I am a mother to three boys. I am a Desmos Fellow. I have a BS in mathematics from Marshall University (Go Herd!) and a MaEd in Mathematics Education from Wake Forest University. I started out as a Math Grad student but discovered my love of teaching when I was teaching night classes to supplement my fellowship at Wake. I switched to MaEd in my second year of Grad school and have had a passion for teaching ever since! I have taught in public, private, and charter schools. I have taught community college, high school, and middle school. I am currently teaching high school at a private school in the suburbs of Charlotte, NC. Find me on Twitter as @jreulbach.
Here is the spreadsheet that I used to figure out and keep track of my pacing for AP Calculus throughout the year. The spreadsheet includes AB and BC. I follow the CED (page 27, Course at a Glance) so that I can use the AP Classroom Progress checks throughout the year. I really like using the Progress Checks throughout the year, instead of saving them for review time. It shows how my students are progressing and what they still need to work on. It gives them consistent practice with AP level timed multiplication problems. And, it shows students (and me) what they still need work on, and which students need the most help.
I picked the lower number of suggested days from the CED, because I never have enough class time! The spreadsheet is for AB and BC. We have about 80 class periods before AP Exam week begins. I need to review more this year, so I blocked off 12 days of review, leaving 68 days for content.
** Please note that the CED recommends 22-23 days for Unit 1, Limits. However, our CPM Precalculus book does a fantastic job with limits, so I cut that in half for my schedule.
The Can I? section is how many days I plan on using for each unit. However, things always change, which is what the Used section is for.
Used is the days I actually used, so I can adjust as I go along. Last year I stole from review days, I am hoping to do that less this year!
I try to stick to this schedule, even if it feels like we are going way too fast. I tell my students that we have to, in order to get it all finished. I have math help almost everyday for students who need more time or help.
This year, I taught AP Calculus AB for the first time, ever.
I was definitely more terrified than excited when I was offered the class. I had wanted to teach it for a couple of years, but remote learning had been incredibly difficult and time consuming for me, and the thought of teaching a very difficult new course during the pandemic was even more terrifying. Oh, and I hadn’t taught Calculus since 1998.
Most of all, I was worried because I wanted to do a really great job for my students. Yes, of course I always feel this way, but I was moving up, again, with the same group of students. I had taught all of them in Pre-Calculus the year before, and most of them Algebra 2 as well. For my juniors, I was the only high school math teacher they had ever had. I did not want to let them down. But, my students all told me our school has had a low passing rate on the AB test in past years. So I was pretty doubtful myself. Additionally, in order to lower screen time and stress for our students during the pandemic, we reduced class time. I would only see my students for one or two 80-minute class periods per week, and about half of that needed to be asynchronous. I was very worried.
Fast forward a year later. We just got our exam results back. I was elated, shocked, and most of all so relieved that my students did well on the exam. (I actually FaceTimed my teacher friend at school crying.) It was like a giant weight had been lifted off of my chest. Most of all, I was so happy for them, and grateful that they trusted me and worked so hard to pass.
I have seen many posts from teachers who will be teaching AP calc for the first time next year. They are as excited and anxious as I was, and like me, they have many questions about how to do this! So, I am writing this to tell other AP Calc newbies out there what I did, as a newbie. Please keep in mind that I am a newbie, and you should also talk to a seasoned AP teacher for much better advice! I was fortunate to have a close friend who is a reader, and got so much great advice from her. I am going to do many things differently this year, but I listed the things below that will stay the same.
I joined the AB Calc Teachers AB/BC Facebook group. This was the single more important thing I did. Even though most of my math teacher friends communicate via Twitter, FB is where you find the AP Calculus teachers. Many teachers in this group are AP readers (which means they grade the exams), so they know what they are talking about. I rarely posted, but many people post great material and/or ask questions, which I greatly benefitted from! * You have to be an AP Calculus teacher to join this private FB group.
I mapped out the entire year so that I could be sure to cover every unit, and have 2 weeks for review. The CED lists how many days every topic should take, so I used that as a guide. I stuck with my schedule even when it was going too fast, because I knew I had to. Some students really struggled with the pace, and I would meet with them before or after school often, but it was still tough. I mapped out my pacing with a Google Spreadsheet.
I used AP Classroom Online extensively. They need to work with the AP material to get used to it, especially the FRQ’s. I gave almost every Progress Check in AP Classroom, as we moved along. The students did the MCQ’s at home, timed, and assigned through AP Classroom. The next day, I would go over the most frequently missed questions in class. I gave the FRQ’s in class, timed, and then we went over them together.
I relied on Mark Sparks free calculus curriculum. It has a good amount of discovery in it, and is conceptual. Most of the AP questions are very conceptual, so I think this helped my students. I modified it heavily, mostly by shortening it as we did not have enough class time. The textbook we had was outdated, and many students didn’t have it anyway, so I didn’t use our textbook at first, then I never used it all year. I also used material shared in the FB group by Bryan Passwater, and Circuits by Virge Cornelius. I loved the Calc Medic material, but I didn’t have enough class days to incorporate their discovery lessons. *Be careful about using Mark Sparks assessments, as kids will find them on the internet.
I timed all of their assessments, all year long. I started out giving them 4-5 mintues per question, and gradually moved the time down. By January, I was using AP Exam timing. They hated this at the time, but they all said it really helped them on the exam.
I gave a full practice exam to kick off our review. I graded the MCQ, and then they graded their own FRQ’s. I put up the solutions and told them, “When in doubt, don’t.” which meant to not give themselves credit for FRQ answers that didn’t match the key pretty closly. I would rather the student underestimate their score than overestimate their score. This showed the kids where they “were” and especially what they needed to work on in the last weeks before the exam. I had a BC student who wasn’t even in my class (who took the practice exam with us) text me after he got his exam score back to thank me for administering the practice exam. He said it really helped.
I taught them how to use their TI’s, not extensively, as we did not have the time. But they knew the basics. I’ve only used Desmos with them in the past, so this one was a tough one for me, and I definitely need to do better next year.
I didn’t grade homework, and I provided fully worked out solutions to all homework I gave them. There is no point in practicing if you have no idea what you are doing, or are doing it wrong. I instruct my students to do a problem, then check the answer. They would come in before or after school if they couldn’t figure out questions (and we didn’t have time in class that day to go over all of their questions).
The following things were my personal preference, and I doubt they made a difference. But I was so short on class time and these things really helped me.
I followed the CED. Since I was new, I was starting at ground zero. I wanted to use AP Classroom, so this seemed like the best route for me.
Assessments: I didn’t give any assessment longer than 30 minutes all year because I just didn’t have the class time. I made my assessments from AP Classroom material and curved when needed. I usually use a square root curve or a kennedy curve.
I didn’t do precalculus review at the beginning of the year. I jumped right into Unit 1, Limits, and reviewed as I went. Students are usually very motived at the beginning of the school year, so I wanted to take advantage of that with new material. Also, since they had me for one or even two years prior, I wanted my students to view this class as a new adventure, and not the “same ol, same ol” stuff.
I used Delta Math for extra skills practice only. I always made this optional.
What I am doing differently and/or need to do better next year:
Chain rule. They had a much harder time with that than I thought they would. And it haunted us all year long.
More work e and ln earlier in the year, and all year long.
Integration using substitution, especially helping kids know when they need to use it. I gave them a ton of Delta Math for extra practice, but they told me that didn’t help as the sets are literally named “integrals with substitution”, so they always knew when they were supposed to use it. This is something that I didn’t realize until almost the end of the year.
Giving more calculator active problems overall, that they actually HAVE to use their calculators on. This was tough this year with remote testing and photo math. So my students did not get enough practice.
More review time at the end.
The AP Classroom videos are available now, so I plan on assigning some of them as required at the beginning of the year. Then, I will make them optional if they need them as the year goes on. I want to require them at first so they will see how helpful the videos can be!
Senioritis: I had a handful of seniors “quit” on me second sememster, after they got into college. We do trimesters, so they weren’t concerned about the grade drop. It espcially broke my heart for kids that worked so hard first trimester, as they could have passed and gotten their college credit. I don’t know how to fix that, but have some ideas in mind for next year. Suggestions are always welcome!
The last time I taugh Calculus was in 1999. And I only had 1 – 2 80 minute class periods per week, and half of that was supposed to be asynchronous to give zoom kids a break.
Apparently our school has a low pass rate. I haven’t seen the scores, as those aren’t shared, but students talk. At the beginning of the year, many kids told me that “They knew they probably wouldn’t pass the test, so why was I making the class so hard? Why should they even try?” Since I had taught them before, I asked them to trust me, and most of them did. Unfortunately Some seniors gave up on after Christmas, after they had been accepted to college. Even the ones that didn’t quit really didn’t believe they had a chance to pass until they did well on the full practice exam I gave in April.
Fifty percent of our students were remote for most of the year, which was an advantage and a disadvantage. I at least got to see most of my kids in person every other week, where many other schools were fully remote.
Our text book was outdated and does not follow the CED, oh, and only a few kids had a textbook to start the year since they were all backordered.
I teach in a private school. Even though we have a very wide variety of students academically, the majority of my kids are privileged. This is huge, becuase even though kids weren’t very successful on the exam in the past, they had strong potential to be very successful.
I have taught most of these students for two or three years. For my nine juniors, I was the only math teacher they have had in high school. This was great for me, as I knew what they had been taught, and we could move right along. But, they were also really comfortable with me, which also was a disadvatange at times. I’m a softy and they know it.
We use CPM at my school. Even though the kids don’t love it, it is very conceptual and challenging, espeically the precalculus series. There are two chapters on Limits in the Precalculus book, so I was able to skip most of that chapter to save precious time.
The school where I teach is moving away from AP. So, that is a culture barrier to get through. Although I discovered this year that many more kids really do care about the AP scores (and getting college credit) than I had previously thought. At the beginning of the year, many of my students (and their parents) told me that they really wanted to pass the exam. Afterwards, every single student who passed contacted me to thank me for helping them pass the exam. So, it really did matter to my students. My students worked incredibly hard this year to pass. I am so proud of their consistent hard work this year. And I am so grateful that I did not let them down.
I don’t believe that I have never worked harder in my life. It had been 20 years since I last taught Calculus, so I did every problem I assigned, and many more problems that I did not assign, so I could see which problems I wanted to give them. I also did all of the MCQ and FRQ questions, in advance. I haven’t had time to write a blog post in almost a year. I even ended up in physical therapy for three weeks in April because I had apparently been grinding my teeth so much at night my jaw completely locked up. But, I have also never had more fun in my life. Calculus was when I first fell in love with math in high school, and it was great to revisit it. I loved teaching Calculus. It was a completely rewarding experience and I can’t wait to do it all again next year!
I often get asked how students can easily type symbols into Desmos. I don’t teach Geometry, so I have not worked to find the best way to do this. I am including what I currently do below, but would love to know if you have a better way. Please comment below if you have a great way that easily enables students to type Geometry symbols.
I use Emojis & Symbols to get things into Desmos that are not in their math keyboard (yet!). I use this often for the arrow key with limits statements.
To include symbols, I go to my top bar (on the browser, not Desmos) and select, Edit, Emoji & Symbols, and then I can input them there. You can copy and paste with Desmos. So to make it easier for the students, you could put the symbols into the text box question, and the students can copy the symbols from your question and paste them into their answer box. Alternatively, you could also code the text input box so students could have the symbols they need already in the box. I created a Desmos to illustrate what I am talking about. It still isn’t great, as you can’t put the symbols over the numbers.
If you have a great way you have students type symbols, please comment below! Thank you!!
I say this every year after a summer of sleeping more, exercising more, and eating better. “This year, I will keep this up. This year, I will take better care of myself once school begins.”
Last year, I even made it one of my official professional GOALS, that I typed into a FORM. I still did not make enough time for myself.
But this year has to be different. There is the stress of hybrid, distance learning, or face to face, and the worry about getting sick. I MUST try harder to take care of myself. We all must. I have seen your tweets and your Facebook posts. I know how you are feeling. I feel it too. We need to be healthier, more well rested, and in good shape, so that we will feel better physically and mentally. Then we can better take care of ourselves, and also our dear students and colleagues that will need our support this year.
I know this, we all know this. We just need to try harder to do this. It won’t be easy, as I have worked more this summer than I ever have in my career. I do not know what this year will be like. I feel like a first year teacher. And that is stressful. You know what helps relieve stress?Sleep! And exercise!!
So, I am pledging to myself to do better for myself. Because only then can I be better for everyone else.
I am going to get enough sleep.
I am going do my 30 minute workout at least 5-6 days a week.
I am going to take 30 minute walks with my dogs a few times a week.
I am going to meal plan on the weekends.
I first typed “I am going to try to”. But then I changed it to I am.
I don’t know who else needs to hear this right now, BUT I SURE DID. So I am going to return the favor and tell you. Teachers, you are STILL enough. Whether or not you are making videos, bitmoji classrooms, or researching every available technology for this fall, you are enough. For some people, doing these things is what they need to do right now. For others, it is not. Both of those choices are ok. It is great if you are doing those things, and it is great if you are not. I am not doing those things. And I am enough. And you are enough, especially if you are doing what you need to do to take care of yourself, before another semester of teaching in an actual worldwide pandemic begins.
Last week I found out that we would be going back face to face, with a hybrid model, 50% of the students at a time. Our students will be in school for a week, and then home for a week, with at home students logging on synchronously. I thought it would invigorate me to know, but instead it has me stressing.
I am feeling overwhelmed and anxious about the coming school year. I’ve been having back to school nightmares. I have been short with my kids, and especially my poor husband. I cry easily. But this just isn’t me. I think that many, if not most, teachers are feeling this way right now.
Teachers, it is OK if you are feeling overwhelmed and have anxiety. Every single time I tweet about feeling this way, I have many replies of teachers feeling the same way. So I believe that many more of us feel this way, probably ALL of us. My school is working hard and doing a great job getting us back. We will be 50%, have masks, swivls, and so much support. And yet I still feel this way. And that is ok. It does not mean that I don’t love my job or my students. It does not mean that I am not a good teacher. In fact, I think it is the opposite. It is because I love my job and students that I am worried. I want to do the best job for them, but I feel like I don’t have a complete handle on what I need to do in the fall. And honestly, I may not know until I start actually doing it. I have not done hybrid teaching before, so I don’t know what to expect. I don’t know best practices. And I have a new prep this year. I feel like a first year teacher again. And that is uncomfortable, and scary, especially for an experienced teacher.
I love my work. I have spent most of my summer working through the material for my new prep. And usually, I am especially invigorated and industrious this time of year, right before school starts. But I hadn’t planned for how I am going to teach remotely or hybrid, as I didn’t know what we were doing until last week. As soon as I found out that we were going hybrid, I went to teacher Twitter to ask for suggestions. I got so many wonderful suggestions that I was almost immediately overwhelmed, as I had not done most of the things that so many people were suggesting. I felt paralyzed.
I am reading about teachers who have spent their summer making video lessons for the entire year. I am in awe of the creative bitmoji classrooms I keep seeing everywhere. Other teachers have already used Classkick, Jamboard, Whiteboard, SeeSaw, Flipgrid, One Note … I have done some of these things, but not all of these things, and it makes me feel that I have not done enough. I makes me feel like I am not near enough.
But as Sara VanDerWerf and Elizabeth Statmore recently reminded me, I AM enough. And you ARE enough too. They reminded me that in these unprecedented times we cannot expend our energy comparing ourselves to other teachers. Just like in pre-pandemic times, we do not have to do ALL of the things to be enough. Self-care, kindness, and support to each other is what we ALL need to get ourselves mentally ready for this unusual school year. So then we can figure out how to do the things that work best for our classrooms.
I am also scared about getting sick, or one of my students or colleagues getting sick. I haven’t seen my parents since February, as my dad is an 80 year old diabetic, so I’m being cautious. And once I go back to school, I definitely won’t be able to see them. I’m sad. I am so, so sad. I miss my parents. I miss my old life. I don’t like wearing a mask, but I always wear one. I’m so mad at people who don’t wear masks. I’m upset about many things right now.
So please teachers, give yourself a break right now. Hug your family. Take long walks, or do what ever it is that brings you peace. Breathe. We have a busy fall in front of us, and we need to be rested in order to be ready. When the time comes, we will do an incredible job for our students, like we always do, even if we have to work many extra hours each day. We are professionals. Trust yourself. We have got this.
I was using a great locker shelf hack that I saw somewhere on the internets. I highly recommend this set up! But when my internet was running slow it was lagging. And with five people online all day, it was lagging quite frequently, especially during class times. So, I NEEDED to get the iPad thing figured out.
My handwriting is atrocious when I try to write on my iPad because I can’t put my palm down to write. I thought the Apple Pencil with palm rejection could save me, but my iPad is too old, and thus not compatible with either Apple Pencil.
Next stop, a great, inexpensive stylus. I’ve had trouble writing with my iPad since I got it, so I’ve tired every stylus out there. The Apple knockoffs w Bluetooth work and write well, but they make a clicking sound that not only drives me crazy, but is picked up when I’m recording instructional videos. I don’t like the rubber tips, as they are large and don’t slide well across the surface of the iPad. I finally found this amazing fiber stylus for only $14 that I love! It also has that fine tip end with the disk it you need it.
** Note: If you have an iPad Air 2, screen share is found by swiping from the top right corner. That took me forever to find. It’s been a long month….
My house isn’t set up for ergonomic teaching, and my back has been KILLING me after a couple of weeks sitting in a chair that was too low, at a “desk” that was too high. Thanks to Jenn White I reinflated an underused exercise ball to sit on. Then,I bought this small inexpensive desk with an adjustable height top, and wheels! I can sit or stand at it! I love that it is small, but has a place for storage where I am keeping my binders as I roll it around the house.
Desmos JUST released a new feature that give teachers the ability to give feedback to students INSIDE Desmos activity builder! This will be such a helpful feature now that we cannot interact with our students in person, and especially for classes that are only able to do asynchronous distance learning.
** Your students MUST be signed in to the activity, with either with a Google or Desmos account, to be able to go BACK into an activity and read the feedback. **
Yes! It works on previous activities! Just today I went into our last activity and added some feedback for students to look at on our first day back. I figured it would be a great way to review, and ease into distance learning.
The feedback is very easy for students to access, as it puts all of the feedback you give them in one place, and they can click to go directly to the screen.
1. You have to TURN on the feedback option in Desmos Labs. Click on your name in the top right corner > Desmos Labs. Then check all the Labs you would like to have.
2. Once in an activity, click the text box at the top of the screen to leave feedback.
3. ALL of the feedback is in one convenient place for your students. And they can just click on the “Go to screen 3” to look at the screen or edit their work.
I am planning on putting a Feedback screen at the end of each activity where students can ask questions once they finish an activity. I am so excited to be able to answer my students questions, right in the activity!
I’m still on “Spring Break”, and we do not start online learning at my school until March 26th. I am glad that my school community has this time to process, as I am not ready to think about online learning yet. I don’t know what online learning looks like for my school yet. And I think that some students may crave the structure, but that others will need compassion, and space.
I do not want to assess my students. I am sure that they are feeling the stress of uncertainty just as I am, and I do not want to add to their stress. I want kids to feel connected to each other, especially if they need that. I would also like to mix up my students online learning, so they they are not just watching online videos and doing practice problems. I would love for their online learning to be creative, and not too monotonous.
I plan on using Desmos Activity Builders that connect students to each other, like Point Collector, and especially activities that contain Gallery Slides.A Desmos Gallery is a screen at the end of an activity where students get to create their own challenge for their classmates. And then their classmates pick each others challenges to solve. I feel that doing these galleries will not only allow students to be creative, but also feel connected to other students. I plan on encouraging them to reach out to the “creator” while working on a challenge, or providing feedback after.
I’ve created a Collection of Desmos Activity Builders that contain gallery slides here. I am sure there are more I am not aware of! Please let me know and I will add to this collection. I would love to know how it works out for your students, and the ways that you are incorporating galley slides, and all Desmos in general, in your online learning. Enjoy!
Last month, I started making short videos for my students after one of my precalculus students told me that she would LOVE it if I would make math help videos. I have made short videos for our test review, new topics we have gone over, and answered homework questions. I am still very new, and still learning. But my students have really appreciated it. They tell me that they like to hear me explain it again, instead of searching for and then watching other math videos when they need help (or missed a day of school).
Then, at our last faculty meeting, our head of school told us that if we were not comfortable getting in front of a screen for students, either recording ourselves or going online for instruction, then we needed to get comfortable, just in case. Immediately, my teacher bff texted me…
So, I made a video to teach her how to make instructional videos. Again, I am still very new! I know there are much better videos and methods out there. But the good news is that I have been able to make many videos, very easily, and in short time. What I do is not difficult, or complicated. And that is important to me as I do not have much time to spare (#TeacherTired). So, I thought other tired, overworked teachers may appreciate knowing how I make videos quickly and easily.
Mac:I use QuickTime to screen record on a Mac. QuickTime is already on all Macs so this is very easy to do right away! I only use this method when I want to screen share and record my voice. There is no writing. This would be great if you wanted to give a lecture using your Mac and a PowerPoint. (Example below).
iPad: I use my iPad and the app ExplainEdu for almost all videos that I make. I love this app because I can add pictures, videos, pdfs, included clipart, and even a browser to screen share. I can write, hi-light, use a laser pointer, and draw shapes that the app will recognize! The app is $13.99, but was worth it as there are no other hidden charges. The Explain Everything website has video tutorials that are probably much better than mine! 🙂
My school does not use Google Classroom, so I save the videos onto my iPad, because then I can upload them to Google Drive or YouTube. If you want to upload to YouTube you just need to create a free account.
My iPad Video Recording Method:
I do much of the work in advance of recording, to cut down on recording time.
I take screen shots of each example problem I want to explain to my students.
I put each problem on it’s own page.
I annotate by adding formulas we will need or things I want to hi-light.
When I am all finished, I record. This is where I work out the problems for my students.
I upload my videos to YouTube
I add the videos to playlists I have created.
Sometimes I will embed the videos into PowerSchool on the “Math Help” page.