Saturday, June 3, 2017

Integration by Parts Circuit

Let's face's hard to keep kiddos engaged after the AP exam. Especially when they already took their final, know they got a "5" on it, and are starting to hit up the graduation party circuit. Luckily, I have great kids who are buying in to the whole "If I learn this now it might make my first week of college a little less stressful." (Huge shoutout to my former student rocking his engineering major at NC State whose email from the beginning of this year I've been able to show them!)

After learning Integration by Parts, I wanted to give the kids something self checking that they could work on with peers for practice, so I created this quick little circuit. I ended the lesson by having one student put a question on the board where tabular was appropriate and one student put a question where it wasn't and we talked more about why they made the decision they did. 

Feel free to use as is or modify! I got all the problems from this Kuta worksheet.  It took the kids about 15-20 minutes to complete. 

Wednesday, May 24, 2017

Standards Based Review in AP Calculus- Student Feedback

After reading through 50 thoughtful and heartfelt course evaluations from my kiddos, I have pulled out the major themes from the section on standards based review. Overall, the reactions were very positive. These were their favorite parts:

  • Liked opportunity to improve grade
  • Pushed kids to study what they didn't know, not just what felt easy
  • Getting a "4" on a topic built confidence for the exam on that topic
  • Loved having to take them "cold"- gave a real picture of current understanding without stress of low score
  • Gave accurate portrayal of what AP questions would be like
  • Enabled you to correct your mistakes and feel okay being wrong/asking questions

As expected, it wasn't all sunshine and daisies....the kids has some (mostly) constructive feedback on things they didn't like too:
  • Didn't like having to remediate to retake; just wanted to be able to retake
  • Deadlines for retakes stressed some kids out since we were doing multiple per week
  • Frustrating for students who understand concepts but make small algebraic or arithmetic errors and don't get the "4" they want so badly
  • Wanted time in class to retake since finding time outside class can be difficult
  • "Annoying" (Such helpful feedback, I know)
  • Hard to find motivation with senioritis kicking in big time

Overall, I thought it was a success and will definitely be using this strategy again in the future. I was able to see a huge amount of growth in the students that took it seriously and we were able to comb through misconceptions with a fine-toothed comb. I was able to grade extremely critically since students were striving for a perfect "4" instead of settling for a 95% or 97% and not really examining what they did wrong. I whole-heartedly agree that it was a lot condensed into a small time period and the deadlines were constrictive for some students and I'll be adjusting for some of that next year. 

The Google Form I used as a sign up was an absolute must - I could check it daily and was able to track student data through it, as shown here:

Overall, kids took 82 retakes on the 9 quick checks. Most kids said they wish they'd done more. And the growth mindset message seems to be getting through:

Can't believe we're so close to the end! 

Friday, April 28, 2017

Math Teachers at Play Blog Carnival #107

The Math Teachers at Play (MTaP) blog carnival is a monthly collection of tips, tidbits, games, and activities for students and teachers of preschool through pre-college mathematics. We welcome entries from parents, students, teachers, homeschoolers, and just plain folks. If you like to learn new things and play around with ideas, you are sure to find something of interest.
I'm so excited to be hosting this edition of the MTaP Blog Carnival at Give Me a Sine! If this is your first carnival, welcome! This is a great way to find some new bloggers you'll love and even share your ideas in the future! I am a high school teacher, so it has been particularly awesome for me to get to explore so many new middle and elementary level blogs as I prepared to host this month. 

Want more information about the MTaP Blog Carnival?  Want to host it at your blog?  Want to submit a favorite blog post?  Click here for more info

Since this is edition #107, let's ask the question on everyone's mind....What's so special about 107? 
  • 107 is a jackpot for prime number trivia! 
    • The 28th prime
    • A Chen prime (since 107+2 is also a prime!)
    • A safe prime (is of the form 2p+1 where p is also a prime)
  • The smallest positive integer requiring six syllables in English (if you include the "and")
  • The atomic number of bohrium
  • The "911" of Argentina and Cape Town
  • The number of legal acupuncture points
  • 33 states and the US Virgin Islands have a highway numbered 107

And now, on to the posts! 

Talking to Parents about Math Explorations
While this post contained only a copy of a letter sent home to parents after a recent Math Exploration event, I loved the message that mathematics continues outside the classroom walls. So often, kids conceptions of math are influenced by their parents prior knowledge and experiences. I love the intentional outreach to parents to embrace the math of every day life! 

Playing with symmetry in kindergarten
a) As a high school teacher, my heart basically melted here
b) I love all the different explorations the students used here to explore symmetry- from pattern blocks to mirrors to modeling with their bodies. The idea of symmetry is an integral part of my geometry and calculus classes daily, so building these intuitive understandings young is so promising! 

"Who Wants To Count My Windows?"

This great post from Joe Schwartz on working with constraints in a 5th grade classroom. He builds off the "Ant Hotel" problem to create a fun-filled learning experience for his kiddos! 

Practice Math Facts Using Your Voice!

Cool and definitely fun to play with, this tool allows you to practice math facts with your computer just using you voice. Did my husband wonder why I was yelling numbers to myself in another room? Probably. But I can see littler ones loving this for practice! Just make sure you allow it to access your microphone. 

Origami Math Game {Tutorial}

I think making cootie catchers is a right of passage in the elementary days. Crystal Wagner shares a tutorial for turning this into a math game for your kids! 

Middle School

My husband and I just closed on a house this week and I am so thankful to be a math teacher. I've gotten hit over the head with all the mathematics around me daily- even just buying the right amount of shelf liner for the kitchen or getting the right sized fire extinguisher. This post made me laugh out loud given all the high school math we've been doing and would be a great launching point to get kids talking about the geometry around them. You can also check out this one, on combinations, from the same blog: Three Sisters And Their PJ’s

Sort Students into Groups using Percents, Fractions and DecimalsThis fun activity will sort kids into groups AND get them thinking in the process. I can even see using this at the high school level- we all know fraction skills can always use a boost!
This activity draws on the proportional relationship that exists in linear functions and gets kids reasoning proportionally. This would provide a huge booster to the discussion of slope, too! 

High School

Denise Gaskins shared this fun Patty Paper Trisection activity (complete with Hints and Solutions: Patty Paper Trisection). This puzzle gets the participant thinking about how to trisect an angle, using simple tools. Straight edge and compass aren't going to help you here, folks. Give this one a try! 

MULTIPLE REPRESENTATIONS FOR TRIGONOMETRIC EQUATIONSSam Shah is one of my go-to's for quality and thought-provoking material in my upper level courses. This activity gets kids thinking conceptually about my all time favorite thing- the unit circle! Trig equations can be hard, but with the right conceptual understanding....BAM! You've got magic! 

To Whom it May Concern: Learn to Love the Why.This one is a keeper. Read the whole thing and listen to the voice clips. Kids can sometimes be our most honest and necessary feedback sources.

This isn't new, but it's been circulating in my mind for the past few weeks as we approach AP exam time. This is a Tuft's study that advocates practice testing as a shield from memory from stress. I've tried to integrate more practice testing into my review this year and I see a difference in what my kids are willing to take on. I don't have a fully formed opinion yet, but it definitely got me thinking. 

A Brief Ode to Blank PaperSometimes we give too much info to our kids. This piece by the amazing Tracy Zager (whose book is sitting on my nightstand and a must read) and advocates that by giving less, we cause kids to think more. 
General Mathiness

These 2 posts from Mike Lawler will get your wheels turning with unsolved problems and the bridge between "pop math" and real math:

This post explores linear congruential generators and how they could be a source of mathematical play. It delves into computer programming, modular arithmetic, and more! Definitely worth an exploration! 

Let me know if you had any other favorite posts of April and submit your posts for next month's carnival! Happy Math-ing! 

Monday, April 10, 2017

Call for Submissions: Math Teachers at Play Blog Carnival, April 2017!

I am so excited to be hosting the Math Teachers at Play (MTaP) blog carnival for April at Give Me a Sine! 
If you haven't heard of it, the blog carnival is a monthly collection of tips, tidbits, games, and activities for students and teachers of preschool through pre-college mathematics.
Have a post you loved from a colleague that really shaped your practice? Find a puzzle, logic problem, or other fun math-related post that caught your eye? Want to get a few more clicks on a post you are particularly proud of writing? Submit them all!  
The deets: Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up through first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival.
To submit an entry, fill out this form: SUBMISSION FORM
I can't wait to see all the amazing posts you all have to share! 

Wednesday, March 29, 2017

Justifications Gallery Walk

As we get closer to the AP Exam, I'm working on helping my kids "play the game" in the way they can benefit themselves most- to be as mathematically precise in their language as possible. Although I've emphasized it all year, students tend to rely on their long term memory once you start review and that tends to be a little less precise than we might hope.

To get students thinking again about technical justifications for curve sketching today, I started with this warm up gallery walk. 

1)  Students did a silent, individual gallery walk to critique justifications (some close, some very off, maybe even some right!?). They left a post it under each one with their feedback on how to make it better.


2) Next, I grouped students and had them each work on one particular justification. Students read through the feedback and sorted it, using it to generate a new and improved justification.

3) Each group presented the feedback they'd seen on their problem and their new and improved justification to the class. This gave us an opportunity to talk as a class about what could be improved and to examine some common issues. 

After that, we did a released AP problem that required multiple justifications and I saw a huge difference in the precision of their language. It was a good jump back into more extensive mathematical writing. It could also be applied pretty easily to EVT, MVT, and IVT justifications, among other things! 

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 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!