Looking Back and Moving Forward

I probably couldn’t even list, let alone discuss, all the things that I have learned this semester. I have gotten so many opportunities to push myself, to fail, to succeed, and to grow as a teacher. I’ve had some of the best times as an educator and some of the worst and I walked out of this semester feeling more passionate and excited about teaching than ever. These are some of the most important things I’ve learned about myself as a teacher.

This semester, I taught two sections of Honors Geometry and two sections of Honors Algebra II. As I moved forward, I found myself teaching a different lesson to my second section than my first. I chalked it up to having different students. But, that wasn’t the case. I realized that I was evaluating myself in the first section and noting things that I should change for the next class. Before this semester, I had not really known the benefits of reflection. The next time I would be teaching a class would be next semester and I would have time to improve it. I realized that the best time to improve lessons and to make changes is right after you teach it. I made little changes, like the order of activities or the way I worded something, in order to increase the opportunities for student learning. That’s a piece of advice that I will be sharing with others and taking with me in the future. Reflect, change, improve, alter, and better your lessons each day. Ensure that every time you teach it, it gets better. We shouldn’t move forward as teachers teaching the same lessons day in, day out, year after year. We should be constantly improving. The best way to do this is reflection.

Teaching an honors class was hard. There’s no way to hide that. It is. The pace is faster, the material more difficult, and the expectations more steep. The freshman students I had were doing math that I, and most people, didn’t see until junior year or later. I had these assumptions about freshman students and what they could or couldn’t handle in terms of mathematical challenge. I was wrong. I taught lessons that, by the time I reached the middle, I realized I needed a bigger challenge for them. These students thrive through challenging tasks and I wasn’t doing them justice. I wasn’t challenging them. Over the course of the semester, I improved on this. I learned how to find where my students were at with material and what types of challenges to throw at them. By the end of the semester, every time that I wrote a lesson, I went back and made it a little more difficult. The benefits of this were amazing. My students were coming up with solutions, explanations, and mathematical conversations that blew me away. As freshman they were thinking more critically than I had until college. From this, I learned an important lesson. We’re teaching for the students, so we should be creating lessons for the students. I should be making lessons that challenge my students every single day, whether they are low-achieving students or honors students. Challenges are what create rich mathematical learning.

One of the best strategies I have used this semester is implementing technological demonstrations. During a unit on angle theorems for circles (chord-chord, inscribed, etc.), I used Geogebra Tube to illustrate to students the concepts. These technology applets allow me to spend less time constructing examples for students, give students the opportunity to discover ideas,  provide the opportunity for increased engagement, and give more accurate depictions of concepts. Before this semester, I was tired of hearing about implementing technology. I felt like it was just people talking just to talk, who didn’t have any evidence that implementing technology would actually benefit student learning. In my own classroom, I was proved so wrong. I felt like my students gained a deep understanding of the concepts and some even wanted to continue playing with the programs at home! New teachers, especially student teachers, should use technology in their classrooms. Try certain programs to see if they work in your classroom.

Finally, I have found that think-pair-share works great for me. I really want students to be able to convey mathematical ideas to one another, both through writing and discussion. When there were conversations that I wanted to have with students, I always asked them to do a continuous write for 2-3 minutes to get their ideas solidified. Then, they would get into table groups and each share. Finally, we would discuss the ideas as a class. I love this strategy for many reasons. First, students are able to write about math. Students don’t get to do that very often, and they should. Second, the solidifying of ideas before class discussion really helps students to have something to say. At times when I have just tried to start a discussion, very few students would contribute. After a think-pair-share, I usually had to stop conversation or it would last all class. Finally, I think that it allows for group collaboration. Once students shared their ideas, many groups would discuss different ideas and build on them. The think-pair-share just elicits so many characteristics that I want my students to have.

Overall, I can’t imagine trading this experience for the world. I’ve learned countless lessons, met some amazing mentors, made connections with students that will last forever, and found myself as a teacher. I love this career and I can’t wait to move forward.


Middle School vs. High School

Let me preface this post by saying that I have always wanted to teach high school. Since I started my career in education, I have been thinking of my “perfect” job and it was always in a high school. Every time.

And then I was placed in a middle school.

When I started teacher assisting at a middle school, I was hesitant, to say the least. I went into it having these assumptions about middle school teaching and about middle school students. In the first weeks of observations and planning, I began to think about the lessons that I would want to teach. All my assumptions about middle school education led me to believe that the way that I wanted to teach wouldn’t work. That I couldn’t do student-led instruction, that I couldn’t use collaborative work, that I couldn’t maintain a looser classroom management plan. Then I just realized that these were assumptions. I could teach however I wanted. So I did. I began to create collaborative lessons and student-led lessons. At first, my coordinating teacher was hesitant. she let me try it anyway. And it worked, most of the time. The students that I had were so much more capable than I had been led to believe. All of my assumptions got in the way of being a good teacher. After I had let them go, I was able to focus on the teaching and on the students.

Don’t get me wrong. This wasn’t all rainbows and butterflies. It was hard. I was in a middle school rich with diversity and filled with students from various socio-economic backgrounds. There were classroom management issues. There were motivation issues. There were issues with student abilities. The experience taught me to just push through these. Good teachers don’t settle with what has always happened or what is easy. Good teachers push their students to their limits, no matter what age they are. When I entered that middle school, I thought my students couldn’t handle certain things, like rich mathematical tasks and collaborative work. But I challenged them. I threw it at them anyway and they exceeded my expectations.

During this placement, I fell in love with the middle school level. The students were young enough to be playful, interested, and still new at mathematics. They were also old enough to have complex mathematical discussions, use collaborative work effectively, and rise to the challenge. It’s an age that I am so endeared by and it’s content that I am so excited for.

This semester, I was placed in a high school in a setting that was almost the polar opposite of my middle school setting. There was very little diversity and not as large of a gap between SES of students. I was also teaching only honors classes, meaning the mathematical ability of my students far exceeded some of their peers.

In my student teaching, I had far different issues than I had before. Classroom management was hardly an issue. But, now, I had to worry about appropriately challenging students who were above the norm in their age group. My strategies for this were different than in a middle school. In a middle school, I had focused on allowing for a little bit of a struggle before students gave up. And this happened quickly in my middle school room. Now, I allow students to struggle far more. The high school students can struggle longer and harder before they will give up, allowing me to challenge them further. I love this aspect of high school teaching. These students aren’t that far from being “adults.” They’re capable of struggle and perseverance and I can use this productively in a math classroom.

Another thing I learned in a high school setting is how different classroom management can be. In my middle school, I had to maintain a more strict policy than I would have liked. But, students needed more order to maintain focus. In the high school, I had a loose classroom management policy. I treated my students as adults and they rose to that expectation. They were missing homework? They made it up on their own time and got it to me. They needed help? They came before or after school to ensure that they understood concepts. I fully believe that students will rise to the expectations you have for them. While this works in the middle school, I think that their social and emotional development is working against them during this time.

Overall, I really learned to stick with my passion, which is teaching. I loved both of my placements and I think that I will love any school that I am at. I want to teach and I want to inspire and I want to take everything that I learned with me to be the best teacher that I can be. And I don’t think that I could choose between a middle or a high school. I used to only imagine myself happy in a high school. Now, I know that I will be happy wherever I am teaching.

Math-team-matics Competition

A couple weekends ago, I was able to be a math coach for Rockford’s Math Club at the Math-team-matics Competition at GVSU. Earlier in the year, a group of students decided they wanted to bring the math club back out of retirement, where it has been for the last few years. Their love of math is infectious and inspiring.

As we walked into the competition, one of the students said “I just hope we don’t get last.” For their first ever competition, I would say that was a reasonable goal. Throughout the day, I didn’t get to follow the Rockford math team, but I got to follow Northview. Seeing these students made me remember why I wanted to become a teacher and why I fell in love with math. For an entire day, each of these students put other plans on hold in order to do math. And they had SO much fun. I think that somewhere, along the way, the fun has gotten sucked out of a lot of mathematics classrooms. But, sometime in our lives, every math teacher had that moment where they fell in love with math, with the pure enjoyment of it. We need to bring that back into the classroom.

The students at Grand Valley that day were inspiring, to say the least. But they were also incredibly impressive. The challenges that were thrown at them weren’t easy, but they were able to use their reasoning skills and their creativity to work through the problems. One of my goals as a mathematics teacher is to be able to challenge students and to force them to think creatively and reason their way through problems. Classrooms should be more like this. They should throw problems at students that encourage them to think, to reason, and to be inspired.

As much as I took away from this experience as a teacher, I think the greatest benefit was seeing how happy it made my students to be a part of the competition. They were so excited that I agreed to take them and they were having so much fun all day. Their goal of not placing in last was achieved. They took third! This was such a huge accomplishment for them and I could not be more proud.

“Thank you for being their teacher.”

Recently, I had the opportunity to lead my first Parent Teacher Conferences. Most teachers dread these, or at the very least, they’re definitely not excited. I guess I’m not most teachers. For days leading up to them, I couldn’t help my excitement. I think that parent-teacher interaction is so important and I was excited to be able to tell parents what I had been seeing in their children.

Much of my conference time was spent with my not icings of students. I told parents how their students were doing both academically and socially in my classroom. I made sure to not start each session with the student’s grade. To me, grades really aren’t that important. And, they aren’t the best indication of students’ learning. So, I began with each student’s positive contributions to class. And I had a lot of them. Throughout this process I found out just how lucky I am to have every one of my students. They each contribute something so unique to class and it was easy to tell their parents what positives they brought each day. These qualities ranged from the fact that students were vocal in class with their ideas about mathematics, they worked well in collaborative groups, they brought a positive energy and interest each day, etc.

One of the most amazing things about PT Conferences, though, was hearing from the parents about my students. Some parents shared their concerns about their student with me. Since I teach all honors mathematics courses, it was typical to hear that students were striving for an A that they didn’t quite have yet. But, what I found to be the most amazing thing was hearing parents say that this was their student’s first honors class, that they never expected this track, and how proud they were. It was inspiring hearing parents talk about how happy they were at their child’s success. A lot of the parents thanked me for what I had been doing in class, which was so rewarding.

My entire life I have wanted to be a teacher and it’s the most amazing thing to hear the words “thank you for being our son/daughter’s teacher.” My goal in this field is to help students be successful, no matter how they define success. For some of my students, success is that A. For others, it’s learning what they need to know to be prepared for their future careers. For others, it’s to just do their best, no matter what grade that brings. I want to help all of them get there. PT Conferences really hit me hard. They made me realize how important what I’m doing is. I’m affecting these students, their parents, and their lives. I don’t take that lightly. I also realized how special each student is. Everyone says that, but I never really knew what it meant until I got the opportunity to discuss each of my students. They are all such inspiring individuals and I’m proud that I get to be a part of their lives, even if it is only for a semester.

Road Trip Across the USA

Last week, my students worked on mastering the distance and midpoint formulas using a really amazing lesson, linked here:


My goal in this lesson was for students to practice using the distance and midpoint formulas while staying engaged, working in collaborative groups, and applying math to real-life scenarios. Students worked in groups of four to plan a trip across the United States. They were given a map with a coordinate plane and were required to travel through ten states over a 5 day period. Students were to find the distance traveled each day using the formula. Then, they had to stop each day exactly halfway between their start and endpoints for gas. They were to find this pit stop point using the midpoint formula.

Students in both of my classes were incredibly engaged throughout the lesson. They were discussing mathematics and were actually excited to do the project. Students were on task, focused, explaining mathematics to each other, working together to solve problems, and getting a lot of practice with the concepts. My favorite lessons involve controlled chaos and this one had a lot of it. As it became one of my favorite lessons to date, I wanted to know what my kids thought. Were they as excited about this lesson as I was? Here’s a sample of their feedback:

“I really enjoyed this project because it wasn’t just boring problems.”

“I prefer packets over projects like this because I can work independently and I can solve things problem by problem without having to pull many things together.”

“I enjoy the bookwork because everyone gets the same answer, but I really like a break once in awhile with a fun project that applies the math with the real world”

“I enjoy doing bookwork because it is very orderly. But I enjoy projects because they allow me to do math differently and be away from the norm. I like both equally.”

“I like this activity because it puts math into real life and it is easier for me and less boring.”

“Well I like the project itself because it’s a more interesting way to practice the concepts. I really don’t like how we had to work in groups.”

“I liked this better than packet work because there were far less problems, but I feel I learned the same info.”

“I enjoyed doing the map because it was a lot more hands on and the book is not. I feel like I learned more and in the book I would not understand things as well.”

“I love working on projects like this. I understand what we are doing better and I love to work in groups.”

“I prefer doing activities like these because they help me use real things which help me understand the info better.”

“I find doing an activity like this was fun. But I also learn well by writing notes and trying examples in class. So, I think I would like doing both (like doing these activities every now and then).”

My favorite response is the one that said that they had far less problems to do, but learned the same info. Isn’t that the point? Students in math are so used to getting drowned by repetitious practice problems. Instead, we should be giving students problems like these. Ones that give students an opportunity to learn the material, practice the material, and master the material without feeling like they just did 100 problems. My CT even mentioned to me that I should ensure that students had actually learned the formulas, as opposed to just skating through the activity. The next day, part of my warm-up asked them to write down the formulas without looking in their notes. Almost universally, every single student had the correct formulas written down and knew how to use them.

I couldn’t imagine how much my students’ responses would impact my teaching. So many teachers just do their jobs without realizing that we really work for our students. We are there simply to ensure that they succeed. How are we supposed to do that without asking them what they need and what they prefer? I could spend every single day of an entire school year doing activities like this USA activity and be perfectly happy. Some of my students probably could too. But not all of them. We need to be listening to students and seeking out their input. In this case, I was thankful that my students loved this lesson as much as I did.


#MichEd in the Classroom

#MichEd in the Classroom

A couple weeks ago, I had the opportunity to work with Brad Wilson and #MichEd, an effort to connect Michigan teachers and students and highlight the amazing things going on around Michigan schools. If you want to know more about them, head here: http://miched.net/. You can also check out more pictures from his visit by clicking on the picture above.

This experience has, by far, been one of the best I’ve had in the world of education. Brad visited the classroom that I am currently teacher assisting in to highlight what new teachers are bringing into the classroom. The lesson that I taught was a hands-on activity in which students were to create their own hubcaps, focusing on maintaining rotational symmetry. This served as an introduction to the concept, forcing students to use manipulatives in order to understand the ideas behind rotational symmetry. Students used paper plates, angle rulers, and wooden shapes to construct artistic hubcaps that were rotationally symmetric. They learned about what it means to have rotational symmetry, what an angle of rotation was, and the order of rotational symmetry. My students gained so much from this activity. They were having fun, talking about mathematical concepts, and working collaboratively to achieve their goal. (Plus, we got some pretty awesome new decorations for the classroom out of it too.)

The main reason Brad was there, both in my classroom and later in a discussion with other Grand Valley teacher assistants, was to understand what new ideas future teachers were bringing to the table and how we were implementing them in the classroom. One of the main ideas in the lesson that I taught was working with manipulatives. Were they necessary in building an understanding for my students? Why did I choose to use them? I truly believe that students need to construct their own understanding. Too much of mathematics education of the past has focused on teachers spewing out information and hoping students would absorb it. This isn’t how people learn math. That’s not how people learn anything. Instead, we need to be guides in students’ education. Throughout my lesson, students were constructing their own meaning on what rotational symmetry meant. They had guidelines to follow, but were forced to make decisions on how to place shapes in order to maintain the symmetry they desired. Some students split their hubcap into 8 slices and made each slice rotationally symmetric. Some students made 8 slices but made every other slice rotationally symmetric. And they could argue why it worked. The student who made all 8 slices identical only had to rotate their hubcap to the next slice to reach a point of symmetry. The student who skipped slices had to rotate two slices. But, still, they both had rotational symmetry. It’s these ideas that students develop THEMSELVES that are important. I could tell them what rotational symmetry was. I could show them examples. But, that doesn’t teach them how to DO mathematics. They aren’t DOING anything.

During our discussion with Brad, all of us GVSU students discussed how we have seen math change. We’ve been lucky enough to have the opportunity to be a part of the movement toward better math teaching, and better teaching in general. When we were in school, we were part of the “old” ways. We were set there to absorb information that our teachers spit out. We were sponges. Which also meant that we could wring ourselves out after a test and forget everything we learned. Until college. That’s when it changed for all of us. We had professors and classes that changed almost everything we knew about math education, what DOING math really was. We were using manipulatives for the first time since elementary school. We were constructing pictorial representations. We were explaining our thinking. FOR THE FIRST TIME. As 21-year-old college mathematics majors, we were doing math for the first time. Why? Why didn’t our teachers teach us in the way we were learning now? So much has changed since we learned math that we had to learn it all over again. And, it’s for the better. We’re taking this new idea of doing math into classrooms with us. We’re teaching our students what it means to do math and not just absorb information. We’re teaching them how to be problem-solvers, how to work together. We’re teaching them how to construct their own learning and discover ideas. We’re teaching them how to explain their thinking, develop conceptual understandings, and really DO math.

Brad is creating a podcast with all of the things we talked about over at #MichEd in the near future, so I won’t give everything away. But, we’re focusing on the future and we’re focusing on the students. We’re doing what’s best for them, not what’s easy, and not what our teachers of the past have done. There are so many great teachers in Michigan flooding our schools with great ideas, innovative strategies, and a passion for teaching students. This next generation of Michigan teachers feels the same.