It's stories like this one that validate for me what teaching is all about. I know the relationships we form with students and the connections we help them make with each other and the kindness we show them are far more important than the math formulas we ask them to memorize or equations we show them how to solve.
In my earlier years of teaching my focus was on covering the standards and making sure we got through all of them by the time the spring test came around; sometimes we would have to rush to get through some things. But as the years have passed, my worries about these standardized tests have gone down significantly. I still value the information they provide for us. I want to see that my students are learning and growing; however, I also want my students to love learning and feel cared for in my classroom.
I do my best to connect with every student in my classroom every day. Currently, I have an algebra 2 class of 37 students and I'm finding it is barely possible to talk to every student and that's frustrating to me. Large class sizes take away from the personal learning experience; it feels more like a lecture hall than the interactive classroom I am more comfortable teaching in. In fact, I despise public speaking; it gives me major anxiety and having a class of 37, I feel some anxiety bubbling up. My typical classroom is an on-going dialog; I need the interaction. With 37 students interaction varies from no one will participate (due to the large audience I'm also scared of) to everyone talking at once. It's a new balance I'm having to figure out to get a classroom culture that works for my students.
One thing going for this large class is that we started the student reflection blogs. I think that through my students' blogs I am, in a round about way, connecting with every student. It may not be directly, but everyday my students are sending a message to me through their blog. I have been reading them everyday, responding when appropriate or when questions arise. I create a prompt a week that includes something unrelated to math; letting the students have some fun with different topics and talking about themselves. I am also writing my own posts to help students get to know me in blog world.
I like the idea that is shared in this article. I am very passionate about connecting with those students who sometimes feel/seem disconnected. Everyone has something to contribute, it's critical that teachers give students the platform on which students feel they can contribute.
Great Teaching Story
Friday, January 31, 2014
Math Activity Turned Social Experiement
In the college course that I am teaching, one of the big units we cover is probability. We talk multiplication counting principle, permutations, combinations, theoretical probability, empirical probability, independent events, and all that good stuff. It's a hard unit; students struggle with many of these concepts, mostly the counting piece. I wanted to add in something that was a little lighter but very related. I was struggling to think of something at first, but then, at the very last minute (which tends to be where my best ideas come from) I decided to create a lottery system that we would play throughout the course of the unit. Every student was given $20 to start the unit and could spend it the best way they thought they could with the goal of having the most money at the end of the unit to get some extra credit on their unit test. The drawings and payout rules we followed are below.
It was a fascinating experiment to watch. You learn a lot about students and their spending habits. There were students who dove right in and thought they would surely win big, and there were others that sat back quietly and held tight to their money, hoping others would spend and they would win with their original $20.
The best part was the last day.
On the last day, there were a few students who still had their original $20, one who had a questionable $22 (some were accusing him of stealing someone else's $2) and the rest were all less than $20. So, most with less than $20 went all in, they knew their only chance at the extra credit was to win the lottery. I say most went all in because not all of them did. There was an interesting turn of events that changed their minds for how they wanted to use their money.
One student in the class received a pretty low score on the test and at first in jest, requested that everyone donate their money to him because he needed the extra credit the most. (Note he had saved his money, and hadn't spent it gambling in the lotto in hopes he would have the most.) Quickly questions came to me about whether that was legal or not for our game. I said, it's your money, it's up to you how you spend it. Suddenly this student had himself about $100 and would easily win the extra credit as long as no one won the last drawing. Not surprisingly, no one won the last drawing and this student bought his extra credit. The lesson we wrapped up the class with outside of the probabilities of lotteries was if you are going to give your money away, which made you feel better, giving it to the lottery or giving it to charity? Some students were glad to give it to the lottery because it upped their own chances of winnings, and others were more happy to give it to someone else who they knew would benefit from their funds.
I do have to say that there was yet another lesson learned in all of this. After this charity student got his money collected from his kind peers, he came over to me and asked if he could buy tickets with all the money. Really buddy? You just got that money donated to you and you are going to toss it at the lotto? His donors were not pleased and he decided that perhaps that wasn't the best idea and held onto his money, but I appreciated that he gave us yet another social experiment to discuss. If you are donating to charity, it doesn't feel as good if the funds aren't going to where you were led to believe they would be going.
All in all, this was an awesome class activity. After going through the entire process once now, I am so excited to do this in the future. The discussions that took place about probability were good, but the discussions that took place about real-life, gambling, saving, donating were unexpected and meaningful.
I love it when something turns out really good and students feel good about it and got more than just a math concept from it.
Here were our lottery rules:
It was a fascinating experiment to watch. You learn a lot about students and their spending habits. There were students who dove right in and thought they would surely win big, and there were others that sat back quietly and held tight to their money, hoping others would spend and they would win with their original $20.
The best part was the last day.
On the last day, there were a few students who still had their original $20, one who had a questionable $22 (some were accusing him of stealing someone else's $2) and the rest were all less than $20. So, most with less than $20 went all in, they knew their only chance at the extra credit was to win the lottery. I say most went all in because not all of them did. There was an interesting turn of events that changed their minds for how they wanted to use their money.
One student in the class received a pretty low score on the test and at first in jest, requested that everyone donate their money to him because he needed the extra credit the most. (Note he had saved his money, and hadn't spent it gambling in the lotto in hopes he would have the most.) Quickly questions came to me about whether that was legal or not for our game. I said, it's your money, it's up to you how you spend it. Suddenly this student had himself about $100 and would easily win the extra credit as long as no one won the last drawing. Not surprisingly, no one won the last drawing and this student bought his extra credit. The lesson we wrapped up the class with outside of the probabilities of lotteries was if you are going to give your money away, which made you feel better, giving it to the lottery or giving it to charity? Some students were glad to give it to the lottery because it upped their own chances of winnings, and others were more happy to give it to someone else who they knew would benefit from their funds.
I do have to say that there was yet another lesson learned in all of this. After this charity student got his money collected from his kind peers, he came over to me and asked if he could buy tickets with all the money. Really buddy? You just got that money donated to you and you are going to toss it at the lotto? His donors were not pleased and he decided that perhaps that wasn't the best idea and held onto his money, but I appreciated that he gave us yet another social experiment to discuss. If you are donating to charity, it doesn't feel as good if the funds aren't going to where you were led to believe they would be going.
All in all, this was an awesome class activity. After going through the entire process once now, I am so excited to do this in the future. The discussions that took place about probability were good, but the discussions that took place about real-life, gambling, saving, donating were unexpected and meaningful.
I love it when something turns out really good and students feel good about it and got more than just a math concept from it.
Here were our lottery rules:
Lottery Rules:
Each student will start with $20.
There will be 5 lottery drawings, students can buy any number
of lottery tickets they can afford on any of the days there are drawings.
Drawings:
#1: 4 numbers will
be randomly selected from 0-9, numbers will be replaced after each draw, must
match the order the numbers are drawn
#2: 4 numbers will
be randomly selected from 1-20, no replacement, order does not matter
#3: 4 numbers will
be randomly selected from 0-9, numbers will be replaced after each draw, order
does not matter
#4: 4 numbers will
be randomly selected from 1-15, numbers will be replaced after each draw, and
then one PowerNumber will be selected from numbers 1-10
#5: 4 numbers will
be randomly selected from 1-15, no replacement, and then one PowerNumber will
be selected from numbers 1-30
Winnings:
For 4 number drawings:
1 out of 4 numbers right: $0
2 out of
4 numbers right: $1
3 out of
4 numbers right: $2
4 out of
4 numbers right: Jackpot (Shared equally
among all Jackpot winners)
For games with a PowerNumber:
PowerNumber
right: $3
1 out of 4 numbers right: $0
2 out of
4 numbers right: $1
3 out of
4 numbers right: $2
4 out of
4 numbers right: $10
4 out of
4 numbers right AND PowerNumber: Jackpot
Wednesday, January 29, 2014
"I give up."
Oh that phrase causes all of the muscles in my body to tighten and frustration starts to boil over. Right along with other phrases like, "I am bad at math" or "I can't do this."
I will admit, I'm not one to always accept every challenge that is thrown my way with a positive attitude, but man, who taught you that it's acceptable to just give up on things?
I currently am teaching a course of math basics with all special education students. Most have not had a lot of success in math in the past and I'm trying to embrace their past experiences and create for them an environment where it's OK to not know everything and meet them at a mathematical level where they currently reside and help them have some success.
Last week went OK. We worked through some basic material together, place value, writing numbers in digits from words, etc. They were feeling success. Many of them had a decent understanding and a few just had to have a little reminder to get them going. They all did pretty well.
But today...ugh.
Today took all my energy. Half of the class was absent today due to other testing that was taking place, so I thought we'd do some fun problem-solving together. Apparently that is not considered fun for these kids. I found problems that were close to their level, maybe just a bit above on some of them and a bit below on others. I put them into teams, had prizes and everything and it was a no-go for some of them. "I give up" was a frequently used phrase. I even said, perhaps we should make this Phy Ed-Math and every time you say that phrase you owe 10 push-ups. They didn't find that entertaining.
How do you teach perseverance? How do you get students who are 15-18 years old to change old habits of giving up on math? How do you teach them to work together? They have the resources, why don't they tap into them?
Calculators were given to everyone, pencil and paper in all hands, iPads with Google at the ready....but still, "I give up."
I know the research that says they can change their ways of thinking, but I feel like they have to want to change it and they are completely and totally convinced that they will forever be bad at math. Perhaps I should pull out some of that research and share it with them.
Regardless of my frustration today, I am NOT giving up. We'll start again tomorrow, we'll give it a go again. We'll see what happens.
I will admit, I'm not one to always accept every challenge that is thrown my way with a positive attitude, but man, who taught you that it's acceptable to just give up on things?
I currently am teaching a course of math basics with all special education students. Most have not had a lot of success in math in the past and I'm trying to embrace their past experiences and create for them an environment where it's OK to not know everything and meet them at a mathematical level where they currently reside and help them have some success.
Last week went OK. We worked through some basic material together, place value, writing numbers in digits from words, etc. They were feeling success. Many of them had a decent understanding and a few just had to have a little reminder to get them going. They all did pretty well.
But today...ugh.
Today took all my energy. Half of the class was absent today due to other testing that was taking place, so I thought we'd do some fun problem-solving together. Apparently that is not considered fun for these kids. I found problems that were close to their level, maybe just a bit above on some of them and a bit below on others. I put them into teams, had prizes and everything and it was a no-go for some of them. "I give up" was a frequently used phrase. I even said, perhaps we should make this Phy Ed-Math and every time you say that phrase you owe 10 push-ups. They didn't find that entertaining.
How do you teach perseverance? How do you get students who are 15-18 years old to change old habits of giving up on math? How do you teach them to work together? They have the resources, why don't they tap into them?
Calculators were given to everyone, pencil and paper in all hands, iPads with Google at the ready....but still, "I give up."
I know the research that says they can change their ways of thinking, but I feel like they have to want to change it and they are completely and totally convinced that they will forever be bad at math. Perhaps I should pull out some of that research and share it with them.
Regardless of my frustration today, I am NOT giving up. We'll start again tomorrow, we'll give it a go again. We'll see what happens.
Tuesday, January 28, 2014
Blogging in Math Class
Part of my plan for this blog is to keep track of my own progress in adventures I have in my classroom. I am always one for trying new things to improve my students' learning. I tend to be the math teacher in my department that doesn't quite fit the typical math teacher mold. I don't love the traditional style of teaching, but sometimes feel tied to it because that's what comfortable to students and to myself even (since that's the way I learned and have seen math most often presented). However, I know it's not the most effective way of teaching all students, so I try to mix things up. Sometimes new things work, sometimes they don't. Sometimes those things may have worked if I would have stuck with them long enough, but I admit that in teaching, if something is too cumbersome, sometimes you just run out of time or energy to keep with things. If students aren't catching on or buying in, it can be really hard to keep pushing them; it takes a lot of energy and teachers are human too...
But, recently, I started what I think is a great plan. This one I am determined to stick with to the end.
Recently, I also started graduate school, which has given me the extra push I may have needed to really think through and implement some ideas that have been floating around in my head for a while. I have also had a great mentor who has been an excellent encouragement to me in my adventures as I sometimes feel as though I am swimming against the current in the world of math teachers.
So the new plan...
My classroom is a place of learning. It is not a place where students get hoops that they have to jump through (daily homework), but a place where they will spend time exploring, discussing and practicing mathematics. Students in my class are given suggested problems to do each day, but these problems are not "required" and students do not receive points for doing these problems. These problems are practice, you don't get trophies when you practice basketball, you shouldn't get a fake trophy for practicing your math either. You should practice because you need to or want to improve. You also don't lose in practice; you practice to get better. You shouldn't be punished for a bad practice. So if practice doesn't go well, we find another way to practice or work hard to practice better next time.
That's my new theory. However, if you just tell students they don't have to do homework, many of them won't do it at all. So, to put the focus on the act of learning, my students are creating a math journal or portfolio via Kidblog.org. Their blogs are an on-going conversation between student and teacher. Students are given prompts daily and have a minimum of 10 minutes each day to respond to those prompts. Prompts include requests to summarize concepts that have been covered, explain how to solve specific problems, or to reflect on their progress of learning.
Students have also been given an "I Can" document that outlines the things that they will and should be able to do by the end of the unit. They will use this "I Can" document as a guide to produce evidence that they have an understanding of the concepts that we have been exploring. Before we get to the summative assessment portion of the unit, students will have used their blog as a place to collect evidence of their learning and understanding of the "I Can" statements. The daily practice problems can serve as evidence as well as videos they record of themselves explaining concepts or solving problems, etc. My hope is that all the focus on what they know or don't know will prepare them or help them better prepare for that summative assessment.
We are only 4 days into this process. So far, I've gotten the students trained in on blogging everyday for at least ten minutes in class. I think thus far my completion rate on the blogs is about 95% for all students over the course of 4 blogging days. I believe if I were to go back to last semester and look at the daily work grades, the completion rate for the homework would have been around 75%. In the blog, it's harder to hide if they aren't understanding. I am able to hear from EVERY student in my classroom about their understanding. Those students that often sit quietly and don't ask questions are very clear in their blogs. They can't say they didn't have time, as there are ten minutes dedicated everyday to blogging. Right now, they are all talking to me. That's where we are starting.
This week, the focus is going to be on great blog entries. Some students gave me one-liners last week. "I understand everything" is not going to be quite enough this week. I found a great rubric we are going to use as a guide for our entries. I am looking for evidence of learning and a statement saying you understand it doesn't prove it. So, this is where things will get tough. Pushing through the learning of how to write a good entry in their blog will take patience on my part. It will also take diligence to read the entries thoroughly and with 37 students in my one class it will take time.
But I've got this one. I am sticking with it to the end. I know that this has the potential to be a great opportunity for students to really learn some math and learn how to learn math. It's algebra 2. It's full of great concepts that have been covered a little in algebra 1. It's a great opportunity to try something new and get to know ourselves as learners. We'll see how it goes.
Math Blog
Here goes nothin'.
I have been toying with the idea of starting a teaching blog for a long time, and today a co-worker and friend convinced me that this is the thing to do. I can now document this awesome journey I am on and perhaps see some growth over time. That's the goal.
A little about me:
I'm a ninth year math and computer programming teacher.
Wow, that sounds about as nerdy and boring as you can get. But I like to think of myself as a fun-lovin', cool nerd; if such a thing can exist. I am out to give math and computer programming the cool status they deserve.
I spent the first five years of my career in 8th grade. Eighth grade is quite the place to start your career. You learn a lot about how uncool you are and how brilliant you are all at the same time. Eighth graders are awesome and awful. They know everything and nothing. They want to be treated like adults, but need to have someone hold there hand. It was a life adventure, one that provided me with many great experiences and laughs.
I was the only 8th grade math teacher which allowed me the freedom to teach any way that I felt was best for my students. I got to experiment with different ways to approach teaching algebra. I learned algebra really well; I hope some 8th graders also learned algebra really well. I did get the opportunity to find out how well my 8th graders had been learning algebra when I got to replace a retiring teacher in the high school within my district and had many of the same students again. I learned that some of my techniques worked well, and some did not work so well. I think all schools should have teachers move from level to level to truly know what students know and need to know as they progress through our system.
The last few years I have been a high school math teacher, I have been given a number of new opportunities to try new things. I created a computer programming course that is in it's second year of existence and now even has a programming 2 course that follows it. I have learned a lot about web page design, teaching that course a few times. Advanced algebra, college algebra and a basics course called math fundamentals have also been on my plate at some point. I have taught all levels at the high school math except the highest ones, pre-calculus and calculus, and have some personal thoughts and ideas about math and what should and shouldn't be taught and how it should and shouldn't be approached.
Through this blog, I hope to get my thoughts out of my head and onto paper, or screen if you will. I like to play around with thoughts, seeing them written will hopefully help me get a handle on what I really believe about math education and technology education. My beliefs are always changing. It's hard to know what to believe in this world of education. I want what is best for my students; I want to teach them skills that go beyond my classroom. If they don't remember the Pythagorean Theorem, that's fine, but I want them to have perseverance to tackle any difficult problem that comes their way.
Welcome. Not sure what kind of a ride this one is going to be, it might be irrational at times, but it'll be real.
I have been toying with the idea of starting a teaching blog for a long time, and today a co-worker and friend convinced me that this is the thing to do. I can now document this awesome journey I am on and perhaps see some growth over time. That's the goal.
A little about me:
I'm a ninth year math and computer programming teacher.
Wow, that sounds about as nerdy and boring as you can get. But I like to think of myself as a fun-lovin', cool nerd; if such a thing can exist. I am out to give math and computer programming the cool status they deserve.
I spent the first five years of my career in 8th grade. Eighth grade is quite the place to start your career. You learn a lot about how uncool you are and how brilliant you are all at the same time. Eighth graders are awesome and awful. They know everything and nothing. They want to be treated like adults, but need to have someone hold there hand. It was a life adventure, one that provided me with many great experiences and laughs.
I was the only 8th grade math teacher which allowed me the freedom to teach any way that I felt was best for my students. I got to experiment with different ways to approach teaching algebra. I learned algebra really well; I hope some 8th graders also learned algebra really well. I did get the opportunity to find out how well my 8th graders had been learning algebra when I got to replace a retiring teacher in the high school within my district and had many of the same students again. I learned that some of my techniques worked well, and some did not work so well. I think all schools should have teachers move from level to level to truly know what students know and need to know as they progress through our system.
The last few years I have been a high school math teacher, I have been given a number of new opportunities to try new things. I created a computer programming course that is in it's second year of existence and now even has a programming 2 course that follows it. I have learned a lot about web page design, teaching that course a few times. Advanced algebra, college algebra and a basics course called math fundamentals have also been on my plate at some point. I have taught all levels at the high school math except the highest ones, pre-calculus and calculus, and have some personal thoughts and ideas about math and what should and shouldn't be taught and how it should and shouldn't be approached.
Through this blog, I hope to get my thoughts out of my head and onto paper, or screen if you will. I like to play around with thoughts, seeing them written will hopefully help me get a handle on what I really believe about math education and technology education. My beliefs are always changing. It's hard to know what to believe in this world of education. I want what is best for my students; I want to teach them skills that go beyond my classroom. If they don't remember the Pythagorean Theorem, that's fine, but I want them to have perseverance to tackle any difficult problem that comes their way.
Welcome. Not sure what kind of a ride this one is going to be, it might be irrational at times, but it'll be real.
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