Improvising…

Today, I did one of my old favorite lessons with Algebra 1 – Inequality Speed Dating. By this time of the year, students are starting to think that they either have mastered solving equations or have no idea how to solve equations, and if we do any sort of straightforward practice they will be either bored or won’t try, based on which group they’ve sorted themselves into. So I like to use this activity to kind of jostle them into life a bit and force them to take more accountability for their work.

On Friday, we completed the first portion of the activity, which is for students to “become experts” at one single inequality. This year instead of gluing them into their notebooks, I gave them each a post-it with an inequality written at the top. Once they’d solved it and had it checked by me, they stuck it on the most recent page in their notebooks.

Today, we took out the post its and I explained the rules. Find a partner, write your inequality at the top of their whiteboard, 3 minutes to solve, then 1 minute for each partner to “coach” the other on how to fix their solution. If you read my post about this activity from last year, I changed several things about how I ran it.

And it fell apart a bit.

1st hour, I had two girls who flat out refused to participate, plus a small class, so those who were participating ran out of problems quickly after they had matched with only a few partners. Luckily, I had extra inequalities because my other classes are larger, so I gave them all new sticky notes with new problems and we managed to continue. Improvisation #1.

2nd hour, my students were super grumbly once they could no longer find a partner who was within their immediate vicinity and it became clear that they would have to move, God forbid. Cue Improvisation #2, where I put 5 new inequalities on the board and asked them to attempt all 5, then consider those 5 and the ones they had been coached on by their partners and tell me: 1 thing they felt they understood, 2 things they needed to work on, and 1 action they were going to take to improve. The last thing is inspired by that class period’s unwillingness so far to take responsibility for their own learning – they still have very fixed mindsets so we’re trying to work on them taking actions when they don’t understand.

4th hour, students were more receptive and almost all participated willingly and appropriately. We ran out of new partners with about 15 minutes left in the period, so in came Improvisation #3: I put two new inequalities on the board and asked them to solve them, then tell me 1 thing they felt good at and 1 thing they needed more practice with. This group, I encouraged them to write an example for their “one things” because I realized in glancing quickly at 2nd period’s that most of them did not have words to describe either what they were good at or needed to work on.

I was kind of upset, because this activity is usually one of my favorites and it…didn’t go well today, and I had many students so reluctant to participate. So, part of this post is taking credit for my own teaching improvisational skills. I don’t know what I would have done if this had happened 2-3 years ago, because I didn’t have the background knowledge to realize that pressing on was not the right choice, or the skill and capacity to come up with an alternative on the fly. So I’m proud of all three improvisations and I think they helped increase the effectiveness of the activyt.

 

But mostly, I want to reflect on why it didn’t go as well this time and how I’m going to regroup.

  1. Since my room isn’t set up in rows or a U shape of tables this year, I decided to have them move around to find their own new partners. This was clearly a mistake because it was where almost all of the refusal came in. “I don’t want to work with any of these other people”, “I don’t want to get up”, “I only want to work with this person”….there are less excuses if I set it up like I have before and set it up with chairs across a table with an inside and outside ring, and have one ring rotate each turn. Definitely worth rearranging my classroom for half a day to organize this rotation.
  2. Last week had a lot of absent students, as about three different viruses were going around. A few of those that were here on Friday weren’t confident about their solutions, and I had several students that I just had to hand a worked out solution to today so they would have a problem to exchange with their partners. Not really much I can do about that, but I’m acknowledging that it contributed to some reluctance to participate and low confidence today.
  3. I think the recording sheets I’ve used previously are necessary to this activity. As much as I love nonpermanent surfaces (whiteboards), and as much as our district is pushing us to make less copies, I think the accountability of “I actually solved the problem my partner gave me” and “I actually checked and coached them through their solution” are needed here.
  4. Good change: I think specifying 3 minutes to ONLY SOLVE, then 1 minute to coach the first partner through their solution and 1 minute to coach the second partner through theirs was really helpful. It led to less rushing than in previous years because they weren’t allowed to look at each other’s solutions until the first timer went off. I think I need to be even more explicit about this next year though, with NO MOVING ON to the next stage until the timer GOES OFF. We need to cultivate more time for thinking.
  5. Good change: problems on post-its instead of glued in notebooks. No need to bring the entire notebook with you around the room unless you wanted your notes. No constant flipping back to the right page because you shut it.
  6. Good change: we had a talk about “coaching” beforehand, along with an example conversation you might have with someone whose solution was incorrect.
  7. Idea: One thing students always get confused on in this activity is multiple solution pathways. That’s part of why this is a great activity, because it starts those discussions, but I get students coaching their partners that their solution was incorrect because they moved their variables to one side before they undid adding 7, or because they moved the variables to the opposite side that their partner had. I think it would be nice to solve an inequality like 2x + 5 < 4x  – 7 several different ways on the board to start class – perhaps something like 3 correct solutions, and 1 incorrect one, and then discuss how the coaching period would look for each of the solutions.

I want to remind myself that I still really like this activity – and that some of my favorite benefits of it did still happen for some students today, but I also want to acknowledge that I did something that didn’t go so well publicly, and I want to reflect on those failures to continue making my teaching better. I already feel better after typing those reflections out! And see, still some good coaching and solving going on in these pictures I took!

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2018-2019 Teaching Goals

Oh my goodness, this summer has FLOWN BY?! I had grad school classes for the first five weeks, then did some curriculum writing with my district for two weeks, mixed in with a lot of concerts and a trip to NYC to see Harry Potter and the Cursed Child and visit the Museum of Math and a really awesome MC Escher exhibit. And now teachers report back next Monday, students come back next Thursday, and I am NOT READY but also very ready.

I miss students in my life, which as always reminds me that I’m in the right profession. I miss making dumb algebra jokes with them, I miss singing Toto’s Africa or Sia’s Chandelier with them (what will the theme songs of this school year be???), I miss laughing and learning and loving with them. I’m stoked to have a bunch of new freshmen in Algebra 1, a ton of kids I had two years ago in Algebra 1 for Algebra 2, and the entirety of last year’s Algebra 2 class that was one of my favorites of all time is going to be the first ever Pre-Calculus class in our school!

I’ve been thinking a lot this summer about changes I want to make in my classroom, as always. I learned so much in my grad classes this summer (real analysis, an assessment course, and Geometry pedagogy) and am excited to apply those ideas, plus talking to other teachers and reading books and continuing to expand my worldview have me itching to try some things out.

I want to keep my goals attainable – we talked in grad school about not changing too much at once, for several reasons. You don’t want to burn yourself out trying to totally overhaul your entire teaching style at once, and you also can’t tell what effects the changes have if you make a bunch at one time. So I’m going to set three larger goals for things to change this year, and then goal 3b is to check in on those goals regularly throughout the year on this blog (midterms and end of terms, possibly?)

Goal 1: Grade less papers

My assessment course and our district’s transition to standards based grading have made me think a LOT about how I grade things. I am a big believer in giving feedback in a timely fashion, because how are students supposed to improve and learn if they don’t have feedback on what they are doing well or what they could work on until two weeks after they did something? Last year, this had me grading papers for almost every class I taught almost every night. I’m going to go ahead and admit that this was not that bad because I just did it while I watched tv in the evenings, and I did not have much of a social life on most weeknights. I seem to have developed much more of a social life over this summer and I…well I really don’t want to be stuck in my house grading papers every night.

I had the realization during the assessment courses we took the last two semesters in my grad program that feedback =/= grading. Wow! Some of you might be thinking that that’s obvious, but I had been thinking of them as synonymous in my mind for the past five years. We talked a lot this summer about oral feedback, checklist feedback during work time in class, partner feedback, and other ways to get students the feedback they need without them necessarily having to turn in a piece of paper (or digital work) daily. With the population of students in my building (at risk students), I try not to assign homework, so there are plenty of opportunities to give them feedback on their work during class without me taking a bunch of grading home. I will still grade paper assignments sometimes, I am sure, but I want to develop checklists of problem solving skills / math skills (based on our SBG rubrics for each standard) that I can quickly fill out during class as I walk around observing student work and I can carry my chromebook around the room also to input proficiency scores for practice assignments, which don’t count towards their grades anyways.

The goal is to take grading home two days per week or less.

Goal 2: Experiment with non-traditional assessments

I started doing this a tiny bit at the end of last year, with poster projects for both Algebra 1 and Algebra 2 asking them to synthesize the information they had learned about sketching polynomials or solving quadratics. They got to choose problems from a list, or draw random problems from a hat. They got to consult with partners. They were much less anxious and stressed and I felt that the results were a much more accurate depiction of what they knew than the paper-and-pencil tests I typically give.

Those aren’t going to disappear, but I want to try more different approaches to help decrease some of the test anxiety I see. I’ve read a lot about giving timed consultation periods at the start or end of a testing period – a few minutes, long enough to discuss something you need to clarify or get validation on, but not quite long enough to have your partner explain how to solve the whole problem. When talking about our SBG implementation, our district curriculum specialists have mentioned combining several individual skill quizzes into one assessment score that encompasses an entire standard. I want to think about having students make a mini-portfolio by choosing problems from the textbook with certain criteria to demonstrate their knowledge.

Basically, I want to incorporate more collaboration and choice. Fundamentally, this is based on two beliefs I have about mathematics. In the “real world”, 1. my students are rarely if ever going to be forced to complete math work in isolation. There will always be an option to ask someone for help or use a resource. 2. they will rarely ever be told they have to solve a specific problem. The problem will present itself in a non-math way, and they will have to select the math that will best help them solve the problem and that they feel capable of doing.

The goal is to have at least one “alternative” form of assessment every half term in at least one of my classes.

Goal 3: Class time to discuss completed work

I think this is one of my biggest teaching weaknesses, honestly. Since we do so much of our work in class and also have issues with attendance, I tend to leave this kind of task to happen individually during our intervention period or during work time. So two things here. One, I want to bring a common misconception or work done by a student to the whole class’ attention at the end of class on a practice day to have a more solid conclusion to the work. Using the checklists I described earlier will help with this effort since I will be able to see boxes that I didn’t check for many students and find things to address easily.

Two, I want to really commit myself to taking ten minutes the day I hand back assessments to discuss them and have students ask questions. My students often don’t want to discuss their work as a class, so I’m thinking I will have to format this as a challenge: I want one question about why something you tried didn’t work, I want one person to share a solution method they think was unique, etc. Open to ideas on that!

My action research project to complete my masters degree will take a look at how self-assessment impacts student achievement, so part of this is also making sure to USE the SBG rubrics that I use to grade with my students and having them assess their own work using them, or rating their understanding of learning targets, etc. Mostly, I want my students to reflect more on their own work and not just turn in and move on.

The goal is to have some sort of activity that forces my students to actually look at their work every time I hand a summative assessment back.

Book Recommendations (Vol. 06)

Uh, 2018 is halfway over? I don’t think I’ve stopped doing, doing, doing since…. (*insert some time probably before I started grad school here*)

BUT, I always make time for reading, and not just for grad classes. I always get asked how I have “so much time” to read for fun, and the truth is that it just isn’t a choice for me not to. I read for at least half an hour most nights before I sleep, because otherwise…I can’t sleep. If I end my night watching a show or doing something “productive” or whatever, I lay awake for hours and am worthless the next day. Reading helps me dump all the things that are stuck in my brain out so I can shut down and rest. Also, I am a very fast reader, so that does help.

ANYWAYS, you can read previous posts from this series here:

Vol. 01 | Vol. 02 | Vol. 03 | Vol. 04 | Vol. 05

books

In the first quarter of 2018, I read 13 books. I’m sitting now at 32 books for the year according to my Goodreads, so I’ve read 19 books this quarter! Here’s the best five, featuring a good bit of poetry that I read during April (Poetry Month):

The Witch Doesn’t Burn in This One – Amanda Lovelace

The poetry collection sequel to The Princess Saves Herself in This One. The poetry series is called Women Are Some Kind of Magic, and if Princess is the story of lost love and finding your strength, this collection is the story of finding your anger and fighting for your worth with all you’ve got.

When I read Amanda’s poetry, I literally lay on my couch and read the poem once. Then I yell out loud a bit. Then I read the poem out loud to my cat. Then I cry sometimes. Then I scream a bit more. Then I clutch the book to my chest and then read it one more time, stroking the page before moving on to the next one. Honestly, that is what happens when I read her work. It’s stunning and truthful and perfectly captures the experience of being a woman in 2018 America. As much as it’s a collection of poems and can be read separately, I highly suggest reading Princess first if you haven’t – plus both are short reads that will take you forever to get through because of the above described process for reading each poem.

 

Long Way Down – Jason Reynolds

Will’s brother Shawn was just murdered, and now Will has Shawn’s gun. He’s going to get revenge. He gets in the elevator…and it’s a long way down, as Will has to come face to face with people from his past – Shawn’s past.

Usually I read a novel written in verse and feel like it conveyed all of the emotion but none of the character strength, or that it’s otherwise missing something. This felt whole, and strong, and entirely gripping. It felt real, even the parts that weren’t. Remarkably, this entire story takes place on one single elevator ride, and yet it took me to tears and rage and sorrow and more and back. I literally did not move from the start to the end of reading this one – which was only a few hours.

 

The Poet X – Elizabeth Acevedo

Xiomara feels like she doesn’t fit anymore. She doesn’t fit her body, she doesn’t fit her mother’s religion, she doesn’t fit in with her old friends or her classmates. Her English teacher persuades a reluctant Xiomara to join the slam poetry club, and she slowly shares her words, despite all the fear and threat of consequences from her family.

This verse novel is absolutely stunning. Xiomara is such a dynamic character and her family issues feel so real and relevant. You feel the pressure from her parents the whole time and fear for what will happen if they find out that she’s trying to live her life outside of their expectations. I especially love the two sides of each of her assignments from English class – the one she wanted to write and the one she turned in. You really get to see the struggle of her wanting to share her words and her story with the world but being so afraid of what will happen if she does. You’ll be rooting for her the whole time.

 

All American Boys – Jason Reynolds and Brandon Kiely

Rashad is just trying to get a bag of chips before the weekend party. He trips over a woman in the store that he doesn’t see. The situation gets misinterpreted and he ends up getting beat up by a cop. Quinn sees it. The two boys both try to come to terms with what happened, including the protest scene that builds up and the racial tensions throughout the school, further provoked by the fact that the officer’s brother is a student on the basketball team with Quinn and many of Rashad’s friends.

Everyone is raving about The Hate U Give (deservedly so, it made this recommendations list after all), but this has something that’s missing from that and Dear Martin and other books in this vein of Black Lives Matter / police brutality exploration novels. The dual perspective in this is critical. Rashad is the oppressed party, but also trying to figure out what in the world just happened to him. Quinn is getting a wake up call to a lot of behavior that he has passively condoned his entire life – realizing his privilege and trying to figure out what he can do with his newfound awareness. The perspective of both boys really gives the full picture, and the fact that it’s co-written by two authors who can speak to each of those positions is key to the resounding emotional bullseye this book hits.

 

A Memory of Light – Robert Jordan and Brandon Sanderson

There’s not a lot I can say about this summary-wise, since it is the FOURTEENTH and final book in the Wheel of Time series, but basically: Rand, Mat, and Perrin vs. the forces of evil, this time it’s FINAL.

I started reading this series almost two years ago now – one of my good friends from college really loves it, but also my uncle who died of cancer two years ago this month loved this series, and his death was what pushed me to finally start it. Reading these books over the past few years has helped me to grieve for him and to feel a closeness with him even though he’s been gone, and I am really going to miss that now that I’ve reached the end. The books are 800 pages long each, but they are so worth investing your time in. This last one hit home with messages of the importance of choices in a way that devastated me yet invigorated me over, and over, and over. There is everything you could ever want in this series, from magic to fighting to romance to fantastical creatures to the whole overarching good and evil battle. When Robert Jordan died before completing the series, Brandon Sanderson took up the role without missing a beat and the transition between authors is so seamlessly done. I fell so in love with so many of these characters (Perrin and Nynaeve and Loial are THE BOMB.COM) and this final volume was just perfect.

Algebra 1 Unit 8 Interactive Notebooks: Forms of Quadratic Functions

This year I’ve committed to posting each unit of both my Algebra 1 and Algebra 2 INBs.

My district is moving to a standards based curriculum, and has identified priority standards for every course. These are the standards we are required to address and assess our students over, so they pretty much form our units.

You can find my Algebra 1 (year long class) INB posts here:

Unit 1 | Unit 2 | Unit 3 | Unit 4 | Unit 5 | Unit 6 | Unit 7

And my Algebra 2 INB posts here:

Unit 1 | Unit 2 | Unit 3 | Unit 4 | Unit 5 | Unit 6 | Unit 7 | Unit 8

And finally, my posts from a 2nd go around I’m teaching of Algebra 1 here:

Unit 1 | Unit 2 | Unit 3 | Unit 4

 

The 7th priority standard we have in Algebra 1 is F.IF.8:

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

I think the last three units of our Algebra 1 year tell a great story. They cycle back into each other, each one pushing a little further, and it all comes together (in the next unit!). This unit feeds off of a lot of the solution methods from the last unit, because we utilize some of these methods to rewrite a quadratic in another form.

IMG_4251

Skill 1: I can rewrite a standard form quadratic function in a form that reveals the zeros

We begin this unit by introducing the three forms of quadratic functions and what information they can reveal to us. We won’t actually be graphing them until the next unit, but there needs to be a goal – why do we want these quadratics in different forms? So I introduced the parabola, and some of the vocabulary surrounding it.

Rewriting a standard form quadratic in factored form is pretty much the same as solving a quadratic by factoring, so I just took the chance to address some of the most common mistakes students had been making (not factoring out a GCF, misplacing negatives, getting confused by positive or negative factor pairs) and to go over the process again.

Skill 2: I can rewrite a standard form quadratic function in a form that reveals the vertex

IMG_4254

Again, this process is fairly similar to solving a quadratic by completing the square, so I again took the chance to address some common misconceptions, and we emphasized throughout that our goal was to end up with something that looked like vertex form, so the students came up with a lot of their own ideas about what to do after they completed the square.

Skill 3: I can rewrite a factored form quadratic function in a form that reveals the y-intercept

 

The notes page for this is pretty basic – but I tried to emphasize as we went through it what we were actually doing. What operations are implied in the factored form function? If there’s multiplication implied, how do we multiply the two factors? What should I do with that extra coefficient?

At this point, I wanted to bring in the idea that we need to be able to 1. recognize what form a function is in by looking at it and 2. identify what form we are being asked to rewrite it in. So the last page of these notes throws in a standard form to vertex form problem, and then asks students to identify forms of some other functions and to make observations about how they can quickly identify the form (it’s all about the parentheses, right?)

It was also revealed to me that I apparently don’t know what half of 7.5 is…so just ignore all of those scribbles on that problem where I had to fix my mistake…

Skill 4: I can rewrite a vertex form quadratic function in a form that reveals the y-intercept

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Something that we really focused on when looking at this skill was identifying when you were “done”. Right after you multiply out the squared binomial, it looks like you have standard form already. But, you haven’t used all of the components of the original function! So we made a point of constantly checking back in with the original function – did we use all the parts of it? If not, what parts have we not used and what should we use next in our rewriting?

Skill 5: I can rewrite a quadratic to reveal any key feature

The triangle on the front of this proved very useful as a summary of the unit – I saw students looking at it constantly as they reviewed and did their project for this unit, and I think it really helped them gain confidence that they were looking at the right set of notes and doing the right thing. I accidentally included a standard form to factored form problem that is not factorable, and although that led to a good reminder that not all quadratics are factorable, I did change it to vertex form on the file for next year.

By the end of this unit, my students for the most part felt really comfortable with the processes involved in factoring, completing the square, and multiplying out polynomials.

 

You can find the files for these pages here, in PDF and Publisher form.

Learning, Growing, Laughing, Healing – A Year of Math Class

I recently wrote a post about my fifth year teaching. In that post, I talk about how my school building has come to feel like family. And right now, we’re down to 5 days left with that family for this year.

This time of year, I like to take one class period to pause, and give my students some time to reflect. I want them to take a minute to think about all the actual stuff they’ve learned this year, because I know they don’t realize in the day to day how much it adds up to. I want them to have time to remember all the times in our classroom together, their favorite and least favorite parts. I give this assignment under the guise of them helping me become a better teacher, and it definitely does give me lots of things to think about and consider every summer, but the real purpose of it is to give them a chance to be proud of themselves. Because they should be.

The past few years, I’ve made a post with some of the highlights from this assignment. You can read those posts here and here. Below, you can see this year’s highlights.

Math

  • I learned that vertex form can’t be turned into factored form without going to standard form first
  • Something that will always stick with me is my revitalized interest in math, and the feeling of accomplishment when I understand concepts I believed to be far beyond my comprehension
  • I understand slope much better than I did last year. Most of these concepts didn’t make sense to me before but you really helped me understand math better.
  • The thing that will probably stay with me is factored to standard and vertex to standard form. I could explain those things to other people because I love those things
  • [Graphing] polynomials with no calculator was my favorite!

Life Skills

  • I learned that there is no shame in asking questions, even if they seem obvious or repetitive
  • My notes will stay with me for the entire summer vacation so I won’t forget how to do math equations
  • I learned I’m good at organizing my notebook. I love my notebook so much and all the stickers I got.
  • Thought I’ve made multiple mistakes, but I asked for help when needed which I always do get help.

Community

  • My favorite part was all the jokes with the squad
  • I like that you give us house points to motivate us
  • I like most staff members, they are very nice. I like how Miss Mastalio is very helpful and explained my math problems better. There was never a dull moment at Mid City
  • I also like how the groups are arranged by Hogwarts characters [houses]. It makes me feel like I’m actually in a cool class and I’m proud to be a Ravenclaw!
  • I liked how Mid City does their fun stuff and actually wants/makes sure the students are happy
  • I liked the way you taught and how patient you were, and that you’d always help
  • Something that is going to stay with me this year is the great memories of this class and how much we laughed
  • I have also learned a lot of great 80’s music. Thanks [student name], [student name], and Mastalio for singing them
  • I loved calling Mastalio a vampire [note, this is a part of my Algebra 2 class’ intensely elaborate inside joke about my backstory, which involves me being a 2,000 year old vampire witch catwoman who had George Washington’s baby. Maybe just don’t ask about it]

Everything’s fine, I’m just crying

  • In all seriousness I really appreciate you, and I looked forward to your class every day. You’re the best
  • I learned that some teachers actually love me
  • I learned ANY ONE CAN BE A MATH PERSON
  • I like how calm, understanding, and accepting both this school and you have been I’ve never been more than average at math so it was nice to have a teacher and environment that was helpful and very motivated. I certainly feel like I’m much better at math than I would be without that.
  • [I learned] that anybody can be a great math magician

 

Overall, my students commented that they liked when we did poster projects instead of quizzes or tests, which is motivating me to work on different assessment styles for next year (I really want to experiment with group or partner assessments, or assessments where students get 5 minutes to talk with a partner before they start, etc, and with portfolio style assessments). A lot of them also commented that their least favorite practice assignments were when we just had a list of problems to solve, so I’ll also be working on replacing more of those with interactive activities like Question Stacks or card sorts or dice games.

Many of these students comment about things that seem like they should be a given in any classroom, but I know they’ve come from traumatic experiences with math classes before – classes where their teacher told them to their face that they’d never be successful, classes where they asked for help and did not get it, classes where instruction they missed was never explained to them. Reading what they wrote about feeling comfortable asking for help in my class, knowing they’ll always get it, understanding and making sense of notes…it makes me really proud of them for working to heal their math trauma. I read a twitter thread recently in which someone referred to their realization that their students DIDN’T have math phobia, they had math trauma. It’s a realization I’ve also come to. Someone, or several people, DID THIS TO THEM. They did not just start out afraid of math. There’s a reason they don’t like it, feel they can’t do it, won’t even try. It’s my job to try to start healing that. It’s a process that often can’t be completed in one year, but their words on these reflections provide evidence that it is happening, it is possible, and we just have to keep working to make math a positive experience for them.

 

Five Years.

FIVE years ago, at this time, I had recently accepted a job at a place called the Kimberly Center.

I was unsure of my decision. I had applied for jobs in various parts of Eastern/Central Iowa, knowing I didn’t want to move too incredibly far away from my parents (Iowa City) and sister (Davenport), but mostly just wanting a job. A classroom to teach in, finally.

I had been offered positions at a few other schools. I had laid awake on sleepless nights trying to decide, talked to my mom, my best friends, my cooperating teacher for student teaching. I had to decide: middle school? Freshmen at a big high school? Various 9-12 in a small town? Or, this “alternative school”.

I don’t think anyone else’s first choice for me was the alternative school (besides the principal who wanted to hire me). People told me it sounded really challenging, the words “scary” and “dangerous” were used. But I’ve always had a stubborn streak, and so I think in the end I chose it mostly to prove I could.

 

Fast forward to my first day of school – my first month, my first year even. There were so many sleepless nights. I was so overwhelmed. Also, I was terrible at asking for help. Poor Heather would come to my classroom after school and ask if I needed anything, I would say no, she would leave with a kind reminder that I could always ask her, and then I would go home and cry. I just didn’t know what I was doing, plain and simple.

My students had been through so much that I didn’t even know existed when I was their age. It took me most of that first year to really understand how their priorities worked and to shift from a whole ton of sympathy (feeling sorry for them and for myself) to true empathy.

 

In the past five years, I have learned more than I did in the 22 years that came before them. I have grown as a person into someone that I am really, truly proud of being.

In this school, now Mid City, I have found another home. I have found a family. I have found so, so much more than I ever thought I would walking through the doors for the first time five years ago.

My coworkers have become good friends – friends who get me and my band obsessions, my outrage at sexism in the sports world, my need for time away from people, my need for data and information. We have theme days and staff socials that turn into karaoke nights and we have endless, endless inside jokes.

My administration treats me with respect and importance – they make me feel like I am an expert in math education and take my input on changes and ideas. I know I can approach them if I disagree with something, or if I have an idea.

 

My students. Man, my students. I went from not understanding them at all, and having different goals for them than they did for themselves, to truly trying to work together to reach for whatever they think success looks like for them.

In the past five years, they have made me laugh every single day. From the things you can see browsing #thingsstudentssay on my twitter to more complicated and subtle inside jokes with different class periods.

They have made me cry, for all different reasons. Because they frustrate me. Because I hurt for them. Because they’ve lost loved ones or we have lost part of our Maverick Family. Because I am so incredibly, wonderfully proud of them.

They’ve done math that I know they never believed they could. Statements have come out of their mouth like, “putting quadratics in vertex form is fun!” and “I tried the challenge problem, got out Desmos and put some things in, played around with it for awhile, and I couldn’t get the y-intercepts to match. But can we talk about it later? Because I still want to know how it works.” – statements that they probably wouldn’t have known what they meant when the school year started, and if they had, would have laughed at someone else saying them. They’ve graphed quadratics by hand, gone from not understanding division to being able to complete the square (a certain student’s literal growth from this year), written paragraphs using statistics to compare athletes, won our school’s bracket competition using statistical analysis, and so much more.

They celebrate when we reach page 100 of our interactive notebooks. They take home papers with stickers to show their moms. 4 of my 5 class periods have said they want to do extra dot talks on the last day of school because they didn’t want this week to be their last Mental Math Monday of the year. They form identification with their Hogwarts Houses and do puzzles and challenges and put away my calculators and plug in my chromebooks to earn points for their House.

We’re a family. They’re my people. Some of them call me Mom and bring me dandelions, or cookies, or whatever they make in foods class. They find me in the morning to say good morning, in the halls to say they miss my class from last year. They ask what I’m teaching next year and if they can take that class. They tell me about crushes, girlfriends, boyfriends, breakups, nieces, nephews, college acceptances, trips, concerts, and more.

They push me to be better every single day. A better person and a better teacher. They aren’t scared to let me know when I slip into lowering expectations. They don’t listen to my instructions but they notice when I get frustrated about repeating them fifteen times after they start working. They ask how my day is going and they truly listen to my answer – way more than adults in my life do.

 

And they GRADUATE, something many of them never saw in their futures, they GRADUATE and they walk across that stage and then they become facebook friends and I watch them continue to learn and grow and say such heartfelt things about my classroom.

 

I have grown obsessed with the mathematicians from the Hidden Figures story in the past two years. My mom recently brought me an interview with Katherine Johnson from the paper. The entire thing resonated with me so strongly, but one line in particular stood out. She said, when asked about all the trials and everything she went through during her time at the space program, “I believed I was where I was supposed to be.”

I have days when I wake up and my first thought is “ugh, no, back to bed”. I have days where I still go home and cry from frustration or failure. There are days when I don’t think I can deal with a particular student anymore. “Do what you love and you’ll never have to work a day in your life” is a LIE, and don’t let anyone tell you differently. I work SO hard, many times harder than I should, because I care so much. It’s so hard to be a teacher, and even harder to work with at risk students.  I still love my job. It’s not just a place to go to get paid. It fulfills me and brings purpose and joy and heart to my life.

Five years have passed since I graduated college and accepted this job. Five years of making my classroom my own. Five years of joy, and pain, heartache and pride and laughter and learning and math.

Five years later, I believe I am where I am supposed to be. Here, at Mid City.

Algebra 2 Unit 8 Interactive Notebooks: Sketching Polynomial Graphs

This year I’ve committed to posting each unit of both my Algebra 1 and Algebra 2 INBs.

My district is moving to a standards based curriculum, and has identified priority standards for every course. These are the standards we are required to address and assess our students over, so they pretty much form our units.

You can find my Algebra 1 (year long class) INB posts here:

Unit 1 | Unit 2 | Unit 3 | Unit 4 | Unit 5 | Unit 6 | Unit 7

And my Algebra 2 INB posts here:

Unit 1 | Unit 2 | Unit 3 | Unit 4 | Unit 5 | Unit 6 | Unit 7

And finally, my posts from a 2nd go around I’m teaching of Algebra 1 here:

Unit 1 | Unit 2 | Unit 3 | Unit 4

 

Our 8th priority standard in Algebra 2 is A.APR.3:

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

 

This is a no calculator allowed unit, which makes sense because the goal is to create a ROUGH graph based on the factored form of the function. My students actually found the freedom from calculators nice – as one of them put it, “It makes me feel like I’m not going to make it more complicated than it needs to be, because I know I shouldn’t need a calculator to do it.”

 

Here’s how I broke down this unit into skills (you can see from the index page picture that I changed the wording of one of our goals after I made it):

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Skill 1: I can identify zeros of a polynomial when it is given in factored form

When we had done our solving polynomials unit earlier in the year, my students expressed a lot of confusion regarding the words root, zero, solution, and x-intercept. I decided to address this for this unit – I actually only got really clear about which term should be used in which circumstance when I saw a graphic someone had posted on twitter last year, so I’m unsurprised that students were confused! I took extra care throughout this unit to use the correct terms with the correct situations and I think my students feel a lot more comfortable using each of them now.

After discussing those terms, we practiced finding the zeros of several factored functions, and then matching them to a graph with x-intercepts that made sense. My students found this easy, although we had to take a brief detour into the world of fractions since they couldn’t use a calculator to find a decimal equivalent. There were a lot of number lines and counting by the denominator that you don’t see in these notes, but I think it was a really good revisit of fraction concepts!

Skill 2: I can identify the total number of solutions, maximum number of extrema, and end behavior based on the degree of a polynomial function

This first page on information you can tell from a polynomial function could use some reformatting. I really liked the root types and the possibilities for what degree 3 solutions could look like on a graph, but I want to switch their places on the page. My students also kept forgetting the difference between finding the degree of a factored polynomial function and one in standard form, so I would add that at the top of the page.

The graph shape and end behavior page is the one that got used the most during this unit. Pretty much all of the other information got memorized pretty quickly, but this one was the page they kept referencing. We used Desmos to explore what would happen for each of the scenarios, with them choosing an even degree and a positive leading coefficient, then having another student choose an even degree and positive leading coefficient, etc., which was really helpful for them to see that this end behavior would hold true for ANY even degree and ANY positive leading coefficient. We also got to see some interesting graphs, like y=57x^100…

Skill 3: I can sketch a rough graph of a polynomial using its factored equation

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We’re putting it all together! I liked the organization of the information to identify here. The only struggle my students had was that the zeros don’t always end up in the order that the x-intercepts appear on the graph, so for the example on the front, they kept putting the double root on (4,0) instead of (-1,0) because that was the order it was listed in the equation. I might add a place for them to rearrange the x-intercepts and types in order to try to prevent this.

Skill 4: I can write a polynomial from given constraints

This is going backwards from what we had just been doing, so it went pretty well intuitively for the students. I always frame this section as them being the teachers and trying to come up with problems. For their assignment, I actually had them write functions, then find the roots and initial value and write them on an index card, and then they traded to see if they could get back to the original function! We mostly looked at having each factor having degree 1, but the last example I showed them how you could come up with alternatives by using other exponents on factors.

 

You can find the files for these notes here, in PDF and Publisher form.