#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.

Which Ratio? Activity for Right Triangle Trig

One of the things my geometry kids consistently struggle with each year is deciding just which ratio to use for each problem. They can reliably go from there, but when you get stuck on the set up, it can be a SINE that you're lost!

I tried something new this week to combat this issue and so far, it's been really effective. My lab students are especially benefiting as I see them consistently being able to identify the ratio and therefore gain an entry point into the problem.

Pam Wilson wrote a great blog post about an activity she did with her students- read it here- and I stole the document she created to adapt to my kiddos. I put each one of these on a slide and students are asked to analyze (think-pair-share) style which ratio is represented in each picture.

My favorite part is I gave each student a set of these paddles to participate. They were quick to make....run an exacto knife through some cardboard and hot glue popsicle sticks to the back of each (how most people spend their Sunday nights, right?!).  Instant feedback for me, fun for them....an all around win. I've been just leaving these on the tables as we work and I'll ask the kids to periodically show me which ratio they think we should use before we attempt a problem. This has been especially helpful with word problems because I do a quick analysis before moving on to make sure we've "got it" and know how to approach it. 

Also, I know this could totally be done in a Kahoot or another way, but something about the hands on "auction" style get the kids super engaged and I love that I can continue to use them throughout the unit. A nice tool to keep around whenever necessary, not just on "Kahoot" day.

A small thing but so far, especially for me struggling learners, it's made a big difference! 

Differential Equations CSI

Differential Equations are a topic with so many applications in the real world. Knowing how rough the Potato Question was for AP Calculus AB students last year (49% of students earned 0/9 points), I wanted to bring some more of these applications to my kiddos within our unit. Luckily, I'm married to a scientist and he's overflowing with ideas to help me out! 

First, we looked at rate laws in Chemistry. First order rate laws are a direct application of the law of exponential change. Honestly, these have more to explore when we get into definite integrals, but I wanted students seeing them for the first time now so we can continue to work with them when we start definite integrals. Since about half of my class is enrolled in AP Chem, this was an easy connection for them to make. We also got to discuss why they're called Integrated Rate Laws (oh, THAT'S what the chem teacher was talking about!) and most were able to easily tie this to the derivation we always do for this. 

After this and some more examples, I handed out the lab for the day-

 Determining Time of Death with Newton's Law of Cooling.

I modified it from an old Houghton Mifflin activity, adding in the information about forensic science. I used this article on using ODE's to determine time of death as a resource for what I added, if you're interested. I felt like I'd scaffolded it enough and was excited to get my kids working.

When they walked in, I had the room set up like a crime scene. My goal was that they'd solve the murder before they left. I had a "breaking news" picture of the murderer poised and ready....it was obviously the Night King from Game of Thrones. But I'll be honest....I should have left more time for this. It felt rushed, so we didn't finish it. My students this year struggle a lot more with fundamentals than in years past, so properties of logarithms that should be 2nd nature were taking way more explanation than the time I'd allotted. We got through the first page- the separate and solving for C. We analyzed what C represented. The rest we will save for next class.

I still love the idea and the intrigue it created for the kids- walking into a "crime scene" and being responsible for solving it. Next year, hopefully with less snow days, we will leave ourselves more time to make sure our algebra skills are on point and we have time to really solve the mystery! Next year I also want to tie in temperature probes and have students actually gather their own data, instead of using the data provided in the problem. 

Hands On Slope Fields

Slope fields have always been a weird topic for me...I never loved my approach to them. They weren't hard for my kids, but they weren't particularly engaging and I always saw my student getting frustrated by the "stakes" of doing them on paper and feeling like they were doing it wrong before they got a real feel for it. I wanted to have my kids be able to experiment with it in a hands on way before having them commit anything to paper, so I've been tweaking this approach for the past few years and felt like this week it finally went the way I'd like it to go! 

I started the class by using Rebecka Peteron's Slope Field Activity, where each student is given a coordinate point and then asked to come up to the board and draw a small segment with that slope. We used these discussion questions pictured to talk about isoclines and beginning to see patterns beyond just "plug and chug" methods of determining information from the field itself.

From there, we did some low-stakes practice with the interactive slope fields I built. To make them, I went to Staples and bought washi tape, brass paper fasteners, and a roll of packing cardboard. I cut out 1 ft x 1 ft squares of cardboard, used washi tape to make the axis, and put the fasteners through the back. In class, I showed the students a differential equation and they modelled the slope field for me. We were able to work out kinks and make sure we all understand what they should look like before going any further. Then, I would ask the students to trace a particular solution using their Twizzlers through a point. We were able to discuss the general vs particular solution, the patterns we saw, and more. All of this was followed by a small group exploration where students played with dependence on x vs y, determining particular solutions, and relating differential equations and slope fields in different representations. 

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I still want to work on the type of practice we do after the exploration and relate it to some more applications, but this approach was way effective for my kids than normal. I have a group this year who really benefit from more visual and hands on approaches anyway. 

Do you have any other approaches to slope fields that you love? Share in the comments! 

Learning to Live-Stream: Review Sessions from my Couch

This year has been a hot mess of delays, snow days, and general schedule interruptions that have gotten me a little jumpy about my AP pacing. Yes, I know the exam is a week later this year. Yes, I know I had 5-6 weeks of review the last 2 years. Yes, I know we started behind since our Pre-Calc courses didn't get to cover the final unit as thoroughly as in years past. But like most teachers, I have my "checkpoints" of where I think I should be at certain points in the year and midterm week has gotten me feeling a little spooked. 

My kids wanted a bit more review that I just didn't have the time to give them for our last test, so we came to a compromise....I would figure out how to do a live stream review if they would watch it. We'd try for an hour the day before the test and see how that went. 

Anyone who has been around my blog for a while knows I'm a huge devotee of Notability and knew I wanted a way to live stream my iPad so  I could write by hand. After doing some research, I came across AirServer,  which took my normal airplay capabilites and allowed me to tie in live streaming directly to YouTube. Students saw my screen and a small image of me in the corner....good for the Italian in me who needs to talk with my hands constantly. 

I knew I should have majored in interpretive dance of ladders falling down a wall at a constant rate. I truly seemed to have missed my calling. 

My favorite feature of doing this was that students could interact with me live, so it wasn't just another video they were watching....they could actually chat. I gave them option of either using the chat on the live stream or if they didn't want everyone to see their questions they could send them on Remind. Questions looked mostly like this:

But occasionally like this:

A nice part of having the questions come in Remind meant that I had the power to answer whichever I chose....ignoring the horse sized duck I was about to take down until a more appropriate time in the conversation. 

The kids seemed to enjoy it and I saw big payoffs on their test. I am going to be trying it again this week for my midterm review with younger students...we will see if it's as beneficial for non-AP students. Though more than 2/3 of my class watched and interacted on the live stream, only 6 filled out my feedback form (THANKS, GUYS). Here's what they had to say:

And my final favorite feature?

YouTube archives the live stream so it can be accessed immediately by students who weren't able to watch live or who didn't want to watch live. They can speed it up or slow it down or just skip to the parts they need. 

I will definitely be tweaking for next time, but overall I thought it was a positive first attempt and reached students in a really accessible way for them on a day when they otherwise would have been unable to have the chance to review with the help of a teacher.