The article "Citizenship Education in the Context of School Mathematics," by Elaine Simmt, states that mathematics has a role in citizenship education and is crucial in the development of informed, active and critical citizens in our society. "Mathematics will help us understand ourselves... [and] understand the world in which we participate." Mathematics is embedded into our world from business, economics, time, space, communication, transport and war and our youth must be educated to understand and critique the 'formatting power' of mathematics.
So, how to we teach math to accomplish this. Right now, math is usually taught as:
1) a set of facts, skills and processes - creating consumers who know how to leave a tip.
2) as facts and fact - pushing around numbers and writing them in different ways suiting the teacher.
3) as right or wrong - reinforcing the notion that mathematics must not be questioned and creating no confidence in individuals.
Elaine gives possible methods such as:
1) focusing on problems and questions arising from student interaction with math using a strategy called 'posing variable-entry prompts'.
2) having the students explain their reasoning attempting to prove their assertions. The necessity of student contribution.
The example in this article about making rectangles using 36 square tiles reminds me of the recent video we saw in class about solving two challenging exponential/logarithmic problems using 2 or more methods.
These types of questions would likely take up a lot of time and therefore I would probably limit each unit to one, possibly two activities of this nature. It would depend on the unit and how much worth I see the students actually getting out of the activities.
These activities encourage group work and negotiation, forcing the students to pose questions and hypothesis on how to approach open ended questions. I like the idea of groups of students writing down their solutions on poster paper and then having to present their results. I completely agree that it is important for students to present their results explaining their reasoning's and approaches to the problems. Also, being in groups will provide them more confidence when discussing the results.
Sunday, October 11, 2009
Wednesday, October 7, 2009
What-if-not
What-if-not? Yes, what is that?
It is a strategy to assist you in problem posing. It is a systematic approach that has five levels.
How can I use this technique in preparation for my groups micro-teaching lesson next Wednesday on Logarithms and Exponentials? At the moment, I'm not really sure how it will be of use. However, I am sure we'll be able to use this problem posing strategy to think of some questions that could be useful for the presentation.
As a level 0, we could possibly begin with one of the rules for logarithms, such as the Power Law, or Multiplication/Devision Laws. From there, who knows where it will go?
The strengths of the What-if-not method is that it is a pretty direct way to formulate a lot of questions from a single starting point. It is a tree that keeps expanding and is interconnected with itself to create even more possibilities. Another positive aspect is that fact that it is a systematic approach to problem posing. It walks you through the steps making sure you really analyze the starting point, the topic you chose, by listing all the attributes you can see. For every question you get a what-if-not question and you are forced to analyze to prove/disprove (find out when true/false) each statement before continuing. You will really able to flesh out the topic you are looking at using this method.
The weaknesses of this method is that it can take a long time, and I mean a LONG time. And after putting a lot of hard work into the process, you may find yourself with nothing to show for it. For example, you may create a lot of what-if-not statements similar to Attribute 8 on page 50. Those arn't going anywhere and will prove to be a waste of time (If I'm wrong about that last sentence, please let me know). Nothing useful may come out of the process meaning I could have watched an episode of House instead of using the strategy.
I'll try using this method during the preparation for the micro teaching lesson. I'll see how it goes.
It is a strategy to assist you in problem posing. It is a systematic approach that has five levels.
- Level 0 Choosing a Starting Point: ie. Pythagorean Theorem
- Level 1 Listing Attributes
- Level 2 What-If Not-ing: Take an attribute and ask yourself, 'what if that attribute was not true and was instead something else?' List as many alternatives as you can think of. ie. What if the Pythagorean Theorem was instead written as a^2 + b^2 <>
- Level 3 Question Asking or Problem Posing: What questions come to mind when you write down this alternative form? When is it true? Is it significant?
- Level 4 Analyzing the Problem
How can I use this technique in preparation for my groups micro-teaching lesson next Wednesday on Logarithms and Exponentials? At the moment, I'm not really sure how it will be of use. However, I am sure we'll be able to use this problem posing strategy to think of some questions that could be useful for the presentation.
As a level 0, we could possibly begin with one of the rules for logarithms, such as the Power Law, or Multiplication/Devision Laws. From there, who knows where it will go?
The strengths of the What-if-not method is that it is a pretty direct way to formulate a lot of questions from a single starting point. It is a tree that keeps expanding and is interconnected with itself to create even more possibilities. Another positive aspect is that fact that it is a systematic approach to problem posing. It walks you through the steps making sure you really analyze the starting point, the topic you chose, by listing all the attributes you can see. For every question you get a what-if-not question and you are forced to analyze to prove/disprove (find out when true/false) each statement before continuing. You will really able to flesh out the topic you are looking at using this method.
The weaknesses of this method is that it can take a long time, and I mean a LONG time. And after putting a lot of hard work into the process, you may find yourself with nothing to show for it. For example, you may create a lot of what-if-not statements similar to Attribute 8 on page 50. Those arn't going anywhere and will prove to be a waste of time (If I'm wrong about that last sentence, please let me know). Nothing useful may come out of the process meaning I could have watched an episode of House instead of using the strategy.
I'll try using this method during the preparation for the micro teaching lesson. I'll see how it goes.
Sunday, October 4, 2009
10 Questions or Comments
1) From the text, 'The Art of Problem Posing', I like the line on page 3, '"The answers Gertrude, what are the answers?" - whereupon Gertrude allegedly responded, "The questions, what are the questions?"'
It reminds of a scene in the book 'The Hitchhikers Guide to the Galaxy'. Deep Thought, a super computer created by a pan-dimensional, hyper-intelligent race of beings, was faced with the task of figuring out the answer to Life, The Universe and Everything. 7 and a half million years later he eventually comes up with an answer, 42. Deep Thought then replies, "I think the problem, to be quite honest with you is that you've never actually known what the question was."
There are all these answers and facts out there but there isn't only one correct path to these answers. So what are the questions?
2) x^2 + y^2 = z^2. An interesting way to begin because it is so open ended. You could choose anything, there are an infinite number of possibilities. The book asks you "What are some answers?" and the only way to come up with any is to pose some questions your self. I simply chose some simple numbers so I could move on with the reading. After reading some of the answers written though it got me thinking about the vast number of responses, and the fact that the responses didn't have to do with math at all.
3) When I see x^2 + y^2 = z^2 I think of a circle first then Pythagoras and right angle triangles. It's a tool to get an answer. The triangles that come to mind are the standard 'special' triangles with ratios 1:1:root2 and 1:2:root3.
4) On page 14 they show a triangle with squares on each edge. I have seen this before, but I have never known the reasons, it seems pointless. How does it help? After writing this question I think I may have figured it out. Is it simply a reminder that to relate each edge length you must square each length first?
5) Do you ever give us any of the answers to the questions you pose? Some of the points brought up are interesting but I guess it isn't the purpose of the book to give answers. That's what the internet is for eh?
6) The hand shaking question on page 19. When I hear this problem I instantly think 'the number of people, choose 2'. nC2, where n is the number of people shaking hands. So, with 9 people, we get 36 handshakes.
Yes, I am one of those guys who came up with the question, "How many handshakes were there altogether."
7) It has been so long since the first time we actually learned the properties of isosceles triangles and Pythagoras, etc. It makes me wonder, how did I first learn these concepts? What went through my mind when it was introduced to me? Did I ever think of interesting questions such as "can I make a bicycle hub out of congruent isosceles triangles?" When I read this chapter today, I certainly didn't come up with any questions like that. I agree with what is written on page 22 whole heartedly, those who have been exposed to geometry "find great difficulty coming up with much more than observations relating the equality of the lengths to the equality of angles."
8) If I was given a Geoboard of 25 nails I would get an extremely stretchy rubber band and try to make the most complicated looking picture possible using all of the pins without the elastic ever crossing over itself.
9) Coming up with unique questions for these pythagoras, geoboard, isosceles and handshake problems is tough. I'm sure after teaching a few courses in math and seeing what students come up with I'll be more capable of thinking of questions, both in and out of context.
10) The handy list of questions on page 30. Add ons:
What is the origin of the formula? Is it continuous? Discrete? Is there an average? Are there visual representations? For whom is this useful to? Practical or theoretical? Can we prove it? Do we need to prove it?
It reminds of a scene in the book 'The Hitchhikers Guide to the Galaxy'. Deep Thought, a super computer created by a pan-dimensional, hyper-intelligent race of beings, was faced with the task of figuring out the answer to Life, The Universe and Everything. 7 and a half million years later he eventually comes up with an answer, 42. Deep Thought then replies, "I think the problem, to be quite honest with you is that you've never actually known what the question was."
There are all these answers and facts out there but there isn't only one correct path to these answers. So what are the questions?
2) x^2 + y^2 = z^2. An interesting way to begin because it is so open ended. You could choose anything, there are an infinite number of possibilities. The book asks you "What are some answers?" and the only way to come up with any is to pose some questions your self. I simply chose some simple numbers so I could move on with the reading. After reading some of the answers written though it got me thinking about the vast number of responses, and the fact that the responses didn't have to do with math at all.
3) When I see x^2 + y^2 = z^2 I think of a circle first then Pythagoras and right angle triangles. It's a tool to get an answer. The triangles that come to mind are the standard 'special' triangles with ratios 1:1:root2 and 1:2:root3.
4) On page 14 they show a triangle with squares on each edge. I have seen this before, but I have never known the reasons, it seems pointless. How does it help? After writing this question I think I may have figured it out. Is it simply a reminder that to relate each edge length you must square each length first?
5) Do you ever give us any of the answers to the questions you pose? Some of the points brought up are interesting but I guess it isn't the purpose of the book to give answers. That's what the internet is for eh?
6) The hand shaking question on page 19. When I hear this problem I instantly think 'the number of people, choose 2'. nC2, where n is the number of people shaking hands. So, with 9 people, we get 36 handshakes.
Yes, I am one of those guys who came up with the question, "How many handshakes were there altogether."
7) It has been so long since the first time we actually learned the properties of isosceles triangles and Pythagoras, etc. It makes me wonder, how did I first learn these concepts? What went through my mind when it was introduced to me? Did I ever think of interesting questions such as "can I make a bicycle hub out of congruent isosceles triangles?" When I read this chapter today, I certainly didn't come up with any questions like that. I agree with what is written on page 22 whole heartedly, those who have been exposed to geometry "find great difficulty coming up with much more than observations relating the equality of the lengths to the equality of angles."
8) If I was given a Geoboard of 25 nails I would get an extremely stretchy rubber band and try to make the most complicated looking picture possible using all of the pins without the elastic ever crossing over itself.
9) Coming up with unique questions for these pythagoras, geoboard, isosceles and handshake problems is tough. I'm sure after teaching a few courses in math and seeing what students come up with I'll be more capable of thinking of questions, both in and out of context.
10) The handy list of questions on page 30. Add ons:
What is the origin of the formula? Is it continuous? Discrete? Is there an average? Are there visual representations? For whom is this useful to? Practical or theoretical? Can we prove it? Do we need to prove it?
Friday, October 2, 2009
The Distant Future...
Letter from a student who liked you.
Hello Mr. Thiessen,
My name is Slarty Bartfast and I was in your class 10 years ago in grade 10. You changed my life. I wasn't always a fan of math. In fact I hated it! After your class I was inspired. You showed me how math could actually be and taught. Your student centered lessons really got me involved and had me understanding the material in no time. It made me continue onwards into grade 11 and 12 and beyond.
You most likely recognize my name because I've been on the news constantly this past week. The man who successfully made the calculations for the first intergalactic warp drive system. It was actually my PHD paper.
Thanks Mr. Thiessen. Because of you, mankind can now travel to the stars.
- Slarty
Letter from a student who hated you.
Mr. Thiessen,
My name is Troy McClure, you may remember me from high school grade 10. Math, I hated it and due to that I didn't give you a chance when I walked into your class. Math was tough, equations and equations of nonsense. Plug this number into x and sub that number into y. It made no sense and that's how I wanted it to stay.
During your lessons you'd often talk about understanding this, and understanding that. I didn't care about any of that. I knew that once math was no longer a prerequisite I would no longer enroll into it.
I didn't want to discuss ideas in groups or do any projects. The bare minimum to pass, that's all I wanted. This was the last mandatory year for math and once I finished high school I was set to pursue my future career in TV broadcasting.
Which is what I did. No thanks to you,
Troy McClure
My hopes and worries...
I hope to be a teacher who passes on an understanding of math to my students. I didn't fear math, I enjoyed it, and I hope I can pass that feeling on to my students by being a effective and engaging teacher. However, I know there will be students who will never like math and I hope I can inspire them enough to get them through the courses.
Hello Mr. Thiessen,
My name is Slarty Bartfast and I was in your class 10 years ago in grade 10. You changed my life. I wasn't always a fan of math. In fact I hated it! After your class I was inspired. You showed me how math could actually be and taught. Your student centered lessons really got me involved and had me understanding the material in no time. It made me continue onwards into grade 11 and 12 and beyond.
You most likely recognize my name because I've been on the news constantly this past week. The man who successfully made the calculations for the first intergalactic warp drive system. It was actually my PHD paper.
Thanks Mr. Thiessen. Because of you, mankind can now travel to the stars.
- Slarty
Letter from a student who hated you.
Mr. Thiessen,
My name is Troy McClure, you may remember me from high school grade 10. Math, I hated it and due to that I didn't give you a chance when I walked into your class. Math was tough, equations and equations of nonsense. Plug this number into x and sub that number into y. It made no sense and that's how I wanted it to stay.
During your lessons you'd often talk about understanding this, and understanding that. I didn't care about any of that. I knew that once math was no longer a prerequisite I would no longer enroll into it.
I didn't want to discuss ideas in groups or do any projects. The bare minimum to pass, that's all I wanted. This was the last mandatory year for math and once I finished high school I was set to pursue my future career in TV broadcasting.
Which is what I did. No thanks to you,
Troy McClure
My hopes and worries...
I hope to be a teacher who passes on an understanding of math to my students. I didn't fear math, I enjoyed it, and I hope I can pass that feeling on to my students by being a effective and engaging teacher. However, I know there will be students who will never like math and I hope I can inspire them enough to get them through the courses.
Wednesday, September 30, 2009
Dave Hewitt - Classroom Orchestra
Today we Dave Hewitt demonstrate a alternative method of teaching. A strategy that involve the whole class, one that is dramatic and like an orchestra. In the classroom we saw him tap the walls with his rulers and have the class add and subtract depending on the direction Dave was tapping in. They would all reply by speaking in unison. Clockwise was add, counterclockwise was subtract. His goal was to have the students see that pattern of what is going on.
Dave eventually introduced variables as a starting number. He drew a row of boxes on the chalk board and designated one as x and chose another box as the destination. He then demonstrated that he could do various combinations of left and right taps to get to the desired destination.
Example: x -> x + 2
This could be solved as three taps right and one left or two taps left and four right, etc
On the board he wrote:
x + 2 = x + 3 - 1 = x - 2 + 4 = x + 612 - 610 ...
He did this all without describing what '=' was too. He wanted them to learn by association.
Some good things about it is that it starts simple and goes to complex and it is an introduction to patters. Also, it is interactive and engaged the whole classroom. Also, the classroom was well managed.
However, there are many negatives to this teaching lesson. There would be a good number of children who will be very bored due to the extremely slow pace. There was no note taking involved which could be seen as both good and bad. Bad for some since a few people may get nervous not having anything written down to refer to. I would also like to see this orchestra method used for a more involved topic other than adding and subtracting which is something the students should have already learned.
Certain topics should be taught using traditional style (quadratic equation), some using constructivist style (geometry) and others by using this Orchestra method (counting). I guess the trouble is figuring out which is best suited for each lesson topic.
On a different note, I was talking to Mike after class and we were talking about alternative ways of teaching math. Us both being Physics students too, Mike brought up math labs (ie. Physics). I thought, why not? Especially kinematics, the math involved in physics is very simple and uses math from grades 8 and 9, and a little from grade 10 in the means of trig. I definitely want to explore this more, teaching math but using physics related questions for applications and word problems.
Dave eventually introduced variables as a starting number. He drew a row of boxes on the chalk board and designated one as x and chose another box as the destination. He then demonstrated that he could do various combinations of left and right taps to get to the desired destination.
Example: x -> x + 2
This could be solved as three taps right and one left or two taps left and four right, etc
On the board he wrote:
x + 2 = x + 3 - 1 = x - 2 + 4 = x + 612 - 610 ...
He did this all without describing what '=' was too. He wanted them to learn by association.
Some good things about it is that it starts simple and goes to complex and it is an introduction to patters. Also, it is interactive and engaged the whole classroom. Also, the classroom was well managed.
However, there are many negatives to this teaching lesson. There would be a good number of children who will be very bored due to the extremely slow pace. There was no note taking involved which could be seen as both good and bad. Bad for some since a few people may get nervous not having anything written down to refer to. I would also like to see this orchestra method used for a more involved topic other than adding and subtracting which is something the students should have already learned.
Certain topics should be taught using traditional style (quadratic equation), some using constructivist style (geometry) and others by using this Orchestra method (counting). I guess the trouble is figuring out which is best suited for each lesson topic.
On a different note, I was talking to Mike after class and we were talking about alternative ways of teaching math. Us both being Physics students too, Mike brought up math labs (ie. Physics). I thought, why not? Especially kinematics, the math involved in physics is very simple and uses math from grades 8 and 9, and a little from grade 10 in the means of trig. I definitely want to explore this more, teaching math but using physics related questions for applications and word problems.
Saturday, September 26, 2009
Math Interview Reflections
After listening to the many groups talk about their interviews I have concluded that the most useful and interesting questions were the ones regarding teacher strategies and classroom management. All those questions asking students their feelings about math and such resulted in what I expected. Among students, not much has changed. Well, I am only 5 years removed from high school and that’s not a lot of time to result in large changes. Every school still has a wide range of students with various competencies in math which usually reflects how they grade their teachers. Also, most students don’t know what the purpose of math is other than a requirement for getting by high school or needed for doing taxes. If that was true though, math could be seen as useless since there are computer programs to do our taxes for us now a days. The applications and purposes of math must be better explained to the students during the lessons.
Before I talk about what I found interesting from some of the other groups I’ll go in detail about the responses I got from our own groups interview. The person we interview is a new teacher who just went through the UBC education program last year. He studied math and physics and got a full time job right after graduation at a fairly new school in Surrey.
The first question we asked was about his transition from the practicum to the full time job. He explained how the full time job is a lot more work. Lesson prepping is the most time consuming component of teaching and all of that has to be completed outside of the classroom. I didn’t expect the degree and quantity of work that he made it out to be. The number of different courses he has to teach his first year is amazing, and for all of them, new lesson plans. I didn’t ask, but hopefully he gets lots of help from his fellow educators.
The second question asked about the amount of time the class is devoted to lecture and how much towards seat work. He responded with 20-40 minutes of seat work depending on the lesson. He reinforced the notion that it is very important to vary the class with activities such as math bingo. Many students can’t last the full 75 minutes that a class goes for and need to get up and move around. This is similar to one of the other groups interviews. One teacher said they like to start with a bus driver game, move on to a challenge question, lecture for 25 minutes and end with some time for work. Variety seems to be a common trend among math teachers these days and I think it is a good thing. Another thing was peer tutoring. I like the idea of peer tutoring because lots of times students have different perspectives and methods on how to approach a problem which can be extremely useful. Also, it may be easier for some kids to ask for help from a peer than a teacher. In my old school one of my math teachers was trying to set up a peer tutor system where the tutors would get paid 10 dollars per hour from the school. I believe it got going after the year I graduated.
The third question asked about any visual methods he used in class. To him, algebra tiles are stupid and I’m going to have to agree with him. It depends on the subject. Subjects such as geometry and surface area where kids can physically measure objects are visual methods really useful. Consistencies of notation was the fourth question. His advice, follow the notation in the textbook. Students get lost easily with simple changes such as f(x) = g(x).
The final question asked about special needs students and the alternative teaching strategies used when working with them. As a new teacher he says it is extremely difficult. Be patient and offer time outside of class. Also, use peer tutors!
Keeping students interested is a must as a teacher. I liked one of the responses from one of the other groups. To keep the top students interested, give them challenging problems and have them act as tutors. As for the struggling students, as long as they don’t give up, you’re doing a good job. Keep giving them encouragements as much as possible.
From these interview sessions I have learned a lot of useful information which I should be able to use in my own teaching practices. To end this blog I will mention the secret final question of the interview: What is your favourite pie?
If you answered 3.14… you are on the right track.
Before I talk about what I found interesting from some of the other groups I’ll go in detail about the responses I got from our own groups interview. The person we interview is a new teacher who just went through the UBC education program last year. He studied math and physics and got a full time job right after graduation at a fairly new school in Surrey.
The first question we asked was about his transition from the practicum to the full time job. He explained how the full time job is a lot more work. Lesson prepping is the most time consuming component of teaching and all of that has to be completed outside of the classroom. I didn’t expect the degree and quantity of work that he made it out to be. The number of different courses he has to teach his first year is amazing, and for all of them, new lesson plans. I didn’t ask, but hopefully he gets lots of help from his fellow educators.
The second question asked about the amount of time the class is devoted to lecture and how much towards seat work. He responded with 20-40 minutes of seat work depending on the lesson. He reinforced the notion that it is very important to vary the class with activities such as math bingo. Many students can’t last the full 75 minutes that a class goes for and need to get up and move around. This is similar to one of the other groups interviews. One teacher said they like to start with a bus driver game, move on to a challenge question, lecture for 25 minutes and end with some time for work. Variety seems to be a common trend among math teachers these days and I think it is a good thing. Another thing was peer tutoring. I like the idea of peer tutoring because lots of times students have different perspectives and methods on how to approach a problem which can be extremely useful. Also, it may be easier for some kids to ask for help from a peer than a teacher. In my old school one of my math teachers was trying to set up a peer tutor system where the tutors would get paid 10 dollars per hour from the school. I believe it got going after the year I graduated.
The third question asked about any visual methods he used in class. To him, algebra tiles are stupid and I’m going to have to agree with him. It depends on the subject. Subjects such as geometry and surface area where kids can physically measure objects are visual methods really useful. Consistencies of notation was the fourth question. His advice, follow the notation in the textbook. Students get lost easily with simple changes such as f(x) = g(x).
The final question asked about special needs students and the alternative teaching strategies used when working with them. As a new teacher he says it is extremely difficult. Be patient and offer time outside of class. Also, use peer tutors!
Keeping students interested is a must as a teacher. I liked one of the responses from one of the other groups. To keep the top students interested, give them challenging problems and have them act as tutors. As for the struggling students, as long as they don’t give up, you’re doing a good job. Keep giving them encouragements as much as possible.
From these interview sessions I have learned a lot of useful information which I should be able to use in my own teaching practices. To end this blog I will mention the secret final question of the interview: What is your favourite pie?
If you answered 3.14… you are on the right track.
Battlegrounds School Response
This article talks about the two main stances in Mathematics Education. The two dichotomies are the Conservative approach and the Progressive approach. To keep it short, the Conservative method is what most people know of when they think math class, lectures, homework, memorization, tests and repeat. The Progressive approach is to have the students come to understand math, to see the patterns emerging from lived experiences and to stimulate problem solving skills.
In table M.1, one of the columns is what should drive curriculum design in public schooling. For Conservative it reads: for the masses, the need to do simple, practical calculations. For Progressive it reads: to expand learners’ modes of thought and develop flexible problem-solving abilities.
This article is pushing for the Progressive approach and lists complicating factors which are preventing the switch from Conservative to Progressive. It goes into different times of our history when a change of mathematics teaching was attempted.
I completely agree that people are math phobic in North America. Many people, particularly parents remember math being extremely difficult and meant only for a small elite or the nerds, and mad scientists who are unable to cope with the world of human interactions. Also, these people feel no shame at being incompetent at math. Children become scared of math before they even start and if they find it troubling they are told it’s ok. This fearful approach is the completely wrong approach towards math and has to be fixed.
Who said war wasn’t good for anything... Apparently, because of war, math curriculums were changed to better prepare students in math due to the perceived need of an increasingly scientific and technological populace. Between 1910 and 1940 a Progressivist Reform occurred due to World War I. John “Dewey challenged the Cartesian split between knowing and doing, or abstract and applied knowledge.” Dewey’s progressive education involved that students must form and test hypotheses and perceive patterns and relationships. His ideas only won acclaim in very progressive schools.
In the 1960s due to the USSR beating the US in the space race, “The New Math” was created. This was another progressive teaching method but it didn’t go over very well. Many math teachers themselves did not know this new math and were incapable of teaching. The new math “supported understanding over fluency,” and “inquiry and sense-making over absorbing and applying facts.
In some ways conservative methods of teaching math works. It works for some but not for all and because of that, people have been trying to change the curriculum for the better. But what gets in the way of this change? The math illiterate with their fears. Also, traditionalists who claim that children are being short-changed by teachers experimenting with their education when they use progressive methods.
The traditional methods of teaching works for some students but still too many are being left behind. Progressive methods must be integrated with the Conservative methods to accommodate a larger portion of students.
In table M.1, one of the columns is what should drive curriculum design in public schooling. For Conservative it reads: for the masses, the need to do simple, practical calculations. For Progressive it reads: to expand learners’ modes of thought and develop flexible problem-solving abilities.
This article is pushing for the Progressive approach and lists complicating factors which are preventing the switch from Conservative to Progressive. It goes into different times of our history when a change of mathematics teaching was attempted.
I completely agree that people are math phobic in North America. Many people, particularly parents remember math being extremely difficult and meant only for a small elite or the nerds, and mad scientists who are unable to cope with the world of human interactions. Also, these people feel no shame at being incompetent at math. Children become scared of math before they even start and if they find it troubling they are told it’s ok. This fearful approach is the completely wrong approach towards math and has to be fixed.
Who said war wasn’t good for anything... Apparently, because of war, math curriculums were changed to better prepare students in math due to the perceived need of an increasingly scientific and technological populace. Between 1910 and 1940 a Progressivist Reform occurred due to World War I. John “Dewey challenged the Cartesian split between knowing and doing, or abstract and applied knowledge.” Dewey’s progressive education involved that students must form and test hypotheses and perceive patterns and relationships. His ideas only won acclaim in very progressive schools.
In the 1960s due to the USSR beating the US in the space race, “The New Math” was created. This was another progressive teaching method but it didn’t go over very well. Many math teachers themselves did not know this new math and were incapable of teaching. The new math “supported understanding over fluency,” and “inquiry and sense-making over absorbing and applying facts.
In some ways conservative methods of teaching math works. It works for some but not for all and because of that, people have been trying to change the curriculum for the better. But what gets in the way of this change? The math illiterate with their fears. Also, traditionalists who claim that children are being short-changed by teachers experimenting with their education when they use progressive methods.
The traditional methods of teaching works for some students but still too many are being left behind. Progressive methods must be integrated with the Conservative methods to accommodate a larger portion of students.
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