Ending One Chapter and Starting the Next

Wait, I’m graduating this week?

I cannot believe I am finally reaching the end of my undergraduate career.  It has been a long 5.5 years, with the exception of the past two semesters. You know you’re doing something you love when the days go by faster than you can believe. It wasn’t until this week that it really sunk in that I was ending my time as a student teacher. I was extremely blessed to be offered a long-term substitute position in the classroom I have been teaching in, so my time with my students is not quite finished. However, it is an odd feeling transitioning from “student teacher” to “substitute teacher.” I am so excited for my journey to continue.

I’m not sure how to even begin talking about how I have grown this semester. From my confidence to my relationships with my students, I’m sure I look like a completely different teacher than I did on that first day. It’s a really cool thing to experience what happens to a classroom overtime. Each class has it’s character, but you don’t really see it until about a month into the semester. It is so interesting to see how the students evolve once they feel comfortable. Knowing how each class differs, I am now able to tweak activities from class to class if I know one strategy works better in one class than it does in another. Discovering how students learn best has been one of the most useful things I have learned this semester.

One strategy that has really worked well for my this semester has been “think pair share.” This is a well-known strategy that students often grumble at if you call it by its name, but there are so many different ways to implement it. One of my favorite ways is to have students complete a problem on their own, and then pair up with their partner while they each share their answer and how they got it. This can initiate some really great conversations, and I love watching students learn from other students.

Another strategy that has worked well for me is the implementation of videos – or really anything I can show that is more interesting than me standing in front of the room talking. I’m not talking about instructional videos, but rather a video that sparks interest and that has math embedded. My favorite website for finding these videos is 101qs.com. You can search any mathematical concept, and you will almost always find a video. My favorite part of implementing these videos in the classroom for the first time is the confused look on students faces when I simply ask them to write down any question that comes to mind after watching the video. It took some prodding, but they eventually came up with some. However, the second time I did this in the classroom, it was clear students were already thinking of questions while watching the video and came up with some really great things. After the students share their questions, I tell them which question we are focusing on for this lesson and then their goal is to solve it.

Lastly, another strategy I really love is the use of “expert groups.” Again, this is using the idea of students teaching each other. With expert groups, students are assigned a concept that they are to master. Once they have done this, they pair up with a different “expert” and the students teach each other about their concept. I really love using this in the classroom. Students feel a sense of autonomy over their learning, and they are often proud to share with they know. This worked great in my geometry classroom.

Throughout this semester, I have had good days and bad days, but I have also had great days that remind me of my passion for teaching mathematics. There are so many more things I have learned this semester, but I know there is even more still to learn. I can’t wait to continue this journey of constant learning and endless fun.

Looking Back

As this semester comes to an end, it is so difficult to put into words everything that I have learned and experienced throughout these past four months. I have found myself many times trying to do this very thing, and I end up stumbling over my words. It’s just too much. Too much good. There are so many awesome things happening in math education right now, and I am so excited to be a part of it. Last week, I got the opportunity to take part in some workshops hosted by Dan Meyer here in Grand Rapids. If you don’t know who he is, you can check out his website at http://mrmeyer.com. To get a feel for the revolution that’s going on in math education, I would also highly suggest watching his short Ted Talk at https://www.ted.com/talks/dan_meyer_math_curriculum_makeover.

These workshops were so beneficial to me as a future math teacher, and I am so excited that I was invited to be a part of it. Dan is extremely influential right now in the math community, and he has insights into student thinking that are all too often overlooked. One key thing I took away that I will touch on that I thought was so profound was the idea of giving students information only when it is necessary for them to have it. Meaning, rather then giving students vocabulary words, formulas, or concepts at the beginning of a lesson that they have no idea what they’re used for, give them a problem where, through working on it, they reach a point where they need those vocab words/formulas/concepts in order to complete the problem or do it more efficiently.  This way, students see the purpose of these tools, rather than as just something they have to learn or memorize because you’re telling them too. This makes so much sense, yet why is it that the standard teaching method is to start a lesson by giving students all of their vocab words for that day to copy down into their notes? This idea is definitely something I will take away from this experience and implement into my teaching.

When I first decided I wanted to teach math, I had a completely different idea of what doing math was. I was good at math in school, and to me, that meant being able to simplify a nasty algebraic expression and get the right answer every time. It meant being able to do mental math faster than all of my other classmates. I held on to this belief as I entered my Teaching Middle Grades Math class. When the professor started talking about how “doing math” meant hands-on activities and exploring the deeper mathematical concepts, I wanted to laugh and say, “Maybe this isn’t the profession for me.” However, my tough facade slowly faded away as I began to realize that my previous view was horribly, horribly flawed. Sure, I was good with my multiplication tables and I was fast with solving for x, but I had no idea what I was really doing. I didn’t understand where the formulas in geometry came from or how or why they worked, or where pi came from, or why a triangle always has 180 degrees. I didn’t understand any of this. And frankly, I didn’t care. But that’s because I was good at it. What about the students who aren’t? I had to imagine not being good at math and then not understanding what any of this stuff even means. That’s when I began to realize, students deserve a better explanation than what the average classroom today is providing them with. This semester has fully prepared me to do that very thing, and I could not be more thankful to be in such an excellent program.

I truly can’t believe that this semester is over. Although it was the most challenging semester of my life in so many ways, I feel so accomplished and have gained so much. I absolutely loved the classroom I spent these past four months in, and I learned so much about myself as a teacher. Being in the classroom confirmed my preconceived notion that connecting with the students would be my favorite part about teaching. Although it was a very sad day that last Friday in the classroom, I am so excited for the new experiences that are to come this fall in my high school placement. But first, I am ready to enjoy a much needed summer break 🙂

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“Children want the same things we want; to laugh, to be challenged, to be entertained, and delighted.”

Dr. Seuss

A Look at Another Classroom

A couple of weeks ago I got the chance to observe another math teacher in the school where I’m Teacher Assisting in. After being in the same classroom all semester, it was interesting to get a new perspective of how other teachers conduct their classroom, especially those in the same content area. One of the things I wanted to do was find out what his beliefs were about teaching, learning, and doing mathematics. To do this, the teacher I observed filled out this survey:

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From here, I was primed to observe his classroom. The class started with music playing in the background while students were doing a warm-up from the book. The environment was playful, as he would sing along but change the lyrics to tell students individually what they needed to do. The classroom management style was a bit more relaxed than what I was used to in my own classroom. Students were talking during the warm up and there was a medium noise level in the classroom. After the warm-up, the teacher conducting “good news” with the students. This allowed for a friendly environment in the classroom. After this, the students were reviewing for a quiz the next day. For review, the teacher picked out homework problems from the book to work on in pairs. Each student had a whiteboard, and when they were finished with the problem they would hold up their whiteboard for the teacher to see. He would then either tell them, “yes” or “no.” This was used as a formative assessment for him and a review for the students. The students seemed very eager to share their answers and to get the right answer. If they were wrong the first time, they would quickly erase their answer and try again. The teacher would often ask the excelling students to help the struggling students around them. This went on for the rest of the class period as review.

It was extremely beneficial for me to observe this classroom and the teaching style that this teacher used. Not only was I able to gain some strategies to implement into my own teaching, but I was also able to gain insight on things that I do similarly or differently and might want to change about my own teaching after looking at it from an outside perspective. Every teacher has a different approach to orchestrating mathematics, and they each have their own reasons for doing it this way. It was very interesting to see a teacher use more of a lecture approach during the warm-up, versus someone like my CT who demonstrates and models how to do mathematics on the white board or ELMO. Although I might think that one strategy is better than the other, it is important for me to remember that some students might learn better other ways. I will keep this in mind while teaching in my future classroom.

“The older I got, the smarter my teachers became.”

Ally Carter

It’s Game Time.

I’ve reached the point of my Teacher Assisting career where I am wrapping up my final unit. I was fortunate enough to have a CT that allowed me to take the reigns and teach two full units this semester, so it is crazy that it is coming to an end. However, I am reaching this point feeling extremely accomplished. This also means that this week is Test Week. I had to squeeze in my final observation with  my content-area professor, so I had him observe on Monday when we were reviewing. I had designed my very own review game for the students to play, and even as we were approaching the day-of, I was a little unsure of how I felt about it. I had mixed-feelings about review games, as I’m sure many teachers do. It seems a lot of times students focus more on winning than they do on the content, or the students who aren’t getting it just sit back and let the students who are do all the work. So, one of my goals was to have the students actually gain knowledge from the game that would help them prepare for the test the next day, while also making sure every student was working. My idea was to have them get into the groups that their seating arrangements already had them divided into, after which I would number them off 1-4 in their groups. After they had their number, they had to keep this number the whole game. Each round of the game, a chart would pop up that had 4 different problems numbered 1-4. Each person was responsible for completing whatever problem matched their own number. Once every person in the group had completed their problem, the designated “number” for each group would report each teammates’ answer on the board. After the answers were revealed, we tallied up each groups points.

As I mentioned before, one of my main goals of this lesson was to make sure that every student was engaged during the game. That was the main reason I designed the game the way I did, with having each person complete a designated problem. Overall, I thought it went really well. Each student seemed to be really into the game and doing their own problem every time that a new round started. We had a few issues with a team “perfectionist,” if you will, doing everyone’s problems for them, but after explaining that we needed to let everyone solve their own problem and only help if they needed it, all was well. The game produced the kind of energy in the room I was hoping for; excitement, focus, and a competitive spirit. As my professor pointed out, this kind of game works really well for middle-schoolers because it allows them to release their energy by getting up and writing their answers on the board, celebrating if their answers are right, and then focus all that energy back in to concentrate on the next problem. It was really awesome to see something I came up with on my own come to life (and not be a complete bust). When I asked for honest feedback, I got some really great tips. One thing I wished I had done that my professor pointed out was that my students didn’t have anything to bring home with them or look back on from the activity. If they got any questions wrong during the game, they just moved on and never were able to go back and see why or what the problem was because they weren’t provided with a hard copy of the problems. If I were to do this again, I would definitely give the students a hard copy of all the problems at the end of the game for some type of review before the test the next day. Although the majority of my students were engaged during the game like I’d hoped for, there was one student that seemed to be the outlier. She was sitting off to the side not participating 100% of the time, kind of off in her own world. This made me wonder what I could do to make this activity more engaging to her or what I could have done to help her better understand what was going on if she was lost. So even though the majority of the class was engaged, it was still my goal to make sure the entire class was participating. For next time, I will try to be more alert and aware of what I can do to make sure this happens.

Here is my review game:

“If a child can’t learn the way we teach, maybe we should teach the way they learn.”

Ignacio Estrada

 

Time Management

Over the course of the past month a half or so that I have been teaching, it has become clear that I tend to spend more time on things than my TA partner. There have been a couple times where I am pressed for time towards the end of the lesson and find myself trying to squeeze the last piece of information in before I let the students burst out of the classroom. When my content-seminar professor was coming in to observe me and asked what I would like him to focus on, I decided this would be perfect. I had him time how long I spent on individual tasks throughout my lesson. It was extremely interesting to get the data back and see where I dedicated my time throughout the lesson, and perhaps where some of that time could have been better spent.

After my observation, my professor and I took part in a coaching session where he really helped me dig into how I felt the lesson went and especially with what I wanted him to focus on, in this case, time management. The data he collected showed that I spent a pretty even amount of time on each task throughout the lesson, with the majority of the time being spent on the more complex example of the lesson (which I was okay with). However, there was one time where I spent a couple minutes with a student who was struggling with a concept. On this particular day, I was extremely pressed for time and was trying to fit a lot in, so these two minutes were very crucial and could have been better utilized with whole class discussion. It’s not that it wasn’t important that I talked with this student, but there might have been a more appropriate time where he could have gotten help and the rest of the class could have benefited. I also noticed how if I would have just spent maybe 30-45 seconds less on each task, I would have had 4-5 extra minutes left at the end of class instead of being pressed for time like I was.

So what does this all mean? I’ve been trying to look at what’s best for the class as a whole rather than just seeing individual students in need. This might sound a little bit harsh at first, and that’s exactly what my problem has been. I have been so worried about making sure every single student gets it that I’ve ignored the fact that the majority of the class has moved on which in turn causes my classroom management to flounder because they have nothing else to do. It’s hard to find that magic number of students that you want to understand a concept before you can move on, but I’m not sure there is a universal number. You have to assess what is best for your students, as well as what material you have to cover before the year is up. This is going to be different for every classroom, and unfortunately, hardly ever will this mean that all of your students understand every concept. Of course, you still need to make accommodations for students who need extra help, this just sometimes needs to happen outside of class time.

This was extremely helpful for me to reflect on and really get down to the root of why I seem to spend a little extra time on my lessons. My yearn to have every student understand is something I value about myself as a teacher, and I will implement this into my teaching. This also helped me to think about what is truly important in a lesson. If I’m running out of time during a lesson and this is the only day I can spend on it, what things do I absolutely need to cover? These are things I will definitely be conscious of when planning a lesson from now on. By using differentiated instruction as well as simply continuing to improve my instruction as a whole I hope to cut down on the number of students who struggle all together and hope that this will be less of an issue. I will also explore other instructional techniques that allow me to meet and work with those struggling students while still allowing the excelling students to work and further their learning. Overall, this was a very helpful experience in allowing me to analyze how I manage my time in the classroom and how to better myself as a teacher.

“Teaching kids to count is fine, but teaching them what counts is best.”

-Bob Talbert

 

Math and Chocolate Go Hand in Hand

As I was sitting in class on Tuesday, I began to look at the calendar. This isn’t something I’ve had a chance to do much this semester, as I usually focus on what’s happening week to week rather than looking at the bigger picture (and let’s be honest, I’m avoiding the giant projects due at the end of the semester). So as I’m sitting in class filling in my planner with all of my assignment due dates, I decide to count up the number of weeks we have left. FOUR. FOUR WEEKS. THAT’S IT. Excluding Spring Break, we only have four weeks of classes left. That is terrifying and exhilarating at the same time. I am also extremely sad to be leaving my students in such a short period of time. Although I have only been with them for two and a half months, I have grown very attached. Anyway, that’s not what this blog post is supposed to be about and I’m getting all sentimental, so let’s move on. The point is, the semester has flown by, and without even realizing it I have compiled a collection of awesome activities that I can’t wait to use in my future classroom. I decided to create one this week that dealt with exploring the Pythagorean Theorem. I had heard about a jelly bean activity on Pinterest, so I decided to tweak it a little to fit my classroom setting. It went really well, and the students thought it was pretty cool. Plus, they got candy, and what middle-schooler doesn’t love that?

My goal behind this activity was to get the students to derive the formula for the Pythagorean Theorem on their own, and by doing this, extend their retention rate of the formula. The activity allows them to see the formula visually represented as well as numerically. By using multiple representations, my goal was to allow diverse learners to all get something out of the lesson and understand the formula as well as its application. Here are some pictures from the activity:

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I asked the students to see how many whole M&Ms fit on the sides of each triangle. I labeled the sides a, b, and c. I then had the students find the squares of a, b, and c, as well as the sum a2 + b2 . The students recognized that this was equal to c2, so it was easy for them to derive the formula from this.

We have done quite a few “quick-proofs,” as I like to call them, at my placement and I can not stress enough how beneficial I believe it has been for the students. When they come up with formulas on their own, they are so much more likely to not only remember the formulas but also understand the underlying concepts and the actual math that these formulas come from. I will continue to do this in my future classroom to help my students get a deeper conceptual understanding of the math they are doing before they become procedurally fluent. If I can throw some chocolate in here and there, even better.

“Teaching should be full of ideas instead of stuffed with the facts.”

-Author Unknown

Let’s Talk

Last week, my content seminar professor asked us to explore some different blogs of fellow math educators on the Five Practices for Orchestrating Productive Mathematics Discussions – which is a fancy way of saying, “Let’s talk!” A blog I found to be extremely interesting and helpful with understanding this process was Christopher Danielson’s, which you can check out on the following link: http://christopherdanielson.wordpress.com/2011/08/30/five-practices-in-practice/

The five practices are:

1.Anticipate     2.Monitor     3.Select     4.Sequence     5.Connect

So basically, you first anticipate the strategies you think your students will use to solve a given problem. Doing this allows you to be a step ahead in the classroom so you will hopefully know what to prompt and say next. Next, you monitor your students’ work. This allows you to see if what you anticipated was correct. It can also help you to start making mental (or physical) notes of who you will call on when it’s time for the actual discussion. Next, you select. This is where you make your final decision on who you want to have share their findings to the rest of the class. This is extremely important, because the rest of the students are (hopefully) listening and will be learning from their fellow classmates. Also extremely important, is sequence, or order. The order in which you have students present their findings is crucial in that you want student learning to be optimized. And finally, connections. It is extremely crucial that students make connections between strategies of what has just been learned, especially if that means explicitly pointing them out as teachers.

This really inspired me to want to have a great discussion in the classroom. I tried my hand (slightly) at this on Tuesday. It wasn’t planned, but I had read the blog recently and it popped into my head as something that might work with this particular lesson. We were doing an exploration activity that was aimed at getting the students to discover the direct relationship between angle measures and opposite side measures of a triangle. I went around from group to group and wrote down on a note card which groups had different findings, and I had the order that I wanted them to share. What I hadn’t accounted for was that I already had the students set up in groups and discussing it amongst themselves, so when it came time to discuss as a class – they were about all talked-out. This was a classic case of beating a dead horse. However, I definitely won’t let this stop me from using this strategy many, many times in the future. I am really excited to see what kind of discussions can come from this.

“Spoon feeding, in the long run, teaches us nothing but the shape of the spoon.”

E.M. Forster

Making Connections

I’ve been reading a book called The Teaching Gap by James W. Stigler and James Hiebert, and I must say I was pleasantly surprised. I’ve actually been pleasantly surprised with a few of my required texts this semester, and I’ve found I truly am learning a lot from them and actually enjoying the readings. This book in particular has been comparing and contrasting U.S., German, and Japanese math lessons. The findings are extremely…interesting. Granted, this book was written over a decade ago,but it is really giving me great insight into what types of lessons allow students to actually learn. Or as we math educators like to say, do math. 

One thing I have learned this semester, and that this book encourages as well, is the importance of making connections between lessons. I think so often this is where unneeded confusion in the classroom comes from, and almost always this could be easily avoided by the teacher. When students aren’t able to understand how each lesson fits together, all they have is scattered information from multiple different days that they’re trying to keep straight rather than being able to see the bigger picture and how it all fits together. As educators, it is our job to not only allow the students to make these connections but to explicitly point them out to them. I tried to focus on that this week while I was teaching, and I think it went pretty well. At first, I think the students were a little annoyed with how many questions I kept asking them, but they’re getting used to it now. Today, we were learning about regular and irregular polygons and we had just finished a lesson last week on triangles. I asked the students if they could tell me what type of triangle would be a regular polygon. Right away a few hands shot up and I got the answer I wanted; an equilateral. Knowing the students could still recall the classifications of triangles and connect it to the idea of a regular polygon was reassuring, and it felt really good to use a question I had thought about before my lesson and have it go over well. This will continue to be something I work on, as I feel it is one of the most important aspects of teaching mathematics.

Oh yeah, and I received this lovely green apple at the GVSU Green Apple Ceremony welcoming me to the College of Education. Much to our dismay, it was not edible.

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“Tell me and I forget. Teach me and I remember. Involve me and I learn.”

Benjamin Franklin

Engagement

We’ve been talking a lot about engagement in one of my seminars, and I couldn’t help but notice the lack-there-of from my students during certain parts of the day. It actually kind of surprised me the first time I noticed it. I was absolutely appalled that there was a possibility that every single student didn’t find me completely entertaining at all times. However, I think it was the multiple looks that resembled (more or less) this adorable picture of a baby that gave away their lack of amusement.

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I first noticed this lack of amusement when I was going over specific homework problems with the class. It seemed that only a few students needed help with these questions and the rest of the class was either bored because they knew the content or didn’t care to follow along. Now that I have taken over and started teaching, I wonder if I want to stop going over specific homework problems as a class all together. It seems that this class time might be better utilized doing something else based on the engagement level I have noticed during this time. There have been other times I have noticed a lower engagement level, and I am still working on figuring out how to keep the students engaged as well as what classroom management techniques I want to utilize in my future classroom. For now, I am going to try to use faces such as the ones above as a sign that maybe I should be analyzing my lessons and figuring out how I can make the activities more engaging.

“The object of teaching a child is to enable him to get along without his teacher.”

Elbert Hubbard

Diving Head First

After only two successful full weeks of Teacher Assisting and two weeks cluttered with five snow days, I officially start teaching my very own unit tomorrow. I. Am. Terrified. Or, at least I should be. I’m not really sure why, but I today I have had a strange sense of calmness about tomorrow, and I’m actually really excited. Maybe it’s because my partner and I get to debut what we have been working on for the past couple of weeks. Are you ready? FOLD-CABULARY! Okay, so maybe I came up with the cheesy name, (which, by the way, has yet to be claimed by any source on Google.) but it is a way for the students to keep track of their Geometry vocab for the unit and I am really excited about it. To get a feel for why the “Fold” part of Foldcabulary makes sense, here’s a picture:

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So basically, we will have the students write each vocab word on a tab of paper all with a picture explaining the word, and on the reverse side of the paper will be the definition. And then you FOLD it all together! Genius, we know. Unfortunately, we cannot take credit for all of the genius behind this credit. You can find the basis for this awesome idea at this link: 

http://www.wolcottschool.com/files/2613/7833/2551/Vocabulary_Foldable_.pdf

Dominic and I are extremely lucky to have such an awesome CT that is willing to give us such independence and allow us to teach this early in the semester. By doing this, we will each get to teach at least 2 units this semester. Right now, Dominic will be teaching first block and I will have second. I am so excited and a little nervous, but I’m really excited to get this first lesson out of the way. I’m really going to focus on classroom management, because I’m pretty sure these bundles of joy are going to try to push the limits once the “new teachers” are in charge. I hope they are ready to learn about the wondrous world of Geometry! Because everyone loves Geometry, right?

“Much of education today is monumentally ineffective. All too often we are giving young people cut flowers when we should be teaching them to grow their own plants.” 

John W. Gardner