“Battleground Schools”, by Susan Gerofsky is an interesting read that discusses what styles of mathematics are taught, and historically have been taught. Political lines have been drawn since long before we had formal education, continuing to this day, and it is unsettling to know that they clearly do not stop at the entrance to the classroom.
Most people are probably quite oblivious to the idea that there are different ways to teach mathematics. Surely, it seems quite standard to the layperson; there are numbers and letters and equations and identities and if you put them together in a classroom you get math. While this is true, most people can probably also recall different math teachers that taught them as students and the different methods that they used. Some of these teachers relied heavily on memorization work to learn concepts and, hopefully, some used different types of methods so that concepts were understood. I am sure it would be found that those exposed to the latter would have a better appreciation of the beauty of mathematics.
As stated in the essay, “mathematics education has oscillated between two poles“; that of “progressive and conservative”. These political stances are quite clear outside the North American classroom – you are either liberal or conservative, democrat or republican with little agreement between the two sides. It is upsetting to find these stances have serious impacts on a child’s learning. Gerofsky points out “few progressivists would argue against some necessary degree of fluency in basic mathematical procedures, and few conservatives would be as radical as to advocate fluency exclusively to the point where understanding would be discouraged.”
“Battleground Schools” discusses a political/educational issue where, like formal politics, few are comfortable discussing. There seems no end to the conflicting decisions that will be made regarding mathematics in the classroom. One can only hope that individual teachers are finding a balance and teaching mathematics so that not only will their students learn concepts, but they just might start to enjoy them.
Wednesday, September 30, 2009
Monday, September 28, 2009
Reflection on Teacher and Student Interviews
My group, also consisting of Amelia Landon and Sam Douglas, took on the task of asking a teacher and a student five burning questions in an effort to discover teaching styles and methods that will work well for us. We were able to set up an interview with John Yamamoto, the Secondary Practicum Program Coordinator for the Education Faculty at the University of British Columbia. While he is not currently a secondary teacher, he taught for many years in Trail and Burnaby, in the regular, correctional and special needs school systems. Our current high school student was Sam’s younger sister who attends grade ten.
The interview with Mr. Yamamoto was very interesting as he has seen many different teaching environments over his career.
Our first question for him was, “what did you find to be your biggest challenges with your early teaching experiences?” He discussed his early issues with classroom management and working around the noise of the classroom as opposed to controlling it. He discussed his solution was to make the expectations of his classroom as clear as possible.
Another good question was, “what accommodations have you made to help students with learning difficulties?” This question struck a chord considering his diverse previous experience. While working with the deaf, he was forced to consider the pace at which he spoke, especially when working with a translator. Although, he said with practice this was not an issue at all. Working in the correctional system, he was forced to deal with many personality issues and said in all school systems, “their problems usually have nothing do with you (as the teacher)”.
Our final question asked Mr. Yamamoto what he enjoyed most and least about teaching. He said he loved the interactions with the kids and enjoyed watching them grow, but it was always tough to see them move on to new phases in their lives beyond high school. He also indicated poor balance in the curricula and teaching large class sizes as things that made teaching difficult, but he said overwhelmingly that the good outweighed the bad.
The interview with our grade ten student also provided some interesting responses. She was asked how her first impressions of a teacher are formed. Her answer listed a good sense of humour and a healthy level of classroom organization as being important for making a decision.
Our grade ten student was also asked how she felt about incorporating more group activities in Math class. She was not fond of the idea saying that she prefers to work alone and that group work can lead to confusion. While some students do like group work, it is good to note that there will be many who will feel uncomfortable.
Finally she was asked about a memorable way that a teacher has helped you to understand a tricky concept. She relayed a funny story used to help the understanding of solving an equation. It is nice to hear that sometimes a little ingenuity and humour can go a long way with adolescents.
There will never be a universal agreement on which is the best teaching style from either the teacher or student perspective, but it is very helpful to note things that tend to work and be well liked. While only interviewing one teacher and one student, this was a great exercise to find what some perspectives are on both ends.
The interview with Mr. Yamamoto was very interesting as he has seen many different teaching environments over his career.
Our first question for him was, “what did you find to be your biggest challenges with your early teaching experiences?” He discussed his early issues with classroom management and working around the noise of the classroom as opposed to controlling it. He discussed his solution was to make the expectations of his classroom as clear as possible.
Another good question was, “what accommodations have you made to help students with learning difficulties?” This question struck a chord considering his diverse previous experience. While working with the deaf, he was forced to consider the pace at which he spoke, especially when working with a translator. Although, he said with practice this was not an issue at all. Working in the correctional system, he was forced to deal with many personality issues and said in all school systems, “their problems usually have nothing do with you (as the teacher)”.
Our final question asked Mr. Yamamoto what he enjoyed most and least about teaching. He said he loved the interactions with the kids and enjoyed watching them grow, but it was always tough to see them move on to new phases in their lives beyond high school. He also indicated poor balance in the curricula and teaching large class sizes as things that made teaching difficult, but he said overwhelmingly that the good outweighed the bad.
The interview with our grade ten student also provided some interesting responses. She was asked how her first impressions of a teacher are formed. Her answer listed a good sense of humour and a healthy level of classroom organization as being important for making a decision.
Our grade ten student was also asked how she felt about incorporating more group activities in Math class. She was not fond of the idea saying that she prefers to work alone and that group work can lead to confusion. While some students do like group work, it is good to note that there will be many who will feel uncomfortable.
Finally she was asked about a memorable way that a teacher has helped you to understand a tricky concept. She relayed a funny story used to help the understanding of solving an equation. It is nice to hear that sometimes a little ingenuity and humour can go a long way with adolescents.
There will never be a universal agreement on which is the best teaching style from either the teacher or student perspective, but it is very helpful to note things that tend to work and be well liked. While only interviewing one teacher and one student, this was a great exercise to find what some perspectives are on both ends.
Reflection on Group Interviews
An eventful day of group presentations has given us some reports on the real world thoughts from both the teacher and student perspective. These reports included answers from teachers who loved their jobs and also those who did not, it seemed. They included stories of teachers who loved teaching in a 'new-age' classroom with alternative media usage and students teaching themselves to some degree. There were also teachers who liked teaching in a very traditional classroom using traditional methods.
From the student perspective, there were reports of those who loved mathematics, and their teachers who taught that subject, and those who did not. There were those who enjoyed learning in a traditional classroom setting and those who liked learning with group and modern teaching methods. This began to sound familiar.
It seemed that the only thing that stays constant across the outlook of both the teacher and student is that there is no such thing as a universal perspective. People will think different thoughts about different areas and the methods of no one teacher will be liked by all. It makes me think to my own future teaching days where I will simply bring to the table those methods and strategies that I feel are most effective and try to keep most of the people happy, most of the time.
From the student perspective, there were reports of those who loved mathematics, and their teachers who taught that subject, and those who did not. There were those who enjoyed learning in a traditional classroom setting and those who liked learning with group and modern teaching methods. This began to sound familiar.
It seemed that the only thing that stays constant across the outlook of both the teacher and student is that there is no such thing as a universal perspective. People will think different thoughts about different areas and the methods of no one teacher will be liked by all. It makes me think to my own future teaching days where I will simply bring to the table those methods and strategies that I feel are most effective and try to keep most of the people happy, most of the time.
Wednesday, September 23, 2009
Response to “Using Research to Analyze, Inform, and Assess Changes in Instruction” by Heather J. Robinson
It seems clear that the image of the teacher standing at the chalkboard or overhead projector lecturing for an hour, or at least its effectiveness, is dead. However, in thinking back to some of my own teachers that I had in high school, this idea should have been dead a long time ago. I believe many teachers have known for a very long time that their teaching methods were largely ineffective; that they were only ever reaching a small percentage of the students. The others would have to pick it up on their own or through tutors. If these teachers had done some research into their own teaching methods as Robinson suggests, it would have been easy to see where they were failing.
I liken teaching without doing self research to a workout plan where nutrition is neglected and results are never studied. If a workout schedule of any kind were followed like this, success would surely be minimal. To not constantly be reviewing your methods and testing their effectiveness is to not complete the job of being a teacher. In order for learning to occur across the classroom, with strong students as well as weak, effective teaching methods must be adopted. It is the individual teacher that must figure out what these are.
I liken teaching without doing self research to a workout plan where nutrition is neglected and results are never studied. If a workout schedule of any kind were followed like this, success would surely be minimal. To not constantly be reviewing your methods and testing their effectiveness is to not complete the job of being a teacher. In order for learning to occur across the classroom, with strong students as well as weak, effective teaching methods must be adopted. It is the individual teacher that must figure out what these are.
Two Memorable Math Teachers
Mr. Fraser – I will never forget sitting in a grade 12 math class with the legally blind Mr. Fraser at the front. I was sure at the beginning of the year that students would be taking advantage of his easy going personality and his blindness to cheat on exams and assignments - very few ever did. I believe this was because of the incredible amount of respect that students had for the man. His large amounts of time that he devoted to helping students understand concepts after class and the respect that he showed for each and every one of them is something that I will never forget.
Mr. Ritchie – Grade 9 math was very enjoyable thanks to Mr. Ritchie. His soft spoken and easy going nature made learning fun and it was an approach that I had not seen previously. His keen interest in extra curricular activities and engaging conversations in the classroom made him a very memorable teacher.
I will try to implement things from both of these great teachers. They both had similar, easy going styles that were well liked by students and I hope I can use mine to be as good of a teacher as they.
Mr. Ritchie – Grade 9 math was very enjoyable thanks to Mr. Ritchie. His soft spoken and easy going nature made learning fun and it was an approach that I had not seen previously. His keen interest in extra curricular activities and engaging conversations in the classroom made him a very memorable teacher.
I will try to implement things from both of these great teachers. They both had similar, easy going styles that were well liked by students and I hope I can use mine to be as good of a teacher as they.
Monday, September 21, 2009
Self Assessment on Microteaching: How to Juggle in 10 Minutes or Less
My first teaching assignment for MAED 314A was a fun one that was well received by my group of five.
My BOOPPPS style lesson plan (see previous blog) was followed closely and I managed to fit the lesson nicely into the ten minute time frame. I was happy to find that no one had previous juggling experience. This would have made for a slight complication, but one that I would have had a plan for. I was also happy to see that each of my four students (Amelia, Mina, Nathan and Sam) was, or at least pretended to be, keenly interested in the activity. In the beginning – using one ball and then two - it was rewarding to see each of the students making progress with the skills. I did my best to give good feedback as this occurred and made suggestions where needed.
I received great feedback from my “class” which included, “great demo”, “great step by step instruction”, good “starting easy to progressive to hard” and “good use of descriptive terms”. These were very nice to hear and made it feel like my teaching session was a success.
The constructive feedback I received was unanimously to use something other than tennis balls for this lesson as they were too bouncy. I agree completely with this recommendation and would try to use bean bags or something similar to avoid the balls bouncing away from those learning the skill. I was also able to pick up some ideas for how I would instruct in the future that I hadn’t thought of when I planned the lesson. Amelia noticed midway into the lesson that when jugging three balls, the beginning hand had to contain the two balls and not just one. This would be highlighted in a future session.
Overall, this microteaching assignment was a success and was seen as rewarding and confidence building to myself and to those I was trying to teach. I can only hope that I teach classes in the future that are as interested and well behaved.
My BOOPPPS style lesson plan (see previous blog) was followed closely and I managed to fit the lesson nicely into the ten minute time frame. I was happy to find that no one had previous juggling experience. This would have made for a slight complication, but one that I would have had a plan for. I was also happy to see that each of my four students (Amelia, Mina, Nathan and Sam) was, or at least pretended to be, keenly interested in the activity. In the beginning – using one ball and then two - it was rewarding to see each of the students making progress with the skills. I did my best to give good feedback as this occurred and made suggestions where needed.
I received great feedback from my “class” which included, “great demo”, “great step by step instruction”, good “starting easy to progressive to hard” and “good use of descriptive terms”. These were very nice to hear and made it feel like my teaching session was a success.
The constructive feedback I received was unanimously to use something other than tennis balls for this lesson as they were too bouncy. I agree completely with this recommendation and would try to use bean bags or something similar to avoid the balls bouncing away from those learning the skill. I was also able to pick up some ideas for how I would instruct in the future that I hadn’t thought of when I planned the lesson. Amelia noticed midway into the lesson that when jugging three balls, the beginning hand had to contain the two balls and not just one. This would be highlighted in a future session.
Overall, this microteaching assignment was a success and was seen as rewarding and confidence building to myself and to those I was trying to teach. I can only hope that I teach classes in the future that are as interested and well behaved.
Friday, September 18, 2009
How To Juggle, in 10 minutes or less
Microteaching Assignment Sept. 18th, 2009
1) Bridge – Introduce simple 2 and 3 ball juggling with tennis balls (approx 1 min.).
2) Teaching Objectives – To introduce students to the art of juggling through display and participation exercises.
3) Learning Objectives – Students will be able to understand the movement of the balls in basic 3 ball juggling and will be able to master the skill through their own practice after the session. Students will understand that juggling cannot really be learned in 10 minutes, but it was sure a catchy name for the task.
4) Pre-test – Students will be asked if any have previous juggling experience (approx 1 min.). In this case, exercises will be set up to practice two person juggling, under the leg juggling or 4 ball juggling.
5) Participatory Activity – Students will each receive one ball and practice the simple tossing from one hand to the other and back again, working on keeping the ball at an ideal, consistent height (approx 1 min.).
Then, another ball will be introduced and students will practice “one, two, nothing to throw”. (approx 4 mins)
Those that feel comfortable can then try with 3 balls and those who do not can continue with two ball juggling with one or two hands. (appox 2 mins).
6) Post Test – Ask students how they enjoyed the activity and ask each to display the new skills they have learned. (approx 1 min).
7) Summary - Reiterate to the students that much additional practice will help them attain the skill. Thank them for their time and efforts and wish them well in their circus careers if teaching does not work out.
1) Bridge – Introduce simple 2 and 3 ball juggling with tennis balls (approx 1 min.).
2) Teaching Objectives – To introduce students to the art of juggling through display and participation exercises.
3) Learning Objectives – Students will be able to understand the movement of the balls in basic 3 ball juggling and will be able to master the skill through their own practice after the session. Students will understand that juggling cannot really be learned in 10 minutes, but it was sure a catchy name for the task.
4) Pre-test – Students will be asked if any have previous juggling experience (approx 1 min.). In this case, exercises will be set up to practice two person juggling, under the leg juggling or 4 ball juggling.
5) Participatory Activity – Students will each receive one ball and practice the simple tossing from one hand to the other and back again, working on keeping the ball at an ideal, consistent height (approx 1 min.).
Then, another ball will be introduced and students will practice “one, two, nothing to throw”. (approx 4 mins)
Those that feel comfortable can then try with 3 balls and those who do not can continue with two ball juggling with one or two hands. (appox 2 mins).
6) Post Test – Ask students how they enjoyed the activity and ask each to display the new skills they have learned. (approx 1 min).
7) Summary - Reiterate to the students that much additional practice will help them attain the skill. Thank them for their time and efforts and wish them well in their circus careers if teaching does not work out.
Thursday, September 17, 2009
Commentary on Richard Skemp's "Relational Understanding and Instrumental Understanding"
As a former mathematics student who plans to teach mathematics in the days ahead, I found Richard Skemp’s essay, “Relational Understanding and Instrumental Understanding” very interesting. Skemp introduces the idea of a difference between these two types of understanding, by relating the idea of “Faux Amis” or false friends – words in two different languages that look very similar but have different meanings. Skemp claims, “I now believe that there are two effectively different subjects being taught under the same name, ‘mathematics’”. It is interesting to realize this statement is something I had thought about in the past, but only as it related to different learning styles. I am sure anyone who has studied math at any serious level has identified themselves as someone who understands relationally, although most, if not all, have used many instrumental ‘tricks’ along the way.
Skemp goes on in the article to take the “Devil’s Advocate” position in an attempt to understand the benefits of Instrumental Understanding (It is clear early on that Skemp favours Relational). Under this position he states, “instrumental mathematics is usually easier to understand”, “the rewards are more immediate”, and “one can often get the right answer more quickly and reliably by instrumental thinking”. He counters his own opposing stance by claiming relational mathematics “is more adaptable to new tasks”, is easier to remember”, “it can be a goal in itself”, and its “schemas are organic in quality”.
Skemp continues with good reasons for why the two types of understanding should be understood by math teachers and the benefits of both in different situations. Skemp’s article highlights a very interesting theory behind why the teaching of mathematics may cause its dislike for so many people, and not the mathematics itself.
Skemp goes on in the article to take the “Devil’s Advocate” position in an attempt to understand the benefits of Instrumental Understanding (It is clear early on that Skemp favours Relational). Under this position he states, “instrumental mathematics is usually easier to understand”, “the rewards are more immediate”, and “one can often get the right answer more quickly and reliably by instrumental thinking”. He counters his own opposing stance by claiming relational mathematics “is more adaptable to new tasks”, is easier to remember”, “it can be a goal in itself”, and its “schemas are organic in quality”.
Skemp continues with good reasons for why the two types of understanding should be understood by math teachers and the benefits of both in different situations. Skemp’s article highlights a very interesting theory behind why the teaching of mathematics may cause its dislike for so many people, and not the mathematics itself.
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