It seems a little ridiculous when I'm writing about it, but there are so many times when I'm teaching that I assume my students already know the material. Maybe it's because I already know it. Or maybe it's that they have seen information like this in previous grades. But I'm always afraid I'm teaching them something they already know.
What happens then is I begin to think, "We should move quickly through the material so that I don't bore them." So I begin going faster, working through fewer examples, and going over less of the simple problems.
Of course, my students don't know the material. So my faster pace is too much for them, and since I'm doing fewer examples they have less idea about how to use the information given to them. They become confused and frustrated and begin to ignore me, and that's when my discipline problems pop up.
I think that was the biggest problem with my block 4. How do I know? Because after their test yesterday I had them fill out a questionnaire telling me how I could improve as a teacher. I was surprised that the students were as nice as they were. (I had been preparing to read about how horrible I am.) But it turns out that all they really wanted me to do is slow down, explain things more thoroughly, and do more examples. It was nice to read.
I think they appreciated being a part of my learning process as well. Today we had a pretty good class - in part because I didn't assume they knew anything. (I gave them a pre-assessment for the triangles unit along with the questionnaire.) It made me feel good to know that I was actually reaching their needs.
The other piece on the questionnaire was about their participation in the class. They answered honestly (mostly-I think-because they didn't have to put their names on the paper), and came up with good ways of solving their participation problems. Perhaps that reflective piece is what made today so much better than usual.
Friday, September 28, 2007
Wednesday, September 26, 2007
MathPad
I went to a lecture at my alma mater tonight called "When the pen is mightier than the keyboard" given by Andries van Dam of Brown University. What an incredible talk! The main idea was that the interface between a person and a computer (generally a mouse and a keyboard) hasn't changed in over 40 years, but that we should be investigating ways to make the computer more "natural" to use. This is a very popular idea right now. The iPhone, even with its unpopular, single-service capability, is a very hot item right now, and is probably the most wide-spread example of good implementation of a computer that's "natural" to use.
I've heard this rant many times, though, from many different people. (You know who you are.) And, while it's definitely both valid and interesting, it was not the most important part of the night for me.
Van Dam spoke about using computers more effectively in the classroom with the use of a program he and his colleagues at Brown are working on, called MathPad. He demonstrated (in real time, even) the incredible capabilities of this program, which uses a stylus rather than a keyboard to enter information. (Thus making the program more natural to use; like you're actually writing math on paper rather than typing it in as on a calculator or in mathematics modeling software like Maple.) The program recognizes your writing, translates it into mathematics, and solves problems or graphs equations or runs mathematical models with a quick strike of the pen. It was very cool. (When's the last time you heard an entire auditorium ooh and gasp for the creation of a graph?)
This lecture made me very excited about technology in education. I really believe that by using technology, teachers are able to truly reach most students of the current high school population. Their entire lives they are inundated by technology, after all. It's how they communicate and how they relax. Why shouldn't it be incorporated into how they learn?
Despite these strong opinions, however, I have yet to include so much as training in using calculators into my classroom. I'm beginning to feel like a hypocrite. So I'm making it my mission to try to incorporate some form of technology into my lessons at least once each week.
... These resolutions are beginning to stack up.
I've heard this rant many times, though, from many different people. (You know who you are.) And, while it's definitely both valid and interesting, it was not the most important part of the night for me.
Van Dam spoke about using computers more effectively in the classroom with the use of a program he and his colleagues at Brown are working on, called MathPad. He demonstrated (in real time, even) the incredible capabilities of this program, which uses a stylus rather than a keyboard to enter information. (Thus making the program more natural to use; like you're actually writing math on paper rather than typing it in as on a calculator or in mathematics modeling software like Maple.) The program recognizes your writing, translates it into mathematics, and solves problems or graphs equations or runs mathematical models with a quick strike of the pen. It was very cool. (When's the last time you heard an entire auditorium ooh and gasp for the creation of a graph?)
This lecture made me very excited about technology in education. I really believe that by using technology, teachers are able to truly reach most students of the current high school population. Their entire lives they are inundated by technology, after all. It's how they communicate and how they relax. Why shouldn't it be incorporated into how they learn?
Despite these strong opinions, however, I have yet to include so much as training in using calculators into my classroom. I'm beginning to feel like a hypocrite. So I'm making it my mission to try to incorporate some form of technology into my lessons at least once each week.
... These resolutions are beginning to stack up.
Tuesday, September 25, 2007
Professional Development Meeting
I had a professional development meeting today with other new-to-district teachers. It was very low-key; something I was thankful for. And I left feeling as though I was in a similar place with my students as the other new teachers were. Even those teachers who were new-to-district but not new-to-teaching were having their own difficulties. It was nice to be reminded that just because I don't have perfect classes each day, that doesn't mean I'm not doing an O.K. job.
I had a great day with my fourth block class today, which is a strange occurrence. Aside from the moment when half the class was called down to the gym for an announcement, I felt as though I was actually getting through to them. Everyone seemed to understand the material. They seemed to be interested. Perhaps this is due to the nature of this new material. Perhaps it's the full moon tomorrow. But I was very excited when I left that class.
The leader of our professional development, D, left me thinking about the idea of perfect teachable moments: those moments in time when dispositions are perfectly aligned so as to be receptive to new knowledge. Today's class was one giant teachable moment.
Thinking back on it now, though, I feel as though I was more excited about today's material. I was definitely bouncing around at the front of the room. Not that that's out of place for me, but generally by fourth block I'm running low on energy. I think maybe I was so excited about the material that my students couldn't help but watch and listen.
I left my professional development meeting today thinking about an idea that I've heard many times before. "Whoever is working the hardest in a classroom is doing the most learning." It's always nice to be reminded of this, and I've always believed it to be true. But I think that I need to reassess my understanding of how to implement the idea. I generally have my students lead themselves through investigations in order to discover important postulates and conjectures. The same is true for block 4. But I've always assumed that once my students have gone through the investigation, there's no need for me to repeat what they've already learned. This is certainly not the case with block 4. While I don't want to be the "mathematical authority" in the room, I've realized that my students won't believe a concept is true without my say-so.
I need to investigate ways to lead my students into trusting their own discoveries in the classroom.
I had a great day with my fourth block class today, which is a strange occurrence. Aside from the moment when half the class was called down to the gym for an announcement, I felt as though I was actually getting through to them. Everyone seemed to understand the material. They seemed to be interested. Perhaps this is due to the nature of this new material. Perhaps it's the full moon tomorrow. But I was very excited when I left that class.
The leader of our professional development, D, left me thinking about the idea of perfect teachable moments: those moments in time when dispositions are perfectly aligned so as to be receptive to new knowledge. Today's class was one giant teachable moment.
Thinking back on it now, though, I feel as though I was more excited about today's material. I was definitely bouncing around at the front of the room. Not that that's out of place for me, but generally by fourth block I'm running low on energy. I think maybe I was so excited about the material that my students couldn't help but watch and listen.
I left my professional development meeting today thinking about an idea that I've heard many times before. "Whoever is working the hardest in a classroom is doing the most learning." It's always nice to be reminded of this, and I've always believed it to be true. But I think that I need to reassess my understanding of how to implement the idea. I generally have my students lead themselves through investigations in order to discover important postulates and conjectures. The same is true for block 4. But I've always assumed that once my students have gone through the investigation, there's no need for me to repeat what they've already learned. This is certainly not the case with block 4. While I don't want to be the "mathematical authority" in the room, I've realized that my students won't believe a concept is true without my say-so.
I need to investigate ways to lead my students into trusting their own discoveries in the classroom.
Sunday, September 23, 2007
The Importance of Reflection
Ok, ok. So I had high hopes of coming home each day after work with my head full of new insights into the teaching profession. I would sit in front of my Inspiron 6000 and let my newfound knowledge loose to the world; enriching the lives of all who seek wisdom about the field of mathematics education.
Clearly, that has not happened. Finding time for just about anything other than planning for the next day has been difficult as of late. (See previous blog entry.) But my resolve, at least as far as reflecting often on this first year of teaching, has recently returned.
I am fortunate to work in a school system with a strong professional development program. One of the perks of this program is having a veteran teacher, D, whose current and sole responsibility is to help other teachers by giving them guidance or at least ideas. I've been having classroom-management issues with my fourth block class. And, after expressing my frustrations to D, she volunteered to observe the class.
While I didn't gain much from this observation in the way of suggestions for classroom management, what I did gain was an understanding of the need to step back and view the class as a whole. At one point during the observation, D called me over and asked whether my students were always vigorously engaged in their tasks the way that they were at that moment. Up until then I was thinking about the 4 or 5 off-task remarks I'd just heard. But her comment forced me to step back and look at the class as a whole. What I saw truly amazed me.
My students, almost all of them, were thoroughly engaged in their tasks. Some of the boys in the front of the room had even begun to argue about the mathematics! I was taken aback, to say the least. That moment forced me to remind myself of the importance of reflecting on both the good and the bad in my classroom each day. I've felt discouraged too many times after school when I've only thought about all that went wrong during the day. Thankfully, D's comments during her observation and in her email afterward reminded me of why I love to teach.
Furthermore, D's observation reminded me of the importance of reflecting on my daily teaching. When I truly sit down and think about each day and each lesson, I gain insight that I can always use to improve my teaching. So here comes another resolution...
I resolve to use this online journal at least twice each week to reflect on topics pertaining to my own teaching and to education in general.
Clearly, that has not happened. Finding time for just about anything other than planning for the next day has been difficult as of late. (See previous blog entry.) But my resolve, at least as far as reflecting often on this first year of teaching, has recently returned.
I am fortunate to work in a school system with a strong professional development program. One of the perks of this program is having a veteran teacher, D, whose current and sole responsibility is to help other teachers by giving them guidance or at least ideas. I've been having classroom-management issues with my fourth block class. And, after expressing my frustrations to D, she volunteered to observe the class.
While I didn't gain much from this observation in the way of suggestions for classroom management, what I did gain was an understanding of the need to step back and view the class as a whole. At one point during the observation, D called me over and asked whether my students were always vigorously engaged in their tasks the way that they were at that moment. Up until then I was thinking about the 4 or 5 off-task remarks I'd just heard. But her comment forced me to step back and look at the class as a whole. What I saw truly amazed me.
My students, almost all of them, were thoroughly engaged in their tasks. Some of the boys in the front of the room had even begun to argue about the mathematics! I was taken aback, to say the least. That moment forced me to remind myself of the importance of reflecting on both the good and the bad in my classroom each day. I've felt discouraged too many times after school when I've only thought about all that went wrong during the day. Thankfully, D's comments during her observation and in her email afterward reminded me of why I love to teach.
Furthermore, D's observation reminded me of the importance of reflecting on my daily teaching. When I truly sit down and think about each day and each lesson, I gain insight that I can always use to improve my teaching. So here comes another resolution...
I resolve to use this online journal at least twice each week to reflect on topics pertaining to my own teaching and to education in general.
Cutting Down the Over Time
As most teachers probably know, the first year of teaching is ridiculously time consuming. For a while I felt as though my entire life was spent planning, creating handouts or tests or quizzes, responding to parents' or other teachers' or administration's emails or phone calls, and photocopying like a madman. I would get to school at 6am and leave at 8pm. After a couple weeks of that even a work-a-holic like myself begins to feel as though they need to schedule time away.
Last week, however, events in my district forced me to arrive at school no earlier than 7am and leave no later than 3pm. While I still planned at home, I needed to use my planning period efficiently in order to prepare myself for the following day's lessons. (For those who know me, the ToDo lists were abundant.) To my surprise, I was able to accomplish most of my in-school work in time.
Now, don't be fooled into thinking that I was able to finish everything at school in my one prep block. I still planned and graded and recorded information and emailed from home, but there were no early-morning or late-afternoon copy sessions. It required a little more forethought on my part, but in the end I was less stressed out about the next day because I'd already planned for it. It's funny when extreme circumstances can force you to raise your expectations of yourself and perform better than you thought you could.
The best part? I was able to spend a small amount of time each evening on relaxing and doing the things I needed to do for myself. I found that, by doing this, I was better rested and happier when teaching classes.
Last week, however, events in my district forced me to arrive at school no earlier than 7am and leave no later than 3pm. While I still planned at home, I needed to use my planning period efficiently in order to prepare myself for the following day's lessons. (For those who know me, the ToDo lists were abundant.) To my surprise, I was able to accomplish most of my in-school work in time.
Now, don't be fooled into thinking that I was able to finish everything at school in my one prep block. I still planned and graded and recorded information and emailed from home, but there were no early-morning or late-afternoon copy sessions. It required a little more forethought on my part, but in the end I was less stressed out about the next day because I'd already planned for it. It's funny when extreme circumstances can force you to raise your expectations of yourself and perform better than you thought you could.
The best part? I was able to spend a small amount of time each evening on relaxing and doing the things I needed to do for myself. I found that, by doing this, I was better rested and happier when teaching classes.
Wednesday, September 12, 2007
Easy Vocab Review
While looking around for review day ideas I found the Discovery School's website, which has great resources for creating vocab and math puzzles. I created a crossword for my Tools of Geometry unit. It was very easy to use!
Definitions Galore
The problem with the beginning of Geometry is the sheer number of definitions. My students have started to groan when I say we have more definitions to talk about. There must be a better way to get these definitions down. I feel as though I spend so much time trying to get them to copy down notes that they have no time to actually try to work with the concepts. And that's the part with which I feel I would be most helpful. Perhaps students' homework time would be better spent by getting the definitions for the next day. Then they can work on solving problems in class.
Perhaps I'll try that approach for the next unit.
On a semi-related topic, I just received an email linking me to a page that piqued my interest in using technology to teach. This one was about wikis. The podcast, found here , talks about using a wiki to communicate and collaborate with students and parents. It's not a bad idea. I'm just not sure how to use it within mathematics. It would be interesting to try it, though. Apparently teachers can get free wikis at http://www.wikispaces.com. Even more of a reason to try.
Perhaps I'll try that approach for the next unit.
On a semi-related topic, I just received an email linking me to a page that piqued my interest in using technology to teach. This one was about wikis. The podcast, found here , talks about using a wiki to communicate and collaborate with students and parents. It's not a bad idea. I'm just not sure how to use it within mathematics. It would be interesting to try it, though. Apparently teachers can get free wikis at http://www.wikispaces.com. Even more of a reason to try.
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