What makes a teacher?

This semester was not easy for me by any means. There were times when dealing with troublesome students and parents that really made me question if I was going into the right field or not. What I always seemed to come back to and ask myself was; why am I doing this? What makes this something that will be more rewarding in the end than not? I always found myself answering with “it’s the kids who have ‘ah-ha’ moments, it’s the kids who never say a word but walk into your classroom and smile or simply say hello, or the kids who ask if you could talk to them after class just because they need someone to talk to and they trust you.” It’s those kids that make this profession worth it. The fact that I am able to help and influence so many kids throughout my career is a blessing and makes all of the hardships and helicopter, finger pointing parents and students worth it. I’ve known since the third grade this was what I was meant to do, and though it might be hard sometimes, I still am confident that this is exactly what I should be doing with my life and exactly where I should be. This semester has helped to give me even more confidence in my decision to become and educator and made me want to strive to continually learn of ways to improve myself and my classroom.

This semester has really shaped my teaching philosophy and classroom management style. I have a much better understanding of what it means to control a classroom and the variety of techniques I can use to do so. I understand now the importance of establishing the respect of your students before relaxing and having fun. I also gained an understanding this semester of the effect communication has on the classroom. I think communication is key to dealing with student behavior issues and I’ve learned the power of a phone call home.

Classroom management isn’t the only thing I’ve learned this semester though. I’ve learned how to continually assess my students and adapt my lessons on the spot depending on the information I receive throughout the lesson on my students. I have a better understanding now of how to approach various lessons and how students learn. A strategy that I’ve noticed shows up often in my approach is constantly finding time to work with students individually. Throughout the lesson students are given time to work independently, this is when I take advantage of the down time and meet with students individually to assess their progress and use this to clarify any misconceptions individually or make note to clarify them as a group. I also then take the information I’ve gathered and use it to adjust the next portion of my lesson. I use it to decide how quickly to move with the next material and how many examples should be covered as a group, in pairs, or individually.

Another technique I’ve found I use often is collaboration/discussion. My classroom is loud, students are constantly talking and collaborating. I think this is key to learning; students should be able to discuss mathematics and the critical thinking involved in it. If a student is able to explain how to solve a problem to someone else, this solidifies their own knowledge. This works for me because this gets students actively participating and creates a more welcome atmosphere for students. My students aren’t afraid to make mistakes and are willing to learn from them together as a class. This, in my opinion, leads to a deeper understanding of key ideas and more critical thinking.

Overall, this semester was filled with so many more learning experiences than I could have ever imagined. And I’ve walked away with so many more teaching techniques than what I started the semester with. I couldn’t have asked for a better support team and I definitely could not have accomplished as much without them. 

Learning to let other's speak

With this next unit, my placement partner and I decided to try and co-teach the lessons. We also decided to use guided notes and start the chapter off with an activity. The best part of all of this...we chose to throw all of these changes at the students on a half day that just so happened to be PJ day and the day my placement partner had his last observation by the COE. Needless to say it was a fiasco! But man did me and my partner learn a lot about what we needed to change for our other class before we threw all those things at them. I also learned that I have a very VERY hard time letting other people speak, I tend to want to take over the lesson and present that material how I want without letting my partner know what's going on. This lead to quite a bit of confusion at first because though we both knew the activity we were doing, we took it in a completely different direction. This just made our first day that much more confusing to students and meant we had that much more to address before presenting the lesson to our other class.

Learning for our first fiasco we decided to change the following:

1. I needed to learn to let my placement partner teach. This meant that I needed to hold my tongue when he's talking and not interrupt him because most likely what I have to say is what he's going to say it just takes him a little longer to actually say it. We also needed to tell students that we're trying something new (co-teaching) and help them understand that we're going to make mistakes and we're learning how to co-teach and it's not going to be perfect.
2. We needed to introduce the guided notes at the beginning of the hour and warn students about them. We also needed to demonstrate to students how to fill in the guided notes. We decided this meant that one of us (me) would fill out the note on the ELMO with students while the other wrote on the board.
3. We needed to get on the same page about the activity and what it was we wanted to students to do. This meant putting together a worksheet that outlined these things. It also meant that we needed to do the lesson which the activity covered BEFORE doing the activity (the opposite of what we did initially). 

Once we had all of these changes plotted out and ready to go we came into our other class quite a bit more prepared than our initial class and with the hope that it would be much less of a fiasco. Especially since we were both being observed by our content supervisor...Now I'm sure you're asking, "Welllllllll! How'd it go?!?!?!?" I'm glad to report, it went great!

First of all, we did the lesson the activity covered the day before. This was first of all because of how horribly the activity and lesson went the other way around with our other hour. And also because we didn't want to give a lesson the day before spring break and felt the activity would be more engaging for students. Once we presented the lesson to students we were a bit worried because nearly every student seemed to really understand the lesson and we didn't know what this would mean for their engagement in the activity the next day.

Our activity dealt with fractions and decimals and converting them to percents. Students were first split into groups of two or three. Each group was then given the worksheet along with a cup full of (fake) coins. Each cup contained a dollars worth of the following coin values: quarters, dimes, nickels, and seven pennies. First we worked with students to make sure they knew how many of each coin value it took to make a dollar 4 quarters, 10 dimes, 20 nickels, 100 pennies). Next we took that and worked through the "Quarters" portion of the worksheet which had students first find the fraction used to represent one of the four quarters it takes to make a dollar. Then come up with this coin value in regards to the dollar amount (25/100) and finally the decimal and percentage representation of this. 

Once students understood this section and what we were asking them to do in the other sections we let them go and explore on their own. Since we were worried students would rush through the worksheet without thinking about it we made sure to tell them that it wasn't a race to finish the worksheet but more of an investigation to test their understanding and that they should work together to complete the worksheet. This was really important I think, because it forced students to work together and not simply take a portion of the change and work on their own. It was really neat to see the students actually physically using the change in the activity too because in all honesty the students didn't NEED the change to complete the worksheet but they chose to use it so they had something to manipulate and see. 

Me and my placement partner went around and asked students questions throughout their exploration to make sure they were understanding the activity and to gauge their understanding of the material and the underlying concepts. This activity proved to be a big success, every single student was able to answer our questions any way they were asked, they were able to explain their thinking, they were able to work collaboratively to understand the activity and concepts, and finally they had fun! Students were very engaged from the beginning of the lesson until about the last 20 minutes of class. I think this was because many students finished the activity early and didn't have anything else to work on. This is something that I would like to work on more in my activity structures. How do I create an activity that's long enough for my students to complete in the time allotted but also not discouraging and still is engaging? This is something that I plan on working on and collaborating with other educators on to figure out what works best for me and best for my students. 

Overall, I think being able to be observed and then have a coaching session about how our lessons/activities/etc went has been really helpful. I know I'm really hard on myself and tend to think that the lesson didn't go nearly as well as it actually did. And to sit down and take a step back and see the lesson written out by an observer and see the engagement level has been really helpful. It shows me where I need to focus more attention because there was lesson engagement and what I'm currently doing well. I think it's important for me as an educator to take the time to reflect on my lessons, even when it's not required of me, so that I have a better understanding of my strengths, weaknesses, and where I can grow the most. This semester has taught me so much about myself and my teaching style and I cannot wait to have my own classroom, to learn more about myself as a teacher, and to try new things. 

Observing and Learning

I think it's important to take the time to go and observe other teachers teaching styles and methods of instruction. This helps us grow as educators and opens us up to different ideas, which is really important. This past week I observed the geometry teacher at my school and was able to see how her approach to the classroom was different. She started the class off by writing the "I can.." statement on the board for the lesson of the day. This is very similar to what I do in my classroom but in my classroom I have the students create the "I can..." statement. After this she went through the lesson using google docs that the students had created the day before. The students had gone home and found proofs of a geometric property they were working on as a class. These proofs were found online and were suppose to be proofs that made the most sense to the students. Once the students posted the proofs to a google doc and shared it with the class they came in the next day to present the proof they found to the class and walk through the proof together. This was interesting to me because the students lead the class in a way. They were able to find something online that helped them make more sense of the topic at hand and then present this to the class. This is really helpful for the class to see what helps other students understand a concept in hopes that this might help them understand it better as well. The remainder of the class was the discussion of the proofs and tying this back to the topic for the day.

After observing this course and how it was run I had the teacher tell me about her thoughts of what teaching is, what our roles are as educators, and her view of the students. This was really interesting when looking back on the way the classroom was run. She viewed her role in the classroom as more of a 'coach' which was clearly visible in how we saw her 'give' control over to the students and allowed them to explore the concepts she presented in their own way but coached them through the process, clarifying any misconceptions. She said she see's that each student comes into the classroom with a different amount of talent and it's her job to form a classroom where each students' talent. She also said she viewed mathematics as like doing an experiment. This is evident in her classroom structure as well when we look at how she has each student explore a different means of proving one concept. She allows student to find other's "experiments" and discover if this type of experimenting makes sense to them and learn why this works for them as well.

This whole experience was eye opening to me because I had never thought to run my classroom through google docs and student presentations of found proofs. I think this is something that only works with very small class sizes (this class only had 4 students) and advanced students who are able to be held accountable for this proof search and presentation. Having students explore others' proofs would be something I might like to implement in my own classroom.

Discovery through Orange Peels

Today was by far the most excited I've been all semester about giving a lesson. The lesson was covering the surface area and volume of spheres. Kind of a tricky lesson if you want to do it correctly and not simply give students the formulas, which I think is ridiculous and would much rather take the risk of students not following the 'discovery' of the formula versus simply giving it to them. To me, it's important that students see where the formula is coming from and make connections from the formulas they already know to the new ones in the lesson of the day. That being said, before yesterday I had no idea how to do this with the formulas for surface area and volume of spheres. I decided my best option was to google activities on the discovery of the formulas. By doing this I found what I wanted to do; for the volume formula, which I chose to do first.

I decided to lead the discovery by starting with what we had used the previous two days to find the formulas for other 3D figures; the volume formula for a cylinder. From here I constructed an example on the board of a cylinder and a sphere with the same height and radius. I then label the height of the cylinder, and the radius of both the cylinder and sphere. My students then came up with the formula they already knew for the cylinder which I wrote on the board. Next, I told students to keep this in mind as we watched the following YouTube video dealing with actual objects representing the cylinder and sphere I drew in my example. Throughout the video I stopped to ask students questions to make connects to our example on the board. Initially we stopped to talk about what the black tick marks on the cylinder were breaking the cylinder into and after pausing here I told students to also keep this in mind as we continued.

We watched as the volume (water) of the sphere was poured into the cylinder. Students then noted that the volume filled up two of the three sections the cylinder was broken into. I asked students what this would mean for the formula we already know for the volume of a cylinder. They said this mean that the volume of the sphere was 2/3 the volume of the cylinder (yayy! exactly what I wanted students to conjecture/discover). Next, together we worked through the algebra of replacing what was the value h in the cylinder formula in terms of the radius of the sphere. Students got a little tripped up on the more complex math of these steps but once I had a student come up and explain the steps most (if not all) of the class caught on.

Link to the video: http://www.youtube.com/watch?v=aLyQddyY8ik

It should be noted that initially I was confused on how to go from the video to the formula I knew for the volume of the sphere. Once I presented this to my placement partner, Josh and we talked through what I was thinking, Josh had an Epiphany and realized the connection (the algebra portion of the discovery). There also was a joke along the way in the algebra about "how many R's ARE there?" or something of the sorts which I caught and laughed at and students caught on and we all enjoyed a good laugh together.

After I felt students understood this, we moved onto the really fun part of my lesson, which I was super stoked about all morning, surface area. This activity involved an orange, a piece of paper, a marker, and team work. Before even handing out the materials I first reviewed with students the formula for the area of a circle. Once we decided that the formula was pi*r^2 and not 2*pi*r (after much debate) I decided students were ready to move forward with the activity, students were told to work with their table partners on this activity. The basic steps of the activity are covered in the pictures below but generally it goes as follows: trace the circle four times onto your sheet of paper (one student holds the orange while one traces), next talk about the area of the circles and what relationship the circle has to the sphere (same radii), after this is solidified I had students peel their oranges. It's recommended that students break the peels into the smallest pieces they can (not ridiculously small but not large), this helps with the next step which is placing the peels into the circles that the students traced from their oranges. At this point some groups started working faster/slower than others so I gave students the directions for the next step and had them try and use what they knew (area formula for circles) to find a formula about the surface area of our 'sphere'. I walked through the class to check the progress of my students whether that be in fitting the peels into the circles or finding the formula.

I told students that they needed to remember their circles they traced from the orange were not going to be perfect, thus how the peels fit into the circles was not going to perfect but should be very close. Students were also told that their four circles 'should' be the same size (or very close) since they're coming from the same sphere. Once every group was done, every group was able to come up with the formula for the surface area of the sphere, 4*pi*r^2. I had one student come up to the projector and use my 'set of peels' to walk her classmates through WHY this works and how it worked. I could not believe how well my students understood this portion of the lesson and was extremely impressed with the students' explanation of the activity, how it worked, and why it worked. Needless to say but the end of the activity I was feeling like a proud mama bear because my students not only took away from the activity exactly what I wanted them to but they gained a deeper understanding of the why behind the math, had fun doing so, and were able to do all of this without their safety net of a PowerPoint which simply gives them the formulas and examples. I was able to create a lesson where students worked together, discovered, had fun, and still took notes**! What an accomplishment!

**For this chapter, the students are putting together flip-books with drawings of each 3D shape, the names, and the formulas for surface area and volume all in one place. This is where students took their notes for this lesson along with a separate sheet of paper where they wrote the examples I gave them once the formulas were found.

The following are the step-by-step pictures of the second activity:
Step One:

Step Two: 

Step Three:

Note that once you peel half the orange you should be able to fill two of your circles with peel.

Step Four: 

Ta-dah! Once the whole orange is peeled, all four circles should be filled with the peel.

Overall, I'm so proud of my students, myself, and how well this lesson went and am happy to share any lesson materials with anyone who would like them. I hope if you choose to do this lesson that it goes as smoothly for you as it did for me! :)

Wrapping Up

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!

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...

"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.