Monday, July 31, 2017

#tmc17 Reflection!

Confession: I almost didn't go to #tmc17. I didn't really know anyone and went back and forth about whether it would be worth it to eat alone at lunch and feel super awkward and out of place. But I decided to do it anyway. I decided to branch outside my comfort zone and it was one of the best decisions of my life.

Let's back up. This year I'll be starting my first - that's right FIRST - year of teaching! Prior to TMC I had been incredibly anxious about my first year - the kids I'll have, teaching classes I've never taught before, how to structure my classroom, and so much more! But, as Graham Fletcher said in his keynote on Friday, I hope to surround myself with people who are smarter than me, and this has made me rest easier and fill with joy for the upcoming year. The nerves are still there, but I have hope in having just surrounded myself with 200 of the teachers I hope to be.

I couldn't quite think how to put all my thoughts into words, so I'm just going to write a list because I LOVE lists!


  • I will never be able to fully understand my students' stories, but that does not mean I cannot fully love them.
    • I had actually been processing this very thought prior to coming to TMC. As a white, straight woman from an upper-middle class background, I will never be able to know what it's like to go hungry, be in a foster home, or not have a roof over my head. Grace Chen's keynote reminded me that my students' stories started long before I had them in my classroom and they will continue long after they leave my classroom. I cannot always change the political injustices that have affected my students, but I can create a space in which they are wholly and fully loved, despite not being able to fully comprehend what they are going through.
  • Putting yourself out there is one of the most powerful things you will ever do.
    • Throughout the course of TMC, I asked questions to strangers, engaged in conversations, went out to dinner with strangers, asked for a MTBoS mentor on Twitter, and connected with people via Twitter. I found that through the simple act of engagement, I have been overwhelmed by power of community and the willingness of others to lend their time, resources, and encouragement.
  • As a math teacher, I want words, not numbers, to transform my classroom.
    • This point is two-fold: relational and instructional. I have always firmly believed in the power of words to build relationships in the classroom. I got the idea from another teacher awhile ago to have kids write letters on the first day of school where they can write anything they want to me! Last year, letters ranged from feelings about math to religion to death and it gave me a glimpse into who they are. I'll be taking this one step further this year by writing ALL my kids back within the first couple of weeks. This lets them know they are seen, they are heard, and they have something valuable to say. SO I LOVE WORDS! I'll be implementing Elissa Miller's "two nice things" in my classroom this year where if a student says something rude (even about themselves), they then have to say two nice things about that person. I love that it establishes a classroom culture of respect and creates a microcosm of the world I want to see (per Grace Chen's talk). As for the instructional power of words, I attended Tina Cardone's "Finding the Words" afternoon session and it identified the power of words in teaching mathematics specifically. My #1TMCThing comes from her session which is journaling! She has students journal at the end of each class by responding to two questions - 1 math related and 1 not math related. The non-math related question may be establishing a goal for the week, responding to a quote, etc. I loved the aspect of asking a math question for students to respond to so that I can get a sense of whether students conceptually understand the material or if they are just going through the procedure. It also adds closure to my lessons where I can give a quick re-cap of what was discussed and then have students write a few sentences. Note: we are on 90 minute block scheduling every day which gives me the opportunity to have them journal the last 5-7 minutes. I realize this may not be possible/tight on a traditional 45 minute schedule! 
  • Students forget....a lot.
    • Even with the best teachers and the best lessons (neither of which apply to me), students will forget what they have learned. I realized that it is not something to be feared, but something that I do need to work with. Through all the things that I've learned, I'm hoping to implement Delta Math as weekly problem sets to review on past material. I've glimpsed through the program, but never used it before so I'm sure there will be some hiccups along the way. But here's to trying new things, right? I am also hoping to use Delta Math as a previewing tool for upcoming material. Before a systems of equations unit, this might mean giving some example problems on solving equations or some basic systems of equations practice before it is taught. Since we are integrated (Math I, Math II, Math III), many topics such as systems and factoring come up in multiple courses and this can be a useful tool both for retention and previewing upcoming material for those who forgot from the previous course. 
  • There are thousands of great ideas out there. You don't have to use them every single day.
    • The greatest relief of my life was when Sean Sweeney was doing his "My Favorite" and he said he gives his kids a worksheet sometimes. WHAT A RELIEF. I try to incorporate investigations, Polygraph for vocabulary acquisition, activities, and more, but sometimes I end up falling back on the traditional worksheet and feel like a horrible teacher. I remind myself to strive to be better every day, but that it is okay. A worksheet doesn't make a horrible teacher just as much as a Desmos activity doesn't make you a great teacher. It's what your students are learning from it and the classroom culture around mathematics. I just remind myself that it's okay, I'm working, and I'm getting there.

Friday, January 6, 2017

MTBoS My Favorite Thing

Jumping into a new semester and starting as a full time student teacher (ahhhh!) means looking for new ideas/favorite things that I'm excited to implement in the classroom this semester! I'll be teaching Math I and AP Statistics and I can't wait to jump in and get started!

One thing I am always looking for is new ideas and ways to practice that are better than just printing out worksheet after worksheet of exercises. Math I is an EOC course and I know that students need practice with these types of exercises, but I want to do it in a way that incorporates the collaboration and talking about mathematics that I want my students to embrace.

Enter: two-column partner practice. I stole this idea from Julia Finneyfrock who uses it in her geometry classes so this idea can work for lots of different math topics, but I'm planning to start out using it with practicing multi-step equations. The idea is that one partner completes the first column while the second partner is working on the second column. The catch is that the solutions in each corresponding row are the same. Students then compare the answers with their partner and have to talk through any answers that don't match to figure out which solutions are incorrect.


I'm excited about this idea because it allows students to be able to check their own work with a classmate and talk through their mistakes with someone else and have accountability for their misunderstandings. They'll have immediate feedback that something has gone wrong and they'll have to 

I can't wait to try out this idea this semester and see if it can get my Math I students talking and engaging more with each other and math!

Wednesday, November 23, 2016

Learning from the Best

These past few days I have had the JOY to get to observe two amazing 6th grade science teachers: Allison Stewart and Nicole Cesari. After one of Nicole's classes, one of her sweet girls came up to me and asked why I would spend my break coming into school. I definitely don't enjoy waking up at 5:45 in the morning, but I told her that Nicole was awesome and I wanted to become a better teacher. I'm secondary math and these two are middle school science, but one key thing that I learned is that teaching is teaching no matter where you go. Also these middle schoolers FOR REAL stole my heart so now I'm super confused about where to teach next year.

Here are some great things that I learned!

Both Allison & Nicole

  • Greet them at the door
    • Now I won't be requiring any high school students to line up outside the door if I end up teaching high school, but I think there is so much power in just saying "hello" or "good morning" to each student as they walk through the door. Students in any grade level bring so much baggage from outside sources into your classroom, and a simple smile as they enter class can change the tone of your classroom. 
  • Recognize students doing well.
    • When I have students struggling, it's so easy to focus all of my attention on those students and put the students are doing well in the background. However, it's important to recognize the students who consistently do what they're supposed to be doing, those that are growing, just celebrate the little successes in my classroom. Sometimes that may be as little as turning an assignment in, but that can be HUGE for some students and it's important to encourage that for them to continue to grow.
  • Each teacher has their own style - you have to find yours.
    • It was incredibly interesting seeing two teachers that teach the exact same grade and subject back to back with two completely different styles. I consider both Allison and Nicole to be successful teachers (hence why I chose to visit them), but they didn't interact with their students in the same way. There is no one way to be a successful teacher and I think that's important to remember.
Nicole

  • Sometimes caring is more important than content.
    • I honestly have never seen a teacher with such positive teacher-student relationships as Nicole. These students absolutely adore her and her former students will come to her after school to talk about life, which I think is incredible. This point is difficult for me, not because I don't believe in the power of love and care (if you know me you know I'm crazy about loving and encouraging everyone around me), but because I feel so much pressure from outside sources to get everything accomplished. We have a test, they have to learn, etc. And yet Nicole reminded me that students have deep-rooted problems in their lives outside of the classroom and sometimes these issues are more important than what's on the whiteboard.
  • We have to be solution-oriented.
    • Whether it is working with students with IEPs, 504s, or behavioral difficulties, we cannot stop at the challenges that they are having, but instead work at what we can do to help that student succeed. We must work to establish a relationship among students, parents, and teachers so that the student can be the most successful that they can be.
  • Noise is okay.
    • To be honest, I think some teachers and administrators would have had some control issues with all the noise in Nicole's classroom on the day before break. But, the kids were so excited and so into what they were doing. We have this idea of school that it should consist of students sitting in desks and absorbing information all day, everyday and that is what is destroying our children. In order to learn how to succeed, students need to learn how to collaborate, to communicate, to think critically, and to discover ideas on their own. I don't know many jobs that require people to just sit and copy words all day, without any critical thinking involved, but that is what we ask our students to do every single day.
Allison

  • Differentiation maintains high expectations for all students.
    • A misconception about differentiation (that real talk sometimes I even struggled with before visiting Allison) is that differentiation is about lowering expectations for students with disabilities and ELLs. I realized however that differentiation really requires you to know your students well and know what they are capable of. It maintains high expectations for their capabilities, but understands that high expectations may be different for different students for various reasons. 
  • Tough love is incredibly important for students to reach their full potential.
    • As I'm sure is common in many classes, Allison's students were struggling to complete assignments and turn in high quality work. Rather than continue on with unacceptable behavior and work, she discussed expectations. I think that resetting expectations on occasion can be so powerful for students to know that it's not okay to continue on an unsatisfactory path. I also believe that it's not helpful to just be mad at them, but as people they deserve to be explained why you are disappointed in them - just like you would in any personal conflict. Passive-aggressiveness will only weaken teacher-student relationships.
  • Student conferences can be powerful tools for reaching students.
    • After discussing her disappointment, Allison didn't stop there but instead allowed her students to have voice by asking the question - What motivates you? She then discussed with students via student conferences their answers to this question and asked what she could do to help them be more successful. As teachers, it's incredibly easy to put the blame on students, but exceptionally more difficult to realize our own shortcomings. After school Allison said something that I'll remember for the rest of my teaching career because it resonated with me so deeply. Neither Allison nor I were the type of people to turn in assignments late when we were in school and sometimes it's difficult for her to understand the reasoning of why they are doing it and really to empathize and understand their reasoning. I don't want to lower expectations for turning in work certainly, but I do think this recognition of my own blind spot will be extremely helpful in my own teaching.
All in all, could not be more THANKFUL to these two fantastic people for teaching me so much! They are wonderful teachers & even more wonderful human beings.

Monday, October 10, 2016

Teaching is Hard - An Open Look at My Heart

As a student teacher (that's not even full time yet!), I know what you're probably thinking...how can YOU think teaching is hard? You don't even have the paperwork, the parents, the lesson plans, etc. And you're right. I am just now seeing a glimpse of what it is like to enter into the world of teaching.

But I mean that teaching is hard emotionally.

Almost every single day that I go to my classroom I learn something new about the home lives of one of my kids. As someone who cares deeply for the well-being of others, I can't help but take on their pain as my own. I desperately wish that I could shield them from the hurt in their lives and take away the pain that they have all gone through, but I can't.

I struggle with classroom management with these kids. How can I be strict with them when this might be the only place that they have where they can feel loved? I've heard the quote, "Students who are loved at home come to school to learn, and students who aren't come to school to be loved." I have to constantly remind myself that holding high expectations of my kids is a manifestation of my love for them and that they will realize that. To set the bar high is to realize that they are capable of something GREAT.

These kids deserve the world. Often I feel that they deserve a teacher that is so much better than I'll ever be. Because of the lack and scarcity in their lives, I want to overcompensate by giving them some superstar teacher that knows everything and gets all the kids in the class to love math and love learning. But that isn't who I am and that isn't realistic. This is the population that I feel called to teach not only this year, but after graduation as well. In order to be a successful educator, I have to realize that I can't try to overcompensate for their home lives by trying to be more than who I am. I am enough because of who I am and because I will commit each day to loving and learning alongside each one of my kids.

So teaching is hard emotionally. There have already been days when I have come home crying and days I've come home smiling and filled with joy. It's a roller coaster of emotions but that's simply what teaching is.

"The best thing about being a teacher is that it matters. The hardest thing about being a teacher is that it matters every day."

Thursday, September 29, 2016

Order of Operations Misconceptions

Recently, I had the opportunity to interview a student going through a math problem and I was able to discover several misconceptions about how students think about a common topic in mathematics: order of operations.

I chose this problem and this topic because order of operations is found in mathematics courses from middle school through college. However, some students still have many misconceptions about it and how it is solved.

Here's what I learned about student understanding of order of operations:


  • Other grouping symbols are often not recognized as forms of parentheses in PEMDAS.
    • When students are just taught to memorize the acronym PEMDAS, they may fail to recognize the connection between other grouping symbols and parentheses. In this example, the brackets caused some confusion because of lack of immediate recognition. 
  • Students taught to memorize PEMDAS may always simplify parentheses first, even when they don't need to be simplified.
    • In the example above, -5 and -2 are in parentheses, but they cannot be simplified further because they are only a number in parentheses rather than an expression. However, if students just memorize an acronym and do not have a deeper understanding, they will immediately jump to anywhere that they see parentheses rather than knowing that it really involves simplifying within the parentheses.
  • Students can have difficulty associating the exponent with the entire grouping symbol, rather than the last number of the group. 
    • Students in the example above may want to square 5 or -5 rather than the entire group because it is in closest proximity. Students who are able to immediately recognize other grouping symbols as parentheses in PEMDAS in Misconception #1 are better able to avoid this misconception.


Other things that I learned from this interview:
1. I noticed that I frequently interchanged the words SOLVE and SIMPLIFY when asking the student about the problem. This can be so confusing for students because they are not synonymous! I need to check my use of mathematical terms if I want my students to understand the true meaning of the vocabulary.

2. I need to ask questions about the right answers as much as I ask questions about the wrong ones. Students can become conditioned when they hear questions to know that they are wrong and immediately correct their response, rather than develop deep thinking about the material. They will search for what they think you want to hear instead of thinking critically about whether their answer was actually correct or incorrect. If I question their correct and incorrect thinking, they become accountable all the time, not just when they are mistaken.

This was a huge learning opportunity for me to check my own difficulties with questioning and learn order of operations misconceptions from a student perspective.

Thursday, September 15, 2016

Quizzes and Tests and Warm-ups oh my!

For my assessment class, we had the opportunity to interview two teachers at our school about what assessment was and how they assess in their classes. In our EDU 315 assessment class we have read a lot of articles about formative assessments, summative assessments, and the importance of checking for understanding in our classrooms. However, there are only so many articles I can read before my head starts spinning. Hearing from other teachers first-hand about how they institute assessment practices in their classrooms helps me to visualize how I can implement my own assessment practices someday.

Collaboration among teachers is incredibly crucial and I learned so much with talking with these two math teachers about what they do in their classrooms. This practice, although not through formal interviews, is definitely something I want to bring to whatever school I will be teaching at next year. I want to hear the opinions of others in order to learn and develop my own assessment philosophy.

A few things important I learned:

  • Modifications aren't only for students with IEPs.
    • This can look different for varying students but can be anything from circling only certain problems to complete, not counting it against a student if they don't finish, etc. For example, we had a student who worked tirelessly on a quiz today but didn't have the opportunity to finish the last two problems. My CT said that instead of just counting those questions as wrong she would simply take the number correct out of the number that he completed. Obviously I knew that I should/must accommodate students with IEPs, but I didn't know how to accommodate others who struggled in the classroom. If a student works slower than the other students and automatically gets the questions wrong that they don't get completed, as a teacher I am not setting them up for success. Often times we are asked the question of being "fair" in the classroom, but through my assessment interviews I learned that fair sometimes has to look different and you have to meet every kid's learning needs. 
  • Assessment can look different in different classes.
    • Prior to my interviews, I had the misconception that the same teacher would assess similarly in all of their classes. However, I learned that although teacher preferences certainly determine how students are assessed in the classroom, the course structure is also a factor. The teachers at Williams assess frequently in Math I and Foundations of Math I because it is an EOC course, the students are mostly freshmen, and schools often look at Math I EOC data. However, in a Math II course, the assessments are much less frequent. The structure of Math II and other math courses doesn't lend itself as much to the daily quizzes and check-ups that you see in Math I. 
  • Assessment should be data-driven, generate data, and have a purpose. 
    • One surprising thing that I heard is that we shouldn't just assess for the sake of assessing. In my assessment course, we have talked about how great assessment is and why we use it, but we haven't really talked about when we don't use it. When should we not assess our students? I think that this point will help me think about why I am using a particular assessment, how it ties back to the standard I am trying to address, what data led me to that decision, and what data I hope to gain from that assessment.
  • Self-assess! Total class failure is a reflection of you, not them.  
    • It's okay to admit that you failed. Reteach! That is what assessment is supposed to teach you. The goal is that the students obtain mastery of the material, not that they make good grades on the assessment. If this means that you have to take a day and reteach a lesson, then do it. Learn from your assessments so that your students can learn from you.
I could certainly write more about all that I learned about assessment through these interviews, but these were some of my greatest take-aways. I can't wait to learn more about assessment and how it will drive instruction in my classroom!

Thursday, September 8, 2016

Let's do this!

I've been browsing through Twitter and reading blog posts by math teachers that are rockstars, plain and simple. I figured I might as well give it a shot so I can pretend to have my life together as well. This blog will hopefully serve as a way to highlight the highs, lows, and everywhere in between of my classes, methods, and student teaching experience at Williams this year - as well as into my future as a teacher after that!

As for the title of my blog - exponential growth. I chose this title for three main reasons. One, it's just a great function. Two, I want my students to grow exponentially in my classroom through engagement and learning opportunities. And finally, I want to continue to grow exponentially throughout my time as a teacher whether I am a student teacher or have been teaching for thirty years. I am a firm believer that I can always learn how to become a better teacher for my students from the people around me through reaching out and asking questions. We as teachers are always encouraging our students to ask questions, but how often do we take the time to ask questions for ourselves to improve our own learning? I believe this is the only way for exponential growth to happen.

As for how I'm going to achieve this growth, I am so fortunate to have some of the best professors, CT, Elon alums, and classmates. I have already learned so much in both my methods and assessment classes about asking the right questions and how to implement formative assessment effectively. My CT is awesome! I just started at Williams this past week, but she has such a positive demeanor with her students. Every class period she starts off with "good news" and encourages her students to share something good in their lives with the class. The relationships that she forms with the students encourages me to build the relationships with my students as I remind myself that students don't care what I know until they know that I care. Next: ELON ALUMS. The most helpful people on the planet. I have reached out to several in the past few weeks and have received lengthy emails with wonderful advice, tons of resources via Twitter, and I'm actually interviewing one alum for my assessment class who currently teaches at Williams. It is so incredibly encouraging how sweet these people have been to me when they have their own lives and worries as teachers, but instead have taken the time to care and invest in me as a teacher as well. I cannot put into words my gratefulness and cannot wait to "repay" (if it is even possible) to all of the younger Elon teachers. Finally, the people going through this with me. We're gonna make it. Even if some people tell us teaching will give us the worst days of our lives, it will also give us the best days of our lives. I'm thankful for classmates who push me, who let me tell math jokes, and who most importantly ask questions with me about what it means to be a teacher.

2 weeks of classes down, 1 week in the school down, a lifetime to go.
LET'S DO THIS.