Know Your… (#DCSDblogs Week 4)

It’s the last week of the #DCSDblogs challenge for our district! I’m really proud of myself for coordinating this challenge and it’s been so fun to read and write blog posts with other awesome teachers in the district!

This week’s prompt is Tips and Tricks, which asks us to write a post with advice for a brand new teacher.

I think this is pretty hard to tell from the outside unless you knew me well that year, but I spent a lot of my first year teaching being extremely overwhelmed, stressed, lost, and anxious. The hope is that my advice could help some other brand new teacher avoid feeling like that!

It all boils down to:

#DCSDblogs week 4-April 23 - april 29



Know Yourself:

I knew going in that one of my biggest struggles in teaching and in being part of a school staff was going to be the fact that I am a huge introvert. I often prefer being alone to being with people and I’m not going to be the one to begin a social interaction. So the first thing I knew was that it was going to be difficult for me to get to know my coworkers and feel like a part of the group. So my mantra for year one was say yes to everything. Every time a staff email went out to invite people for drinks after school, I went (unless I already had plans). When people asked me to eat lunch with them, I did. If they requested volunteers for a district math curriculum writing, I went. I took every opportunity I could, even when I just wanted to go home and be alone.

And I made friends. Not as many my first year, but as my second year started, I realized that because I had said yes to all those things year one, people started inviting me to other things. Birthday dinners, barbecue at their house, to go to the play at another high school with them.

That worked for me because I’m introverted and knew I needed to force myself to get to know everyone, but it could be something else for you. Figure out what your barrier becoming a part of your school staff group is going to be and find a way to combat it.


The worst piece of advice I’ve ever heard for teachers, and I keep hearing it, and I’m sure you’ve heard it, is “don’t smile until November”. What the heck?! People kept telling me that, and I knew it wasn’t me. I’m never going to be a strict disciplinarian, it’s just not my personality. (I’m not even going to get into the fact that I think this is horrible advice even if you are a stricter teacher – especially if you’re working with disadvantaged students. They need smiles.) I knew that advice didn’t fit me, so I ignored it.

You need to know yourself to be an effective teacher. You can’t pretend to be someone you’re not in front of a classroom of students. They will know, and they will not respect you.


Know Your People:

Teaching is an incredibly unique profession. It’s a job that everyone thinks they understand, because everyone went to school and had teachers, but that’s not the same thing at all. We carry all the burdens and celebrations of our students with us, and no matter how hard we try not to, teachers often take the failures of individual students to heart.

It’s been proven that psychologically, teachers suffer many of the same effects of PTSD just by being exposed to all the struggles of all of their students. That was a fact that totally floored me when I first learned it.

I’ve discovered that what you need is your people. You need to find people on your staff, just two or three, that you totally and completely trust. And sometimes, when you’re having a really rough patch, you need to go find one or two of your people and just vent it all out. You need to know that these people won’t judge you for your frustrations, you need to trust them to not gossip about what you’ve told them.

These vent sessions should be contained – once all parties are done venting, you move on and leave it all there. It can’t turn into a negativity spiral, which is sometimes hard to do. But what I’ve found is that you need people like this THAT ARE TEACHERS, THAT WORK AT YOUR SCHOOL. You can’t take all of these burdens home and place them on your family and friends. Plus, they won’t completely understand anyways, because they aren’t within the climate of your building. You need someone who will understand what you’re frustrated about, and why it’s frustrating.

Then these people are also the people you can go to when you want to celebrate something – get really excited about a student who answered a question about something that happened three units ago, or show them this really cool lesson you’ve developed.

Find your people. Share the ride with them.


Know Your Students:

Getting to know your students as people is so, so important. They aren’t just vessels to dump content into. They. Are. Humans. Should I throw my favorite quote in here again? I think I should:

Every human life is worth the same, and worth saving.

– Harry Potter and the Deathly Hallows

If you can think of your students as people, it becomes a lot easier to find worth in all of them, even the ones who aren’t doing as well in your class. You should definitely do surveys at the start of the year, or find some activity that fits you that lets you get to know them as people.

This is my favorite section of my intro surveys:Capture

Many of my students struggle to fill in 10 things that make them happy, which is telling in itself, but it definitely shows their priorities immediately. The personality traits one I use to roughly sort them into a Hogwarts House (did you see that one coming????). I do that because as someone who is very invested in the series, it works almost like a Myers-Briggs type personality test would and tells me a lot about how students will work best and what methods will probably help them understand content the best. If I know they’re a Gryffindor, I know there’s probably a lot of pride involved, and that they most likely will struggle to ask for help when they need it, for example.


I also mean know your students in another way. The thing I most wish I had learned about in my teacher ed program and didn’t at all was mental health and childhood trauma. I do work in a specialized environment where all of my students are at risk students and so most if not all of them deal with either mental health or childhood trauma, but I think it is so, so important to know about even if you don’t work with a specialized population with a high incidence of that type of student.

If you’re a new teacher (or a not so new teacher) who feels like you haven’t been trained on mental health or childhood trauma, I strongly suggest you seek out your school counselor and ask them for resources. In the meantime, two of the things I’ve found most helpful are below.

The Adverse Childhood Experiences (ACEs) study, originally done in the 1990s in California, explores the link between different types of childhood trauma and the effects on later life. It’s shocking and upsetting how prevalent these are and what they can do to people’s brains. I’ve now taken a class on it, watched two documentaries, and read a lot about it and it’s quite literally changed my life. It’s all about the fact that this isn’t a choice; trauma truly affects your brain’s development and changes the ways you encounter the world.

Mindfulness exercises can really help students who struggle with anxiety, but also any student, as they struggle to focus and keep themselves calm during stressful class situations. Our mental health therapist did a professional development with our staff on mindfulness, and I’ve linked to some of the resources she gave us, including a mindfulness toolkit.


Note to Self (#DCSDblogs Week 3)

The theme for week 3 of the #DCSDblogs challenge is Oops! The goal is to talk about a mistake you made in your classroom recently and how you addressed it.

This year is the first year I’ve taught Algebra 2. Starting last summer and throughout the year, I’ve made sure to start my planning for this class a bit earlier than normal so I can process the content I need to teach and get my mind around the best way to present it. This is also the first class I’ve used Interactive Notebooks in, which has actually overall helped me with finding the core ideas of the content and finding the pieces that are going to resonate most with students.

The unit we just finished covered rational functions. I took a bit to re-acquaint myself with the process of finding asymptotes, adding/subtracting/multiplying/dividing and solving these functions. However, this unit came right in the spring break / Iowa Assessments time of year, and so my planning all got a bit wonky.

I definitely didn’t leave myself enough time to do the planning of these lessons justice, and it showed. Here are my notes to myself for teaching this unit in the future:

We started with sketching graphs of rational functions. The very first thing I realized is that my students, while proficient at factoring quadratics, have not gotten very efficient at it. This meant that every single problem seemed more complex, because pretty much regardless of what you’re doing with a rational function, the first thing you need to do is factor the numerator and denominator.

*note to self: more practice factoring quadratics to enhance efficiency

I also realized that in my process of sketching a graph – finding x and y intercepts, vertical and horizontal asymptotes, holes, etc., I had them finding the intercepts first. This ended up not making sense, because if there’s a hole at one of the intercepts, that point isn’t actually an intercept, so the holes need to be the first thing you find. This one was a fairly easy fix because I just had them write on the inside of the foldable “move step 2 to after step 4” and explained why we needed to do it in a different order. Everyone was fine, and we moved on.

*note to self: use a few examples to make sure the order of your process makes sense

Then, we hit the exit slip problem I had included on their foldable. They were feeling okay about finding the characteristics of the graphs, not so great about actually sketching the final curves amongst the asymptotes, intercepts, and holes, but I figured we could give the exit slip a shot and then come back and discuss it the next day. Rookie mistake: I had taken the functions I used for the foldable from one of their textbook’s worksheets for the section, and I hadn’t graphed the exit slip one myself because I wanted to leave it blank in my teacher INB since the students were supposed to complete this one on their own.

Turns out, this particular rational function has no asymptotes, which we had not seen any examples of and so every student completely panicked. They correctly found that there were no vertical and no horizontal asymptotes, but then they all just stopped working because they were convinced that wasn’t possible for a rational function and they had done something wrong.

*note to self: check the exit slip problem. Also, don’t assign a unique case example for an exit slip!


Next, we covered simplifying, multiplying, and dividing rationals, along with complex fractions. This section actually went really well, and my students felt really good about themselves after having a freakout when they saw the complex fractions and then realizing that they had all the skills to deal with them already! The only thing I want to change here is…again…the order of the steps. It makes more sense to rearrange the problem into a multiplication problem before factoring. My students were the ones who figured this out, because they’re awesome.

*note to self: seriously, check to make sure the order of your process make sense.


Adding and subtracting rational expressions is probably the most complex process in our district’s Algebra 2 curriculum. Either that or factoring polynomials above degree 2. Regardless, I did not do a good job of presenting this, or practicing it, or anything. I kind of botched this one big time.

First, the foldable didn’t leave enough room for anything to happen.

*note to self: give students enough room to do math on the paper!

Then there’s the fact that I just…didn’t explain this well. There’s really no way around it. I did not teach this well. My students didn’t know when they were finished with a problem, what to do next, they kept getting lost in calculations.

*note to self: spend some time doing more problems with adding and subtracting rationals yourself, so you can break down the structure better

*note to self: search the #mtbos and other online resources to see how other people break this skill down

*note to self: really, just scrap this section and start over from scratch for next year

I can end this post on a good note, though, because I made sure to set aside extra time to plan for the last skill in this unit, solving rational equations, and I think that turned out pretty well. My students loved making the pockets for their INBs and getting to stick the practice problems in them, which we also did for simplifying rational expressions, and it was a good way to fit more practice problems into their INBs without taking up more pages.

They also showed me that they really had mastered solving quadratics earlier this year, because that’s what you end up having to solve when you’re solving a rational equation. I was really proud to see them pulling out the Quadratic Formula or factoring again and just going at it!

*note to self: good job on this one 🙂


I learned from this section that I need to be more intentional about planning, especially with content I haven’t worked with myself in a while. I have stellar students in my Algebra 2 class, so we were able to overcome my shortcomings in planning without too much trauma, but they did get lower quiz scores over this content than I’m used to from them.

I’m hoping to have a bit of time left at the end of the year to come back to this content before their final, but I don’t think it would be productive to keep pushing forward with it right now. They need a break from it after the train wreck I put them through.

Please let me know if you have any great lessons over rational expressions and functions – I would love the help in improving this unit for next year!

*note to self: word processing systems don’t think asymptote is a word and it’s incredibly frustrating.

You Won’t Do This Alone (#DCSDblogs Week 2)

Last night, I went to see one of my favorite bands, With Confidence (and also Don Broco and State Champs) in concert.

One of my favorite songs by them is called Voldemort – this is also one of the ways they originally caught my attention, because obviously I’m going to be intrigued by any band who titles their songs after a Harry Potter theme!


As I thought about what I would write for this week’s #DCSDblogs post (The theme this week is Teachers Learning from Teachers), I started to realize that this song encompasses a lot of the things I wanted to talk about.

I remember the first night that she said
“Oh maybe I can do this on my own”

I am an incredibly stubborn and independent person, which is sometimes a flaw and sometimes an asset. When I set out on my first year of teaching, I was convinced that I could do everything myself. If I didn’t know how to do it, I could figure it out. The song is from the perspective of a friend who insists on being there for the girl described, even when she says she can do it on her own.

And I will try to hold you up
Through those times when you are gone
Despite the weather, it gets better
You won’t do this alone

In case any of you out there didn’t know yet…teaching is hard. My first year, I was overwhelmed and barely keeping afloat at times, and yet I continuously refused to ask anyone for help. Most of it was a little voice in my head that went, “you don’t have a specific question to ask, so you’re fine. You’ll figure it out.”

Heather, one of the other amazing math teachers in our building, worked herself into the cracks in my stubbornness over the course of the year. At the start of the year, when I refused all of her offers of help, she left me alone for awhile. As the year wore on, she would drop in occasionally and ask how things were going. Her questions got more and more specific – “do you need help with anything?” started to become “Which class is your most difficult this quarter? Is there anything you wish you could do to work with that?” and she made it harder and harder for me to just brush her off and pretend like I had everything under control.

I won’t even pretend this is a finished process today, because I still tend to think I can do things for myself, but Heather has helped to convince me that it’s not weakness to reach out for help in your classroom. We’ve built a relationship of bouncing ideas off of each other that now often will start a conversation off with “Okay, so I’m going to tell you this idea and I want your honest opinion even if it’s bad.”

I remember the first night that she went
To find her little place inside this world

The other piece of advice I’ve gotten that has hugely impacted my teaching was from one of my cooperating teachers in student teaching. On my first day in his classroom, Brian told me “I never take any work home. Home is my family place. If I bring things home, it starts to bleed into my time with them and hurts my relationship with them.”

Over the time I spent with him, he expanded on this idea to say that it doesn’t work for every teacher to take nothing home – he preferred to stay a little bit later at school in order to keep his home a work-free zone, but that the main point was to build boundaries for yourself.

It’s far too easy as a teacher to occupy yourself with the goings on of your classroom and your students every waking moment (and as I’m sure you can all relate, sometimes they spill into the sleeping moments too!). Obviously, this can be harmful to our existence as humans outside the classroom – our relationships with friends and family, our outside interests, etc.

In my first few years of teaching, I firmly adhered to Brian’s model of taking no work home – I didn’t mind staying at school later if I knew that when I got home, I wouldn’t have any work responsibilities at all. It’s only in the last year that I’ve been able to reflect on and reshape the model a little bit to better fit my own mindset and lifestyle – I still usually stay at school to do most of my lesson planning and grading, but now I’ll throw in a spare hour here and there at home to blog, or read blogs, or get the ideas down for a new activity before I forget them. The point is that you need your “little place inside this world”, like the song says, that separates your work from your personal life. We’re in a weird profession where the work follows you everywhere, and for our mental health it’s important to create those boundaries – whether they are physical, mental, or both.

As of right now, my boundaries are pretty much that I complete all must do work at school, and then extra things like blogging or a new idea or possibly getting ahead of the game if I have spare time and really feel like it can be done at home. That’s what works for me!


There’s a lot of things I’ve learned from other teachers so far, but those are the main few.

  • you need help, and other teachers can give it to you (admitting it is not weakness)
  • create some boundaries between work and your personal life
  • having a teacher you can trust to bounce ideas off of that will respond with honesty and without judgement is golden

And I know that you’re holding out for better weather
And I can’t promise you that I’ll be round forever
If there’s one thing I know it’s that we’re good together

We’re good together. The people around you have a lot to offer you, I promise 🙂

Book Recommendations (Vol. 01)

Reading is my favorite hobby.

At the end of 2016, I posted a wrap up of the year and when I wrote it, I wanted to include a top 5 books list. Two things stopped me – first, it didn’t seem like it fit with the theme of “professional top fives”, I just really wanted to make book recommendations to people. Second, I had read too many books to choose five from the whole year.

So this year, I’m going to try making these book recommendations posts every 3 months (a quarter of a year). They say “everyone is a teacher of literacy”, so here’s math teacher me, trying to convince you to read more for fun. Amazingly, the first three months of 2017 have already passed?!

As a disclaimer, the summaries are probably going to be pretty vague because I don’t like to go into books knowing too much about them, but I’ll give you the gist!


I’ve already read 15 books this year – here are my 5 favorites:


The Problem with Forever – Jennifer L. Armentrout

Mallory is starting her senior year, returning to public school for the first time in several years after being homeschooled following a trauma she endured while living with a previous foster family.  She encounters a face from that time that she never expected to see again, who was a light in the darkness of that home.

This book hit me really hard emotionally and I ended up crying through much of the last third or so. It is a very realistic portrayal of many of the hardships that our underprivileged, at risk, and traumatized students face on a daily basis. It is very painful to read at times, but it is also full of hope and the path of rebuilding trust and connection after it has been lost.

We Are Okay – Nina LaCour

Marin left her entire old life behind when she left California for college in New York. It’s now winter break and she finds herself alone in the dorms, the only one who didn’t go home or on a vacation. Her best friend from California, Mabel, shows up to visit and forces her to confront everything she left.

This book is such a short read, and is a really raw examination of everything that comes with grief and change. It’s another one that’s about broken connections and how to rebuild them, and how to re-imagine your life when you discover that things aren’t exactly as you thought they were. It’s written so that you feel all of the emotions along with Marin, and go on the journey with her of confronting what happened.

The Hate U Give – Angie Thomas

This book was inspired by the #blacklivesmatter movement and starts out with high schooler Starr witnessing one of her good friends be shot and killed by a police officer. The rest of the story follows the unrest in Starr’s neighborhood, her struggles to reconcile the world of her mostly white and privileged school with her friends and family in her mostly black and lower class neighborhood.

This one is really powerful – I read the whole thing in pretty much one sitting. “What’s the point of having a voice if you’re gonna be silent in those moments you shouldn’t be?” It really calls into question how you can sit in your privilege and not address something that really matters, and shows you the people who don’t have that choice. This is one I think everyone, but especially every teacher, should read.

Homegoing – Yaa Gyasi

Homegoing begins with the stories of Effia and Esi, half sisters who have never met and don’t know of each other’s existence, at the start of the slave trade in what is now Ghana. It follows the trail of their descendants to present day.

This is one of the most beautifully written books I have ever read and I keep raving about it to everyone who will listen to me. Every chapter gives you a brief glimpse into the next descendant down the line and in every chapter I found myself wanting to read a whole book about that character. In the end, it’s not a spoiler to say the two lines find a way to intertwine again and it is lovely and wonderful. It also gives a very interesting glimpse into different perspectives on the slave trade and the history of some of the ancient (and modern) Ghanaian people. But wow, is this book lovely to read.

The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life – Alex Bellos

It’s basically various stories about the histories of different math concepts – including how Kepler and Galileo used to send each other anagrammed riddles of their new discoveries, a giant survey to discover the world’s favorite number, and more!

It was just a really fun read. I had previously read and loved Bellos’ Here’s Looking at Euclid and also loved it. As is evident from those titles, he’s great at puns, and I also think he’s pretty great at explaining the math from a layperson’s perspective – so if you find math fascinating, but don’t feel super confident in your skills, this one’s for you! It’s just really interesting and will make you think about things you never considered. I know a lot of people don’t love nonfiction, but this is a pretty easy read for nonfiction.


So there it is – my top 5 books of the first quarter of 2017. Please, if you’ve read anything great, leave me a comment and hype it up for me – I love recommendations! Also, if you end up checking any of these out, report back and tell me if you loved it as much as I did!

The Pride Bubble (#DCSDBlogs Week 1)

!!! It’s the first week of the district wide blogging challenge that I created !!!

I’m really excited for this blogging challenge – to see teachers in our district who have wanted to blog have a reason to finally get started.

Anyways, the theme for week one is One Good Thing – to share something good that happened in your classroom in the past week and explain how it was celebrated.


It feels like on a daily basis, I’m carrying around my pride in my students within this bubble. I’m always proud of them – I teach a population of students who are in a daily fight with the low expectations the world has placed upon them, and every day that they show up in my classroom gives me pride that they haven’t given up yet. So the bubble always exists.

Sometimes it’s very fragile and small, and sometimes it inflates more and more.

And then sometimes it bursts, because it’s just too full of pride to be contained anymore.

My pride bubble burst on Friday.


My Algebra 1 students came into my class at the start of the year with little to no mathematical success in their histories. The challenge at the start of the year was to get them to even try. Throughout the year, we’ve slowly started doing some explorations/investigations at the start of new material in an attempt to expose them to the ‘real mathematical world’ where you aren’t just told a rule or formula; you discover it. When we first started doing these, most of what I would get were complaints like “how are we supposed to do this, we haven’t learned it?” and the like.

On Thursday, we began an algebra tile exploration on solving quadratics by completing the square. We’d already learned to solve quadratics by factoring and using inverse operations, and I’d alerted them to the fact that by the end of the year, we would have FIVE different methods for solving quadratics. I even warned them that this particular method would possibly be the least favorite for many of them, because that’s been my experience in the past with students.


We began looking at some problems together as a class – I explained that our goal was to make one side of the equation into a perfect square of algebra tiles, and we reminded ourselves that if we add extra tiles to one side, we must add those same extra tiles to the other side to keep the equation balanced. My pride bubble started swelling when we reached the point where we wrote the factored form of our first example as (x+2)(x+2) and one of my students offered, with no prompting, “couldn’t we write that as (x+2) squared?”


Then another student noticed that the problem suddenly looked like the ones we had been solving the previous week using inverse operations, and asked if we could solve it like those.


The next day, they were off, using their algebra tiles to complete the square and solve quadratics, on their own or in pairs. As I circulated, I kept hearing things that made my pride bubble swell more and more.

“No, remember, you have to split the x tiles evenly because we’re making a square”

“Wait, in this one the ones tiles are with the other tiles to start. Don’t we want them separate? Can we just subtract them to move them to the other side?”

“We’re always going to add positive ones tiles, right? It’s either negative times negative or positive times positive.”

“I don’t think we even need to use the tiles for this one. I know what’s going on.”


And these kids, who fought so hard against these investigations when we first started doing them in first quarter of this year, started asking me and each other extra questions that weren’t even part of the written instructions.

“Wouldn’t it be cool if there was a set of algebra tiles with an x cubed tile? What would that look like? It would have to be 3D, but how would you decide which side should be red and which side would be the other color, because there would be more than two sides but only two colors.”


“Hey, all of these have an even number of x’s.”

Me: “Would it be harder if there were an odd number?”

“Yeah, because you have to split them evenly”

Me: “We’re going to talk about that on Monday”

“Oh, man, that’ll be cool!”

(This was a student who just last quarter frequently sat in class mumbling under his breath about how pointless the class was and how much he wished it were lunchtime and failed over half his assignments)


“Are there problems that you can’t do like this? What would those look like?”


At this point, I was sitting at a table grading the previous class’ investigations because they were moving along so well without any prompting from me. The pride bubble was pretty huge at this point, and I was just sort of smiling to myself in the corner.

They started to get to the last two questions of the investigation, which asked them to look over all the problems they’d completed and try to find the relationship between the number of x tiles in the original problem and the number of extra tiles they’d had to add to complete the square. These types of questions have always defeated them in the past – I don’t think they’ve ever been asked to generalize before they got to me, and so they just fight against having to do it. They also hate to actually read instructions, so I was expecting all sorts of questions just because they didn’t want to read the fairly large block of text of the question.

Instead, they started to read the instructions aloud to each other. They started flipping through their packets to look at examples. They read the instructions line by line and paused to consider each piece.

All of them at least found the pattern that we were splitting the x tiles in half.

Many of them found the whole pattern and were able to use it to correctly solve one last problem without using the tiles.

One student, considering all his examples, asked, “Miss Mastalio, what’s the word for the answer to a division problem?”

This was his final answer:


This was when my pride bubble burst. I wanted to cry so many happy tears. These kids have fought and fought and fought thinking about how math works this year. Somehow, the dam has broken and they’ve worn down.

For some reason, this investigation wasn’t a fight. It was a triumph.

It was a great reminder to just keep trying. That they need practice grappling with new ideas, with finding patterns, with expecting math to have logical conclusions. That it will eventually pay off.

These kids are getting a school wide shoutout on Monday – these are read over our announcements and I individually named each student in the one I wrote after class ended. They were my #teach180 tweet for Friday and I’m so excited to do our formal notes on completing the square tomorrow and be able to say, “I know several of you already found this pattern; what was it?”


I love fourth quarter, when everything starts coming together.




(Here is the investigation I used, which is adapted from the exploration from section 9.4 of the Big Ideas Math Algebra 1 curriculum)