#MTBoSBlaugust Day 8: Oh The Places You'll Go!

I have been lucky in all my years of teaching to have a "senior" level class each year. For a few years, it was 8th graders- top dogs going off to the wide world of high school. For the majority, it's been Pre-Calculus or AP Calculus with some of the most wonderful 18 year old humans the world has ever seen.

One of the things I try to do with my seniors is give them a space in the classroom that is all their own. I bought this poster as a heading for the corner:

I chose it for a few very specific reasons:

• Dr. Seuss is a boss
• It was available as a Prime item (an instant sales tactic)
• I like that it doesn't specifically mention "college" or anything else like that- just "the places"

I keep a set of blank "pennants" in a folder near the wall and I encourage kids to post anything they're excited about there. They can decorate to their hearts content or they can just fill it in. They can fill out as many as they want.  For some, that looks like this. 

Always an added bonus when you get to celebrate an acceptance to your alma mater (Go Bearcats!)

Some students have upwards of 10-15 pennants on the wall by March, posting every acceptance they want to share there. This board has seen big names: Yale, Cornell, Duke, Syracuse, UNC Chapel Hill, University of Texas, and many more. But I wanted this board to be a place to celebrate anything that my seniors are celebrating about their life outside high school. For some of those kids, that doesn't mean a 4 year school. I've had kids post military commitments, jobs, community college, missionary work, and gap years. Not only is this good for my seniors- giving them a sense of pride and ownership- but it's also a place where my underclassmen can get inspired by the things their older counterparts are accomplishing. Most fun for me, it brings kids rushing into my room first thing in the morning- sometimes long before their class-  to share happy news with me or confide in me if they're disappointed. They ask their friends to "wait up" after class so they can stay and share something with me. It's such a simple thing, but it's been a powerful tool in helping me connect to my kiddos at a scary and exciting time in their lives.

If you teach seniors, I really recommend trying this. I don't have pictures of last year's wall since my room is being used for summer school, but I'll take some and post them in the future! 

#MTBoSBlaugust Day 7: Using Google Drawings to Encourage Student Independence with Technology

One of the things that was most daunting about beginning to integrate technology into my every day instruction was the thought of having to do any instruction in the actual use of the tech. As much as we think our kids are digital natives, there's a cruel reality we must face. For many our my kiddos, this was the extent of what they could do with technology:

If it wasn't social media or a video game, my kids weren't buying it. And trying to explain the things that need to be clicked in the correct order to a class of 30 kids who may or may not be listening was daunting. I can vividly remember saying the same thing over...and over...and over...and over the first few times I tried a new tech tool. And while some of the kids caught on quickly, I found it hard to balance the kids who were moving ahead of me and the kids who were lagging behind. 

Looking for a tool to create more student independence, I started playing with Google Drawings and it's been my go to tool ever since! If you haven't tried it before, start in your Google Drive: 

See how you just did that....on your own? 

That's because you just used a Google Drawing I made to show you exactly where to look! 

It's very easy to insert images (often screen captures of the tool you're using) and then edit then by adding text, shapes, arrows, callouts, and more. You can also add multiple pictures to one drawing, add charts and diagrams, and add word art. 

You can download the image as many different things, but I usually use JPEG since it's easily inserted into a Word document or uploaded to my website. 

Here are some examples some I've made for my kids in the past:

These can be easily copied, pasted, uploaded, and shared! I put them into student worksheets so kids can work at their own pace and I'm free to move about the cabin and help as needed! It's been a life saver for me (and my own sanity) when teaching with tech! 

#MTBoSBlaugust Day 6: Continuity, Limits, & L'Hopitals, Oh My!

PLT PICs at NASA

I was extremely lucky to have an out of this world (get it, get it???) PD experience this summer- going to Houston to attend the Advanced Placement Annual Conference. On top of that, I got to attend with my Calculus PLT PIC (yup....professional learning team partner in crime- because there are never enough acronyms in a school setting). She just finished her first year of teaching AP and I finally have enough under my belt to apply to be a reader, so we were coming from slightly different perspectives. Both of us knew one thing for sure, though....we could not stand to hear another word about L'Hopital's Rule by the time we left.

Anti-L'H's sentiment on conference notes

The big issue was this- there's been a lot of debate online all year about the way L'Hopital's rule is justified. Understandably, the College Board has asserted that it is mathematically incorrect to say that something equals 0/0 since 0/0 is indeterminate. This caused some unrest in the Calculus community, since many teacher have allowed students to write this for years. Easy enough adjustment for my PLT to make...make sure students evaluate each limit separately. But we got a new curve ball this year that brought some amazing scoring statistics with it. Question #5 from the AB exam was a relatively straight forward question- average rate of change, evaluating derivative, candidate test for absolute extrema, L'Hopital's Rule. 

So why oh why did only 0.013% of students (under 30 worldwide) get full credit on this question? 

The answer came from the scoring guidelines, which allocated 3 points to part d instead of a more typical 2 points:

If a student didn't state that g was continuous, they missed a point. Any while logically we know that this must be true, I think very few of us as Calculus teachers would have expected our students to state this explicitly. This was discussed ad nauseam in many sessions and left me thinking how I could better prepare my students for this type of more rigorous justification. I knew it needed to start during my limits unit and then continue throughout the year. Most importantly, it needed to have my students analyzing why a limit can be evaluated and when it does not exist vs cannot be evaluated because we are missing necessary information. 

Here's the activity I designed to start my students thinking about this during the first unit. 

Limits & Continuity Justifications (PDF)

Limits & Continuity Justifications (Word)

I've attempted to use multiple representations, lots of notation to build fluency, and to scaffold up to 2 questions more like the part d on the AP. I also am trying to help kids distinguish between when we need more information, when we have enough information, and how to justify all of that. I will be emphasizing that it doesn't just saw "evaluate," but it also says justify! Please feel free to send feedback! This is still rough and a work in progress! 

#MTBoSBlaugust Day 5: Be Prepared! (For Parent Teacher Conferences)

My husband and I went to visit Cornell this weekend, where one of our friends in finishing his PhD. While looking out at the view beneath the clock tower, we were stopped by an older couple admiring our dog. 

Them: "Your dog is beautiful"

Me: Thinks "Duhhhhh. Most beautiful animal in the world. Glad everyone else sees it too." 

Them: (Petting her) You're a sweet old girl! 

Me: Thinks "Wait did you just call my dog old?" Fiery rage starts to burn at the proposal that my dog is anything other than a young whipper snapper who will live forever. 

Anyone who knows me could guess this would be my reaction...

To all the parents who trust me with their kids everyday: thank you. I just cried leaving a dog boarding "resort." God help me as a parent 🙄

— Caitlyn Gironda (@Caitlyn_Gironda) August 30, 2016

I can't help but equate this scenario to the way some parents must feel when they walk into a parent teacher conference. They are being told the way other people view their child- a true extension of themselves. I don't have children so I cannot even fathom what they must really be experiencing. I only know that no one calls my sweet puppy old! 

No one has ever accused me of being underprepared, especially when it comes to dealing with parents. My first years as a private school teacher in "the crucible that is our very scrutinizing...parent clientele" (my former principal's word....in my actual letter of recommendation) trained me well to come prepared and leave with parents feeling over-informed. It also taught me a lot about being able to give constructive feedback without someone feeling attacked or criticized. Since those days, I've always seen parents as an ally- someone I want on my side. Some may not help their children's attitude towards my class, but they can certainly hurt it. If I get them on my team from the start, it's never bad news for the student. 

This relationship is more difficult when a student struggles throughout the year, as many parents are at a loss about how to help their students. They want tangible things they can do to help their child or that their child can do to improve, as well as real feedback on specific struggles. With that in mind, I started using this form at each parent teacher conference:

Parent Teacher Conference Form

The form leads with the positive: naming students' strengths. 

I try to not only address my concerns, but also list some ideas of things students could do to make improvements. From there, I include extra help opportunities, missing assignments, and upcoming assignments. Here are 2 examples from previous meetings:

I then attach a multitude of items to this- a copy of the printout from my online grade book, a copy of the schedule for our Math Learning Center, and any other information that I want the parents to get directly from me. One of the things that I like most about this packet is that it frees parents to actually have a conversation with me, rather than frantically jot down notes. One of the other things that I love is that it emphasizes just how many opportunities for extra help the students have, which has effectively eliminated the "what are you doing to help my student" accusation that can rear it's ugly head sometimes. 

A simple form, but one that's been really effective for me! New teachers, don't fear parent conferences! Just make sure you're prepared, informed, and speaking with love and respect about someone's baby! 

#MTBoSBlaugust Day 4: Graphing Calculator Bootcamp & DIY Breakout Boxes

"No Calculator"

We all know that these 2 words, in combination, can cause pure terror in some students. Our kiddos have developed a dependency on technology in many arenas of life and math class is definitely one of them. Graphing calculators are a powerful tool, but I find when most students walk through my door in September they are using them for one thing and one thing alone- arithmetic.

One of my first tasks with my students in upper level classes (Pre-Calc, Calculus, AP Calculus) is to test their fluency in using their graphing calculator for more than just arithmetic. While other tools like Desmos provide much better worlds to explore mathematics, the reality is they will need to use their handy dandy TI's when we get to the exam. I want to be able to both pre-assess what they already know and help remind them of skills on which they might be rusty. In the past, I've used this:

Graphing Calculator Bootcamp

I decided to take it to a new level this year, so I am turning it into a "Breakout" activity a la Breakout EDU or an "Escape the Room" at your local mall.

I started by building "Break Out" kits. Each one contains:

• A Toolbox
• A Bike Lock (Numerals)
• A Combo Lock
• 2 Padlocks
• A small plastic container (tupperware-ish)
• A fabric sunglass case
• A laundry bag

Here are the containers that can be locked:

And here are the locks: 

That makes 4 different types of locks and 4 different things that can be locked. Total, these cost me $42 at my local Dollar Tree, but they can reused for any course and topic and my husband can steal them for his Chemistry classroom too. I thought it was worth the investment and still way cheaper than the name brand one that Breakout EDU sells.

My plan is to adapt the "Bootcamp" to be a set of clues and problems whose answers make up the numbers in the 2 number-dependent locks. Then, the padlock keys will need to be accessed by solving other problems. It won't add a ton more time to the Bootcamp activity, but should considerably up the engagement and competitive nature. I'm still in the process of writing it, since each lock has a different code and each box needs to be personalized, but this is a start! Everything is organized in a spreadsheet & color coded with colored stickers so it can be tracked and put back easily. I'll share more when I have the final activity finished and when it's implemented, but I'm excited to try this out, especially with my non-AP Calc kids!

#MTBoSBlaugust Day 3: Thinking About Retrieval Practice

I try not to go overboard with how many instructional routines I change each year so I can make sure I actually follow through on the things I believe are most important. This year, retrieval practice is high on my list. Ever since I read Make It Stick, I've been on a mission to make retrieval practice part of my daily routine in class. This post from Class Teaching is a pretty good summary of the book's discussion of spacing and interleaving.

I screenshot this photo from Twitter on July 5th (and that is really all I know about it...This would not pass a turnitin.com test right now, I know) and I loved the structure that it presented for integrating retrieval practice as part of a routine in the classroom.

Mrs. Mahoney used this as a warm up with her classes and she was very positive about the results. I like her addition of a "conundrum," but don't want to take on too much too soon. It might be something I'll add in later. 

I also liked this post from That Boy Can Teach, where he advocates for the following when engaging in retrieval practice:

• Make it challenging - ensure that it incorporates desirable difficulties ("certain training conditions that are difficult and appear to impede performance during training but that yield greater long-term benefits than their easier training counterparts" - https://bjorklab.psych.ucla.edu/research/#idd).
• No grading - any form of grading, such as the teacher collecting in scores, will begin to make the activities feel like they are high stakes which has the potential to make students feel anxious which isn't conducive to remembering.
• Mistakes are learning's friend - students will learn from their mistakes (as long as feedback is given which highlights their mistakes) and when asked to complete another retrieval practice exercise will be more likely to remember something they previously had got wrong.
• Feedback must be given - see above; students won't know what they have got wrong or have missed out if feedback is not provided either by a teacher or a fellow student.

I do believe that some grading at specific time intervals could be helpful, but I like the idea of it being low stakes at first. He shares a lot of strategies that could be implemented easily and my wheels really started turning.

I felt very inspired by this post from Love to Teach, where she discussed using Retrieval Practice in her history class.  Each color corresponds with a time frame (Last lesson, last week, etc) and the further it was in the past, the more points it would be worth. 

These are some templates for challenge grids that could be adapted to any subject area. I like that these are already saved into different formats, depending on what you use. 

Here's what I've decided will be my start this fall:

• I am adding a section like this to the bottom of each homework assignment. These will be brief questions, but will address a variety of mixed topics. Students can ask questions and see solutions throughout the week.
• On Thursday or Friday of each week (I only see my students every other day), we will have a retrieval challenge. I anticipate coming up with the most witty name imaginable for this new tradition. Each of these will only cover material from the retrieval practice on the homework.  I have never been one of those teachers who says "it's all fair game once, no matter what"...probably because I was an anxious student and I think it's only fair to give some warning. 

I'm still working out the kinks, but see this as something that could be really helpful for my students and see pay offs in test scores and in how much they remember as they move forward in mathematics. If you use any strategies like this already, please feel free to comment below about what's worked for you! 

#MTBoSBlaugust Day 2: Similarity in Right Triangles

As I write this, I'm currently sitting in the public library- my second home for the summer- waiting for my next tutoring student to show up. I looped for about 30 minutes to find parking, so I've dug in with my Algebra II books for the better part of the day and am happily working away on my plans for the coming year. 

But what am I tutoring? Geometry. Always Geometry. 

Geometry is so full of definitions and theorems and can be taught in a way that requires an unrealistic amount of memorization....to the point where students write it off without ever getting to know it. I was one of those students. It wasn't until I taught the course, saw the conceptual structure lying below the surface, and understood that I could eliminate so much memorization if I focused on a few key concepts that I started to appreciate it. 

As a Geo teacher, one of the topics I remember feeling the least satisfied with the resources I found to help my students with this was similarity in right triangles. Most textbooks would have a picture like this, showing the similarity between the triangles:

Followed by a picture like this, with the geometric mean formulas to be memorized:

And then we would wonder why students can't remember the very important leg and altitude rule. Where the heck did these come from? What did they mean? Can anyone explain what x and y are anyway? 

When I first taught Geometry, a teacher told me they'd discovered the KEY to teaching this topic! Get out your colored markers, folks. 

Depending on what you knew and what you wanted, you'd color code either the altitude or the leg one color. Then, you'd color the 2 pieces of the hypotenuse that touch that color....so for an altitude, it would be either side of it and for a leg, it would be the piece closest to the leg and then the whole hypotenuse. Then, you set up a proportion where the thing that is it's own color repeats. Boom! You always get the right proportion!

This worked for some kids, but was no where near the level of conceptual understanding I expected from my kids typically and was unsatisfyingly difficult when the topic we were really talking about was just good old similarity! 

One of the joys of tutoring to me is seeing the approaches other teachers have towards specific skills. I can share my best strategies with the kids, but sometimes they wind up sharing a strategy with me too. This one- simply drawing a table to organize- was a real eye opener for me and made the topic a "no brainer" for most of my kids. 

We start the way I would have anyway, with doing a hands on exploration that you can find here:

Right Triangle Similarity Activity

This was created by my amazing coworker, not by me! But I LOVE it and can't imagine teaching this topic without it anymore. Students cut out the pieces of the triangle and orient them in the same direction, writing both proportional relationships and similarity statements between each triangle.  Then, there are coordinating cards to go with each of the questions on the exploration. Students are then asked to hypothesize about any patterns they see (which was admittedly very hard for my kids this year, but easier for many of the honors teachers). 

Since these could be flipped, turned, rotated, and mapped onto each other, this activity also hit on the idea of rigid motions (which I always love!) and got kids thinking about corresponding parts. from there.

And now for the stolen part (and a huge thank you to whatever teacher my tutoring student had that taught them this). Have students create a table for each triangle with the 2 legs and hypotenuse. When set up correctly, BAM! A wild proportion will appear! (This Pokemon reference may someday get old, but I'm hanging on to it for dear life until then).  Here's 2 examples:

No more special "rules" kids need to memorize. No more "oh yeah you just color this one and this one" and then color the wrong ones. Just a simple understanding of corresponding parts and proportional relationships.

Should this have been a "duh" idea for me??? Maybe. But it's made teaching this topic so much easier for me and for kids, so I'm passing it along in case anyone else hasn't used this idea before.

#MTBoSBlaugust Day 1: Triangle Concurrency & Food Deserts

Happy Blaugust! If you're reading this and not participating, I highly encourage it! I've been on a blogging hiatus since February and I can honestly say I'm a better teacher when I'm writing. It's my second Blaugust and I can think of few things that get me more prepared and excited to go back to school! I can't wait to reflect more for myself and steal all of your wonderful ideas, MTBoS!

It's been 2 years since my days in a STEM Magnet School, writing interdisciplinary PBL's on the regular to submit to our $3,000,000 federal grant. Having the pressure off and not needing to write these monthly was a relief at first, but I slowly started to miss it. The idea of a geometry project married to the concept of food deserts has been kicking around in my mind for years, since I first learned what a food desert was. I loved that it was real world, community based, and gave kids an opportunity to interact with actual government officials.

I did a test run this year, where I had students discover the properties of points of concurrency in this context, without the added "project" element. It looked a little like this...

Looking at local food deserts & proposing new grocery store locations in #GeomChat today using triangle center constructions #MTBoS pic.twitter.com/1jzHcuSn9Z

— Caitlyn Gironda (@Caitlyn_Gironda) February 13, 2018

And every kid came to the same solution- build at the circumcenter of the region, since it was equidistant from each vertex.  I was surprised by this....I actually thought there'd be more debate, especially since every student had suggested a different triangular region near their house.

Knowing that I won't be teaching Geometry this year, I wanted to pass on the full project I've drafted to someone who could either use it or adapt it and make it better.

Combatting Local Food Insecurity: Points of Concurrency in Triangles

This lesson is in a 5E(ish) format- I'm working on a graduate certificate in STEM Leadership and I wrote this for a class I just finished. Throughout the "Engage" process, I used this video to help students see what a food desert is and the experience of someone who lives in one:

I then utilized the USDA's Food Access Research Atlas and Google Maps to identify local food deserts (which was actually prevalent in my district, which is perceived to be affluent by many outside the community). As you can see from the map here, these exist throughout the country, and not just in urban or predominantly minority neighborhoods. Students tied in their study of biology and body systems by researching the short and long term side effects of poor nutrition. Finally, they conclude by writing a report to send to local city council suggesting a new location for a community resource and giving a strong mathematical justification of the location. While some local governments might just ignore these, I've working in districts before where local politicians made a point to either write back or come speak to students about their proposals to make them feel validated and help them see the importance of participating in local government. And let's be honest- my first graduating class from the STEM school got a patent on a project from their freshman year, so I see no limit to where this type of real world project could take our kids.