## Wednesday, September 30, 2015

### Post-it Queen

I am definitely the Post It queen of my department. My desk is constantly littered with a minimum of 12 different pads of brightly colored notes. I have a pad that I leave in each group's "supply basket" for daily group work (because you never know when you will NEED them!). I got heart-shaped post-it's from my high school best friend as an engagement gift to help keep me organized as I planned the wedding. You get the picture.

To throw gas on the flame, I was gifted over 15,000 Post-its as part of the Reddit Teacher Gift Exchange (THANK YOU!) 2 years ago. They have become a regular part of my class games, activities, and assessments.

My favorite way to use them right now is together with the (free!) Post-it Plus app. I post questions around the room that the students need answer in pairs or groups and ask each set of students to post their answers, one per note.

Today's was a pre-assessment on laws of exponents as we movie into our logarithms unit in Pre-Calculus.

I posted 6 problems, one on each of the major laws. I could instantly look at the Post-its and get a general idea of where the strengths and weaknesses in prior knowledge exist. Kids all got it right, we can briefly discuss and move on.

Our biggest problems seemed to be rational exponents, so from there we can delve further into the type of misconceptions the students have.

Here is where the app kicks in! You use the app to take a picture of the post its (Pro-tip: Ask the kids to use pen or marker- pencil doesn't photograph very well), as seen here.

From there, the app creates a "board" of the notes so you can scroll through them and assess student misconceptions. It's anonymous so kids are more willing to be wrong, which I love.

From there, I've had kids do group responses to common errors, identify patterns, and do "find my mistake" activities. I'm sure there is so much more I could do, just haven't tried yet.

It's a fun formative assessment that the kids instantly think is "cool" because of a simple app.

 The "board" of answers through which we can scroll!

Happy Hump Day!

## Saturday, September 26, 2015

### Introducing the Derivative (The Italian Way)

I'm from a big, loud, Italian family and all our biggest celebrations always involved pasta. Imagine my excitement that I can share one of the most exciting days of Calculus with my students and bring pasta along for the ride!

Inspired by Math Teacher Mambo's post about relating graphs of f and f', I couldn't wait to test this out with my students. I was amazed- a concept with which they were likely to struggle was suddenly accessible and they were having great conversations with their partners.

I really tried this as an experiment and spent less time that I wish I had actually manipulating the pasta, so I may re-write this to give them more practice with the "approaching" idea.

Side Note: One of the reasons I love teaching so much with pasta is my now infamous "pasta speech." I did an activity with pasta my first year of teach about something (triangle inequalities maybe?) and haven't had to buy a new box of pasta yet. In that time, I've moved classrooms and moved schools and, quite frankly, not been concerned about the food safety of said pasta. I always give a very impassioned speech- a pasta-biography of sorts. It's humble beginnings on a grocery store shelf....it's long summer in a hot storage unit while I slowly moved trunk-fulls of stuff to my new city in my '92 Subaru....it's residency on the bottom shelf of my bookcase, close to the not so cleanly environment that is a high school classroom floor. All of this to lead to the moral of the story- don't you DARE put that pasta in your mouth! I even had a student buy me a box of pasta for Christmas and leave it on my desk with a note that says "Thought you could use an upgrade." Never gets old.

The Lesson:

To get kids thinking about average vs. instantaneous velocity, I started with this question....

As a group, answer the following question & justify on your whiteboards numerically, graphically, algebraically, or verbally:

Alex and Erika both live next door to each other, 13 miles from school. Alex leaves home at 6:30 am and arrives at 6:45 am. Erika leaves home at 6:50 am and arrives at 7:00 am. Who passes the gas station halfway to school in a shorter amount of time?

This led to a pretty lively debate and helped me pre-assess their knowledge of physics a bit. Eventually, one student convinced the rest of the class that since we don't know their instantaneous velocities that we didn't have enough information to answer this question- which I love, because it leads them to questioning how we get that information.

The next activity was inspired from a University of Washington activity, but I modified it heavily so my kids could really build the knowledge themselves (without quite so much jargon).

We did get to some practice with the limit definition and I'm going to use this Derivatives Match Up as a warm up activity in class on Monday to give them some more partner practice. Derivasaurus Rex is very excited about all these rates of change (more on him later)!

## Friday, September 25, 2015

### Once in a While...

...you get a message like this from a kid.

Taking risks in the classroom is exhilarating, but sometimes you're not sure if you're helping anyone (especially yourself) by taking on so much extra work. Teaching in daunting and exhausting and some days you just feel ready to break.

Thankful for this student and the others who make a point to remind me why I do this (even if sometimes it's harder for me to see the reminders). Such a happy note to end my week.

## Thursday, September 24, 2015

### Rational Functions Challenges!

I always find my Pre-Calculus class the most challenging to teach at this time of year. Yes, even more so than prepping for AP Calculus for the first time and teaching a blended class with 50 students and about 10,000 things to grade every night.

We run on block scheduling and there are few things which I think are more of a challenge for mathematics teachers than the gaps in background knowledge that happen from skipping semesters (or YEARS) of math in high school. By the time the kiddos get to me in 11th or 12 grade, all those "must know" skills have been forgotten. My goal is to try to remind them of those skills without having to reteach the concept completely. I know it's in there....we just need to bring it back to the surface!

We are currently studying rational functions, a topic which is so vital to their study of limits and later calculus. The whole idea of discontinuities....so important!

This year for some of the review topics, I'm using some classroom flipping (with videos I made with Educreations). Kids who remember the material can speed through these and demonstrate mastery while kids who need the extra remediation have the opportunity to get it. My kids had 2 "flips" last night- a brief video on holes vs. asymptotes and one on horizontal asymptotes. Having the preview of these topics allows me to group the kids strategically and have them really practice in class.

Desmos PolyGraph Activity
Think "Guess Who?" for functions (the one pictured above is quadratics)! I loved that it let me move around the room and assess the comfort level with mathematical vocabulary.

We had a big discussion about what questions would be considered appropriate for pre-calculus level students. Here's what we decided...

From the teacher perspective, I could follow each conversation and make sure they were using academic vocabulary. I was able to circulate around the room and listen and ask probing questions to kids who needed it. It was competitive, but fun! Every single one of my students said on their feedback form for the activity they'd want to do it again.

What the kiddos are saying....

"It was fun and helped strengthen my math terminology"

"I like the fact that you can ask questions to better understand the topic and also get asked the questions. It's easier to understand and more fun with being partners with some random person :)"

"It was a fun, creative way to show what we know with out the stress of a quiz, or test."

Once I felt confident that they had mastered the vocabulary and were ready for more collaborative practice,  the students had to complete a graphing mini-project on my giant laminated graph paper! The first 2 questions were a mini-review from rational expressions and equations and the 3rd was the actual mini-project.

(Is the domain and range bothering anyone else?? Have some more work to do with that group, still!)

## Monday, September 21, 2015

### Authentic Engagement with Mistakes

One question I've been grappling with a lot this year is trying to help students authentically engage with their own mistakes and misconceptions. My first year of teaching I was the queen of corrections, letting students correct every test and quiz to try to realize what they did wrong and learn from it. My middle schoolers were generally very honest about this, but when I switched to high school I saw the huge desire for good grades outweigh the desire to learn from errors. I saw more and more cheating and less and less studying for the initial test and I cut it off.

I know there are such huge payoffs for kids who learn to analyze their own mistakes, though!! And telling a student who genuinely wants to learn from what they did wrong and is proud to demonstrate to you that they've mastered a concept that they are out of luck? It makes my stomach turn!

This is very much a first draft, but here's what I'm thinking....
Things I'm considering:

• Only allowing students to re-test on a set number of assessments per semester (2....3....suggestions?). This allows the opportunity to make up for a "bad day" but not get used to failing the first time and making it up the 2nd time around. Does this go against the whole idea of always being able to learn from their mistakes?
• I only want to offer 1 re-test....what if a student in genuinely absent? Do you start making exceptions?
• About 1,000 things I haven't even thought to worry about yet
Has anyone come up with a system they really love for allowing students to learn from their mistakes and prove mastery without sacrificing the high expectations on the first assessment?

## Sunday, September 20, 2015

### Back At It

THREE YEARS AGO: I was a 2nd year teacher at a private middle school in a very affluent area. I lived in a new city 2 hours from my now husband and 12 hours from all my family and friends, was the youngest person on my staff by at least 30 years, and had a whole lot of free time....which I filled with school work! That's where this blog was born and, for a while, actually thrived. I was working 90-100 hours a week and it generally wasn't a very balanced life. Something had to give (Spoiler: it was the blogging!).

TODAY: I'm starting my 5th year of teaching and my 3rd year at the school I moved to when I decided to finally be near my aforementioned husband. I fill my days with much more balance- teaching in a STEM magnet program, piloting a blended learning class for our district, tackling AP Calculus for the first time, satisfying my dog's desire for an infinite quantity of adventures, and enjoying being in my late 20's with an amazing husband and group of supportive coworkers and friends.

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After a 3 year hiatus, I'm working on getting back into blogging. I am excited to build my PLN and share ideas with a supportive community worldwide who share the same passion that I do- designing activities and curriculum to make math exciting and engaging for our students.

Consider this post a bridge between these 2 phases of life....
• Post before this (some of which have been deleted....because gosh I was bright-eyed and overly excited about every moment of my day) are the thoughts of a young, excited teacher who has lots of autonomy, no standardized tests, and is still learning exactly what good teaching looks like to her.
• Post after this are the reflections of a (slightly) more seasoned teacher who believes that the students should be in the driver's seat in their own education, that experimentation and failure are a good thing, and that I still have a ton to learn!
Let's get mathy, y'all!