grade levels. In the case of Phoenix Park, and I would venture to say in all cases, students were disruptive not because of the approach to learning, rather because of a lack of motivation to learn. As educators, the challenge for us then is to employ methods so as the unmotivated are motivated. As is stressed in the approach to differentiated instruction, it is important to meet the needs of all diverse learners in our classroom. For the disruptive students at Phoenix Park, this may mean reducing the amount of freedom they had by assigning particular questions to be complete (this seemed to be their preferred method of learning).
I think the open-ended approach to learning is great, but I question how or if it would work in some of the more rural areas of Newfoundland and Labrador. In these areas teachers already have a heavy workload, and in some instances are teaching outside their teachable areas. As well, there is the issue of multi-grading, which is a common component of many small rural schools.
I, like many of my classmates, would have loved to have had the opportunity to experience a learning environment similar to that encountered by the students at Phoenix Park. Instead, my learning consisted of traditional methods in which teachers introduced a particular topic, leaving little or no room for student self exploration. In comparison, students at Phoenix Park were introduced to a topic via open ended questions, which gave them opportunity to be as creative and in depth as desired. Students were responsible for their own learning, which in turn provided them with a sense of pride and accomplishment, which is sometimes lacking in the more traditional learning environment. This sense of pride and accomplishment led students to be more successful in mathematics, simply because they understood the mathematics. Boaler emphasizes this success in her following statement “The Phoenix Park students did not seem to have this shallow view of mathematics; they were aware of the depth of the subject-the different layers that may be encountered. The student also demonstrated an unusual awareness of the diversity and breadth of mathematics. They did not regard mathematics as a vast collection of sums; they seems to have a richer and more balanced view of the subject.” (Boaler, pg. 77)
As an educator, I questioned whether or not the techniques employed at Phoenix Park would be applicable to classrooms throughout Newfoundland and Labrador. My initial response was absolutely NOT, however, after much thought and discussion I am confident this open-ended approach to teaching would definitely work in our classrooms. That being said, in order for this approach to learning to work, a great amount of support from students, parents, administrators and board officials would be required. It would be a very time consuming process, and one which requires the teacher to be well organized and to have an extensive understanding of the subject material. As Sharon mentioned, it is not necessary that we do a complete program overhaul in one year, rather we could implement this particular technique at a rate comfortable to us. As well, a transition period for students is necessary as they move away from the more traditional methods of “drill and practice” and “practice makes perfect” towards an open-ended learning experience in which they are responsible for their own learning.
An area of concern for myself, as well as one pointed out by Boaler, is that of disruptive students. This particular type of student is present in all classes, across all grade levels. In the case of Phoenix Park, and I would venture to say in all cases, students were disruptive not because of the approach to learning, rather because of a lack of motivation to learn. As educators, the challenge for us then is to employ methods so as the unmotivated are motivated. As is stressed in the approach to differentiated instruction, it is important to meet the needs of all diverse learners in our classroom. For the disruptive students at Phoenix Park, this may mean reducing the amount of freedom they had by assigning particular questions to be complete (this seemed to be their preferred method of learning).
I think the open-ended approach to learning is great, but I question how or if it would work in some of the more rural areas of Newfoundland and Labrador. In these areas teachers already have a heavy workload, and in some instances are teaching outside their teachable areas. As well, there is the issue of multi-grading, which is a common component of many small rural schools.
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