This week I wrapped up my unit with my sixth and seventh graders. This unit has been such a learning experience for me. First of all I cannot believe that I just TAUGHT actual students a whole chapter of math content. Holy FREAKING cow. This is what I've known my whole life that I wanted to do and this is what I've been working my butt off for five years to do with my life. The sense of excitement I get from knowing how close I am to being a certified teacher is out of this world and the pride I get from how well my first ever chapter went is ridiculous. I could not have asked to be placed in a better school nor have better students to be my so called guinea pigs for my first teaching experience. I didn't expect to be so thrilled to be in a middle school let alone look forward to waking up every day and going to school to touch the young minds of my students. It brings tears to my eyes just thinking about how much I love the career path I've chosen for myself and everything that comes with it.
It blows my mind how receptive and open my students were to a new teacher coming into their classroom and just taking over and teaching them material that they'd never seen before. To me, that's a terrifying amount of responsibility, especially having no experience doing so before. The students were so helpful to my first 'learning to teach' experience and gave me great feedback about what worked for them and what didn't. And through this I figured out how good I am at gauging students understanding simply by reading body language. I think this was one of the biggest things that helped convince me that I'm going the right direction with my life. I feel the best teachers come with a 'feel' and so called 'nack' for teaching and I'd like to think that with teaching my first ever lesson I found my 'nack' and 'feeling' for teaching; and what an amazing feeling that was.
I guess I should probably start blogging more specifics about my lessons and gushing about my love for teaching a little less. I'll give it a try...
My lesson was over geometric figures and was the first time that many of my students learned any sort of geometry (or at least the first time they learned the figures as specifically as I taught them). The first section covered the basic vocab: Point, Line, Plane, Line Segment, Ray, and Congruent. Students seemed to grasp this lesson pretty well and when they came to class the second day I was able to ask them to come up with real life examples of each and got some very creative responses (Line: the equator, Line Segment: a flag pole). The next lesson (section 2) covered angles (acute, obtuse, straight, right, supplementary angles, and complementary angles), the students struggled the most with supplementary and complementary angles but I was able to give them a helpful "reminder" that straight angles had 180 degrees so supplementary angles add to 180, this seemed to help. They also struggled with reading the protractor, I gave them steps to finding the measure of angles when reading the protractor and those seemed to help but worst case students ended up counting off the "fives" between the rays of the angle. Section 3 was the longest section of the chapter and proved to be the one I struggled with teaching the most. It covered parallel, perpendicular, skew, transversals, and angle relationships formed when a transversal intersects two parallel lines. The first four terms weren't too tricky for students (especially since many had seen them before) but the angle relationships were the most difficult for students and for one hour I ended up having to reteach that portion of the less the next day because they didn't understand it the first time and I was too rushed the first time to do teaching it justice. When I retaught this to second hour I did a much better job of explaining the material using vertical and adjacent angles (which we covered with parallel and perpendicular). And because I knew what not to do for third hour I was able to not have to reteach the lesson for them.
The final two sections on angle measure sum of triangles, quadrilaterals, and polygons and congruent polygons went very well. I did an activity with each class dealing with finding the angle sum of triangles using a straight angle and ripping off two angles of a triangle to lie along the straight angle and find the three angles along the straight angle fit perfectly (aka add to 180, or the measure of a straight angle). (See my other blog post for more on this). Students seemed to really enjoy the activity and hopefully with my next chapter I'll be able to do more of them.
I was really pleased with how all of my assessments of students understanding went throughout this lesson and though the first class didn't do so well on their first quiz (which I had them all correct and explain the correct answers to receive points back), second hours second quiz that I gave them went exceptionally well and no one received below an 80%. And on the test second hour had an average of 83% and third hour had an average of 94%. Which though it's not all about the test scores, it's still a sort of gauge and confirmation of how well the chapter went. And dang, for my first time teaching I'm pretty stinking proud of how well my students seemed to understand the approach I have to teaching and the material I taught them. I can't wait to get back in front of the classroom, but sadly have to give my placement partner a chance to teach now. Which in fact, it's much more difficult to relinquish control now, I don't know how my CT does it every year! I just want to jump back up there and teach my kids!
Once I get my materials from my unit scanned in I'll attach them to this post. Until then, off to the next learning experience!
Thursday, February 27, 2014
Are Smartboards 'smart'?
In my content seminar we've been asked to do weekly(ish) readings from The Teaching Gap. In the recent chapter we read about the use of projectors vs. chalkboards in Japanese classrooms vs. American classrooms. The authors talk about how in Japanese classrooms there is no projector simply a chalkboard, which provides record of problems and solution methods. This is the opposite in American classrooms in which there is a projector that's used to focus students attention and demonstrate the procedures. These different methods of "projecting" the lesson really speaks to the approach that each country takes in mathematics education. In the U.S the approach is very much review, demonstration, practice, and corrections. Whereas in Japan the approach is review presentation of a problem, student work through the problems, discussion of solution methods, high lights and summarize. The learning is much more student centered in Japanese approaches which speaks to the minimal use of the chalkboard. If the chalkboard is used it's used to help enforce the importance of student discovery not teacher demonstration.
This use of projectors and boards tends to lead one's thinking to the newest 'board', the Smartboard. How would Japanese teachers use this in their classrooms? Would they even find it helpful? Or would they think were more of a hinder than a help with the 'normal' structure in the classroom? My thoughts are: Smarboards can be very helpful when used to show demonstrations of concepts, especially when they involve figures which one can manipulate on the Smartboard. I think when looking at their use like this, Japanese teachers would see the benefits of the board to help students discovery and understanding.
The use of the Smartboard in classrooms tends to bring teacher's practices to more demonstrations and presentation because with the board the presentations are much more interactive and teachers are able to manipulate the figures used, which is very helpful in geometry lessons. I think that it's really important that teachers don't take using the Smartboard to the extreme and refuse to differentiate from that method of instruction. Yes the use of Smartboards can add to the effectiviness of lessons and lead to deeper understanding of the material but it's important to keep in mind when using them that it's not the ONLY effective method of instruction...
This use of projectors and boards tends to lead one's thinking to the newest 'board', the Smartboard. How would Japanese teachers use this in their classrooms? Would they even find it helpful? Or would they think were more of a hinder than a help with the 'normal' structure in the classroom? My thoughts are: Smarboards can be very helpful when used to show demonstrations of concepts, especially when they involve figures which one can manipulate on the Smartboard. I think when looking at their use like this, Japanese teachers would see the benefits of the board to help students discovery and understanding.
The use of the Smartboard in classrooms tends to bring teacher's practices to more demonstrations and presentation because with the board the presentations are much more interactive and teachers are able to manipulate the figures used, which is very helpful in geometry lessons. I think that it's really important that teachers don't take using the Smartboard to the extreme and refuse to differentiate from that method of instruction. Yes the use of Smartboards can add to the effectiviness of lessons and lead to deeper understanding of the material but it's important to keep in mind when using them that it's not the ONLY effective method of instruction...
Monday, February 17, 2014
"Murdering" Triangles
One of the biggest benefits of having two classes learning the same material at different paces is that I get to teach the same lesson twice but not one right after the other. This proved to be very helpful when going outside of my comfort zone and teaching a more hands on lesson/activity to help students learn the angle sum of triangles and then find a formula for the angle sum of other polygons. Initially when I did this activity with 2nd hour which is the students who are at level for seventh grade I found there were a few things missing which I thought could be helpful to students for the next time. It also just so happened that the first time through this activity I was observed by COE a second time. My coordinator thought this activity was very fun for the kids and even told me that he was able to learn something from the lesson he didn't know before. He thought the lesson was refreshing to see since it was so different from the lesson I had done the first time he observed me. He did suggest that I provide some sort of closure for the students, which I failed to provide for second hour and he felt that they might not have fully grasped what I wanted them to from the activity and a good way to gauge that would be asking them simply "So, what did we learn today?"
When I did this same activity with 3rd hour I knew that I wanted to provide more closure with the students and also have them help develop a formula we could use to find the angle sum of polygons. I figured since 3rd hour is the more advanced students they would need less guidance than my first class and would be able to come up with this formula with much less help than second hour would have needed (I didn't do this generalization with 2nd hour). Knowing how chatty 3rd hour can be and having the lesson on a Friday AND that Friday being Valentines day AND being the day I was observed by my content coordinator...well needless to say this activity was either going to be great and productive or a total flop.
While in the lesson I felt that though the kids were SUPER chatty, I was able to reign them back in and keep them focused enough to take from the activity what I wanted them to...
Funny side note: when I asked students to rip off the two angles of their triangles whose vertices they hadn't placed on the straight angle, many students responded by gasping and complaining that we were murdering triangles by doing such a thing. Thought that was something only math loving middle schoolers would come up with and had a good laugh with them about it.
The students asked lots of questions that I wasn't really prepared for, and I like to think that I think of nearly every question before going into the lesson but this really shouldn't have surprised me since this class is so witty and can come up with enough questions to fill an hour just full of questions. There were many questions that students asked about which I wish I had had more time to address and especially after meeting with my content coordinator and talking through how to answer the questions. I think I'd really like to take the time (if I have it) to go back and discuss with students WHY we can't/can divide the polygons into triangles a variety of different ways and have students explore different ways of dividing up our polygons and how to make those work (if possible). I'm hoping to spend some review time having students look into this along with go back and look at more variety of triangles to solidify our "proof" of the sum of the angles of every triangle equaling 180. I think next time I would also remove the last two polygons (lightning bolt and star) from the hand out until students had already gained a deep understanding of how to find the sum of the angles, then (especially with an advanced class) I might give them those last two polygons to find the sum of the angles as more problem solving types of questions to push the limits of their understanding.
The activity didn't go poorly by any means; it actually went very well there's just a few things I would like to change. With a little guidance from me the students were able to come up with a general formula for finding the angle sum of polygons at the end of the lesson. Which my students before weren't able to do and didn't have the time to do. At the end of the lesson as I was passing out the worksheet with a reflection and take home piece, I had students cover with me possible answers they could have for their reflection piece on what they learned from the activity. By doing this I was able to get all the students involved and thinking about the lesson along with gauge their comprehension of what we'd just done and know if they were taking away from the lesson what I wanted them to. This wasn't something I did with 2nd hour and was really helpful because I realized how much my students had taken away from the activity and even though they were chatty they really learned a lot from the activity and had a lot of fun.
There are definitely ways that I could shorten or extend this activity based on how in-depth I want my students to explore and how much I think my students can handle. But overall I think for my first time stepping outside my comfort zone and doing an activity with students I was able to create an activity that engaged students, was fun, and had them learning and taking away from the activity exactly what I wanted them to.
When I did this same activity with 3rd hour I knew that I wanted to provide more closure with the students and also have them help develop a formula we could use to find the angle sum of polygons. I figured since 3rd hour is the more advanced students they would need less guidance than my first class and would be able to come up with this formula with much less help than second hour would have needed (I didn't do this generalization with 2nd hour). Knowing how chatty 3rd hour can be and having the lesson on a Friday AND that Friday being Valentines day AND being the day I was observed by my content coordinator...well needless to say this activity was either going to be great and productive or a total flop.
While in the lesson I felt that though the kids were SUPER chatty, I was able to reign them back in and keep them focused enough to take from the activity what I wanted them to...
Funny side note: when I asked students to rip off the two angles of their triangles whose vertices they hadn't placed on the straight angle, many students responded by gasping and complaining that we were murdering triangles by doing such a thing. Thought that was something only math loving middle schoolers would come up with and had a good laugh with them about it.
The students asked lots of questions that I wasn't really prepared for, and I like to think that I think of nearly every question before going into the lesson but this really shouldn't have surprised me since this class is so witty and can come up with enough questions to fill an hour just full of questions. There were many questions that students asked about which I wish I had had more time to address and especially after meeting with my content coordinator and talking through how to answer the questions. I think I'd really like to take the time (if I have it) to go back and discuss with students WHY we can't/can divide the polygons into triangles a variety of different ways and have students explore different ways of dividing up our polygons and how to make those work (if possible). I'm hoping to spend some review time having students look into this along with go back and look at more variety of triangles to solidify our "proof" of the sum of the angles of every triangle equaling 180. I think next time I would also remove the last two polygons (lightning bolt and star) from the hand out until students had already gained a deep understanding of how to find the sum of the angles, then (especially with an advanced class) I might give them those last two polygons to find the sum of the angles as more problem solving types of questions to push the limits of their understanding.
The activity didn't go poorly by any means; it actually went very well there's just a few things I would like to change. With a little guidance from me the students were able to come up with a general formula for finding the angle sum of polygons at the end of the lesson. Which my students before weren't able to do and didn't have the time to do. At the end of the lesson as I was passing out the worksheet with a reflection and take home piece, I had students cover with me possible answers they could have for their reflection piece on what they learned from the activity. By doing this I was able to get all the students involved and thinking about the lesson along with gauge their comprehension of what we'd just done and know if they were taking away from the lesson what I wanted them to. This wasn't something I did with 2nd hour and was really helpful because I realized how much my students had taken away from the activity and even though they were chatty they really learned a lot from the activity and had a lot of fun.
There are definitely ways that I could shorten or extend this activity based on how in-depth I want my students to explore and how much I think my students can handle. But overall I think for my first time stepping outside my comfort zone and doing an activity with students I was able to create an activity that engaged students, was fun, and had them learning and taking away from the activity exactly what I wanted them to.
Monday, February 10, 2014
Home run or strike out?
I realize that it's been quite some time since I've posted; with taking six classes, TA-ing Monday-Friday, and working four jobs I'm pretty much using more time than I even have available. Plus! This past week I began my unit with 2nd hour on Monday and 3rd hour on Thursday. After hardly sleeping through the night Sunday night, I woke up bright eyed and bushy tailed ready for my lesson with second hour (mind you this is sarcastic and I was actually terrified). I've learned that all my past experience with kids babysitting, nannying, and tutoring has really helped make me feel comfortable being in front of the kids and I find that what I most worry about is how much influence I have over these young minds. It's absolutely terrifying how some students hang on nearly every word I say and how much influence I have over their lives and minds; but this is also an absolutely amazing feeling. I cannot put into words how amazing this week was for me, every day I love teaching more. People always say that it's the "ahhh-haa" moments that are some of the most memorable and rewarding and after hearing my students have these moments this week I have to agree with them. It truly gives me butterflies to hear my students say "ohhhhhh! That makes so much sense now!". And just the fact that in my first week of teaching I was able to give many students moments like this is just mind blowing (I can't help but be a little proud of myself).
That being said, this does NOT mean that the week went flawlessly. Monday and Tuesday went very very well, and this was a big bonus seeing as Tuesday I was observed by the College of Ed. Needless to say, I was more nervous/terrified going in to teach Tuesday than I was Monday. But I also came out of Tuesday with more confirmation that this exactly where I'm suppose to be right now and I'm doing exactly what I'm suppose to be doing. The first thing my COE coordinator said to me in our meeting after my lesson was, "You're going to make a great teacher". Just hearing that from someone who's been in the profession for so long was so great and encouraging. I'm so hard on myself when it comes to my teaching that I can convince myself of things being much more terrible than they actually are. I ended up getting a voice mail from my coordinator later in the day telling me how great my lesson was again, and saying he couldn't get my lesson out of his head. Isn't that what we want from our "students" and ourselves? Our lessons to be so great that our students go home and talk about them to their parents or apply them to aspects outside of our classroom...
What made Tuesday even better was how great the students were and how receptive they (typically) are to the lessons I give. They're so willing to learn and interact with me and are not afraid to ask questions and I really can't ask for a better group of students to try out all my crazy activities on and begin my teaching career.
After Tuesday's lesson came Wednesday lesson; which I went into knowing I had a TON of material to cover and fingers crossed I'd have time to cover it all. Sadly, that lesson didn't go as smoothly as Tuesday's and because I spent majority of the period covering the beginning vocab, this left little time at the end of the lesson for the more complicated portion of the section. I only had a few minutes left in the period and quickly gave a simple example of the end material with little explanation. This proved to be fatal mistake. I knew at the end of that lesson that students were NOT comfortable with the material and did not come away from that lesson with an understanding of what I wanted them to. This is where the idea that teachers need to be 'flexible' came into play. I decided that what was best for my students was to recover the material (mostly the end of the lesson) again the next class period and give them two days to do the homework. It was when I was giving the lesson for a second time that I had nearly every student saying "Ohhhhhhhh! I get it now!" and though it was frustrating for students to be so confused on the homework assignment and lesson initially and it was frustrating for me that I was unable to give a clear, precise, and involving lesson the first time around this really was a good learning experience about being flexible when lesson planning. Being able to cover the material a second time, a day later, was also really helpful for me to get an understanding of where my students got tripped up and come up with a different way to present the material.
Moral of the story: though a lesson might strike out the first time it's presented, this is an important step in the learning process of becoming a teacher and it's important that we're able to be flexible and pay attention to our students needs. You never know, the same material presented in a different way might just be a home run the next time around.
That being said, this does NOT mean that the week went flawlessly. Monday and Tuesday went very very well, and this was a big bonus seeing as Tuesday I was observed by the College of Ed. Needless to say, I was more nervous/terrified going in to teach Tuesday than I was Monday. But I also came out of Tuesday with more confirmation that this exactly where I'm suppose to be right now and I'm doing exactly what I'm suppose to be doing. The first thing my COE coordinator said to me in our meeting after my lesson was, "You're going to make a great teacher". Just hearing that from someone who's been in the profession for so long was so great and encouraging. I'm so hard on myself when it comes to my teaching that I can convince myself of things being much more terrible than they actually are. I ended up getting a voice mail from my coordinator later in the day telling me how great my lesson was again, and saying he couldn't get my lesson out of his head. Isn't that what we want from our "students" and ourselves? Our lessons to be so great that our students go home and talk about them to their parents or apply them to aspects outside of our classroom...
What made Tuesday even better was how great the students were and how receptive they (typically) are to the lessons I give. They're so willing to learn and interact with me and are not afraid to ask questions and I really can't ask for a better group of students to try out all my crazy activities on and begin my teaching career.
After Tuesday's lesson came Wednesday lesson; which I went into knowing I had a TON of material to cover and fingers crossed I'd have time to cover it all. Sadly, that lesson didn't go as smoothly as Tuesday's and because I spent majority of the period covering the beginning vocab, this left little time at the end of the lesson for the more complicated portion of the section. I only had a few minutes left in the period and quickly gave a simple example of the end material with little explanation. This proved to be fatal mistake. I knew at the end of that lesson that students were NOT comfortable with the material and did not come away from that lesson with an understanding of what I wanted them to. This is where the idea that teachers need to be 'flexible' came into play. I decided that what was best for my students was to recover the material (mostly the end of the lesson) again the next class period and give them two days to do the homework. It was when I was giving the lesson for a second time that I had nearly every student saying "Ohhhhhhhh! I get it now!" and though it was frustrating for students to be so confused on the homework assignment and lesson initially and it was frustrating for me that I was unable to give a clear, precise, and involving lesson the first time around this really was a good learning experience about being flexible when lesson planning. Being able to cover the material a second time, a day later, was also really helpful for me to get an understanding of where my students got tripped up and come up with a different way to present the material.
Moral of the story: though a lesson might strike out the first time it's presented, this is an important step in the learning process of becoming a teacher and it's important that we're able to be flexible and pay attention to our students needs. You never know, the same material presented in a different way might just be a home run the next time around.
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