"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! 

A Little Bit of Thanks

Y'all....how 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?!?!

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. 

Downside

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. 

Downside

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.

Downside

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.

Downside	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.

Applications of Derivatives Slap Jack

Triangle Congruence Theorems- Why Not ASS?

First of all, kids, yes. We are going to write the word ASS. We are going to write it repeatedly. I can insist you write it as SSA, but we all know that isn't going to happen OR help you remember it nearly as well. Get your giggling out now. 

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! 

Here's some of the resources I've used throughout the unit. I'll continue to add if I see anything else unique: 

• 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.

I haven't taught triangle congruence in 5 years, so I'm slowly starting to get back into the groove. So many things I'll change for next year! 

Tangent Line Approximation Discovery

You guys, what is it with me and blogging this year? What are your best tips when you feel like you just can't get into a groove with your blog?! I miss it! 

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. 

I knew my kids were more than capable of discovering this phenomenon and explaining it to each other without much help from me, so I wrote up this very simple activity for them:

We wrapped up with a discussion about what students had discovered, focusing heavily on part (f). I love seeing kids have these "duhhhh" moments- when something seems so simple that it's barely worth mentioning. It reminds me of those moments in college when a professor calls something trivial that was anything but trivial to you. When my students can start to view concepts in Calculus as so obvious they barely deserve explanation, I'm a happy teacher. 

Here's a link to the document! 

Tangent Line Approximation Discovery

Justifications and Curve Sketching in AP Calc

Have I mentioned that I love curve sketching? (Yes, I know, only every 5 minutes). To me, it's a giant puzzle that students can approach from all different angles. There are so many small parts that individually contribute to the big picture and I love those moments when you see it all come together for a student. It's one of the only units in Calculus where I can look around on any given day actually see the lightbulbs lighting up for each kid- each one benefiting from a different perspective or activity. Today we did some serious curve sketching challenges!

#1: Justification Graphic Organizer

Students worked in small groups to complete the graphic organizer with calculus explanations for each of the features in the chart. 

We returned to their chart over and over throughout the lesson and it's something they can keep to study from in the future. Next year I think I'd like to revise it to to include explanations of what happens on f, f', and f''...maybe a sketch or description box?

#2: Quiz, Quiz, Trade

This is an activity that is right from the College Board modules and I love it! I gave the students time to work on their own problem silently and then check their answer. They needed to be prepared to teach it to another student. If they didn't feel prepared, they got to come hang out with me at a side table to go over it once the activity started. I set a timer for 5 minutes and told students to interact with as many other students as they could in that time. They worked diligently, explaining their problem to those who needed help and solving each others problems. It brought out common misconceptions, too (which is always vital).  

Quiz Quiz Trade Student

Quiz Quiz Trade Teacher

#3: AP Justification Challenges

Next we worked on scaffolded activities to get students building arguments. Here we discussed what implications f, f', and f'' all have on each other more specifically and began to see common AP style questions. We didn't finish all of these in class, but the nice thing is you can pick and choose what your kids need to most help with while you work. 

Here's the whole document that we used!  AP Style Justifications

Let me know if you have any other activities you love for this unit! 

AP Calculus Curve Sketching Tips & Tricks

One of my favorite times of year in AP Calculus is that moment when we finally have enough mastery of derivative technique to start seeing the "why" to our last few weeks of "what."  These are some of my favorite conversations I get to have with my kids (and my kids get to have with each other) as we move into curve sketching. 

Extreme Value Theorem (aka Wolf Blitzer's Celebrity Jeopardy Meltdown)

Extreme Value Theorem always seems to fall around election day in my curriculum and the the obvious connection between that and the candidate test are often staring me directly in the face. However, I've found that this analogy often only helps students remember the name of a test- not that actual idea of what it does. 

My husband and I are both secretly 87 years old and we watch Wheel of Fortune and Jeopardy every night together. When I was recently reminded of Wolf Blitzer's total meltdown on Celebrity Jeopardy, I had a sudden ah-ha moment:

• 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. 

Mean Value Theorem(aka the E-Z Pass Conspiracy Theory )

Kids love a good conspiracy theory and what better tool to scare a new driver than the prospect of an undeserved speeding ticket. I've posted before about how I introduce Mean Value Theorem, but this year I added a new layer of intrigue. This Snopes Article linked above was written about the area in which I am teaching (Upstate NY) and I remember being a teenager and hearing family members talking about "big brother watching" with all the new technology that was being developed. I may or may not have given my students an article about this to read before showing them that Snopes had verified it wasn't true. They may or may not have freaked out a little. It definitely got them talking about what type of proof they would want a police officer to present to them if they knew that when they were clocked on a radar gun they weren't speeding, but the cop was giving them a ticket anyway. 

Rolle's Theorem (just think "Tootsie Roll")

My husband still talks about the day he learned Rolle's Theorem in BC Calc. He can't tell you anything about what it meant, but he remembers that his teacher gave them all dinner rolls. I thought about doing this and was talking at a dinner party one night about where to buy dinner rolls in bulk (because math teachers at a dinner party are notoriously cool). After resigning that I'd need to look like a crazy lady at a wholesale club the next day, someone I barely knew suggested I just buy Tootsie Rolls instead. I had another mini-epiphany:

• 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:
  

First Derivative Test- Let's Get Talking

The first derivative test is a pretty intuitive idea when you break it down....a maximum has to happen when slope changes from positive to negative and a minimum has to happen when slope changes from negative to positive. It's something you could talk about at a much lower level than AP Calc. However, it's something we need to be able to justify correctly at the AP level, so the more I can get my students to understand the intuition, the easier this will be for them. I used this activity this year:

Increasing/Decreasing Speed Date

I gave out cards like this to my students. 

Each one has:

• The graph of a derivative on it
• A prompt to help students generate discussion
• An answer key on the back.

First, I had students work individually on their own problem to make sure they were the "experts" in it. Then, students "speed-dated" students with different problems, trying to determine intervals of increasing and decreasing on each. Then, in small groups, students were asked to identify what happens at the points where the intervals meet. We wrapped up with a whole class discussion to debrief and develop our final conjecture. 

We still have a lot more to do in curve sketching, but these are just some of my favorite little tricks for introducing a collection of really fun ideas! 

Post It Challenge Review Game

I am PICKY when it comes to review. I have a very long list of "must haves" that make it almost impossible for me to be happy with a review activity. I want an activity that....

• 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
• etc

I've kissed a lot of frogs (Chutes & Ladders, I'm looking at you) with review activities that just didn't work for me. I've been in classes observing games that don't meet all of my criteria and some teachers make it work so well, but I know without my buy-in it's not going to look so pretty in my own room. This idea was adapted from my amazing mentor my first few years and has blossomed into one of my favorite review activities that ALMOST meets all my criteria.  

Post It Challenge!

Teacher Set Up: 

1) Make a presentation of questions (any type, any sort of answer, anything subject area!) that are relevant to the topic you're reviewing. No need to do any crazy formatting....the goal is to go over each question after you do it anyway. Not have the answers available adds to the suspense of seeing if your group was right. 

2) Think strategically about how you want students grouped. Heterogenous are 100% the way for me here....get kids with different strengths talking. Never set up a group to be behind! 

Materials: 

1) Your presentation

2) Sticky Notes

3) Whiteboards for scratch work (optional)

Rules: 

1) All work must be shown on the sticky note

2) One answer per group; make sure your answer represents your whole group! (Teamwork is an important part of this rule)

3) You must turn in your answer within the allotted time for that question

3) After each round, the sticky notes get passed so a different person writes for each questions

4) You must put your group number on your sticky note or your group will not be eligible for credit

Game Play:

1) Assign each group a number. Make sure they write it on the top of each sticky notes, 

2) Put the first question up on the board and let students know the amount of time they will have. I use this time to circle around the room encouraging groups and helping out the strugglers. I also use Traffic Light Cups here to make sure I'm hitting the struggling groups. 

3)  Collect answers from groups as they finish, making sure to keep groups informed of how much time they have remaining. 

4) After collecting all answers, actually go over the problem. Create suspense. They might not care if they got the math concept, but they care if they got the points.....let it build. 

5) Put the next question on the board and repeat. As the groups work on the question, put up any sticky notes that were correct next to that group's number. You can also give half credit by ripping a sticky note in half.

This isn't perfect, but I tend to find that it gives me a lot of control of variables. I can control the group size, game pace, types of questions, and have the flexibility to add in "bonus questions" quickly if I see something the kids need immediate help on. No one is being put on the spot up in front of a group...if they get something wrong, their sticky note just doesn't get put on the board. 

Another simple post to get my blog train rolling again. Happy Monday! 

Derivatives of Trigonometric Functions

I. Stink. At. Blogging.

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.....

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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.

Then, I had them use the quotient rule and trigonometric identities to derive the other 4 trig derivatives.  

Like I said, not groundbreaking, but it got them talking and thinking about the magical fact that Calculus is, in fact, not just magic. It should all make sense! 

Derivatives of Trigonometric Functions Discovery

#MTBoSBlaugust Day 19: Thoughts for Starting Geometry

Second to last post of #MTBoSBlaugust! This has been an incredibly rewarding experience, gotten me ready for back to school, and helped me see how much blogging increases my critical thinking about my teaching. 

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:

• curfew
• school rules
• other awesome things they might come up with?

And just generally things like these:

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. 

Then, we can get into a brief overview of who Euclid was and how this attention to detail was incredibly important to him. We are going to think like mathematicians in this class and in order to do that, we need to be sure we're being precise. 

2) Students work in pairs to complete this investigation from Discovering Geometry: An Inductive Approach (Key Curriculum Press) and wrap up with generating class definitions

3) Give students a list of geometric terms and have them work with their partner to generate the most precise definition they can given their prior knowledge. This will not only get them communicating, but hopefully help me pre-assess what they remember and give me time to walk around and talk to kids individually. 

4) Discuss their definitions as we generate our own class definitions. Culminate with filling in notes for the day that address notation. 

Thoughts? Favorite ways to address such a vocab-heavy course? Favorite Euclid videos? Feel free to comment! 

#MTBoSBlaugust Day 18: Good Signs

Today I finally got a chance to get into my classroom and start setting up. My mind has been spinning since orientation with questions and ideas, especially since my husband was able to get into his classroom weeks ago since it wasn't being used for summer school. We spent last week hearing a lot about admin's stance on education and I genuinely felt like this was a group of educators who, at least in intention, were there for the kids. There was encouragement to take risks, to try new things, to innovate, and to advocate for the students. It all sounds so good in theory, but you never know what things look like in day-to-day practice. I hoped I would be meeting other colleagues who wanted to challenge themselves, innovate, and bring a positive attitude to collaboration.

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. 

#MTBoSBlaugust Day 17: The Power of Yet Poster

A while ago, I saved this poster on Pinterest because I loved the sentiment! I knew I wanted something like this to go into my classroom this year, but when I found out I'd be floating I figured it would be a nice idea for the future. (The pin was a dead link, so not sure where this originated. I'm happy to give credit if it was yours- let me know!!)

Since I just found out that I do in fact have a classroom and was reminded of the poster by this tweet tonight:

When kids ask for something, we expect them to say "please."

When they say they can't do something, we should expect them to say "yet."

— Justin (@JustinAion) August 26, 2016

I decided it was time for me to make one of my own! 

Printable Poster:  The Power of Yet Printable Poster

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! 

#MTBoSBlaugust Day 16: Designing for Growth Mindset

I just finished a few days of New Teacher Orientation and it was invigorating, albeit a little overwhelming. We talked about so much that it's hard to keep track, but one of things that stuck with me is a word that came up over and over today in our discussion of the district vision: intentionality. 

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:

1) Homework

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:

Grading Homework for Accuracy or Completion? Yes!  

I totally agree that neither system promotes analysis of mistakes and I like the author's proposal to use those mistakes as teaching tools. I like the idea of student ownership over their own work and assessment, but I know there are loopholes here for students who want to take any easy way out. 

I am sooooooo open to suggestions on this. Please share your homework grading practices and why you love them. I want to be inspired, #MTBoS! 

2) Assessment

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

I know the arguments....that kids need to learn responsibility and shouldn't ever be allowed to do corrections or take retakes. I don't disagree on summative assessments- there has to be some type of deadline in our 180 day calendar. However, that doesn't mean I can't help my kids see their learning as fluid (and growing) along the way. 

I know there are tons of resources on this out there, but this is the one that got me thinking:

Promoting Growth Mindset Through Assessment

Again, give me your suggestions!! How do you use assessment to send a growth mindset message to your kids? And how do you do this in a PLC environment if others don't necessarily agree? 

TL;DR

Thinking about growth mindset...want your best ideas! 

• How do you use homework as a growth mindset learning tool?
• How do you use assessment to promote growth mindset?

#MTBoSBlaugust Day 15: #ObserveMe Goals

Here are my #observeme goals for this year! 

I am still picking out a rubric I like and I'm not sure where I'll actually put this (maybe attach it to my back as I masterfully and gracefully float between classrooms? attach it to some currently unpurchased cart I wheel back and forth? get a tattoo of them?), but I love this idea so much. It is not only good for us as teachers to seek the feedback, but it models for our students that we should always been looking for ways to improve! 

My district orientation starts tomorrow and I can't wait! Wish me luck! 

#MTBoSBlaugust Day 14: Balloon Geometry

Time for a fun Friday post and a break from a lot of heavy curriculum lately! 

Every year my former STEM program put together a giant kickoff for our students. These events were designed to promote collaboration, trust, and community while getting to explore some awesome STEM ideas. One year we themed the entire kickoff around sustainability as our students would be engineering with repurposed materials in their design class. Another year, we had groups design boats out of cardboard and then we tested them out in a pool at the end of the day. 

SEAFARING STEM! from justin pierce on Vimeo.

Last year, we decided to go with a more diverse plan. Each teacher designed their own mini-PBL and students were able to select which they wanted to attend. It reminded me of the excitement of going to a big state or national conference- the hardest part was deciding what you should skip! This gave us all a chance to nerd out a little in our respective subject areas and do things we might not normally have time for with a diverse collection of grades and ability levels. 

I settled on using the time to have my kids explore Balloon Geometry. Besides spending two hours before school blowing up balloons and having incessant popping sounds coming from your classroom, it was fun & a great engineering challenge. I saw groups work together to problem solve, play to each other's strengths, and just have fun thinking critically about geometry. 

Here are my slides: Balloon Geometry

You could make this way more structured to ensure that kids are building "pretty looking" polyhedra, but this was only an hour activity and I liked seeing the kids work together to decide what figures would work the best. 

There are TONS of great resources online for this, but here are a fun of the ones I used:

• Ballon Polyhedra
• Mathematical Balloon Twisting for Education 
• Balloon Numbers
• And this video: