Saturday, March 25, 2017

What's New for AP Review 2017?

New Year, New Curriculum, New Review! 

I'm revamping my review system this year and trying out some changes with my kids. We have about 15 total 80 minute classes for review (assuming Mother Nature gets her act together and doesn't send us any more huge storms), which is a pretty healthy amount. I'm trying to integrate much more mixed review this year to get my kids thinking wholistically about the curriculum and am also using a standards-based approach to topical review to get them to key in on where they are struggling. Here is my basic outline so far:

Pre-Assessment (2012 Practice Exam)
I am very much against a prescribe approach to review, as every class I've ever taught has varied in their strengths and weaknesses. Moreover, I vary in my strengths and weaknesses in teaching and need to be realistic about where those are. I started this year by giving my kids a full exam right off the bat- something I shielded my kids from until well into our review last year. This is a reality check and a pre-assessment...a confidence builder or a wake up call. I did an analysis of common mistakes and will be going over these with my class when we look at the exam. 

Full Practice Test #dunkinandderivatives
Nothing in schooling really prepares you for the stamina you need during an AP test until you are smacked in the face with a 3 hour marathon and only a set amount of energy with which to work. To get my kids used to the demans and the pacing of the exam, I offered the secure exam during a full session on a Saturday. We made a deal that I'd get them breakfast if they showed up to do it, and so it lovingly became titled Dunkin' and Derivatives. Of the 65 calculus students in the school, we had about 30 show up. The ones who did are already asking if we can do another before the test day, so they have clearly seen a benefit to the experience. I chose a day in the near future and we'll go over it together as a group. I am hoping that this will become a tradition and we can get more kids participating as they years go on.  

Standards-Based Feedback
The problem with offering the secure test as a practice exam is that I can't hand it right back to them to study. I loved during our breaks hearing the kids conversations about what topics they noticed they were having trouble remembering, so while they worked I took the time to put together a topical feedback form for each of them. I left a spot next to each question so I could write my comments there to give general feedback on that particular topic. 

Here's a link to a word version of the file. Feel free to edit/tweak: 

Standards-Based Review Quizzes
Fom my review grade, I decided to use a Standards Based Grading model. I developed
my AP Calculus Learning Objectives last summer and have been using them throughout the year to help guide students' studying. I have consolidated all those learning targets into the big ideas that students need to know and am going to give small quick checks on each topic. I will use the 0-4 grading scale (at left) to mark each one. Students who get a 4 have demonstrated mastery. Anything below that means we have more room for growth, so after completing corrections on their quiz and demonstrating remediation in some way they will be able to re-assess to mastery. Higher or lower, their final re-assessment grade will be what is used in calculating their score. I will average all of their quick checks on the different topics to get one final average.  I stole the formula to convert this to a percentage from Mrs. Poulsen at Lake Placid High School in NY in a recent presentation she gave on SBG: Percentage=15(Average-3)+85

It may not be the most complex conversion option, but it is easy for my kids to understand:
4 translates to 100%
3 translates to 85%
2 translates to 70%
1 translates to 55%
0 translates to 40%

Here are my ground rules, thanks to lots of feedback from colleagues who are thinking of implementing SBG next year:
SBG Remediation Wall
  • Only 1 quick check will be taken in class. All others must be taken by appointment
    • I have a QR code in my room that will take kids to a Google sign up for times when I'm available. They must give me a minimum of 24 hours notice. That way I have quizzes ready to go (so NOT running around like a chicken with my head cut off)
  • Students may re-assess no more than 2 times per quick check (I have mixed feelings about this one, but it's a compromise for people who don't believe in re-assessment at all and also emphasizes learning it sooner rather than later since we have an AP exam coming shortly)
  • Students "ticket" to re-assess is proof of remediation. This can include extra worksheets from my giant Standards Based Remediation Wall (yes, I created this on my bulletin board...like a crazy person), notes from an online video, or extra practice from another resource. I am putting this on them, not me.
  • Re-assessments must be completed within one week of the original assessment.
I am giving my kids this tracking sheet to help them organize:

Topical vs. Mixed Review
Last year I spent a TON of time on topical review and I know it benefitted my students, especially since they were in a specific course that was built to help some of the students who might never take Calculus succeed. However, I think not starting mixed review with them earlier in the year meant that they struggled more when trying to distinguish what to do when. With that in mind, this year I structured my review this year so that each night has mixed review homework from our practice book. Then, students will have a brief worksheet on whatever we worked on in class that day. The first few days it will be topical review as we go back through the course highlights. Then, we will move more towards AP style application and justification questions. Lastly, I left the final few days of my review unplanned so we can do completely mixed review on what we need the most. I also won't give specific homework those days, since APs will be about to begin and they should be focussing on what they need most. 

Here's the review overview I gave my kids: 
Cram Session
This isn't new, but I figured I'd post it again in case anyone didn't grab it off my Twitter last year. Stacey Roshan created this awesome Cram Video for AP Calculus a while back and last year I created a student assignment to accompany it. I make it optional, but it's a great resource for kids that want to do it! 



We're also doing a giant review tournament and the winners get a WWE Tag Team belt (not a joke, got it in the toy section at Target), so that's keeping their attention pretty successfully. I'll write more about that later in the month. 

I'm sure I'll be tweaking and changing as I go, but I'm interested to see what kind of results this gives! If you so anything that you LOVE for review, please pass it along! 

Thursday, March 2, 2017

Area Between Curves Partner Task

We are starting my favorite unit of the year tomorrow....area and volume! 

Not only is it the culminating moment in the course- our very last unit- but it's also just plain FUN! I'm replacing half their test with a performance task, having them build 3D models of anything possible, and just spent way too much money on honeycomb party decorations on Amazon Prime. You'd think by now my husband would just expect weird and seemingly non-math related items to be shipped to our house regularly, but evidently I'm still surprising him. 
To start off tomorrow, I wanted to get the kids working in partners and visualizing what is actually going on when we find area between curves. We can do a lot with technology, but this one time where I want them to develop the idea by hand. Each group will be given a different set of functions and a different interval on which to graph them. They will then develop the formula for area between the curves with their partner. We can hang them all up and compare our methods to determine area. 


I'm worried about the "big idea" here...once they have that, we can get into the more complicated and interesting things we'll explore this unit. I'm excited to build some models of 3D solids with known cross sections, spend some time playing with honeycomb decor, and revisit my Volumes Performance Task from last year. This will be a unit where I will definitely miss being in a science classroom (I know, I was spoiled), but I'm so excited to get started. Let the fun begin! 



Wednesday, January 25, 2017

Joy Ride: An Introduction to Riemann Sums

This year, I tweaked the order in which I teach integration a lot. Since we begin to talk about differentials when we talk about linear approximation in the applications of differentiation unit, it seemed natural to me to flow directly into differential equations and indefinite integration. Instead of leading with the area problem, we worked on general antiderivatives and differential equations. Since my students are now familiar with moving between functions and their antiderivatives, I am now starting to move into area applications to introduce definite integrals. They are starting to ask about "going backwards" from acceleration and velocity naturally, instead of having to force the area problem somewhere that it seems unnatural. This will also give me time to re-visit u-substitution since I got to teach it without having to worry about changing bounds in our indefinite integration unit. 

For the last 3 years, I've taught in an entirely project based program. The switch back to regular ed has been an interesting one for me, as I can see the ways my pedagogy has changed but don't always have the time, resources, or freedom to implement these changes. I knew when I was given the opportunity to have a 2 hour block for a project instead of giving my AP Calculus kids a midterm that I wanted to jump on the opportunity. I adapted this Gorilla Jump activity from MAA (which is an amazing activity if you've never seen it!) into a project that would require more data collection. It was a real challenge for the kids, but they seemed to walk away with the big idea and were asking the right questions (even if they didn't have all the answers yet). 

Students worked in small groups using this Driving Simulator (made on Scratch from MIT) to generate velocity data over even intervals. 

They were free to decide what intervals to use and needed to be mindful of units as most were measuring in seconds while velocity was in miles per hour. This simulator also has weather and varies the time of day, so I had my kids react to these variables so it would affect their velocity. Some drove responsibly at 68 mph on the highway. Some just accelerated as fast as possible the whole time.  I know who to watch out for in the school parking lot now. 


Using that data, students generated estimates for total distance travelled using the lowest velocity on the interval, the highest velocity on the interval, and the average velocity on the interval. They were asked to represent these estimates graphically, which naturally leads to a rough version of a Riemann Sum. In addition, I asked them to challenge themselves to see if they could write an equation (using sigma notation if they were feeling extra fancy) to represent how to generally find the total distance travelled. This was frustrating for the kids, for sure. I used it mostly as a pre-assessment to see what they remember from the previous year on sigma notation. (Verdict: we've got some serious work to do there). They were able to discuss upper and lower bound and postulated that collecting data over smaller intervals would lead to more accurate results. All in all, it led to extremely positive conversations and I think they'll have a very solid foundation when we attach formal names and notation to these ideas next class. 



A few notes of things that jumped out at me, having implemented it once: 

  • Since units were in mph and sec, there was converting needed. The kids didn't struggle with this, but it caused the outputs to be extremely small decimals for some groups. Just something to keep in mind.
  • A lot of kids discussed ways you could have changed your driving to make your estimate more accurate instead of changing your data collecting methods. While a valuable conversation, some kids got lost on a tangent here and struggled to finish in the allotted time. 
  • Since there was no requirement that their velocity function be monotonic, using the lowest or highest velocity on the interval did not lead directly to a right or left hand Riemann sum. I know that's something that won't be a hard jump for my kids next class, but again it's something to keep in mind. 
  • The kids got really cranky having to make 3 of the same graphs by hand. If you have a way to photocopy them quickly, you'd have a lot fewer cranky 17 year olds on your hands. We didn't at the time (I wasn't in my classroom and we had limited time). 
  • The car has an odometer. It would've been interesting to copy down the actual mileage of the trip and see how far off we were, especially since we're talking about error. Missed opportunity, Gironda. 
  • There's got to be a cooler final product for this. Again, I had a limited time from in which to do this with my kids, so posters were concise and manageable. I know this could get pushed to be a lot better. 
Let me know what else you might do to make this better. I liked it enough and it was worth doing, but would like to improve it for next year! I'll update with finished products from the kids when I get them! 


Tuesday, January 24, 2017

Blended Learning: Lessons Learned


One of my biggest regret after moving districts this year was that I never sat down and put all the lessons I'd learned as a blended learning teacher together in one place. Luckily for me, at the end of last year I got to sit down with the people at Opportunity Culture, the group that had been instrumental in helping my district move towards blended learning. They put together this vignette summarizing my experiences and my best advice to new blended learning teachers. 




Pioneering Blended-Learning Teachers Reach More Students Vignette Series
A vignette written about my experiences with blended learning in Pre-Calculus. If you want my lessons learned (often the hard way), read this! 

I'm so thankful to have had this experience and to have had it documented! 

Hey! I said that! 





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 samjshah.com, 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!