This article presents a brief and concise history of mathematics education from the early 1900's to the present and outlines, and speculates at, the issues, problems, opposing views and struggles that surround math as a subject.
There are three distinct phases to note throughout the past century, the Progressive Reform (1910-40's), The New Math (1960's), and the "Math Wars" NCTM Standards Reform (1990's to present), as well as two main stances, progressive and conservative. A progressive view of mathematics is one of a better understanding and less memorization of strict rules, theorems and algorithms for the sake of fluency, which is more of a conservative approach. I personally believe that fluency will come with a deeper understanding of mathematics and that the two are not separate.
The reasons for the three aforementioned phases of math education throughout the past century are political reasons, i.e. the push for The New Math curriculum during the 1960's was largely influenced by the Cold War era and the Space Race, but they are also due to a number of reasons around a sort of math phobia.
Many people hear the word "math" and cringe. Some reasons for this sort of a reaction given in the article, which I agree with, are because math is hard, only a select elite need to know it, there is no shame felt for not knowing, or "liking" math, and there seems to be a stigma attached to those that like math, that they are socially awkward. Also, it is important to note that there is a flaw with our school system, in that teachers are teaching subjects that they are not really qualified to teach, such as mathematics. By allowing teachers to teach math when they are not qualified to, it is very likely that they may impart a view on their students which adds to this fear of math and a very destructive cycle is formed.
I don't feel that teaching math from either a progressive or a conservative stance really matters, but there should be a mixture of the both and I would probably lean a little towards the progressive. However, whatever way the teacher wants to teach the given curriculum they should have a good knowledge of math and they should have the goal of making math interesting for their students to break down the math phobia which is so prevalent in North American society.
Thursday, September 30, 2010
Wednesday, September 29, 2010
Letters From the Futures Past
Dear Mr. Mathews,
How are you? I hope that you are still teaching. I am writing to you now because I just wanted to let you know how much of an influence you were to me as my teacher. Without your positive classroom atmosphere and all the different fun activities we did in your class I never would have developed an interest, nevermind a love for mathematics. After graduating I went on to successfully complete a bachelors of science with a physics major, which I couldn't have done if it weren't for your inspirations, as many of my professors were atrocious and were very uninspiring. After this I continued on to do further education and now am working at my dream job researching for NASA. Again, I feel as though I owe much of my success to what I learned in your class, both with regards to the subject matter taught and life lessons modeled by you, so thank you.
Sincerely,
John Smith
Dear Mr. Mathews,
After recently attending the ten year reunion, I began to reflect back on my time at high school and I seemed to be really focusing on your class. I couldn't figure out why I was thinking so much about your class until I realized that I used to spend a lot of time thinking up more and more creative ways and excuses to skip your class. This was because your class was so boring and I just couldn't concentrate. You focused so much on students that understood math and so little on students that did not, which I didn't. I feel as though I could have done a lot more with my life if you, or any of my other teachers had done a better job with students like myself that just needed a little more attention and a bit of a push to do more or try harder. I hope that you have been doing a better job since I last saw you.
Sincerely,
Phil Harmonik
The first letter describes the type of feedback I would hope to get from past students. I hope to be an inspiring teacher that not only knows their subject well, but also models a good way to look at ones life and creates a positive school experience. The second letter is the type of feedback I hope not to get as a teacher. I hope to be an exciting, fun teacher that doesn't have a boring class that people try to skip as often as possible, or fall asleep in on a regular basis.
How are you? I hope that you are still teaching. I am writing to you now because I just wanted to let you know how much of an influence you were to me as my teacher. Without your positive classroom atmosphere and all the different fun activities we did in your class I never would have developed an interest, nevermind a love for mathematics. After graduating I went on to successfully complete a bachelors of science with a physics major, which I couldn't have done if it weren't for your inspirations, as many of my professors were atrocious and were very uninspiring. After this I continued on to do further education and now am working at my dream job researching for NASA. Again, I feel as though I owe much of my success to what I learned in your class, both with regards to the subject matter taught and life lessons modeled by you, so thank you.
Sincerely,
John Smith
Dear Mr. Mathews,
After recently attending the ten year reunion, I began to reflect back on my time at high school and I seemed to be really focusing on your class. I couldn't figure out why I was thinking so much about your class until I realized that I used to spend a lot of time thinking up more and more creative ways and excuses to skip your class. This was because your class was so boring and I just couldn't concentrate. You focused so much on students that understood math and so little on students that did not, which I didn't. I feel as though I could have done a lot more with my life if you, or any of my other teachers had done a better job with students like myself that just needed a little more attention and a bit of a push to do more or try harder. I hope that you have been doing a better job since I last saw you.
Sincerely,
Phil Harmonik
The first letter describes the type of feedback I would hope to get from past students. I hope to be an inspiring teacher that not only knows their subject well, but also models a good way to look at ones life and creates a positive school experience. The second letter is the type of feedback I hope not to get as a teacher. I hope to be an exciting, fun teacher that doesn't have a boring class that people try to skip as often as possible, or fall asleep in on a regular basis.
Friday, September 24, 2010
Five Burning Questions
Teacher Questions:
1. How have you motivated students who are not naturally excited about math?
2. Do you make use of different technologies in your class to encourage different learning styles, if so what are they and how do you implement them?
3. How do you feel about the current math curriculum, what is good what isn’t? Do you feel that there is a growing disconnect between math 12 and what is expected/necessary for first year university math?
4. From the time that you started teaching in a high school until now, have you ever been bored? If so, how did you deal with the issue of boredom?
5. When do you plan to retire? Do you plan do go into administration?
Teacher Responses:
I had the opportunity to ask two teachers these few questions; they will be referred to as teacher A and teacher B. Teacher A has been teaching high school math for about 10 years now and has taught mostly in international schools in Asia, namely Macau, China and Korea. She graduated from Australia. On the other hand, teacher B has taught in Canada for a total of 9 years, 2 years in Ontario and 7 years in British Columbia. He is teaching in a large public school in the Vancouver region. He graduated from Ontario.
Response to question 1:
Both of the teachers expressed that they try to give students questions that they can handle, in order for them to feel successful and to gain some confidence, this is where they would gain their interest in math. For example, “working with these students one on one and making sure they know how pleased I am when they do well on tests, quizzes or assignments.” was teacher B’s response.
Response to question 2:
Both teachers use computers and certain softwares to teach their lessons. Teacher A works in a school where all students have a computer and are networked with the teacher’s computer, so she can do things live on her computer in order to teach her students, this is very engaging for students living in a age where they are always around technology. Teacher B does not have the same luxuries as teacher A, nonetheless he also uses a computer and a projector for his class.
Response to question 3:
Teacher A said that AP calculus is the goal for most students at her school, and she feels that it prepares them quite well. She finds no issues of the curriculum that she is teaching right now. Teacher B on the other hand hasn’t found any concerns so far in the new grade 10 curriculum, since it is the beginning of the year. However, he did mention that there is less material to teach so there is more room to explore with new activities that he has thought of so far to help with the students learning. He also mentioned, “I think students learn differently than before internet became available and technology became so advanced. Now, students are accustomed to retrieving information instantaneously and networking in larger groups. There almost seems like an impatience to learn when the Socratic method of teaching is used.” I found this to be the most useful knowledge to know about how students like to learn these days.
Response to question 4:
Teacher A said that she has felt boredom but it was because she was teaching the same things in the same way due to not having much access to resources. However, in order to get over her boredom she started doing more research online for new ways to use technology and read up on tweets about all these things other teachers were doing in other schools to improve her teaching style. Teacher B on the other hand, mentioned that he has never been bored since he has been always creating new lesson plans each year he teaches.
Response to question 5:
Both teachers expressed that they are not interested in administration; however that might change in due time.
Student Questions:
1. Do you think mathematics is useful in life? Why/why not?
2. Why do you think students dislike or like math?
3. When learning math, does it help to see real life applicable examples and applications or is it enough to know that something works and to see an example of it whether or not it has an obvious application?
4. What would you change about the way mathematics is being taught if any?
5. Would doing group research projects be helpful and is it something that would make your math class more enjoyable for you?
Student Responses:
Student who enjoys mathematics (Based on responses given):
Math gives us a basic knowledge to be able do everyday things, such as handling a budget and ones finances and is an important skill to know how to apply math and to show some understanding of simple math in many careers.
For many students math seems to be a rather daunting task, this can be attributed to the “wordiness” of many math problems which makes simply understanding the problem an issue, never mind actually solving it. Furthermore, it is one thing to see a teacher do an example on the board and have it look nice and easy but, for a student to do the math on their own is more difficult, especially when the question is not worded very clearly.
When trying to help students better understand mathematics it often helps to capture their interests by presenting real life examples and applications as opposed to just showing an example that works.
From the perspective of this student, some important qualities that a math teacher should possess are to be well organized, knowledgeable of the subject area and has clear goals for their teaching and learning objectives, and is available and willing to help students as often as possible.
Group projects can be seen as a good way boost marks but more importantly it gives students a chance to learn about math in different ways. A project is a nice change of pace from doing math problems day in and day out. This could be something good to do at the end of a unit, term, or the end of the year. However, it would be a good idea to keep in mind that, especially in the higher grades, most students already have a lot of other projects and larger assignments to do and that we should be aware of this and not overburden them with something that they really wouldn’t appreciate doing at the end of the year. If you are going to give a group project to students in either math 11 or math 12 it may be received better nearer the beginning of the year instead of nearer the end of the year.
Student who doesn’t enjoy mathematics
I was to interview the student who disliked mathematics. Based on his response to our 5 burning questions, it was obvious to note that this student does not favor mathematics. However, even though he disliked mathematics, he was able to admit that mathematics did have useful benefits in reality. An example that he gave was related to purchasing items to renovate a house. The student also mentioned that he was not interested in the applications of mathematics in reality; he would simply be content to know the steps to get to the right answers.
Like many other students who struggle with mathematics, the common issue among them is the need for more time to get their work done and constant practice to help them remember the steps more efficiently. It is true that mathematics is one of the hardest subjects to learn in high school, from this student’s perspective, he seemed to prefer instrumental mathematics over relational mathematics due to the fact that mathematics is not really an interest of his.
Since mathematics is not interesting to this student, he would want to get his work done and over with as soon as possible. Thus he preferred learning and working on mathematics in a private tutoring environment, where it is only him and either a teacher or tutor to teach him the mechanics of solving the math questions.
When I asked him what he thought about the concept of group projects, he replied by saying that he would not be able to concentrate on both talking with group mates and working on mathematics. He preferred sticking to the curriculum and keeping it simple, so that he can finish his mathematics education quickly.
(Niyaz, Howard, Mathew)
1. How have you motivated students who are not naturally excited about math?
2. Do you make use of different technologies in your class to encourage different learning styles, if so what are they and how do you implement them?
3. How do you feel about the current math curriculum, what is good what isn’t? Do you feel that there is a growing disconnect between math 12 and what is expected/necessary for first year university math?
4. From the time that you started teaching in a high school until now, have you ever been bored? If so, how did you deal with the issue of boredom?
5. When do you plan to retire? Do you plan do go into administration?
Teacher Responses:
I had the opportunity to ask two teachers these few questions; they will be referred to as teacher A and teacher B. Teacher A has been teaching high school math for about 10 years now and has taught mostly in international schools in Asia, namely Macau, China and Korea. She graduated from Australia. On the other hand, teacher B has taught in Canada for a total of 9 years, 2 years in Ontario and 7 years in British Columbia. He is teaching in a large public school in the Vancouver region. He graduated from Ontario.
Response to question 1:
Both of the teachers expressed that they try to give students questions that they can handle, in order for them to feel successful and to gain some confidence, this is where they would gain their interest in math. For example, “working with these students one on one and making sure they know how pleased I am when they do well on tests, quizzes or assignments.” was teacher B’s response.
Response to question 2:
Both teachers use computers and certain softwares to teach their lessons. Teacher A works in a school where all students have a computer and are networked with the teacher’s computer, so she can do things live on her computer in order to teach her students, this is very engaging for students living in a age where they are always around technology. Teacher B does not have the same luxuries as teacher A, nonetheless he also uses a computer and a projector for his class.
Response to question 3:
Teacher A said that AP calculus is the goal for most students at her school, and she feels that it prepares them quite well. She finds no issues of the curriculum that she is teaching right now. Teacher B on the other hand hasn’t found any concerns so far in the new grade 10 curriculum, since it is the beginning of the year. However, he did mention that there is less material to teach so there is more room to explore with new activities that he has thought of so far to help with the students learning. He also mentioned, “I think students learn differently than before internet became available and technology became so advanced. Now, students are accustomed to retrieving information instantaneously and networking in larger groups. There almost seems like an impatience to learn when the Socratic method of teaching is used.” I found this to be the most useful knowledge to know about how students like to learn these days.
Response to question 4:
Teacher A said that she has felt boredom but it was because she was teaching the same things in the same way due to not having much access to resources. However, in order to get over her boredom she started doing more research online for new ways to use technology and read up on tweets about all these things other teachers were doing in other schools to improve her teaching style. Teacher B on the other hand, mentioned that he has never been bored since he has been always creating new lesson plans each year he teaches.
Response to question 5:
Both teachers expressed that they are not interested in administration; however that might change in due time.
Student Questions:
1. Do you think mathematics is useful in life? Why/why not?
2. Why do you think students dislike or like math?
3. When learning math, does it help to see real life applicable examples and applications or is it enough to know that something works and to see an example of it whether or not it has an obvious application?
4. What would you change about the way mathematics is being taught if any?
5. Would doing group research projects be helpful and is it something that would make your math class more enjoyable for you?
Student Responses:
Student who enjoys mathematics (Based on responses given):
Math gives us a basic knowledge to be able do everyday things, such as handling a budget and ones finances and is an important skill to know how to apply math and to show some understanding of simple math in many careers.
For many students math seems to be a rather daunting task, this can be attributed to the “wordiness” of many math problems which makes simply understanding the problem an issue, never mind actually solving it. Furthermore, it is one thing to see a teacher do an example on the board and have it look nice and easy but, for a student to do the math on their own is more difficult, especially when the question is not worded very clearly.
When trying to help students better understand mathematics it often helps to capture their interests by presenting real life examples and applications as opposed to just showing an example that works.
From the perspective of this student, some important qualities that a math teacher should possess are to be well organized, knowledgeable of the subject area and has clear goals for their teaching and learning objectives, and is available and willing to help students as often as possible.
Group projects can be seen as a good way boost marks but more importantly it gives students a chance to learn about math in different ways. A project is a nice change of pace from doing math problems day in and day out. This could be something good to do at the end of a unit, term, or the end of the year. However, it would be a good idea to keep in mind that, especially in the higher grades, most students already have a lot of other projects and larger assignments to do and that we should be aware of this and not overburden them with something that they really wouldn’t appreciate doing at the end of the year. If you are going to give a group project to students in either math 11 or math 12 it may be received better nearer the beginning of the year instead of nearer the end of the year.
Student who doesn’t enjoy mathematics
I was to interview the student who disliked mathematics. Based on his response to our 5 burning questions, it was obvious to note that this student does not favor mathematics. However, even though he disliked mathematics, he was able to admit that mathematics did have useful benefits in reality. An example that he gave was related to purchasing items to renovate a house. The student also mentioned that he was not interested in the applications of mathematics in reality; he would simply be content to know the steps to get to the right answers.
Like many other students who struggle with mathematics, the common issue among them is the need for more time to get their work done and constant practice to help them remember the steps more efficiently. It is true that mathematics is one of the hardest subjects to learn in high school, from this student’s perspective, he seemed to prefer instrumental mathematics over relational mathematics due to the fact that mathematics is not really an interest of his.
Since mathematics is not interesting to this student, he would want to get his work done and over with as soon as possible. Thus he preferred learning and working on mathematics in a private tutoring environment, where it is only him and either a teacher or tutor to teach him the mechanics of solving the math questions.
When I asked him what he thought about the concept of group projects, he replied by saying that he would not be able to concentrate on both talking with group mates and working on mathematics. He preferred sticking to the curriculum and keeping it simple, so that he can finish his mathematics education quickly.
(Niyaz, Howard, Mathew)
Thursday, September 23, 2010
Reflection On Teaching How To Make Mushroom Art
According to the feedback received from my peers I came across as being well prepared and organized, there was good flow and pace to the lesson, it was fun and interactive with the use of multi-modal and hands on activities and there were good, clear instructions. Also, was able to inspire a further interest in learning more garnishes.
Things that I could have done better are to stand and hold the mushroom at a better angle so as to improve the visibility of those I was teaching, taken the time to teach a couple more techniques, and to give a little bit more instruction.
From my own point of view I felt that I was well prepared and had a good intro to my lesson. I thought that this was a very interactive lesson and that I made good use of hands on learning with the main activity and good use of visual learning with the short video which I showed a the end of the lesson. The video also helped to inspire further learning.
Some things that I could work on would be to stand in a way such that my demonstrations could be better seen by all, watch the timing closer so that I had time to give a proper summary and check in on everyone more closely to see how they are doing with the task.
Things that I could have done better are to stand and hold the mushroom at a better angle so as to improve the visibility of those I was teaching, taken the time to teach a couple more techniques, and to give a little bit more instruction.
From my own point of view I felt that I was well prepared and had a good intro to my lesson. I thought that this was a very interactive lesson and that I made good use of hands on learning with the main activity and good use of visual learning with the short video which I showed a the end of the lesson. The video also helped to inspire further learning.
Some things that I could work on would be to stand in a way such that my demonstrations could be better seen by all, watch the timing closer so that I had time to give a proper summary and check in on everyone more closely to see how they are doing with the task.
Wednesday, September 22, 2010
Micro-Teaching: Mushroom Art
Bridge: Have you ever looked at any sort of food display and thought, “Wow, that looks so cool, I wonder how they did that?”, or “I wish that I knew how to do that”, and then thought that food really can be an art form?
Learning Objectives: By the end of this mini lesson you should be able to clean/peel a mushroom and know how to make at least one design on a mushroom, as well as have a general idea about garnishes and gain some basic culinary skills, such as knife skills.
Teaching Objectives: To get everyone involved in the task and to spark an interest in the field of culinary arts and to pass on some of my knowledge and skills.
Pre Test: Does anyone know how to make any garnishes out of various fruits and or vegetables? What sort of cooking/culinary skills do you have?
Participation: Hand out knives and mushrooms, give a quick demo of what I am going to get them to do and have them “carve” the mushrooms for themselves.
Post Test: The post test for this lesson will be more of a self-evaluation of the students work. If they feel that they were successful in completing the task and are happy with how their final product looks and feel that they could do this again at home on their own, then that is good.
Summary: Give more ideas about making simple garnishes using other foods by showing a short video.
Materials Needed: Four Pairing knifes
Mushrooms (2 per person)
Cutting boards (1 per person)
Time Needed: approx. 10min.
Learning Objectives: By the end of this mini lesson you should be able to clean/peel a mushroom and know how to make at least one design on a mushroom, as well as have a general idea about garnishes and gain some basic culinary skills, such as knife skills.
Teaching Objectives: To get everyone involved in the task and to spark an interest in the field of culinary arts and to pass on some of my knowledge and skills.
Pre Test: Does anyone know how to make any garnishes out of various fruits and or vegetables? What sort of cooking/culinary skills do you have?
Participation: Hand out knives and mushrooms, give a quick demo of what I am going to get them to do and have them “carve” the mushrooms for themselves.
Post Test: The post test for this lesson will be more of a self-evaluation of the students work. If they feel that they were successful in completing the task and are happy with how their final product looks and feel that they could do this again at home on their own, then that is good.
Summary: Give more ideas about making simple garnishes using other foods by showing a short video.
Materials Needed: Four Pairing knifes
Mushrooms (2 per person)
Cutting boards (1 per person)
Time Needed: approx. 10min.
Monday, September 20, 2010
Dave Hewitt
This form of whole class participation and learning/teaching was something that was very interesting to see being done. It seemed to work very well for this particular teacher and is something that I would be interested in trying out for myself. I think that you really need to be organized and prepared and have a clear sense of where you want to go in order to teach this method, even though it is very loosely structured. I am not too sure if I could teach like this very often however, as I often feel the need for more structure, but I do believe that there is something to be said for this method.
Friday, September 17, 2010
Memorable Math Teachers
When I look back at my past math experiences, good, bad, and mediocre, there are a few teachers and instructors that stand out among the many I have had.
Among them is my old math 12 teacher, a truly brilliant lady with terrible breath. Aside from the bad breath, most students that had her really liked her and found her to be an effective teacher of mathematics. I on the other hand did not enjoy her teaching style nearly as much, I did however enjoy playing pacman on my graphing calculator during class. As someone who really understood and was quick at math I found her style to be rather juvenile and slow, especially for math12, a class which should be taken by serious math students. I would often compare her to a kindergarten teacher, and as a result of this painfully slow pace I would quickly lose all of my interest and ended up doing rather poorly, poorly is of course a relative term here for I am sure that many others would have been very grateful for my mark.
Another teacher that stands out is a professor here at UBC. He also, is a brilliant man and it is easy to tell that he really loves what he is researching and teaching. In his class we would do the usual things one might expect to do in a university math class but, on top of that he was very open to class discussions and he would present open ended and new/current problems which excited in myself a renewed interest and love for math. As well as these things we also would do more that just written homeworks and were able to do exciting fun projects and build various models. Maybe it was because I hadn't done anything like this in a math class for a long time, but this was a very good class and I always looked forward to attending it.
Among them is my old math 12 teacher, a truly brilliant lady with terrible breath. Aside from the bad breath, most students that had her really liked her and found her to be an effective teacher of mathematics. I on the other hand did not enjoy her teaching style nearly as much, I did however enjoy playing pacman on my graphing calculator during class. As someone who really understood and was quick at math I found her style to be rather juvenile and slow, especially for math12, a class which should be taken by serious math students. I would often compare her to a kindergarten teacher, and as a result of this painfully slow pace I would quickly lose all of my interest and ended up doing rather poorly, poorly is of course a relative term here for I am sure that many others would have been very grateful for my mark.
Another teacher that stands out is a professor here at UBC. He also, is a brilliant man and it is easy to tell that he really loves what he is researching and teaching. In his class we would do the usual things one might expect to do in a university math class but, on top of that he was very open to class discussions and he would present open ended and new/current problems which excited in myself a renewed interest and love for math. As well as these things we also would do more that just written homeworks and were able to do exciting fun projects and build various models. Maybe it was because I hadn't done anything like this in a math class for a long time, but this was a very good class and I always looked forward to attending it.
Monday, September 13, 2010
Skemp Reading Response
I found this article very interesting and somewhat thought provoking. It made me think of teaching math in a slightly different way and it made me think about how I understand and approach math and how I hope to teach math.
Something that I got from this article is that a relational understanding of mathematics is more of a conceptual and deeper, more lasting understanding whereas instrumental is more of a mechanical understanding, i.e., here is the formula, "monkey see, monkey plug in".
Skemp argues that relational teaching is far superior but wonders why so many math teachers teach in a more instrumental manner, while I feel that both are equally important and that they are inseparable when teaching math. Instrumental teaching/understanding is often a good way to form a foundation from which to build on and leads to a strong relational understanding.
This being said, I believe that relational teaching and understanding should be something to strive for whenever possible. However, this really may be too much for many students, especially in lower grades where math is still a mandatory subject, as it could be a very slow and overwhelming process at times and when in reality, all that is really needed to be known by the student is the given algorithm and when/how to use it.
Something that I got from this article is that a relational understanding of mathematics is more of a conceptual and deeper, more lasting understanding whereas instrumental is more of a mechanical understanding, i.e., here is the formula, "monkey see, monkey plug in".
Skemp argues that relational teaching is far superior but wonders why so many math teachers teach in a more instrumental manner, while I feel that both are equally important and that they are inseparable when teaching math. Instrumental teaching/understanding is often a good way to form a foundation from which to build on and leads to a strong relational understanding.
This being said, I believe that relational teaching and understanding should be something to strive for whenever possible. However, this really may be too much for many students, especially in lower grades where math is still a mandatory subject, as it could be a very slow and overwhelming process at times and when in reality, all that is really needed to be known by the student is the given algorithm and when/how to use it.
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