1. Bridge: We will begin our micro-teaching presentation with a 'hook', something to grab the students attention. In this case, we have a brief history of the invention of logarithms to show the class.
2. Teaching Objectives: We plan to cover the laws of exponentials and logarithms and then work through a problem along with the class. This will comprise of a number of smaller problems taken from the larger problem and posing them individually to the class for response. Finally, we take all those responses, put them together and graph the result.
3. Learning Objectives: We plan to have the students apply the various logarithm rules to solve a question and display their understanding.
4. Pre-test: We will go over the rules of exponentials and logarithms. We will then have the class answer a few simple questions. We will then show a graph comparing logarithms in various bases.
5. Participatory Activity: We will work through the long logarithm problem with the class and produce a result that everyone is happy with.
6. Post-test: Time permitting, we have a second (shorter) problem for the class to work on and solve.
7. Summary: We will briefly recap the equations and concepts that we have covered.
Tuesday, October 13, 2009
Saturday, October 10, 2009
Citizenship & Democracy in Mathematics
Response to: "Citizenship Education in the Context of School Mathematics" ~ Elaine Simmt.
Elaine Simmt argues in her article that by studying mathematics, one will develop critical thinking and problem-solving skills, that are crucial for a democratic, informed member of society. I certainly see the potential validity of this statement. Having met, and studied under, many mathematicians, I know that people who study math passionately are conscious and critical thinking. There are many personality traits (reserved, patient, analytical, cautious) associated with mathematicians that would suggest that those who study math are affected positively by their extensive study.
But perhaps Simmt has missed a step between critical thinker and global citizen. As much as there are 'problem-solvers' in the world, there can be 'problem-posers', or in a social context, 'problem-causers'. Do we know any bad 'math people'? What about internet hackers, inside traders, card sharks, money lenders and ruthless businessmen? Have they not done the math? Having the skills to manipulate our highly quantized world doesn't pose any limit or moral barriers to those seek wealth or power.
I do agree with Simmt though, that math is very much a part of the human experience. And those who use math, do 'transform' our reality and not just 'transmit' it. Math is a double-edged sword. For every opportunity for constructive processes, there exists the possibility for destructive processes; for every problem solved, a problem posed. The beautiful symmetry of math means that everything has an inverse. Math gives us the skills to examine the world at its most fundamental levels, but the choice of good or bad still exists. All I can hope for, is that I can show my students the beauty, symmetry and good in mathematics and prepare them for the true problems that life will present them.
Elaine Simmt argues in her article that by studying mathematics, one will develop critical thinking and problem-solving skills, that are crucial for a democratic, informed member of society. I certainly see the potential validity of this statement. Having met, and studied under, many mathematicians, I know that people who study math passionately are conscious and critical thinking. There are many personality traits (reserved, patient, analytical, cautious) associated with mathematicians that would suggest that those who study math are affected positively by their extensive study.
But perhaps Simmt has missed a step between critical thinker and global citizen. As much as there are 'problem-solvers' in the world, there can be 'problem-posers', or in a social context, 'problem-causers'. Do we know any bad 'math people'? What about internet hackers, inside traders, card sharks, money lenders and ruthless businessmen? Have they not done the math? Having the skills to manipulate our highly quantized world doesn't pose any limit or moral barriers to those seek wealth or power.
I do agree with Simmt though, that math is very much a part of the human experience. And those who use math, do 'transform' our reality and not just 'transmit' it. Math is a double-edged sword. For every opportunity for constructive processes, there exists the possibility for destructive processes; for every problem solved, a problem posed. The beautiful symmetry of math means that everything has an inverse. Math gives us the skills to examine the world at its most fundamental levels, but the choice of good or bad still exists. All I can hope for, is that I can show my students the beauty, symmetry and good in mathematics and prepare them for the true problems that life will present them.
Thursday, October 8, 2009
Review of "What-If-Not" strategy from "The Art of Problem Posing"
This review is in reference to pages 33-65 of the "The Art of Problem Posing" by Stephen I. Brown and comments on the strategy of "What-If-Not".
The term "What-If-Not", refers to a creative thinking process of examining mathematical/problem elements with a fresh perspective. With each concept, we identify key ideas & problems and then we try to expand on them in new directions, incorporating our own perspectives and thinking processes.
I really like this strategy for problem posing/solving. It's all about asking the right questions. Taking a theorem and changing a variable or condition to create a new situation and then examining it to see where it has taken us. This can be used extensively in the classroom, as we have begun to discover in our other classes. The students learn through inquiry and compound ideas and ultimately will have a more concrete understanding of the concept using this strategy.
We first explored this in SCED 316a with the aptly named 'UnDemo' in which the students were in control of the experimental process and merely guided by the teacher. In this way, the students were allowed to ask "what-if" and then examine "what-if-not". If students can understand what something 'is not', then they have a better understanding of what 'it is'. We next explored this in our Principles of Teaching lecture in which we talked about what it means to define a chair. And then from that, looking at a plethora of objects that were 'chair-like', but not chairs (i.e. thrones, stools, lounges, couches, etc.). In this way, the pythagorean theorem is a chair, but the other equations that were plucked from it, where 'pythagorean-like' and equally valid for examination. And by understanding what the pythagorean theorem wasn't, a student would have a better understanding of where it fit in their theoretical framework.
The only limitation to this method of inquiry, however, is that fact that this type of exploration can often be off 'topic' or time-consuming and may even lead to confusion. We cannot use this strategy like a blunt tool, or it will damage the process. Instead, we must use it as a fine instrument that requires skill and precision in utilizing for best results.
The term "What-If-Not", refers to a creative thinking process of examining mathematical/problem elements with a fresh perspective. With each concept, we identify key ideas & problems and then we try to expand on them in new directions, incorporating our own perspectives and thinking processes.
I really like this strategy for problem posing/solving. It's all about asking the right questions. Taking a theorem and changing a variable or condition to create a new situation and then examining it to see where it has taken us. This can be used extensively in the classroom, as we have begun to discover in our other classes. The students learn through inquiry and compound ideas and ultimately will have a more concrete understanding of the concept using this strategy.
We first explored this in SCED 316a with the aptly named 'UnDemo' in which the students were in control of the experimental process and merely guided by the teacher. In this way, the students were allowed to ask "what-if" and then examine "what-if-not". If students can understand what something 'is not', then they have a better understanding of what 'it is'. We next explored this in our Principles of Teaching lecture in which we talked about what it means to define a chair. And then from that, looking at a plethora of objects that were 'chair-like', but not chairs (i.e. thrones, stools, lounges, couches, etc.). In this way, the pythagorean theorem is a chair, but the other equations that were plucked from it, where 'pythagorean-like' and equally valid for examination. And by understanding what the pythagorean theorem wasn't, a student would have a better understanding of where it fit in their theoretical framework.
The only limitation to this method of inquiry, however, is that fact that this type of exploration can often be off 'topic' or time-consuming and may even lead to confusion. We cannot use this strategy like a blunt tool, or it will damage the process. Instead, we must use it as a fine instrument that requires skill and precision in utilizing for best results.
Saturday, October 3, 2009
10 Questions/Comments on "The Art of Problem Posing"
This response consists of 10 questions/comments regarding pages 1-32 of "The Art of Problem Posing" by Stephen I. Brown.
1. I valued most highly, the idea that problems are very much context-based. The difference between a lousy problem and a superb problem (on the same topic) lies almost solely in context. And I think a student can tell/appreciate when a truely good/unique/intriguing question has been asked (as opposed to a conventional one).
2. I often see my own contextual view of problem posing and solving as being quite narrow. What are some strategies or literature that might best help broaden my contextual view?
3. I like the notion of posing an idea and not a problem. The open-endedness of it is very freeing and allows the mind to explore new possibilities and solutions. I was amazed at how many answers there were to a given idea.
4. I also thought it was very interesting, the idea that the person being asked to respond to an idea like x^2 + y^2 = z^2, was, in a sense, posing and answering their own questions and that the problem-solver imposes their own views on an idea and becomes a unique problem-poser.
5. What do you do when the a student wants the proof to an equation or principle and the explanation of the proof would be too far above that student's current knowledge level? Often times, I think math teachers are compelled to have their students take their word for it, because the beautiful simplicity of an idea is too complex to explain to the student.
6. How strongly should I be emphasizing pattern recognition, rare sequences and phenomena in amongst the standard curriculum?
7. What license do I have as a teacher to assign value/marks to a student's answer that is a unique approach/solution to the problem for which they put the wrong answer? i.e. If I want the answer 5,12,13 and I get the answer -5,-12,-13?
8. I found it very funny in the hand-shake example of the jurors, because my mind immediately jumped to the problem of how many total handshakes. I guess that is my narrow contextual perspective.
9. How far can I probe into a simple concept before I run the risk of undoing the knowledge I taught and confusing my students?
10. What IS the use of examining phenomena?
1. I valued most highly, the idea that problems are very much context-based. The difference between a lousy problem and a superb problem (on the same topic) lies almost solely in context. And I think a student can tell/appreciate when a truely good/unique/intriguing question has been asked (as opposed to a conventional one).
2. I often see my own contextual view of problem posing and solving as being quite narrow. What are some strategies or literature that might best help broaden my contextual view?
3. I like the notion of posing an idea and not a problem. The open-endedness of it is very freeing and allows the mind to explore new possibilities and solutions. I was amazed at how many answers there were to a given idea.
4. I also thought it was very interesting, the idea that the person being asked to respond to an idea like x^2 + y^2 = z^2, was, in a sense, posing and answering their own questions and that the problem-solver imposes their own views on an idea and becomes a unique problem-poser.
5. What do you do when the a student wants the proof to an equation or principle and the explanation of the proof would be too far above that student's current knowledge level? Often times, I think math teachers are compelled to have their students take their word for it, because the beautiful simplicity of an idea is too complex to explain to the student.
6. How strongly should I be emphasizing pattern recognition, rare sequences and phenomena in amongst the standard curriculum?
7. What license do I have as a teacher to assign value/marks to a student's answer that is a unique approach/solution to the problem for which they put the wrong answer? i.e. If I want the answer 5,12,13 and I get the answer -5,-12,-13?
8. I found it very funny in the hand-shake example of the jurors, because my mind immediately jumped to the problem of how many total handshakes. I guess that is my narrow contextual perspective.
9. How far can I probe into a simple concept before I run the risk of undoing the knowledge I taught and confusing my students?
10. What IS the use of examining phenomena?
Response to Timed-write 2
Well, I wrote this timed-write really fast, so I'm not sure how accurately it portrays my feelings. But I do know that it sheds some light on what I think about my future students and what my future performance might look like. A lot of what I wrote is stuff that I've already been thinking about and trying to problem solve. I sit on the bus dreaming up ways to approach topics with kids and how to best teach difficult concepts. Some of my ideas are way out there and that's why it was easy to write a positive and negative 3rd person perspective.
With the positive perspective, hypothetically written by a former student, I wrote it in much the same style that I might have written an actual letter to my former teacher. I admired many of his attitudes on the subject of learning math and I hope to embody some of those same teaching styles. Whether a student ever realizes the quality of my instruction is immaterial, so long as they receive the benefit from a well-suited instruction and curriculum.
With the negative perspective, again written by an imaginary former student, I try to shed light on some of my fears as a new teacher. I can imagine some of my creative teaching methods as being counter-productive, confusing or only benefiting a small portion of the class. So, I'm still struggling to find the right idea, or a least a good working-idea of what an effective (interactive) teaching approach is. Plus, this negative perspective mirrors some of the comments in the positive perspective and attempts to reveal that there can often be goods and bads to any approach. There will sometimes be disparity amongst students as to who really benefits from my teaching.
So, as you can see, my focus continues to be to find an effective and interactive teaching style. I like the picture I portrayed in the positive perspective and I'm going to try to find one-on-one strategies to avoid the picture I portrayed in the negative perspective.
With the positive perspective, hypothetically written by a former student, I wrote it in much the same style that I might have written an actual letter to my former teacher. I admired many of his attitudes on the subject of learning math and I hope to embody some of those same teaching styles. Whether a student ever realizes the quality of my instruction is immaterial, so long as they receive the benefit from a well-suited instruction and curriculum.
With the negative perspective, again written by an imaginary former student, I try to shed light on some of my fears as a new teacher. I can imagine some of my creative teaching methods as being counter-productive, confusing or only benefiting a small portion of the class. So, I'm still struggling to find the right idea, or a least a good working-idea of what an effective (interactive) teaching approach is. Plus, this negative perspective mirrors some of the comments in the positive perspective and attempts to reveal that there can often be goods and bads to any approach. There will sometimes be disparity amongst students as to who really benefits from my teaching.
So, as you can see, my focus continues to be to find an effective and interactive teaching style. I like the picture I portrayed in the positive perspective and I'm going to try to find one-on-one strategies to avoid the picture I portrayed in the negative perspective.
Friday, October 2, 2009
Timed Write - 10 Years From Now
This is a futuristic scenario regarding me as a teacher 10 years from now. At this point, I've been teaching for 10 years and have had an opportunity to teach around 2000 students. The text below describes two students. To the first student, I am their favourite teacher, and to the second student, I am a failure. At this time, it will be 2019 and I'll be 31.
Student #1:
Mr. Collins is my favourite teacher this year. ...and probably ever. I love coming to his classes because he always keeps me interested in what I'm learning and makes things fun. I have to think pretty hard because he poses lots of problems, but at least I know he'll give me the answer in the end if I can't figure it out myself. But most times I can, because Mr. Collins always shows us the 'why' behind math. I'm not the best student in the class, but I still get a chance to contribute and he always has time to hear what I have to say in class. I've chatted with him after class a couple times. Once 'cause I had to ask to extend a due date on one of my math assignments (although I'd finished most of it), but the others were to ask other questions about the concepts we were learning and to show him some of my ideas. I think our class is going to do really well on the provincial this year. And not just me, but all the kids will do well. Sometimes I feel it like a race to the answer, because when he poses the problem, we all know how to approach it. Mr. Collins would make a good professor one day and it'd be cool if he could be my professor in university. The only thing would be that he wouldn't look like a professor, because he's really young.
Student #2:
Mr. Collins is the worst teacher I have this year, but unfortunately, I have no choice 'cause he's the only teacher for our grade. I hate the fact that he always goes on these long-winded speeches about stuff that isn't even important. Sometimes I feel like he forgets we're even there! Plus, he always makes us feel stupid. He makes these ridiculously hard problems and then expects everyone to get them, even though there are only a couple people in the class that are actually passing!! Basically, if you want to pass this course, you have to put in extra time and ask questions outside of class. And I don't have that kinda time. I just want to be able to learn while in the class. Plus, I'm not really interested in all the extra stuff, stuff that isn't part of the textbook. He's just adding more work on top of the work we do out of the textbook and it's not even relevant.
He has questions about spaceships and stuff that's in the future and I don't get why it's so important. Also, Mr. Collins makes us get up in front of the class and solve problems on the board. Like, what's his deal? I don't have the answer, that why I'm learning!! Yet, we have to go up their by ourselves. Sure, the class is allowed to help a bit, but I don't get to go back to my seat until I've put something on the board. Whatever, once I fail, I'll just move on. I won't have him for another course again, 'cause I'll check ahead of time, or else just drop out if I do.
Student #1:
Mr. Collins is my favourite teacher this year. ...and probably ever. I love coming to his classes because he always keeps me interested in what I'm learning and makes things fun. I have to think pretty hard because he poses lots of problems, but at least I know he'll give me the answer in the end if I can't figure it out myself. But most times I can, because Mr. Collins always shows us the 'why' behind math. I'm not the best student in the class, but I still get a chance to contribute and he always has time to hear what I have to say in class. I've chatted with him after class a couple times. Once 'cause I had to ask to extend a due date on one of my math assignments (although I'd finished most of it), but the others were to ask other questions about the concepts we were learning and to show him some of my ideas. I think our class is going to do really well on the provincial this year. And not just me, but all the kids will do well. Sometimes I feel it like a race to the answer, because when he poses the problem, we all know how to approach it. Mr. Collins would make a good professor one day and it'd be cool if he could be my professor in university. The only thing would be that he wouldn't look like a professor, because he's really young.
Student #2:
Mr. Collins is the worst teacher I have this year, but unfortunately, I have no choice 'cause he's the only teacher for our grade. I hate the fact that he always goes on these long-winded speeches about stuff that isn't even important. Sometimes I feel like he forgets we're even there! Plus, he always makes us feel stupid. He makes these ridiculously hard problems and then expects everyone to get them, even though there are only a couple people in the class that are actually passing!! Basically, if you want to pass this course, you have to put in extra time and ask questions outside of class. And I don't have that kinda time. I just want to be able to learn while in the class. Plus, I'm not really interested in all the extra stuff, stuff that isn't part of the textbook. He's just adding more work on top of the work we do out of the textbook and it's not even relevant.
He has questions about spaceships and stuff that's in the future and I don't get why it's so important. Also, Mr. Collins makes us get up in front of the class and solve problems on the board. Like, what's his deal? I don't have the answer, that why I'm learning!! Yet, we have to go up their by ourselves. Sure, the class is allowed to help a bit, but I don't get to go back to my seat until I've put something on the board. Whatever, once I fail, I'll just move on. I won't have him for another course again, 'cause I'll check ahead of time, or else just drop out if I do.
Wednesday, September 30, 2009
Reflection on MAED 314 in-class video
The video presented in class today was a real eye-opener. The grade 8 instruction felt like it was going at a snail pace and it made me remember how much different their learning is. Their speed, approach and objectives are so completetely different and it is something that I'm going to have to refamiliarize myself with if I'm going to be an effective teacher in their class. I can't go at my speed, or even close, or I will lose them for sure.
Some of our classmates commented on the slow presentation as boring, but that is just our minds adjusting to this style. We are used to fast paced information, and no time for repetition and practice. In my opinion, this was a great speed to teach at! The students certainly didn't seem bored! In fact, those students seemed completely absorbed in the process. The teacher was teaching to the slowest student and making sure everyone was on board. I was very impressed with that. In the space of 20min, he had successfully introduced the concept of algebra in an interactive, engaging and relational way. He had given the students the skills to perform algebra slowly and incrementally so that they all got it. He made the knowledge linear and broke it into small enough pieces.
I am very impressed. I plan on using some of his approaches in introducing concepts to my students in the future.
Some of our classmates commented on the slow presentation as boring, but that is just our minds adjusting to this style. We are used to fast paced information, and no time for repetition and practice. In my opinion, this was a great speed to teach at! The students certainly didn't seem bored! In fact, those students seemed completely absorbed in the process. The teacher was teaching to the slowest student and making sure everyone was on board. I was very impressed with that. In the space of 20min, he had successfully introduced the concept of algebra in an interactive, engaging and relational way. He had given the students the skills to perform algebra slowly and incrementally so that they all got it. He made the knowledge linear and broke it into small enough pieces.
I am very impressed. I plan on using some of his approaches in introducing concepts to my students in the future.
Monday, September 28, 2009
Battleground Schools (Summary & Reflection)
Summary:
This article addresses many of the problems that face the system of education of math curriculum in public schools. Primarily, there is a clash between progressive and conservative thinkers on the transmission of knowledge from teacher to student and what math skills should be the focus of instruction. Also, there is a recurring theme of prejudice, misconception and fear of mathematics that has a cripling effect as it propagates through the generations. It is not only socially acceptable to be mathematically illiterate, but there are students and teachers alike who pass through the education system without ever really understanding fundamental secondary math concepts. In this way, there are many math teachers who do not possess the skills to properly instruct their students in math and who are excused on the grounds that the textbook is considered 'teacher-proof'.
In the early 20th century (1910-1940), a Progressivist Reform sought to bring about the unification of knowledge and application. This meant using an inquiry-based approach to learning that had largely been ignored before. This included the facilitation and orchestration of student supported inquiries into learning. Then, in the 60s, spurred on by the launch of Russian spacecraft, the 'space race' became a national issue in America as an unmet demand for qualified and educated scientists was realized. This 'New Math' initiative saw the rewriting of mathematical structure to be based more on set theory. But many teachers struggled to adapt to the new changes and in the 70s, the popular media was denouncing it. Now (1990-present), there is a real reigning-in on teaching standards in an attempt to implement a 'back-t0-basics' approach that lessens the autonomy of teachers and holds them more accountable. The National Council of Teachers of Math (NCTM) produced a definitive set of standards in 2000.
Response:
This article had a lot that needed digesting. I can imagine that there would be incredible difficulties in moderating and regulating the instruction of any subject, but with math, it must be that much more difficult. Not only is it a subject that many people aren't fluent with, but because it is logically driven, discrepancies must be extremely difficult to resolve. If two teachers each believe their competing interpretations of the rules of math are correct, then there is little persuading them. Also, when it comes to the level of autonomy of teachers in the class room, I don't know where I stand. I know that it is essential that no detail of math instruction (either relational or instrumental) be left out, but at the same time, I don't want teachers acting as textbook paraphrasers either. That is why provincial exams are a good idea, because it holds the teachers within the bounds of the material covered therein. What I would like to see is an increase in the expectation of math students and teachers. If we can raise the standard (create a new trend of achivement), then all future generations can benefit.
This article addresses many of the problems that face the system of education of math curriculum in public schools. Primarily, there is a clash between progressive and conservative thinkers on the transmission of knowledge from teacher to student and what math skills should be the focus of instruction. Also, there is a recurring theme of prejudice, misconception and fear of mathematics that has a cripling effect as it propagates through the generations. It is not only socially acceptable to be mathematically illiterate, but there are students and teachers alike who pass through the education system without ever really understanding fundamental secondary math concepts. In this way, there are many math teachers who do not possess the skills to properly instruct their students in math and who are excused on the grounds that the textbook is considered 'teacher-proof'.
In the early 20th century (1910-1940), a Progressivist Reform sought to bring about the unification of knowledge and application. This meant using an inquiry-based approach to learning that had largely been ignored before. This included the facilitation and orchestration of student supported inquiries into learning. Then, in the 60s, spurred on by the launch of Russian spacecraft, the 'space race' became a national issue in America as an unmet demand for qualified and educated scientists was realized. This 'New Math' initiative saw the rewriting of mathematical structure to be based more on set theory. But many teachers struggled to adapt to the new changes and in the 70s, the popular media was denouncing it. Now (1990-present), there is a real reigning-in on teaching standards in an attempt to implement a 'back-t0-basics' approach that lessens the autonomy of teachers and holds them more accountable. The National Council of Teachers of Math (NCTM) produced a definitive set of standards in 2000.
Response:
This article had a lot that needed digesting. I can imagine that there would be incredible difficulties in moderating and regulating the instruction of any subject, but with math, it must be that much more difficult. Not only is it a subject that many people aren't fluent with, but because it is logically driven, discrepancies must be extremely difficult to resolve. If two teachers each believe their competing interpretations of the rules of math are correct, then there is little persuading them. Also, when it comes to the level of autonomy of teachers in the class room, I don't know where I stand. I know that it is essential that no detail of math instruction (either relational or instrumental) be left out, but at the same time, I don't want teachers acting as textbook paraphrasers either. That is why provincial exams are a good idea, because it holds the teachers within the bounds of the material covered therein. What I would like to see is an increase in the expectation of math students and teachers. If we can raise the standard (create a new trend of achivement), then all future generations can benefit.
Sunday, September 27, 2009
Re: Student/Teacher Interviews
Wow... what interesting responses! This has certainly given me a lot to think about. I like the fact that we managed to pose these questions with little overlap between student and teacher responses, so that we could learn as much as possible. The students (all from different schools, cities, backgrounds) gave good reviews of their teachers and that is encouraging to know that they are doing a good job. A couple obvious challenges still to overcome in the classroom and certainly traps that we will be looking out for during our practicum. The teacher gave some good advice and some nice ideas & guidelines for getting started in the classroom. Plus, it's nice to know that we have a resource to look to in the years to come; that there are teachers out there that are willing to help us as we step into the classroom. Now... off we go!
5 Burning Questions to Math Teachers and Math Students (Answered)
5 Burning Questions to Math Teachers and Math Students
Below are the answers we received from our willing student and teacher participants. The answers are candid, honest and anonymous:
Answers:
Teacher:
1. I am much busier at the full time job. Lesson preparation is the most time consuming thing. Lesson plans don't actually get written on the job. For class management, it is easier to be strict at first, then ease up later rather than the other way around. Seating plans can be very useful to break up chatting kids, although I don't use them that often.
2. Students will usually get 20-40 min. of seat work depending on the lesson. It is difficult to avoid a lot of talking and notes but I try to vary it with activities. Things like math bingo work well as a transition from notes to seat work.
3. In math, I don't use much... algebra tiles are stupid. Only when I get to geometry and surface area do I use solids to show concepts. I try to do many short lab-like activities where kids physically measure stuff with rulers or stopwatches. It is important to get them out of the seat once in a while.
4. I typically try to mimic the textbook, although for physics I don't even use the text and then I go with what is in the IRP's or whatever they'll encounter in university. You must keep notation simple. They will get lost at something so simple as f(x) = g(x) and then you lose them entirely.
5. Yes. It's difficult in practice when you are a new teacher and already have enough preparation and marking. Just be patient and offer you time outside of class. Peer tutors are useful if your school has them.
Students:
Student #1:
Grade 9
1. I'm pretty comfortable and math is one of my favourite subjects and I'm comfortable because it isn't super hard and I know how to sorta do it.
2. I remember most of it. It will have to do with my future a lot because it is how to pay taxes and how to know how much space there is in a room so I can place a rug or something in it.
3. Not really slowly, because they want it to get done but you can always come after school and ask for help on the stuff we just covered.
4. Not to much, because it was all really easy and in class we covered much harder stuff.
5. He would do the math for us, not explain and tell us to just do the work sheet.
Student #2:
Grade 12
1. I don't mind math once I grasp the concept, but I have to study hard to completely understand.
2. I remember most of last year's curriculum because most of it applies to this year's course. I don't see much use in this knowledge in the future because I'm not looking into any professions involving a lot of math.
3. Yes, my teacher went at a comfortable pace for me and he covered all the material needed for the exam.
4. I improved my grade with the final exam
5. What I didn't like about my previous teacher's instructing style was that he didn't really like going over the homework if we didn't understand.
Student #3:
Grade 9
1. I actually really enjoy math and I'm mostly comfortable using it because I find it sometimes fun and I understand it.
2. I don't remember everything but I remember a lot of it. A lot of it is important for the future because it was about taxes, fractions and other things that will be helpful for the future.
3. Yeah, she was very good and went over things if people didn't understand. She covered all the material very well.
4. The final exam helped my final grade a lot because it was easier than the work we did in class.
5. She was pretty good but she had a really quiet voice so I had to sit at the front. Other than that, she was a really good teacher.
Student #4:
Grade 11
1. I enjoy math to some extent, I usually don't understand it so I'm not comfortable with using it.
2. My brain likes to do this thing called erasing all memories of things I don't understand or like during the summer... so I don't remember much. I remember learning about certain things, but I don't remember how to do them. I see a use for some of the stuff, but I really don't see when I will need to do factoring and stuff.
3. My teacher went at a very good pace and covered all and more material then was required for our exam.
4. I have to say my exam wasn't even close to representing my course mark. I was getting a solid B (76%) iin the course and then proceeded to get a fabulous 57% on my exam.
5. My math teachers is one of the best around. I don't think there is anything I don't like about his teaching method. Though, he does like to just give us the basic rules of the problem and then we have to take what he showed us and use the same concept for the harder questions. This is one thing that I am still having difficulty with, but that is just me.
Student #5:
Grade 9
1. I really, really like math except last year the text book was all about drawing diagrams and I didn't learn anything so I wouldn't be comfortable using math everyday.
2. I only remember the equations, not the diagrams which would be helpful in the future.
3. My math teacher went way too slow so the whole class began to lose interest and when the finals rolled along, we weren't ready.
4. I did pretty well, it raised my mark a lot, but everyone else who was in our class scored lower than the average mark.
5. I didn't like how my teacher gave notes without explaining them.
Below are the answers we received from our willing student and teacher participants. The answers are candid, honest and anonymous:
Answers:
Teacher:
1. I am much busier at the full time job. Lesson preparation is the most time consuming thing. Lesson plans don't actually get written on the job. For class management, it is easier to be strict at first, then ease up later rather than the other way around. Seating plans can be very useful to break up chatting kids, although I don't use them that often.
2. Students will usually get 20-40 min. of seat work depending on the lesson. It is difficult to avoid a lot of talking and notes but I try to vary it with activities. Things like math bingo work well as a transition from notes to seat work.
3. In math, I don't use much... algebra tiles are stupid. Only when I get to geometry and surface area do I use solids to show concepts. I try to do many short lab-like activities where kids physically measure stuff with rulers or stopwatches. It is important to get them out of the seat once in a while.
4. I typically try to mimic the textbook, although for physics I don't even use the text and then I go with what is in the IRP's or whatever they'll encounter in university. You must keep notation simple. They will get lost at something so simple as f(x) = g(x) and then you lose them entirely.
5. Yes. It's difficult in practice when you are a new teacher and already have enough preparation and marking. Just be patient and offer you time outside of class. Peer tutors are useful if your school has them.
Students:
Student #1:
Grade 9
1. I'm pretty comfortable and math is one of my favourite subjects and I'm comfortable because it isn't super hard and I know how to sorta do it.
2. I remember most of it. It will have to do with my future a lot because it is how to pay taxes and how to know how much space there is in a room so I can place a rug or something in it.
3. Not really slowly, because they want it to get done but you can always come after school and ask for help on the stuff we just covered.
4. Not to much, because it was all really easy and in class we covered much harder stuff.
5. He would do the math for us, not explain and tell us to just do the work sheet.
Student #2:
Grade 12
1. I don't mind math once I grasp the concept, but I have to study hard to completely understand.
2. I remember most of last year's curriculum because most of it applies to this year's course. I don't see much use in this knowledge in the future because I'm not looking into any professions involving a lot of math.
3. Yes, my teacher went at a comfortable pace for me and he covered all the material needed for the exam.
4. I improved my grade with the final exam
5. What I didn't like about my previous teacher's instructing style was that he didn't really like going over the homework if we didn't understand.
Student #3:
Grade 9
1. I actually really enjoy math and I'm mostly comfortable using it because I find it sometimes fun and I understand it.
2. I don't remember everything but I remember a lot of it. A lot of it is important for the future because it was about taxes, fractions and other things that will be helpful for the future.
3. Yeah, she was very good and went over things if people didn't understand. She covered all the material very well.
4. The final exam helped my final grade a lot because it was easier than the work we did in class.
5. She was pretty good but she had a really quiet voice so I had to sit at the front. Other than that, she was a really good teacher.
Student #4:
Grade 11
1. I enjoy math to some extent, I usually don't understand it so I'm not comfortable with using it.
2. My brain likes to do this thing called erasing all memories of things I don't understand or like during the summer... so I don't remember much. I remember learning about certain things, but I don't remember how to do them. I see a use for some of the stuff, but I really don't see when I will need to do factoring and stuff.
3. My teacher went at a very good pace and covered all and more material then was required for our exam.
4. I have to say my exam wasn't even close to representing my course mark. I was getting a solid B (76%) iin the course and then proceeded to get a fabulous 57% on my exam.
5. My math teachers is one of the best around. I don't think there is anything I don't like about his teaching method. Though, he does like to just give us the basic rules of the problem and then we have to take what he showed us and use the same concept for the harder questions. This is one thing that I am still having difficulty with, but that is just me.
Student #5:
Grade 9
1. I really, really like math except last year the text book was all about drawing diagrams and I didn't learn anything so I wouldn't be comfortable using math everyday.
2. I only remember the equations, not the diagrams which would be helpful in the future.
3. My math teacher went way too slow so the whole class began to lose interest and when the finals rolled along, we weren't ready.
4. I did pretty well, it raised my mark a lot, but everyone else who was in our class scored lower than the average mark.
5. I didn't like how my teacher gave notes without explaining them.
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