Monday, December 19, 2016
After that, we're doing the following activity to practice identifying useful u's and du's. I know I got this activity from somewhere, but can't for the life of me remember where. If you know where it originated, please let me know!
My kids are taking a quiz next class on basic integration and we'll start u sub as our send off to winter break. Do you have any ways that you love introducing u subs? Any tips or tricks from years of experience I'm in the process of acquiring?
Wednesday, December 14, 2016
This is a student who went on from my class and is in one of the top engineering programs in the country. They felt the need to email me when they got their Calc II final grade back! 99.999999% of this student's success is from tremendous work ethic and awesomeness, but I am so grateful to hear a thanks for being a small part of that 0.000001% left over.
And also, how awesome is it to know that your kids go on from you and are super competitive and ready to tackle the world?! How awesome are our kids?!?!
Tuesday, December 13, 2016
So what does this all have to do with me and more importantly with teaching?
I have always considered myself a "worrier." Not kidding- I remember being 3 or 4 years old listening to a cassette of "Don't Worry, Be Happy" before bed, scared to death that someone was coming to take my bed if I fell asleep. (Why would they put those lyrics in a song that could possibly be deemed appropriate for my bed time??) It was an endearing personality quirk my family and friends had learned to accept. I had also accepted it about myself and had, as a result, made deliberate choices to challenge my anxieties in hopes of conquering them. I seized opportunities to try new things, study abroad, move across the country, and challenge myself professionally, knowing the whole time that I'd hate the experience until I got comfortable.
Fast forward to last winter: A series of incredibly unfortunate personal events led to me starting treatment for panic attacks and post-traumatic anxiety. Activities that had been commonplace in my day to day life were now terrifying. I'd spend all my energy to get up and put a smile on for my students and colleagues, only to come home and have no energy left for my family or myself. I started to understand the very real struggle people with anxiety and depression face everyday and I hated it. And I also started to realize that I wasn't alone in this- it was all around me.....especially in my students. With the help of doctors, friends, family, and my amazing husband and pup, I've adjusted to a new normal, one that always will have a little more anxiety.
It's easy to look longingly at those people who seem to breeze around the school with a huge smile, charisma oozing from their pores. To long for a life where you didn't battle with your own irrational stressors. But the more I've reflected on my experiences with anxiety, the more I see how it has shaped the teacher I've become. And although I could have done without the panic attack before my first observation at a brand new district a few weeks ago (thanks a lot, brain), there are things that I'm learning to love about the way my brain works. Are there cons? Duh. But there are pros, too.
New situations and interactions can be stressful
I've spent the better part of my life making deliberate choices for this exact reason. I started living by the manta "Do one thing every day that scares you" (which isn't hard when you have anxiety) during my freshman year of college and it's taken me on some incredible journeys. You get used to the fact that you're going to feel scared and you're going to hate it, but hopefully it will be fine. It's the reason I became a TA in college, the reason I studied abroad, the reason I moved across the country to an apartment I'd never seen (twice), and the reason I push myself constantly to do new things in the classroom.
|This is how one looks after fear of volcano boarding on one of the most active volcanos |
in Nicaragua is conquered. I would say I volcano-tumbled more than I "boarded," but I still did it.
Living out every possible way a situation can go wrong in your mind
No one can say I'm unprepared.
I had a professor in graduate school who advised us to always overplan; this has never been as issue for me. When we first started teaching, I remember my husband saying he had 10 minutes left at the end of a block....unimaginable. Since I've always got so much planned, I have a plethora of resources and "other options" to use if needed. It's like a choose your own adventure some days- find out what the struggles are, choose the appropriate course of action.
I also tend to tweak and tweak and tweak my lessons, continually thinking how to make it less likely to go wrong. Can it be obnoxious? Sure. But 9 times out of 10 it does help.
A constant feeling that things "could've gone better"
I'm my own worst enemy when it comes to criticism. I have had to teach myself when to say "this is as good as it's going to get right now" and be okay with that. But I know that this sense of perfectionism is what made me a great student in school and what drives me as an educator. I am passionate about improving things around me and passionate about making sure my kids are achieving. I tweak, I read, I talk, I share, I get feedback. It's all in the pursuit of making things just the littlest bit better.
You have to experience how crippling anxiety feels.
I have a much more profound sense of empathy for those around me than I ever did before my anxiety peaked. I can recognize the day to day struggles and identify small triggers that I never saw before. Working with teenagers? This gives you a whole new perspective. It gave me a bigger heart and bigger ability to teach kids, not just math.
I'm not 100% sure why I felt the need to write this, but it's been sitting unpublished for weeks in my drafts. I feel like there's more of us out there in teaching than we'd often like to admit. I've had to learn to give myself a higher level of self-care as I become more aware of my own anxiety and I hope others who need it can do the same. We are lucky to be in a profession where our weakness can often make us stronger, helping us connect with our kiddos in a new and more profound way.
The basic rules:Here's one I wrote recently for my AP Calculus Class to get them ready for their big applications of derivatives test. It's a mix of released AP questions, questions from review books, and questions from worksheets. Lots of mixed practice on everything from curve sketching to related rates to tangent line approximations.
- Students play in 2 vs. 2 games (so 4 students per group)
- Students look at the 1st card and work with their partner to solve the problem completely on their whiteboard or in their notes
- First group to have a complete solution written can "slap" the deck to indicate they're done. They then have to defend their answer. If they're right, they get to keep the card. If not, the other group gets a chance to "steal" by getting the question right.
- If no one gets it right, the whole group has to work to figure the problem out. No one gets the card, but they're still responsible for the topic.
- Group with the most cards at the end wins!!
We've been digging into triangle congruence proofs in Geometry and I wanted to make sure were digging into WHY, not just HOW.
We started examining why the Side-Side-Side Criteria works, inspired by this post from Math Giraffe. I displayed each step one at a time so groups couldn't rush through and to make it a bit of a game. I offered candy to any group that could create a triangle that was different from the first on they created. Any group who felt like they had done it presented their ideas to the class and we examined each one. Something crazy happened....we could ROTATE, REFLECT, or TRANSLATE them all to be on top of the others. This was handy, as we'd defined congruence using the existence of a rigid motion between the 2 shapes that would match one onto the other.
I knew this trick wouldn't work again (you can't fool kids out of candy twice). So for round 2, we started comparing SAS with ASS. This time, I went pasta! I literally woke up in the middle of the night thinking about this and wrote up my directions when I got to school on the board, so no file to share there. Here's the gist:
1) Each group gets a piece of poster paper & folds it into 4 sections
2) Have kids break pasta into 4 pieces of 2 lengths (you can specify what lengths with your kids or just let them choose.....I think I did 4 4" pieces and 4 5" pieces).
3) In each section on the paper, have kids draw an given of the same size. I did 30 degrees and had kids extend it out to the edge of that section.
4) Challenge the students to use one of each length of the pasta to create 2 different triangles if the angle given is included between the 2 sides. (They can't. SAS for the win here.)
5) Challenge the students to use the remaining pasta to create 2 different triangles if the angle given is NOT included. Don't let them glue until they have tried a bunch of different options- some will try to say this is impossible too.
6) Have students summarize the difference between the 2 scenarios and name them as SAS and ASS on their poster.
7) DECORATE! You have awesome new posters!
- Triangle Congruence Start Up Worksheet from the wonderful Math Teacher Mambo
- Triangle Congruence Warm Up that I made to help differentiate between possible ways to prove triangles congruent.
- Triangle Proof Planning Guide that I created this as a triage for some kids who were struggling with the basics, but wound up being really helpful as a conversation piece for lots of my students.
We just wrapped up our applications of derivatives unit in AP Calc and I wrote this little activity to introduce local linearization and tangent line approximations. It's one of the simplest but most important ideas in all of AP Calc- that if we look close enough, a tangent line at a particular point will be almost the same as the function since functions are locally linear.
Wednesday, November 16, 2016
Friday, November 11, 2016
- There are only 3 candidates here- the people on the show. Are there people yelling the answers from their couch at home? Sure. But they aren't true candidates for winning since they aren't even in the studio. Same thing goes with the candidate test....you have to be in the interval to be eligible.
- While all candidates are eligible, it's pretty clear to see who the winner and loser was in this episode. There's an absolute maximum, an absolute minimum, and another candidate who just gets a "thank you for playing."
- It's easy to talk about ties with this analogy as well. If someone had tied Andy (most likely not Wolf), there would have been 2 winners (2 absolute maximums). The key is they would have had the same maximum value (y value) occurring for 2 different people (x value). It's an easy conversation to revisit when you are distinguishing between an extreme value and where it occurs.
- Roll sounds a lot like ROLLES Theorem (obvious, I know)
- Tootsie Rolls look like a horizontal tangent line if you hold them up to read them correctly. Their slope? Zero!
- The letter o is everywhere here: rOlles theorem, tOOtsie rOll. And what do o's remind us of? ZERO!
- You can even use the Tootsie Roll to demonstrate the theorem by sliding it between the tangent and the secant lines:
- The graph of a derivative on it
- A prompt to help students generate discussion
- An answer key on the back.
Monday, October 24, 2016
- is competitive enough to get kids invested, but not so competitive that it turns struggling students off to playing
- holds every student responsible for their learning, not just the person whose "turn" it is
- covers a variety of representations, from graphs to tables to written expression
- reviews a variety of question types, not just MC
- discourages guessing
- minimizes embarrassment if you happen to be wrong
- promotes debate and teamwork
- allows me to clarify misconceptions early and often
- likes long walks on the beach
Another simple post to get my blog train rolling again. Happy Monday!
Sunday, October 23, 2016
I have been working hard to get to know my new kiddos, my new colleagues, my new town, and still walk my dog and talk to my husband occasionally. Oh, and I've slept in my own bed exactly 0 of the last 5 weekends (#weddingseason). Unfortunately, that meant blogging was the first thing to go.
This post is NOT groundbreaking, nor is it going to be long, but you have to start somewhere. This is me at least showing up at the gym and walking on the treadmill. It's no spin class, but it's a start back to getting in shape! So here goes.....
I have always believed in allowing kids to discovery something whenever it's developmentally appropriate for them to do so; it's a pillar of my educational philosophy. My very first year of teaching high school, I had a student who would stay after school with me to derive formulas that I'd deemed not worth deriving with the class as a whole because it would bother her to not know "why." She understood that these formulas weren't "magic" and that math should make sense and I still think of her often when I am working to discover something with my kiddos.
One of the issues I had my first time as a Calculus teacher was students who had been good at the "skills" of math, but hadn't always been great at the conceptual part. They really say math as a list of things to memorize and as long as they could do that, they would do well. So much is lost when we approach Calculus this way, so I've worked to build more conceptual understanding into a curriculum that an all to often be skills-based.
In the past, I've built up my arsenal of awesome Desmos and GeoGebra activities since I was working in a one to one environment with technology. And while I am loving my new district, it was a jolt back into the real world of having to share computer carts and wait 5-7 minutes for PC's to boot up before an activity could start (I know....I sound spoiled. I am aware I lived in a technological fantasy land for the past 3 years of my teaching career). Sometime, it's just not worth the 7 minute boot up time for a 5 minute activity. So instead of breaking out some Desmos wizardry, I wrote a good old exploration for the graphing calculator to derive the derivatives of trig functions. What I wound up loving about this was the ability to introduce some new functions of the calculator, since that will be their trusty friend during the AP exam anyway.
First I had the students use the calculator to graph the derivatives of y=sinx and y=cosx.
Tuesday, August 30, 2016
I've done a lot of blogging about my plans for establishing a classroom that is more aligned with growth mindset and I intend on letting that inform a lot of my first day activities. I'm going to start both my preps with the Post It Activity I mentioned earlier to get conversation going. The questions have totally changed from my original post, but my goal is have 7 questions that align with the 7 class norms Jo Boaler talked about in Mathematical Mindsets and I outlined in my class norms videos. I'll blog about them more on the first day of school!
From there, my PLC typically goes straight into content. And while I want to make sure I'm keeping pace with a new prep, I also want to set the tone of critical thinking, collaboration, and discussion. I can't stand the idea of having kids copy definitions on day 1....it hurts my heart. Here's what I'm thinking and I'm definitely happy to take any feedback you have!
1) Pair/Share on why precise language is important to the kids personally. I'm thinking:
- school rules
- other awesome things they might come up with?
|Side note: this is my FAVORITE teaching tool for the AP exam. |
It's how I get my kids to finally stop using the work "it" in their answers.
Monday, August 29, 2016
While I was puttering around in my room today trying to figure out where to start, a smiling face popped her head in my door to introduce herself. She was a veteran teacher, someone who had been there for a while and offered to help in any way she could. She assured me that I should ask for help and that it was a math department norm to be asking questions of each other to make our teaching better. We began to talk about sharing classrooms since she hadn't met the other new teacher yet with whom she'd be sharing and then she said something that obviously piqued my interest: that she wanted to talk to the other teacher since she was trying something "new and crazy" this year. Knowing that she wanted to better her strategies in classroom management, she had spent a large part of her summer researching ways to facilitate that through classroom design. She was going to start differentiating her seating options by creating zones: individual desks, groups and pairs, big comfy folding chairs, etc. This way students could work in the most appropriate situation for them, even if that wasn't what everyone else was doing. The craziest part? She doesn't even have her own classroom. She thought this was going to be good for kids, so she was willing to spend the time setting up and taking down the room before she floated to another room. She was working to negotiate the obviously unique scenario with the other teacher using the room.
I haven't been to a staff meeting yet and I haven't even met most of my PLC, but knowing that there are people who are pushing themselves every day to break out of their comfort zone to benefit a student is nothing but a good sign to me.
And obviously, I had to hang my first posters.
Friday, August 26, 2016
Since I just found out that I do in fact have a classroom and was reminded of the poster by this tweet tonight:
I decided it was time for me to make one of my own!When kids ask for something, we expect them to say "please."— Justin (@JustinAion) August 26, 2016
When they say they can't do something, we should expect them to say "yet."
I am playing around with how I like it laid out best and if I want to back them with another color or not, but here is what they're looking like right now (shoutout to my toes in picture #1 and 3):
I will post pictures once I get into my classroom and get decorating....naturally it's the last hallway to be waxed!
Thursday, August 25, 2016
This has been a huge focus for me over the past year and one that I never quite had a word to describe. I like to think that I always try to do what's best for kids with the knowledge I have at that moment and that takes a lot of intentional design. This was a huge factor in piloting my blended learning course, my STEM courses, and will remain a huge factor as I move forward.
I've done a lot of work on mindset this summer and I'm trying to question my own practices as much as possible, always with "What is best for kids?" at the center. I feel like I have wrapped my head around how I want to present my belief in my students and in growth mindset in the opening days and I'm regularly stealing things from around the MTBoS to hang in my room (SINCE I JUST FOUND OUT I'M NOT FLOATING ANYMORE! #yassss). I have spent the last 3 years designing problem-based experiences for my students through STEM and my pedagogical approach tends towards these open-ended tasks and encouraging student collaboration. Of course I have room for improvement, but it's an area I'm more comfortable.
But with growth mindset, I am starting to feel like the devil is in the details. We convey messages to kids through the instructional choices we make every day and these messages are often stronger than anything we say out loud. These are my next 2 devils to tackle right now:
I am particularly not proud of my homework setup. Sure, I give considerably less homework than a lot of teachers and try to select meaningful problems that are worth my students' time. But in general, my students check their answers against a key that is projected and I check for effort. It's plain and it is beneficial to students who choose to use it appropriately, but not to everyone. And I'm going to be totally honest....I'm haven't worked with my whole PLC yet, but I am highly doubting they would be jumping on board to eliminating or drastically changing the nature of homework as defined by Jo Boaler in Mathematical Mindsets. I know the issues that would occur if 1 teacher decided to totally eliminate homework if others didn't also get on board. And I am still working my way towards being 100% comfortable with it. I want to make some changes that will benefit my kids and create more equity, but I need to take some baby steps to do this.
I also want to build metacognitive skills in my class and I know that self-reflection about homework can be a vital place to infuse that.
This NCTM blog got me thinking more about my homework practice:
Let's be real....kids dread assessments. Any assessment. Ask them to take out a piece of blank paper and write their name and you'll see the anxiety on their faces. We need to build a different relationship for our kids, so they can start to use assessments as a tool for growth instead of a judgement of their character.
I have high hopes that someday I can find a beautiful standards-based assessment routine where my kids will see assessment as a tool for learning instead of a judgement. This is a new road for me, as I've started to focus more and more on my assessment practices as I have gone further in my career. But SBG seems daunting to take on, especially in a public school setting where many other people are teaching the same course as you. I'm taking baby steps and I hope these are things I can build on as time goes on:
- Writing "I can" learning targets for each unit so students can self-assess regularly
- Instituting a retake/corrections policy for all formative assessments
- Offering a instant messaging office hours to give students another outlet to ask for help
- How do you use homework as a growth mindset learning tool?
- How do you use assessment to promote growth mindset?