These reports are done for all students who have an average of 50 or less. It is also done, if time permits, for students who are between 51 and 55. This policy is from the Vancouver School Board, and it varies from district to district. If they were failing in Term 1, they not necessarily have it, although some parents may request an intern report EVERY month. Be careful with the info you disclose ( class average of diverse students)
We also talked about adaptations for students with special needs. For example, ESL students are allowed to use electronic dictionary. Other special ed students may be allowed extra time in tests.
Sunday, January 31, 2010
Lesson plan submission
Lesson plans should be submitted 4 days in advance. They will be amended, resubmitted and changes should be implemented during instruction. Lessons should have Intro (pre-requisite, review, warm up puzzle), core (new material) and conclusion (summary, assign homework)
We needs something for marking every week: Quiz, class activity, can be more in order to get an idea where they're at, go to the board in pairs. The point is to assess their learning. 2 things is better. Introduce new approaches to educational (MAED 314, Thinking Mathematically, Week plan and lesson plans. For the week plans just write about the three moments of class. Look at textbook: exercises type "a" (easy), "b" (medium), and "c" (difficult) Bring something interesting.
Look for my questioning techniques. Conclusions: a game, perhaps?, summary. Think of ways of arranging the class environment.
These are the chapters I will teach:
Ch 6 - 6.4, 6.6
Ch 7 - 7.1, 7.2, 7.3 (know theorems but not proving (ktbnp)), 7.4, 7.5 (ktbnp)
Ch 8 - 8.1, 8.2 (ktbnp), p 480 is important, 8.3, 8.4 (ktbnp), 8.5, 8.6
We needs something for marking every week: Quiz, class activity, can be more in order to get an idea where they're at, go to the board in pairs. The point is to assess their learning. 2 things is better. Introduce new approaches to educational (MAED 314, Thinking Mathematically, Week plan and lesson plans. For the week plans just write about the three moments of class. Look at textbook: exercises type "a" (easy), "b" (medium), and "c" (difficult) Bring something interesting.
Look for my questioning techniques. Conclusions: a game, perhaps?, summary. Think of ways of arranging the class environment.
These are the chapters I will teach:
Ch 6 - 6.4, 6.6
Ch 7 - 7.1, 7.2, 7.3 (know theorems but not proving (ktbnp)), 7.4, 7.5 (ktbnp)
Ch 8 - 8.1, 8.2 (ktbnp), p 480 is important, 8.3, 8.4 (ktbnp), 8.5, 8.6
Wednesday, December 2, 2009
Dave Hewitt's Video
I watched Dave Hewitt's video a long time ago. Today I tried, in vain, to look it up online through YouTube. Nonetheless, I shall embark on discussing the video and the ideas presented there.
One thing I still remember was the way he tapped with his stick on the board, and a little bit of theatricality (is that a word? yes, just checked it online), to have students understand the number line and the order of numbers. I think it was a good way because you can see the whole collective engaged at the same time in learning and showing to the teacher that they knew. It was also a non-intimidating way to give students who are falling behind an opportunity to catch up with the rest of their classmates. When they are responding to the teachers prompts is virtually impossible to realize who made a mistake, who didn't... etc. Also, when the collective made a mistake there was no visible students who could be ashamed or not even made to stand out.
Furthermore, the teacher found a seamless way to introduce a concept of unknown and of variable.
One thing I still remember was the way he tapped with his stick on the board, and a little bit of theatricality (is that a word? yes, just checked it online), to have students understand the number line and the order of numbers. I think it was a good way because you can see the whole collective engaged at the same time in learning and showing to the teacher that they knew. It was also a non-intimidating way to give students who are falling behind an opportunity to catch up with the rest of their classmates. When they are responding to the teachers prompts is virtually impossible to realize who made a mistake, who didn't... etc. Also, when the collective made a mistake there was no visible students who could be ashamed or not even made to stand out.
Furthermore, the teacher found a seamless way to introduce a concept of unknown and of variable.
Tuesday, November 24, 2009
Story from the Practicum
It took me a while to post this to my blog. Nevertheless, here it goes.
The title of my story is "School Advisors"
I did not have a good story to tell about my practicum that included students and student-teachers interaction. Now, that might be good, if we look at it as "no news, good news." On the other hand, there were a few happenings that concerned my school advisors.
During my interview with my Faculty Advisor, Katharine Borgen, I was informed that my two school advisors were going to be Seema and Tanya. Then my FA asked me whether I taught Computer Science as well as math. I informed her that no. She then responded to me that she knew Seema and that in fact she knew that Seema was not teaching any other subject this year except CS. So most likely I would have to be assigned to another SA. When I got to the school, Seema asked another teacher, right then and there, if he wanted to have a student teacher. His name is Greg and he accepted. Tanya, he informed me, was on "mat leave," but was due to come back next week. So I worked for the first week with Greg by observing some of his classes and teaching a few. On the next week, I got to meet Tanya. She just came back from Mat leave and asked me if I was willing to teach a class for her. That was Tuesday, and on Wednesday I taught a class. It went relatively well. On that same day, the SAs and Student teachers met with the FA. Katharine told us that we needed to balance the classes so that none of us student teachers would get too many preps. So it ended up being that I would not work with Tanya nor Seema, but Esther, a teacher that I had only observed on a couple of classes, and Greg.
I think that my practicum is going to go well. I like both of my SA's and they seem to be very supportive. Greg gave me very specific feedback, which was something I was expecting from the practicum.
The title of my story is "School Advisors"
I did not have a good story to tell about my practicum that included students and student-teachers interaction. Now, that might be good, if we look at it as "no news, good news." On the other hand, there were a few happenings that concerned my school advisors.
During my interview with my Faculty Advisor, Katharine Borgen, I was informed that my two school advisors were going to be Seema and Tanya. Then my FA asked me whether I taught Computer Science as well as math. I informed her that no. She then responded to me that she knew Seema and that in fact she knew that Seema was not teaching any other subject this year except CS. So most likely I would have to be assigned to another SA. When I got to the school, Seema asked another teacher, right then and there, if he wanted to have a student teacher. His name is Greg and he accepted. Tanya, he informed me, was on "mat leave," but was due to come back next week. So I worked for the first week with Greg by observing some of his classes and teaching a few. On the next week, I got to meet Tanya. She just came back from Mat leave and asked me if I was willing to teach a class for her. That was Tuesday, and on Wednesday I taught a class. It went relatively well. On that same day, the SAs and Student teachers met with the FA. Katharine told us that we needed to balance the classes so that none of us student teachers would get too many preps. So it ended up being that I would not work with Tanya nor Seema, but Esther, a teacher that I had only observed on a couple of classes, and Greg.
I think that my practicum is going to go well. I like both of my SA's and they seem to be very supportive. Greg gave me very specific feedback, which was something I was expecting from the practicum.
Wednesday, November 11, 2009
Two Column Approach to solve a problem
Hey guys, here is my solution to the "Black Friday" problem from the book "Thinking Mathematically"
Wednesday, November 4, 2009
Assessing the Book:
Applied Mathematics 12
SOURCE BOOK
The book is not very heavy, for a textbook. It is not very thick; it has only 420 pages. It would be easy for students to carry it from class to class because the size of the pages is even smaller than letter size.
This seems to be a very durable book because it has a hard cover and the pages are shiny. The binding is already giving up a little and I can imagine that the spine might split from the rest of the book in a few years, but overall this book is stern.
It doesn't smell much, which is good for a textbook. The pages are shiny and the colors used in the pictures are pleasing. The book has not been rebounded and it doesn't seem like anybody has altered it. It has not student-markings.
The book was published in 2002 in Toronto, Ontario by Pearson Education. I don't know any of the authors. They are mostly from Alberta and BC Universities.
This is the "source" book and it seems like it is supposed to be used along with another textbook, the "project" book because in the introduction it includes instructions on how to use both.
The table of contents tells you the name of the chapters and the lessons into which each chapter is divided, and the page where you can find them of course. It does not have a glossary, but instead it has a "Student Reference." It does have an Index and answer sheets. There are no supplementary problems. It has projects which could be used as enrichment material.
It has a good design with many colored illustrations of the concepts that the students must learn. It has many photos, diagrams, and illustrations. Yes it has all the IRP requirements. It has no logical sequence of chapters, but within each chapter there is a logical procedure.
The important concepts are not highlighted in the text part of the textbook. It has, though, boxes where they lay important explanations and/or definitions of concepts.
SOURCE BOOK
The book is not very heavy, for a textbook. It is not very thick; it has only 420 pages. It would be easy for students to carry it from class to class because the size of the pages is even smaller than letter size.
This seems to be a very durable book because it has a hard cover and the pages are shiny. The binding is already giving up a little and I can imagine that the spine might split from the rest of the book in a few years, but overall this book is stern.
It doesn't smell much, which is good for a textbook. The pages are shiny and the colors used in the pictures are pleasing. The book has not been rebounded and it doesn't seem like anybody has altered it. It has not student-markings.
The book was published in 2002 in Toronto, Ontario by Pearson Education. I don't know any of the authors. They are mostly from Alberta and BC Universities.
This is the "source" book and it seems like it is supposed to be used along with another textbook, the "project" book because in the introduction it includes instructions on how to use both.
The table of contents tells you the name of the chapters and the lessons into which each chapter is divided, and the page where you can find them of course. It does not have a glossary, but instead it has a "Student Reference." It does have an Index and answer sheets. There are no supplementary problems. It has projects which could be used as enrichment material.
It has a good design with many colored illustrations of the concepts that the students must learn. It has many photos, diagrams, and illustrations. Yes it has all the IRP requirements. It has no logical sequence of chapters, but within each chapter there is a logical procedure.
The important concepts are not highlighted in the text part of the textbook. It has, though, boxes where they lay important explanations and/or definitions of concepts.
Saturday, October 17, 2009
Reflection on "Division by Zero"
I think it is a good activity to have students free-write about "divide" for four minutes and then have them do the same for the number zero. I think it is a different approach and students appreciate having something different to do in a math class. Usually they are asked to solve problems, find answers, calculate things, fill out worksheets. . . etc. But this activity stands out. It makes the student reflect about their notions of division and of zero and once you explain that the division by zero is not valid in mathematics they will be ready to talk more and understand better this special suituation.
A poem
Divide by zero and see what you get
the smaller the number the greater result
no business dividing by zero
throw out the idea
separate an apple
among all your friends
separate one unit
but among zero?
not cool
not cool
Zero. four minutes worth of free writing
Zero is a cruel number. When you have zero it means you have nothing. When you put zero effort into something it's as if you had done absolutely nothing. Zero can also make something into nothing. If you multiply by zero ANY QUANTITY it will turn into zero. So zero not a good thing. Unless you have something bad. If you have something bad then you want to have zero of it. Or if you have potential to do something bad you need to put zero effort into it and multiply it and then you get zero of that bad thing. Zero is a round number because other numbers throw them zeros around and they roll. What goes in the middle of zero? Nothing. That is a good way to remember its value. Some numbers like to collect their zeros and put them to the right. On the left of the number it's as if they were too late; they don't get to count or value. Zero: a good thing on the right, not good on left.
Divide 4 minutes worth of free writing
Dividing is no good among people. It's OK in mathematics. It means to separate, to do less. But when you divide by a smaller number than one then you might get a bigger number than what you started with, provided it is a number greater than one. One seems to be a very important number when it comes to dividing. If you divide by one it's as if you had done absolutely nothing. When you divide in the real world you usually end up with less. If somebody asked you to divide your sandwich, you might end up with half of it. Dividing in the real world: not so much a good thing, although sharing is important. In Mathematics it is OK, as long as you don't divide by zero.
Wednesday, October 14, 2009
Reflection on the Micro-Lesson (Assignment 2)
One of the things I enjoyed was listening to my fellow students say things like "Oh..." and the way they said it tells me that there is something going on in their heads. Maybe they saw something they had never thought of before, or saw a thing they had seen before but in a different way.
On the other hand I think there were a few things that could have gone better. I think that the delivery of our lesson was not very well organized. I think that there were times when one of us talked too much and when we interrupted each other. That was because we did not plan it thoroughly before. I think that if we had taken more time to plan the lesson and divide more specifically what each one of us was going to do and say, our presentation would have gone much better.
I liked the way we got the students engaged in learning. I think that manipulatives are a great way to give students something to do. The student feel more comfortable doing math, because they can rely on a concrete image to go further in their mathematical development. The manipulatives do not intimidate the student and facilitate the transition from the concrete to the abstract. In this case it helped us go from operations with areas of rectangles to algebraic expressions. Another thing I noticed is that you, as a teacher, have to let the students play for a little while with the manipulatives once you have given them the manipulatives for the first time. If you don't let them play, they will be playing with them when you are trying to explain something. This is why I think that manipulatives take a lot more time than regular lecturing and worksheets, but in the end the benefits are more fruitful.
On the other hand I think there were a few things that could have gone better. I think that the delivery of our lesson was not very well organized. I think that there were times when one of us talked too much and when we interrupted each other. That was because we did not plan it thoroughly before. I think that if we had taken more time to plan the lesson and divide more specifically what each one of us was going to do and say, our presentation would have gone much better.
I liked the way we got the students engaged in learning. I think that manipulatives are a great way to give students something to do. The student feel more comfortable doing math, because they can rely on a concrete image to go further in their mathematical development. The manipulatives do not intimidate the student and facilitate the transition from the concrete to the abstract. In this case it helped us go from operations with areas of rectangles to algebraic expressions. Another thing I noticed is that you, as a teacher, have to let the students play for a little while with the manipulatives once you have given them the manipulatives for the first time. If you don't let them play, they will be playing with them when you are trying to explain something. This is why I think that manipulatives take a lot more time than regular lecturing and worksheets, but in the end the benefits are more fruitful.
Lesson Plan - Factoring
Bridge: By introducing students to the manipulative of algebra tiles in an associative style, we will demonstrate the idea and some simple mechanics behind factoring before actually addressing it in a purely mathematical sense.
Learning Outcomes: Students will gain a hands on association to the mechanics of factoring, which will supply them with an insightful experience to relate to the larger problem of factoring quadratic equations.
Teaching Outcomes: To have the students actively participate in a creative group effort. Expand students experience with mathematics. Learn from the students experiences with the manipulatives.
Pretest: Ask students what kind of simple geometric shapes can be made with the manipulatives. What methods are there to finding the area of those shapes.
Participation: Students will work in groups to form various rectangles with the manipulatives, noting different configurations of their classmates. By introduction the notion of variables as lengths of some manipulatives, students will be asked various ways to find the area of their rectangles.
Post Test: Inquire to students what kind of rectangles were created, and how the areas related to the length and width of the rectangles. Stress the use of symbolic equations in the final steps of their exploration.
Summary: Have students note the findings of their group, the relation between the length and width, and the total area of the rectangle. From this demonstrate that through symbolic equations what they've been doing is factoring simple quadratics.
Learning Outcomes: Students will gain a hands on association to the mechanics of factoring, which will supply them with an insightful experience to relate to the larger problem of factoring quadratic equations.
Teaching Outcomes: To have the students actively participate in a creative group effort. Expand students experience with mathematics. Learn from the students experiences with the manipulatives.
Pretest: Ask students what kind of simple geometric shapes can be made with the manipulatives. What methods are there to finding the area of those shapes.
Participation: Students will work in groups to form various rectangles with the manipulatives, noting different configurations of their classmates. By introduction the notion of variables as lengths of some manipulatives, students will be asked various ways to find the area of their rectangles.
Post Test: Inquire to students what kind of rectangles were created, and how the areas related to the length and width of the rectangles. Stress the use of symbolic equations in the final steps of their exploration.
Summary: Have students note the findings of their group, the relation between the length and width, and the total area of the rectangle. From this demonstrate that through symbolic equations what they've been doing is factoring simple quadratics.
Tuesday, October 13, 2009
Citizenship Education in the Context of School Mathematics
How will I make my class a place where students learn to be a democratic citizen?
I think that, as teachers, we usually lose focus on what our real goal in the classroom is. We are not there to throw knowledge to the students and then assign them grades according to how much they get. Our job is to help them understand the world around them, and how they as students can affect that world. In other words, how they can use what they learn in school to go out and affect their families, their own and other communities, their country and the global community.
In my class I will make sure to have discussions taking place. I think that students need to be able to explain their understandings to the rest of the class so that they learn to make, and at the same time understand, political statements and arguments.
I will also try to incorporate current events into the classroom and show them with a mathematics perspective. For example, we can discuss the current unemployment rate and make arguments on what does this mean and make predictions as to what would happen if it grows or decreases.
I will try to encourage students to build arguments, but in a respectful manner. They need to be able to listen to other students’ opinions and enrich and form one of their own. I will value critical thinking, more so than just getting the "right answer." I will focus on the "how" and the "why." I will emphasize that mathematics is not about totality where an answer is either wrong or right because that would translate into their own minds as if they were able to think right or wrong.
I think that, as teachers, we usually lose focus on what our real goal in the classroom is. We are not there to throw knowledge to the students and then assign them grades according to how much they get. Our job is to help them understand the world around them, and how they as students can affect that world. In other words, how they can use what they learn in school to go out and affect their families, their own and other communities, their country and the global community.
In my class I will make sure to have discussions taking place. I think that students need to be able to explain their understandings to the rest of the class so that they learn to make, and at the same time understand, political statements and arguments.
I will also try to incorporate current events into the classroom and show them with a mathematics perspective. For example, we can discuss the current unemployment rate and make arguments on what does this mean and make predictions as to what would happen if it grows or decreases.
I will try to encourage students to build arguments, but in a respectful manner. They need to be able to listen to other students’ opinions and enrich and form one of their own. I will value critical thinking, more so than just getting the "right answer." I will focus on the "how" and the "why." I will emphasize that mathematics is not about totality where an answer is either wrong or right because that would translate into their own minds as if they were able to think right or wrong.
Thursday, October 8, 2009
The Art of Problem Posing
"What if Not"
I think that the advantage of using the "What if Not" (WIN) strategies is that the teacher can come up with interesting questions. Students are very used to the obvious questions. If the topic being covered is right triangles, then they expect to work around the same type of problems, such as "using the Pythagorean theorem, find the missing lenghts... find the missing angles, find the area..." and they all sound the same, are predictable, and no wonder the students end up being bored. If on the other hand you present the student with a question that seems completely different from what they had heard before you run the risk of having the student engaged into learning.
The way I would use WIN strategy would be when I am coming up with "good" questions when I am lesson planning. A good question has multiple approaches and can lead to rich conversations with many different topics, and at the same time, can serve for the purpose of assessing student progress. I could also use WIN strategies when coming up with a class project. One question might be challenging enough for students to take time, and, why not?, group effort to solve it and then present it to the rest of the class. I think that if I could frame a WIN question with the right real world story behind it, the students might feel motivated to work the problem ahead of them with diligence, enthusiasm, excitement and curiosity as to how the problem is solved.
I think that one weakness of this strategy is that if not thoght thoroughly, when a teacher uses WIN strategies the questions that might arise might not be meaningful or interesting enough. So I think that is why the author even warns the reader on coming up with this questions in a mechanical or automatic way.
I think that the advantage of using the "What if Not" (WIN) strategies is that the teacher can come up with interesting questions. Students are very used to the obvious questions. If the topic being covered is right triangles, then they expect to work around the same type of problems, such as "using the Pythagorean theorem, find the missing lenghts... find the missing angles, find the area..." and they all sound the same, are predictable, and no wonder the students end up being bored. If on the other hand you present the student with a question that seems completely different from what they had heard before you run the risk of having the student engaged into learning.
The way I would use WIN strategy would be when I am coming up with "good" questions when I am lesson planning. A good question has multiple approaches and can lead to rich conversations with many different topics, and at the same time, can serve for the purpose of assessing student progress. I could also use WIN strategies when coming up with a class project. One question might be challenging enough for students to take time, and, why not?, group effort to solve it and then present it to the rest of the class. I think that if I could frame a WIN question with the right real world story behind it, the students might feel motivated to work the problem ahead of them with diligence, enthusiasm, excitement and curiosity as to how the problem is solved.
I think that one weakness of this strategy is that if not thoght thoroughly, when a teacher uses WIN strategies the questions that might arise might not be meaningful or interesting enough. So I think that is why the author even warns the reader on coming up with this questions in a mechanical or automatic way.
Sunday, October 4, 2009
Comments, Questions on "The Art of Problem Posing"
1. Asking students to pose problems has really changed the way I perceive teaching mathematics. It has opened unlimited possibilites for studentsto show their mathematical abilities. I was teaching English in Korea for a few weeks, and teaching English was, at that time, something new for me. My wife is an English teacher and so I borrowed many of her strategies for teaching English. One of those strategies was to ask students to write a "K W L" for each piece of literature as they read it. The "K" stands for Know and so you would write what you already know. The "W" stands for Wonder, and so you would write what you wonder about, and it could be in a form of a question. The "L" stands for what you learned. After asking the students to come up with questions for the "W" column about what they were reading I realized what a powerful tool this is. I was not asking students, on that column, what they knew or prove that you know something, which would have made them feel obligated to bring up something that would be seen as wrong or right. But by coming up with a question, usually about a story we were reading, the student was implicitly showing me that they understood the story.
2. When you ask a student to pose a problem, how do you evaluate him or her? I would think pass or fail. But it is complicated because the teacher is going to go through each problem posed by the kid, think about it and determine whether the student really understood or only paraphrased a problem from the textbook.
3. Are some observations made on a simple statement as "x^2 + y^2 = z^2" more valuable than others?
4. When one comes up with a question, the nature of the question should reflect the level of undarstanding, but it is difficult to judge that.
5. How do the two meanings of undertanding, relational understanding, play into the "Art of Problem Posing"?
6. Is the author aware of the difference between "relational" and "instrumental" understanding?
7. Why does he think that Problem Posing has not taken off in the curriculum and therefore in the majority of the classrooms in North America?
8. Are we going to find great problems in this book?
9. I appreciate the fact that the authors take their time to explain what the book is about, how to read it and who is it directed to (audience).
10. I am really enjoying reading this book, although at some point it can get too hard to understand.
2. When you ask a student to pose a problem, how do you evaluate him or her? I would think pass or fail. But it is complicated because the teacher is going to go through each problem posed by the kid, think about it and determine whether the student really understood or only paraphrased a problem from the textbook.
3. Are some observations made on a simple statement as "x^2 + y^2 = z^2" more valuable than others?
4. When one comes up with a question, the nature of the question should reflect the level of undarstanding, but it is difficult to judge that.
5. How do the two meanings of undertanding, relational understanding, play into the "Art of Problem Posing"?
6. Is the author aware of the difference between "relational" and "instrumental" understanding?
7. Why does he think that Problem Posing has not taken off in the curriculum and therefore in the majority of the classrooms in North America?
8. Are we going to find great problems in this book?
9. I appreciate the fact that the authors take their time to explain what the book is about, how to read it and who is it directed to (audience).
10. I am really enjoying reading this book, although at some point it can get too hard to understand.
Friday, October 2, 2009
Hey you!
Yo,
I did not appreciate being in your class. I was late most of the time and you gave me a total hard time about it. I did not learn nothing. So thanks a lot for wasting my time!
You only cared about math and not about me. I am not good when it comes to math, ok? but I am good for other things and, contrary to what you might think, not everything in life is about math!
I think there was not a single day that I said, "Gees, I'm glad I went into Mr. R's class 'cause I learned something." No. It was always: "What a drag this class is! And what a waste of time!!" 'cause that's exactly what it was.
Anyway, I am out of your class and happy about it. I hope I don't cross paths with you, or better said, if I ever see you on the street, beware! 'cause there's gonna be me, with a bat, and ready to smash your "brilliant" head.
Sincerely,
Me, your EX-student.
I did not appreciate being in your class. I was late most of the time and you gave me a total hard time about it. I did not learn nothing. So thanks a lot for wasting my time!
You only cared about math and not about me. I am not good when it comes to math, ok? but I am good for other things and, contrary to what you might think, not everything in life is about math!
I think there was not a single day that I said, "Gees, I'm glad I went into Mr. R's class 'cause I learned something." No. It was always: "What a drag this class is! And what a waste of time!!" 'cause that's exactly what it was.
Anyway, I am out of your class and happy about it. I hope I don't cross paths with you, or better said, if I ever see you on the street, beware! 'cause there's gonna be me, with a bat, and ready to smash your "brilliant" head.
Sincerely,
Me, your EX-student.
Your student, Bart
Hi,
I was your student about 4 years ago, in 2015. I just want to say that I really enjoyed your class and at the same time I learned a lot. I enjoyed your class because it was really interesting. Even if the topic being covered was not very interesting, you found a way in presenting it that made us want to learn about it and want to learn more about it.
I think I learned a lot because now that I am in college I think I am doing a good job in my calculus classes and I have a good foundation that has supported me.
Anyway, I just wanted to say thanks for your help and hope that you are all right.
Your student,
Bart
I was your student about 4 years ago, in 2015. I just want to say that I really enjoyed your class and at the same time I learned a lot. I enjoyed your class because it was really interesting. Even if the topic being covered was not very interesting, you found a way in presenting it that made us want to learn about it and want to learn more about it.
I think I learned a lot because now that I am in college I think I am doing a good job in my calculus classes and I have a good foundation that has supported me.
Anyway, I just wanted to say thanks for your help and hope that you are all right.
Your student,
Bart
Wednesday, September 30, 2009
Relational Understanding and Instrumental Understanding
I think that the author makes a very interesting point in debating the pros and cons from both views of understanding, more precisely on understanding mathematics. I still think that relational understanding is a more valid goal for a mathematics teacher but apparently relational is not independent from instrumental understanding, as one is helped by the other. Relational understanding seems to promote the independence of students when it comes to showing their mathematical knowledge. On the other hand, instrumental understanding leads to too many rules, that once broken, e.g. making a mistake, it is hard to find the right way.
The idea of seeing math as a town is a new, yet sounded somehow familiar to me. Understanding mathematics relationally is like knowing the city so that one can go from one point to the other, and understanding mathematics instrumentally is like knowing a number of routes between a number of points.
An idea I got after reading this was to maybe ask my students to draw their own "mathematics" maps, to see how they can connect their knowledge. And why limit it to mathematics only? I would like to see how math connects within itself and also how all those concepts connect with other areas like art, science, sports, business...
The idea of seeing math as a town is a new, yet sounded somehow familiar to me. Understanding mathematics relationally is like knowing the city so that one can go from one point to the other, and understanding mathematics instrumentally is like knowing a number of routes between a number of points.
An idea I got after reading this was to maybe ask my students to draw their own "mathematics" maps, to see how they can connect their knowledge. And why limit it to mathematics only? I would like to see how math connects within itself and also how all those concepts connect with other areas like art, science, sports, business...
Monday, September 28, 2009
Interview with Students and Teachers
Interview with the Student
So I interviewed a student from high school, "J." We spend some time together and I taped his answers. I transcribed the interview.
How would you answer the question "why learn math?"
To make you think. There are some jobs that do not really need math, but math just really makes you think. It makes you see a problem in many different ways. They train you to not be closed minded.
How do you best learn math?
Practice. Not just reading. You have to do it.
Do you enjoy learning math? Do you find it interesting? Do you think it is being taught well?
I can't say I always enjoy learning math, I think it is taught pretty well. Math is a hard subject. I don't enjoy it always. It has nothing to do with the way it is being taught that I don't like it; it is a pretty hard subject. Sometimes I don't like it. Sometimes I find it interesting. Sometimes I find it pretty boring.
Which assessment methods are you best at?
I would say on presentations. I just don't have stage freight. I don't really have a problem talking to people.
How would you define mathematics?
Numbers. Lots of numbers. I don't know. . . adding, subtracting, multiplying.
Interview with the teacher:
How much homework do you assign and why?
Just enough to feel over whelmed but they don't break down. Keep them out of my hair during class time, keep them occupied.
How do you deal with difficult students
Use of humor, have the students see you as a person.
How would you improve the teacher education program?
UBC program, shortened to 6 month practicum, focus on practical. No wishy washy theoretical crap, total lack of practicality. Social Justice, Special Ed good.
Boys more willing to experiment and try different things, girls require a lot more structure, less likely to take risks. However they put in more effort.
more hands on work not the answer, math work not being done, not enough theory, more crunching numbers. Overly calculator dependent.
Conversation with a math teacher
Q1: How much homework, do you assign, if any, and how often? Why?
In the lower grades (9 and 8) homework is primarily work not completed in class.
For grades 10 about half and hour per class and grades 11 and 12 about 45 min to 1 hour per class.
Q2: How do you get difficult students or those who just don't show any interest and do not participate
involved?
I try to engage them by doing a wide variety of activities and showing how it applies in their lives. I am finding
the new curriculum (grade 8 last year, grade 9 next year) to be excellent in this regard. The new textbooks are
amazing. When I was a new teacher I thought if I just explained things well enough and loved the students, they
would all succeed. I've learned that the students must bring their own energy to the class in order for them to be
successful.
Q3: What kind of training did you go through before started teaching? Do you feel
it was adequate?
I am an engineer by training and worked in the field for over 15 years. I find that this experience helps
tremendously specifically in making the lessons more engaging. I have a Ph.D. in Chemical Engineering. To
qualify as a teacher, I took the 11 month program at SFU.
Q4: Do you see a different between how and the way boys and girls learn math?
As a profession, teacher are working at incorporating boy/girl learning patterns. More specifically, we are trying
to make lessons more boyfriendly
by allowing a lot of partner work and movement in the classroom.
Q5: What recommendations would you have for mathematics education reform?
The only recommendation that comes to mind may surprise you we
need to make it easier to fire ineffective
teachers. The number one factor for a child's success is the teacher. We need to stop blaming outside factors and
critically look at ourselves in terms of delivering the best lessons in an environment that allows individual students to embrace their own style of learning and thrive.
Conversation with two math students
Q1: How would you define "mathematics"?
Both Isabelle and Gabrielle: Adding, subtracting, multiplying, dividing, fractions.
Q2. If you were the teacher, how would you improve your math class?
Gabrielle:
1. take 5 minute break in between the classs. Her classes are 75 minutes.
2. have students get involved by asking them how to do a step/do the problem before explaining the process.
Q3. How do you best learn math?
Gabrielle: having a quiz after learning a new process.
Q4. How would you answer the question "why learn math?"
Gabrielle: budget, learn about money, taxes, buying things.
Isabelle: we don't need to learn half the stuff we do. We don't need to learn geometry.
Q5. Which assessment methods are you best at (if applicapable): quizzes, inclass assignments, home work, open
book exams, final exams, provincial exams, group projects/activities, inclass assignments, research projects,
openbook exams
Both Isabelle and Gabrielle do best with inclass assignments.
Isabelle says because she is more focused inclass.
Gabrielle home work and inclass assignments are about even re successful learning/marks.
Q6. Do you enjoy learning math? Pls explain your answer.
Gabrielle depends on teacher if the teacher explains and proceeds to new problems at the students' pace and
gives students lots of examples so we understand.
Isabelle no. I don't know why.
Q7. Do you find MATH interesting? Pls explain your answer.
Gabrielle yes, because a specific rule will apply to all numbers. For eg, two negatives multiplied are always a
positive. But it's not interesting like social studies, where you learn something new all the time.
Isabelle it's fun when it's easy. Otherwise it's not interesting.
Q8. Do you think it is being taught well? (comment on both the course materials and the teacher)
Gabrielle the course materials are good this year. My teacher this year is good because he gives us a break to
relax our mind after 35 minutes, he takes time to make sure that he isn't going too fast and he checks to make
sure we are following his steps, he gives a lot of examples, and he tests us as we go along to make sure that we
understand. He also makes sure we are prepared for the chapter tests/quizzes by giving us assignments on the
new material before the quizz.
Isabelle No because we spend too much time marking our homework and tests. We spend about 1/3 of the class
marking each other's work. The class is boring. The teacher teaches straight out of the text and she just tells us to
do the work. If we need help we have to ask.
So I interviewed a student from high school, "J." We spend some time together and I taped his answers. I transcribed the interview.
How would you answer the question "why learn math?"
To make you think. There are some jobs that do not really need math, but math just really makes you think. It makes you see a problem in many different ways. They train you to not be closed minded.
How do you best learn math?
Practice. Not just reading. You have to do it.
Do you enjoy learning math? Do you find it interesting? Do you think it is being taught well?
I can't say I always enjoy learning math, I think it is taught pretty well. Math is a hard subject. I don't enjoy it always. It has nothing to do with the way it is being taught that I don't like it; it is a pretty hard subject. Sometimes I don't like it. Sometimes I find it interesting. Sometimes I find it pretty boring.
Which assessment methods are you best at?
I would say on presentations. I just don't have stage freight. I don't really have a problem talking to people.
How would you define mathematics?
Numbers. Lots of numbers. I don't know. . . adding, subtracting, multiplying.
Interview with the teacher:
How much homework do you assign and why?
Just enough to feel over whelmed but they don't break down. Keep them out of my hair during class time, keep them occupied.
How do you deal with difficult students
Use of humor, have the students see you as a person.
How would you improve the teacher education program?
UBC program, shortened to 6 month practicum, focus on practical. No wishy washy theoretical crap, total lack of practicality. Social Justice, Special Ed good.
Boys more willing to experiment and try different things, girls require a lot more structure, less likely to take risks. However they put in more effort.
more hands on work not the answer, math work not being done, not enough theory, more crunching numbers. Overly calculator dependent.
Conversation with a math teacher
Q1: How much homework, do you assign, if any, and how often? Why?
In the lower grades (9 and 8) homework is primarily work not completed in class.
For grades 10 about half and hour per class and grades 11 and 12 about 45 min to 1 hour per class.
Q2: How do you get difficult students or those who just don't show any interest and do not participate
involved?
I try to engage them by doing a wide variety of activities and showing how it applies in their lives. I am finding
the new curriculum (grade 8 last year, grade 9 next year) to be excellent in this regard. The new textbooks are
amazing. When I was a new teacher I thought if I just explained things well enough and loved the students, they
would all succeed. I've learned that the students must bring their own energy to the class in order for them to be
successful.
Q3: What kind of training did you go through before started teaching? Do you feel
it was adequate?
I am an engineer by training and worked in the field for over 15 years. I find that this experience helps
tremendously specifically in making the lessons more engaging. I have a Ph.D. in Chemical Engineering. To
qualify as a teacher, I took the 11 month program at SFU.
Q4: Do you see a different between how and the way boys and girls learn math?
As a profession, teacher are working at incorporating boy/girl learning patterns. More specifically, we are trying
to make lessons more boyfriendly
by allowing a lot of partner work and movement in the classroom.
Q5: What recommendations would you have for mathematics education reform?
The only recommendation that comes to mind may surprise you we
need to make it easier to fire ineffective
teachers. The number one factor for a child's success is the teacher. We need to stop blaming outside factors and
critically look at ourselves in terms of delivering the best lessons in an environment that allows individual students to embrace their own style of learning and thrive.
Conversation with two math students
Q1: How would you define "mathematics"?
Both Isabelle and Gabrielle: Adding, subtracting, multiplying, dividing, fractions.
Q2. If you were the teacher, how would you improve your math class?
Gabrielle:
1. take 5 minute break in between the classs. Her classes are 75 minutes.
2. have students get involved by asking them how to do a step/do the problem before explaining the process.
Q3. How do you best learn math?
Gabrielle: having a quiz after learning a new process.
Q4. How would you answer the question "why learn math?"
Gabrielle: budget, learn about money, taxes, buying things.
Isabelle: we don't need to learn half the stuff we do. We don't need to learn geometry.
Q5. Which assessment methods are you best at (if applicapable): quizzes, inclass assignments, home work, open
book exams, final exams, provincial exams, group projects/activities, inclass assignments, research projects,
openbook exams
Both Isabelle and Gabrielle do best with inclass assignments.
Isabelle says because she is more focused inclass.
Gabrielle home work and inclass assignments are about even re successful learning/marks.
Q6. Do you enjoy learning math? Pls explain your answer.
Gabrielle depends on teacher if the teacher explains and proceeds to new problems at the students' pace and
gives students lots of examples so we understand.
Isabelle no. I don't know why.
Q7. Do you find MATH interesting? Pls explain your answer.
Gabrielle yes, because a specific rule will apply to all numbers. For eg, two negatives multiplied are always a
positive. But it's not interesting like social studies, where you learn something new all the time.
Isabelle it's fun when it's easy. Otherwise it's not interesting.
Q8. Do you think it is being taught well? (comment on both the course materials and the teacher)
Gabrielle the course materials are good this year. My teacher this year is good because he gives us a break to
relax our mind after 35 minutes, he takes time to make sure that he isn't going too fast and he checks to make
sure we are following his steps, he gives a lot of examples, and he tests us as we go along to make sure that we
understand. He also makes sure we are prepared for the chapter tests/quizzes by giving us assignments on the
new material before the quizz.
Isabelle No because we spend too much time marking our homework and tests. We spend about 1/3 of the class
marking each other's work. The class is boring. The teacher teaches straight out of the text and she just tells us to
do the work. If we need help we have to ask.
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