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.
Saturday, October 31, 2009
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.
Tuesday, October 13, 2009
Experiencing Math at Amber Hill
First I would like to congratulate Sharon on a job well done! I really enjoyed the presentation of material in chapter four and the discussions that followed (and of course, the food was great as well!)
Chapter four provided an introduction to the methodologies used in the teaching of mathematics at Amber Hill. Teachers were very traditional in their approaches to the teaching of mathematics- they used short, procedural and closed questions. When students had questions concerning mathematics, teachers would guide them [the students] through questions step by step, posing multiple choice questions that would eventually lead students to the correct answer. The focus of math learning was on the memorization of rules and formulas, not on the understanding of why or how a concept is derived. The teachers were very focused on student success, and believed the methods they employed were the best suited for the students which they taught.
I suspect the teaching methods employed at Amber Hill are present in classrooms throughout Newfoundland and Labrador. As a new teacher, I struggle with trying to understand why we are still using such approaches to the teaching of math, if we know these methods are not appropriate for all students. I would venture to guess that it is largely because we are afraid of change. We are products of our own learning, in that for years ideologies of “practice makes perfect”, and “drill and practice” were stressed as the only way to teach and learn mathematics. I once asked a teacher who had been teaching math for a number of years (in fact he was nearing retirement age), why he used such approaches, to which he responded by stating that that’s the practice he has used for x number of years, and how well his students did on standardized tests. Through discussions with students, they blatantly stated that they didn’t understand the mathematics, they simply knew how to identify key points in questions which would in turn indicate which formulas/rules had to be applied.
On of the questions posed by Sharon, and to some degree Boaler, was “is there a disparity between what we believe as good math teaching and approaches used?” I believe this to be true. There is a constant reminder from department heads, principles, and board officials of the importance of student success on standardized assessments, which in turn becomes the focus of our teaching. We become less concerned with what “works” for students and more concerned with getting the curriculum covered so as to ensure student success on such assessments. As was the case with Amber Hill, we are concerned about student success, so much so that we lose sight of what’s really occurring in our classrooms.
As teachers, we continually need to step back and evaluate our teaching strategies. It is important that our focus is on student learning, as well as student success.
Chapter four provided an introduction to the methodologies used in the teaching of mathematics at Amber Hill. Teachers were very traditional in their approaches to the teaching of mathematics- they used short, procedural and closed questions. When students had questions concerning mathematics, teachers would guide them [the students] through questions step by step, posing multiple choice questions that would eventually lead students to the correct answer. The focus of math learning was on the memorization of rules and formulas, not on the understanding of why or how a concept is derived. The teachers were very focused on student success, and believed the methods they employed were the best suited for the students which they taught.
I suspect the teaching methods employed at Amber Hill are present in classrooms throughout Newfoundland and Labrador. As a new teacher, I struggle with trying to understand why we are still using such approaches to the teaching of math, if we know these methods are not appropriate for all students. I would venture to guess that it is largely because we are afraid of change. We are products of our own learning, in that for years ideologies of “practice makes perfect”, and “drill and practice” were stressed as the only way to teach and learn mathematics. I once asked a teacher who had been teaching math for a number of years (in fact he was nearing retirement age), why he used such approaches, to which he responded by stating that that’s the practice he has used for x number of years, and how well his students did on standardized tests. Through discussions with students, they blatantly stated that they didn’t understand the mathematics, they simply knew how to identify key points in questions which would in turn indicate which formulas/rules had to be applied.
On of the questions posed by Sharon, and to some degree Boaler, was “is there a disparity between what we believe as good math teaching and approaches used?” I believe this to be true. There is a constant reminder from department heads, principles, and board officials of the importance of student success on standardized assessments, which in turn becomes the focus of our teaching. We become less concerned with what “works” for students and more concerned with getting the curriculum covered so as to ensure student success on such assessments. As was the case with Amber Hill, we are concerned about student success, so much so that we lose sight of what’s really occurring in our classrooms.
As teachers, we continually need to step back and evaluate our teaching strategies. It is important that our focus is on student learning, as well as student success.
Sunday, October 11, 2009
Boaler, Chapters 1-3
It was great to see everyone and back to class routines. I appreciated the opportunity to discuss and examine resources that are applicable to the teaching of math. I have already started the search for Math Curse and The Grapes of Math. I’m sure my students will appreciate these books as much as I will.
In the first three chapters of her text, Boaler introduces us to two schools, both of which employ very different mathematical approaches in the teaching of mathematics. Amber Hill’s approach to learning is very structured. Each class began with the introduction to different procedures in a clear and structured way. Students were then required to complete a series of questions using the methods described by the teacher.
The teaching pedagogies employed at Phoenix Park were much different from those at Amber Hill. From the beginning of year 8 to Christmas of year 10, students worked on open-ended projects in every lesson. This approach allowed students to examine and explore various topics in mathematics. The outperformance of Phoenix Park over Amber Hill students on standardized tests, could be attributed to the different teaching methods.
Through reflection on my own math experiences, and through discussions and observations with colleagues, the methodologies used at Amber Hill are very similar to those used in many classrooms throughout Newfoundland and Labrador. Throughout the years, we have somehow lost track of the purpose of standardized testing. It was/is intended to help identify areas of student weakness, as well as areas of strength. Why is it then, that we often use such assessments as public exams, CRT’s, etc as an indicator of teacher ability?
In the first three chapters of her text, Boaler introduces us to two schools, both of which employ very different mathematical approaches in the teaching of mathematics. Amber Hill’s approach to learning is very structured. Each class began with the introduction to different procedures in a clear and structured way. Students were then required to complete a series of questions using the methods described by the teacher.
The teaching pedagogies employed at Phoenix Park were much different from those at Amber Hill. From the beginning of year 8 to Christmas of year 10, students worked on open-ended projects in every lesson. This approach allowed students to examine and explore various topics in mathematics. The outperformance of Phoenix Park over Amber Hill students on standardized tests, could be attributed to the different teaching methods.
Through reflection on my own math experiences, and through discussions and observations with colleagues, the methodologies used at Amber Hill are very similar to those used in many classrooms throughout Newfoundland and Labrador. Throughout the years, we have somehow lost track of the purpose of standardized testing. It was/is intended to help identify areas of student weakness, as well as areas of strength. Why is it then, that we often use such assessments as public exams, CRT’s, etc as an indicator of teacher ability?
Good Teaching, Bad Results
As a new teacher, one of the most difficult questions I am faced with is how to define or what characteristics a person must have to identify them as being a good teacher. Is it as Romberg and Carpenter suggest- that a good teacher is the one who has ten different ways to say the same thing, ensuring the students “get it” sooner or later? Is it the teacher who has zero discipline issues in his/her classroom, where students sit in parallel lines facing the front of the room, showing respect for the teacher as well as fellow classmates? Or is a good teacher defined by student success on standardized testing? My definition of a good teacher includes some degree of each of the previous attributes. As a student, I labelled teachers as good if they had the ability to make learning fun. Good teachers were those who were enthusiastic about the subject matter at hand, used a variety of teaching methods and in general altered the curriculum to be relevant to our leaning environments rather than altering us to suite the curriculum.
Unfortunately, throughout our province and certainly throughout our country, many define teachers by student performance on standardized tests (more particularly CRT’s and public exams in our province). If students do well, the teacher adequately delivered the curriculum, however if students perform poorly the teacher did not adequately cover material in the curriculum. The validity of this statement was reinforced by my principal in a recent conversation in which he said, “Jennifer, if you’re looking to transfer out of your current position, the first thing the principals and department heads of other schools are going to look at is how well your students performed on standardized assessments like CRT’s and public exams.” At first I was angered by his statement. In the case of the level three students, how could I, after teaching these students for only one year, be responsible for their performance on such assessments? With the jammed packed curriculum, how could I possibly be responsible for ensuring students understood and remembered basic concepts covered in grades 7-11? After the initial anger, I realized the key to student success was to first identify previous knowledge and misconceptions students had, followed by elimination of misconceptions and finally expansion on pre-existing knowledge.
One of the issues raised by Schoenfeld in his article, is that when solving mathematics problems, students have to follow the procedure, whether it makes sense to them or not. This was very prevalent in my educational experiences. My teachers were strong believers of the “practice makes perfect” theory. They would assign large quantities of questions all of which required little to no thought on the student part. The role of the student was simply to “plug” the numbers into the appropriate formula to obtain the correct answer. We were never challenged to think whether or not our answers made sense- it was assumed if you followed the correct procedure then the correct answer would be obtained. If we were given an exercise similar to that of the army bus, as described in Schoenfeld’s article, and obtained the wrong answer, my teachers would state that the problem was “tricky” in its wording or that students made a “silly mistake” by not reading the question carefully. It should be noted that a month and a half prior to CRT’s in grade 6 and 9, teachers would spend every math class reviewing old CRT’s to ensure students did not make the same “silly mistakes” as previous students had. Which leads me to often wonder if my teachers were some of the ones who think the curriculum is too jammed packed.
Schoenfeld’s third result: Students come to believe that all problems can be solved in just a few minutes, is a statement which I have heard numerous times throughout my educational experiences. In my previous teaching experience, I’ve had numerous students who, if they can’t solve a problem in a few minutes, give up, stating that the problem is too hard. Teachers play a large role in the creation and reinforcement of such student beliefs. As mentioned in the article, teachers (myself included) are guilty of assigning a large quantity of questions focused on small chunks of subject matter and to be completed in a short amount of time. If for some reason students still do not grasp the concept at hand, we simply assign more questions. This is true not only of in-class and home work material, but also of questions on many standardized assessments. The mathematics public exam to be completed at the end of level three consists of 50 selected response questions and 10-13 constructed response questions, all of which are to be completed in one three hour sitting. Advice given by fellow colleagues in preparation of students for standardized tests including CRT’s and public exams, is to “move on” to the next question if an answer to the current question is not obtained immediately. Thus reinforcing the belief that all math problems can be solved in just a few minutes. The same is true of in-class assessments in the form of unit tests, quizzes, mid-year examinations and pop quizzes. Students have to answer a set number of questions (usually a substantial quantity) of questions in a given time period, with little or no extra time given.
Schoenfeld’s fourth belief: Students view themselves as passive consumers of other’s mathematics, is an area in mathematics in which we are shifting the paradigm. In Math 3204, students are encouraged to complete investigations which develop the underlying concept in that particular topic/unit. Rather than having the teacher state the formula, students apply previous knowledge which in turn leads to the development of appropriate formulas, theorems, etc. This provides students with the notion that math really does make sense, and has more than one application. Such a process emphasizes the importance of making connections through math not merely on rote memorization.
Schoenfeld’s article discusses valid issues surrounding teaching and learning in our public school systems. As educators we need to move away from passive education, in which we expect students to simply memorize and apply formulas, towards active learning in which student engage in discussions and development of the mathematics.
Unfortunately, throughout our province and certainly throughout our country, many define teachers by student performance on standardized tests (more particularly CRT’s and public exams in our province). If students do well, the teacher adequately delivered the curriculum, however if students perform poorly the teacher did not adequately cover material in the curriculum. The validity of this statement was reinforced by my principal in a recent conversation in which he said, “Jennifer, if you’re looking to transfer out of your current position, the first thing the principals and department heads of other schools are going to look at is how well your students performed on standardized assessments like CRT’s and public exams.” At first I was angered by his statement. In the case of the level three students, how could I, after teaching these students for only one year, be responsible for their performance on such assessments? With the jammed packed curriculum, how could I possibly be responsible for ensuring students understood and remembered basic concepts covered in grades 7-11? After the initial anger, I realized the key to student success was to first identify previous knowledge and misconceptions students had, followed by elimination of misconceptions and finally expansion on pre-existing knowledge.
One of the issues raised by Schoenfeld in his article, is that when solving mathematics problems, students have to follow the procedure, whether it makes sense to them or not. This was very prevalent in my educational experiences. My teachers were strong believers of the “practice makes perfect” theory. They would assign large quantities of questions all of which required little to no thought on the student part. The role of the student was simply to “plug” the numbers into the appropriate formula to obtain the correct answer. We were never challenged to think whether or not our answers made sense- it was assumed if you followed the correct procedure then the correct answer would be obtained. If we were given an exercise similar to that of the army bus, as described in Schoenfeld’s article, and obtained the wrong answer, my teachers would state that the problem was “tricky” in its wording or that students made a “silly mistake” by not reading the question carefully. It should be noted that a month and a half prior to CRT’s in grade 6 and 9, teachers would spend every math class reviewing old CRT’s to ensure students did not make the same “silly mistakes” as previous students had. Which leads me to often wonder if my teachers were some of the ones who think the curriculum is too jammed packed.
Schoenfeld’s third result: Students come to believe that all problems can be solved in just a few minutes, is a statement which I have heard numerous times throughout my educational experiences. In my previous teaching experience, I’ve had numerous students who, if they can’t solve a problem in a few minutes, give up, stating that the problem is too hard. Teachers play a large role in the creation and reinforcement of such student beliefs. As mentioned in the article, teachers (myself included) are guilty of assigning a large quantity of questions focused on small chunks of subject matter and to be completed in a short amount of time. If for some reason students still do not grasp the concept at hand, we simply assign more questions. This is true not only of in-class and home work material, but also of questions on many standardized assessments. The mathematics public exam to be completed at the end of level three consists of 50 selected response questions and 10-13 constructed response questions, all of which are to be completed in one three hour sitting. Advice given by fellow colleagues in preparation of students for standardized tests including CRT’s and public exams, is to “move on” to the next question if an answer to the current question is not obtained immediately. Thus reinforcing the belief that all math problems can be solved in just a few minutes. The same is true of in-class assessments in the form of unit tests, quizzes, mid-year examinations and pop quizzes. Students have to answer a set number of questions (usually a substantial quantity) of questions in a given time period, with little or no extra time given.
Schoenfeld’s fourth belief: Students view themselves as passive consumers of other’s mathematics, is an area in mathematics in which we are shifting the paradigm. In Math 3204, students are encouraged to complete investigations which develop the underlying concept in that particular topic/unit. Rather than having the teacher state the formula, students apply previous knowledge which in turn leads to the development of appropriate formulas, theorems, etc. This provides students with the notion that math really does make sense, and has more than one application. Such a process emphasizes the importance of making connections through math not merely on rote memorization.
Schoenfeld’s article discusses valid issues surrounding teaching and learning in our public school systems. As educators we need to move away from passive education, in which we expect students to simply memorize and apply formulas, towards active learning in which student engage in discussions and development of the mathematics.
Math Autobiography
My experience with mathematics in elementary school was what Schoenfeld defines as very traditional in its approaches. I attended Bonne Bay Academy, a small rural school with a population of approximately 80 students. Many, if not all of the classes were multi-grade. The responsibilities of teachers were vast- they were responsible for teaching numerous courses, often outside discipline areas. Mathematics class was no exception to the multi-grade classroom. This meant that a 50 minute period often resulted in only 20 minutes of instructional time allotted to each grade.
My teachers were firm believers in “drill & practice” methodologies. Student success was measured by how well students could reiterate concepts in the form of worksheets, assigned/homework problems and the end of year assessment- most common being the CRT’s administered at the end of grade 3, 6 and 9. Teachers believed a measure of their ability to deliver the curriculum was based on our performance on such assessment. Teachers were of the mindset that if the students did well, the teachers did a good job delivering the curriculum, however if the students did poorly it was because of their students’ lack of interest or ambition to do well.
Although the classroom walls were covered with displays of student work, none of these displays were math based. There were colourful depictions of proper construction of sentences, grammar rules, and the like, but none pertaining to mathematics. As a teacher, I encourage the display of work from all discipline areas, including math. At the beginning of each unit I encourage students to display information pertaining to the subject matter to be covered in that section, as well as any questions they may have pertaining to that particular unit (as we progress through the unit students are then able to answer the questions). This may range from influential persons in mathematics, to rhymes to help remember formulas, to the display of mathematical rules.
Many of my teachers in primary/elementary school were seasoned teachers. They had been in the profession for more than 20 years, and most were nearing retirement age. They were set in their ways of teaching, and viewed new approaches with poor attitudes and viewed them as being too time consuming. They spent a small fraction of instructional time outlining important concepts, with the remainder of the class spent working independently on assigned problems. Very rarely were we permitted to work in groups, and strongly encouraged from “thinking outside the box”. A portion of each class was spent reviewing the previous night’s homework, where the teacher would call out the correct answer, and only when a student asked, would he review the procedure used to obtain the correct answer. When asked why a procedure was the way it was, the teacher would respond with something like “because I said so”.
This attitude towards math changed in grade 5 when a new teacher was assigned to our school. He was young, and taught math using new and varying approaches. The manipulatives, which up to this point were on the shelf collecting dust, were taken down, and math became fun. Finally, someone to share my enthusiasm! This teacher has greatly influenced my teaching of mathematics. Whenever I find myself using traditional methods of teaching, I reflect back on my learning experiences, and what learning math meant to me. I try to use various methods of teaching rather than the expected norm of demonstration on the board, followed by assignment of exercises from the textbook. (It should be noted that all my math teachers from grade 3 to level III were male. This is much different from the trend we see today, with the majority of math/science teachers being female)
My best memory of math comes from the 5th or 6th grade. As previously stated, I had a math teacher who was young and vibrant. I remember the feeling of being able to deduce for myself some of the major concepts in the units rather than simply being told this is what you need to know and this is how to apply it. Some of my worst memories of math come from my earlier experiences in math class, where the teacher simply stated the objective, demonstrated at the blackboard the appropriate “steps” in solving the problem and then assigning a large quantity of questions. If questions were not completed during class time the remainder were to be completed for homework. This was mentally draining because each problem was the same as the last, with the exception of the numbers involved. Another memory that stands out is that of the feeling of anxiety when called to the front of the class to demonstrate an answer. There was always the fear of being wrong and being ridiculed by the other students in my class or looked down upon by the teacher for not knowing the concepts which he had previously “taught”.
Report cards and teacher comments indicated I was good at math. It was an area in which I excelled, and one which was of interest. In high school, I was enrolled in advanced math and calculus courses, and did quite well in all. Reflecting back, I believe I was good at math for the simple reason that I had the ability to reproduce what the teacher wanted. I never once asked why or how a particular theorem was derived, I simply developed the skills necessary to know when and how to apply it when the time came. For this, some may disagree and say I was not good at math rather I was good at providing the teacher with the answer he/she wanted.
As part of my undergraduate degree, I completed 9 courses in mathematics. These ranged from Calculus, to linear algebra, to statistics, Euclidian geometry, and numerous others.
I think the learning and understanding of mathematics is a very integral part of the curriculum in schools. Basic math operations are applicable and required to excel in many other parts of the curriculum. No matter how well you understand the concepts taught in physics, chemistry, and other sciences in order to be successful you need basic math skills. As well, without the basic concepts developed at a young age, and the continual expansion on such concepts, many everyday tasks such as the calculation of interest rates, or the measuring of materials for carpentry become difficult.
My teachers were firm believers in “drill & practice” methodologies. Student success was measured by how well students could reiterate concepts in the form of worksheets, assigned/homework problems and the end of year assessment- most common being the CRT’s administered at the end of grade 3, 6 and 9. Teachers believed a measure of their ability to deliver the curriculum was based on our performance on such assessment. Teachers were of the mindset that if the students did well, the teachers did a good job delivering the curriculum, however if the students did poorly it was because of their students’ lack of interest or ambition to do well.
Although the classroom walls were covered with displays of student work, none of these displays were math based. There were colourful depictions of proper construction of sentences, grammar rules, and the like, but none pertaining to mathematics. As a teacher, I encourage the display of work from all discipline areas, including math. At the beginning of each unit I encourage students to display information pertaining to the subject matter to be covered in that section, as well as any questions they may have pertaining to that particular unit (as we progress through the unit students are then able to answer the questions). This may range from influential persons in mathematics, to rhymes to help remember formulas, to the display of mathematical rules.
Many of my teachers in primary/elementary school were seasoned teachers. They had been in the profession for more than 20 years, and most were nearing retirement age. They were set in their ways of teaching, and viewed new approaches with poor attitudes and viewed them as being too time consuming. They spent a small fraction of instructional time outlining important concepts, with the remainder of the class spent working independently on assigned problems. Very rarely were we permitted to work in groups, and strongly encouraged from “thinking outside the box”. A portion of each class was spent reviewing the previous night’s homework, where the teacher would call out the correct answer, and only when a student asked, would he review the procedure used to obtain the correct answer. When asked why a procedure was the way it was, the teacher would respond with something like “because I said so”.
This attitude towards math changed in grade 5 when a new teacher was assigned to our school. He was young, and taught math using new and varying approaches. The manipulatives, which up to this point were on the shelf collecting dust, were taken down, and math became fun. Finally, someone to share my enthusiasm! This teacher has greatly influenced my teaching of mathematics. Whenever I find myself using traditional methods of teaching, I reflect back on my learning experiences, and what learning math meant to me. I try to use various methods of teaching rather than the expected norm of demonstration on the board, followed by assignment of exercises from the textbook. (It should be noted that all my math teachers from grade 3 to level III were male. This is much different from the trend we see today, with the majority of math/science teachers being female)
My best memory of math comes from the 5th or 6th grade. As previously stated, I had a math teacher who was young and vibrant. I remember the feeling of being able to deduce for myself some of the major concepts in the units rather than simply being told this is what you need to know and this is how to apply it. Some of my worst memories of math come from my earlier experiences in math class, where the teacher simply stated the objective, demonstrated at the blackboard the appropriate “steps” in solving the problem and then assigning a large quantity of questions. If questions were not completed during class time the remainder were to be completed for homework. This was mentally draining because each problem was the same as the last, with the exception of the numbers involved. Another memory that stands out is that of the feeling of anxiety when called to the front of the class to demonstrate an answer. There was always the fear of being wrong and being ridiculed by the other students in my class or looked down upon by the teacher for not knowing the concepts which he had previously “taught”.
Report cards and teacher comments indicated I was good at math. It was an area in which I excelled, and one which was of interest. In high school, I was enrolled in advanced math and calculus courses, and did quite well in all. Reflecting back, I believe I was good at math for the simple reason that I had the ability to reproduce what the teacher wanted. I never once asked why or how a particular theorem was derived, I simply developed the skills necessary to know when and how to apply it when the time came. For this, some may disagree and say I was not good at math rather I was good at providing the teacher with the answer he/she wanted.
As part of my undergraduate degree, I completed 9 courses in mathematics. These ranged from Calculus, to linear algebra, to statistics, Euclidian geometry, and numerous others.
I think the learning and understanding of mathematics is a very integral part of the curriculum in schools. Basic math operations are applicable and required to excel in many other parts of the curriculum. No matter how well you understand the concepts taught in physics, chemistry, and other sciences in order to be successful you need basic math skills. As well, without the basic concepts developed at a young age, and the continual expansion on such concepts, many everyday tasks such as the calculation of interest rates, or the measuring of materials for carpentry become difficult.
Do Schools Kill Creativity?
In his video entitled “Do Schools Kill Creativity?” , Sir Ken Robinson presents the idea that creativity is as important as literacy, a concept to which I find intriguing and one to which I have never given much thought.
As a teacher, more specifically a Mathematics/Science teacher, I am guilty of stressing the importance of these two particular subjects. During my career, I have found myself numerous times stressing the importance of Mathematics to my students citing the ever familiar “Now John, you need this course to graduate.” I have even went so far as to “borrow” classes that I thought were of least importance, mainly the arts, from other teachers so as to ensure the curriculum was covered and students were well prepared for the upcoming end of year evaluation. Not once, did I entertain the thought that the Arts and Humanities were of equal importance, and that these should be treated with the same status as the Maths, Sciences and Literacy.
If we agree with Sir Ken Robinson, and I believe for the most part we do, why is it then that the Department of Education of Newfoundland and Labrador stress the importance of literacy as opposed to creativity. Why is it, that when recommending time allocations for coursework at the primary/elementary level is the emphasis always placed on literacy and numeracy (40% and 30% respectively) with the remainder of teaching time allocated to social studies, religious education, health, art, music and physical education. The same is true of recommendations of allocations at the junior high/senior high level where students have some choice as to which courses they choose, however graduate requirements still exist.
During the early stages of education, students view schools as a place where learning is enjoyable. However, as students progress through junior and senior high, these opinions and views tend to change. This can be attributed to what Sir Ken Robinson refers to as educating students out of creativity. We encourage students to excel in literature as opposed to creativity, because it is the literature that is required to gain entrance to university, which in turn leads to a career, and hence defines the individual as being successful.
To quote Albert Einstein “The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.”
As a teacher, more specifically a Mathematics/Science teacher, I am guilty of stressing the importance of these two particular subjects. During my career, I have found myself numerous times stressing the importance of Mathematics to my students citing the ever familiar “Now John, you need this course to graduate.” I have even went so far as to “borrow” classes that I thought were of least importance, mainly the arts, from other teachers so as to ensure the curriculum was covered and students were well prepared for the upcoming end of year evaluation. Not once, did I entertain the thought that the Arts and Humanities were of equal importance, and that these should be treated with the same status as the Maths, Sciences and Literacy.
If we agree with Sir Ken Robinson, and I believe for the most part we do, why is it then that the Department of Education of Newfoundland and Labrador stress the importance of literacy as opposed to creativity. Why is it, that when recommending time allocations for coursework at the primary/elementary level is the emphasis always placed on literacy and numeracy (40% and 30% respectively) with the remainder of teaching time allocated to social studies, religious education, health, art, music and physical education. The same is true of recommendations of allocations at the junior high/senior high level where students have some choice as to which courses they choose, however graduate requirements still exist.
During the early stages of education, students view schools as a place where learning is enjoyable. However, as students progress through junior and senior high, these opinions and views tend to change. This can be attributed to what Sir Ken Robinson refers to as educating students out of creativity. We encourage students to excel in literature as opposed to creativity, because it is the literature that is required to gain entrance to university, which in turn leads to a career, and hence defines the individual as being successful.
To quote Albert Einstein “The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.”
1st Meeting
It was great to have the opportunity to have met you all in the first class. This is a my first semister in graduate studies and I look forward to conversing with you, and drawing from each individuals experience.
I am still learning the "in's and out's" of blogging, and although I have spent the past couple of weeks collecting my thoughts I am only now getting the opportunity to post them.I look forward to communicating with you all in the upcoming weeks, and wish you all the best of luck in your graduate work!Jennifer
I am still learning the "in's and out's" of blogging, and although I have spent the past couple of weeks collecting my thoughts I am only now getting the opportunity to post them.I look forward to communicating with you all in the upcoming weeks, and wish you all the best of luck in your graduate work!Jennifer
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