Thursday, January 19, 2017

Choosing a Method of Integration

One of the biggest difficulties my students face when we work through our integration unit is distinguishing between the different techniques we've learned. When told which approach to take, they can nail almost any integral. When given a mixed bag of problems to sort through on their own, the tides start to turn. I tried to spiral in a bit more mixed practice than I did last year, but it still didn't feel like quite a enough this year.

I designed this to have kids work on in phases-
1) Individually evaluate which method you would use (gut instinct, what do you think?)
2) Swap papers with a partner and say whether you agree or disagree and be ready to argue why
3) Work with your partner to try to decide on who is right. Check yourself by evaluating the integral
4) Generate a list of what features helped you identify which method to use!

I wish I'd left more time to do it in class. I will definitely budget more for it next year. 

Any other favorite activities for helping kids with this?

Thursday, January 5, 2017

New Year, New Blog [Re-Blog]

Re-blogging this from Julie Reulbach on the ExploreMTBoS site! I'm excited to participate and encourage anyone who has thought about blogging to jump in for 2017! It will totally change your teaching! 

Welcome to the Explore the MTBoS 2017 Blogging Initiative!

With the start of a new year, there is no better time to start a new blog!  For those of you who have blogs, it is also the perfect time to get inspired to write again!
Please join us to participate in this years blogging initiative!  To join, all you need to do is write just one post a week for the next four weeks.  To make it easier for you, we will post a new prompt every Sunday!  Once you have blogged, please fill out the form below.  Each week, your blogs will be posted on this site for all to enjoy!
This Week’s Theme:  My Favorites
This week, the blogging theme will be “My Favorites”, where you can post about one (or many) of your favorite things!  Called a “My Favorite,” it can be something that makes teaching a specific math topic work really well.  It does not have to be a lesson, but can be anything in teaching that you love!  It can also be something that you have blogged or tweeted about before.  Some ideas of favorites that have been shared are:
  • A lesson (or part of one) that went great
  • A game your students love to play
  • A fun and/or effective way to practice facts
  • A website or app you love to use in class
  • An organizational trick or tip that has been life changing
  • A product that you use in your classroom that you can’t live without!
Blog Newbies!
If you are brand new to blogging, you can read Starting A Blog from the 2015 initiative.  This post will give you specific instructions on how to start a blog.
Hot Tip!  Don’t stress about your blog name!
The hardest part about blogging is often coming up with a title.  Do not let this detail derail you!  A great suggestion is to make your blog address your name.  Then, you can title your blog later – or change the title anytime you want!  To see what this looks like, check out Sam Shah’s blog.  His web address is, but the site name is “Continuous Everywhere But Differentiable Nowhere“.  No one cares about your blog name, they just want to read interesting, inspiring, and helpful posts!
Hashtag it!  #MTBoS #MtbosBlogsplosion 
Don’t forget to tweet out your blog link and add hashtags so other teachers in the MTBoS community can easily find your post!  If you are not tweeting yet, you should be!  There is an amazing community of math educators there just waiting to inspire and support you!  Check out How To Start a Twitter Account to get started!  Also, if you are brand new to Twitter or just want to get more out of it, there are more Twitter tips on Julie Reulbach’s blogpost, Tweet, Connect, Repeat.
This year, we are joining up with the #mtbosblogsplosion.  Special thanks to  Carl Oliver@carloliwitter, for jump starting blogging for many people in our community!
Hashtags to add to your tweets:  #MTBoS #MtbosBlogsplosion
Also, if you have a wordpress blog, please re-blog this post to get the word out!
Deadline: Press submit by the end of the day Saturday, January 7, 2017.
Yes, this is a quick turn around this week – but we don’t want you to put it off or delay!  Once you are finished with your blog post, fill out this form and your blog post will be featured on this site [meaning the MTBoS site this is reblogged from] next week!

Wednesday, January 4, 2017

Indefinite Integration with U Substitution

Happy 2017! 

So much changed in 2016, but one of the things I'm most happy about is that my blogging habits changed! I've always been an #MTBoS lurker, but finally getting more involved in blogging has helped shape me so much as a teacher and I'm looking forward to even more sharing and collaboration this year. Let's just say I'm on an upward trend...
I was happy to see my kiddos on the first day back from break, but watching them attempt u-substitution felt like watching this: 

To be expected, I know. We started u subs 2 classes before break and on the class before break I had a whopping 6 students show up (we went right up until 2:30 pm on December 23rd....most of my kids were off skiing or sleeping until well after my class was over). Knowing that we would be struggling to get back into the groove today, I wanted to come up with an activity that would include checkpoints along the way to encourage students to analyze their work throughout the process, not just at the very end. Cue this awesome activity from Tatia Totorica on TeachersPayTeachers on U Substitution that is FREE! Unfortunately, it used definite integrals and we aren't quite there yet. However, I loved the idea and decided to adapt to make it my own. 

U Substitution 4 Color Activity (Indefinite Integrals)

At it's core, this is a matching activity. Print it out on different color papers and have kids work in partners to find the pieces that correspond with each other. They also work to fill in the columns on their worksheet, which requires them to show their work in the appropriate columns. I liked that the weren't easily matched...they required some thinking and analysis. By the end of class, the students were cruising through these with their partners. 

Happy Integrating! 

Monday, December 19, 2016

"Undoing" the Chain Rule- Intro to Integration by U Substitution

This year I've revised how I'm going to introduce u substitution to my Calculus kiddos. It's an intimidating topic the first year teaching the course, knowing that it's an area in which students can sometimes struggle. Take 2 and I'm much more ready to let my kids do the directing. I'm using the chart below as a discovery activity for students to being to piece together the pieces (u and du) that will be integral to our future study:

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? 

Happy Monday! 

Wednesday, December 14, 2016

A Little Bit of Thanks

Y' do you not get the feels from this?

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

Teaching with Anxiety: A (Complicated) Love Story

Anyone who knows me knows I love a good Netflix binge. Last year during a glorious string of hours with as little voluntary muscle movement as possible, I watched the first 2 seasons of the show You're the Worst. It seemed to be at first to be an irreverent look at the transition from the freedom of your 20's to the "settling" of your 30's, centered around 2 self-destructive people who fall in love against their better judgement. As the series went on, it started to take a more serious turn. It's revealed that the main character battles clinical depression and begins to chronicle the impact her battle with her own mind has on her relationships, career, and life. I found it poignant, hilarious, and an interesting break from my usual Bravo nonsense (#loveyouvanderpumprules). 

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. 

Silver Lining
 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. 
Silver Lining
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. 

Silver Lining
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. 

Silver Lining
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. 

When I'm feeling really annoyed by my own anxiety, I like this article too. 

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. 

Applications of Derivatives Slap Jack Review

I've written before about my Slap Jack review game. It's one of my favorites for getting kids engaged and working together! 
The basic rules:
  • 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!!
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.