Last week Elissa Miller (@misscalcul8) posted this meme about the composition of functions. I just loved the visual imagery!
I am teaching PreCalculus for the first time this year and have enjoyed the rigor immensely. It has, however, been a lot of traditional lecture and assessment. I was getting ready to start composition of functions and thought why not have kids create their own memes to show their understanding? I got with a colleague and we developed this rubric.
When I showed students the example and told them they would be creating their own they were pretty excited. I started grading them today and am blown away by their creativity! Some are food related (a donut dipped in chocolate, another donut with chocolate filling) while others are completely different. One of my favorites is a Christmas Tree with glass ornaments inside paired with a glass ornament with a tiny tree inside of it 🙂
It seems the students enjoyed the assignment as much as I did. I love that they had an opportunity so show their understanding of a concept in such a creative way! I will definitely be looking for other topics in PreCalculus that lend themselves to alternative methods of assessment. This was a definite win because memes > quiz any day 🙂
Desmos has opened the application window for their Desmos Fellowship, and if you are passionate about teaching and math, you need to apply!
When the team at Desmos chose a name for their collaboration with educators, they could not have chosen a more descriptive name than “Fellowship.” From the moment you open the email that you have been selected to be part of this program, you begin to experience a sense of belonging. You gain access to a Slack channel where you connect with other Fellows and share ideas and begin to get to know each other. It’s like a PLC you might have at your school, except it’s a whole group of people like YOU, who are full of passion and ideas and are eager to collaborate and create.
I was overwhelmingly intimidated on the trip out to San Francisco, wondering how in the world I would have something to contribute. These fears may have been very real on the journey out, but every single member of the Desmos team went out of their way to make us all feel valued and appreciated!
Some of my favorite memories from the weekend:
- Dan Meyer met a group of us at the door and welcomed us, and in a heartfelt welcome told us how excited Desmos was to have us there to learn FROM US and talked about how we just needed to be ourselves. This helped put so much anxiety to rest!
- Shelley Carranza modeled how to combine passion and planning when developing activities. Shelley has a gentle soul that just envelopes you and makes you feel so welcome!! She was AMAZING with her organization and hospitality all weekend.
- Eli Luberoff‘s keynote – I first met Eli in Philly during Twitter Math Camp and he spoke of his commitment to ensuring money doesn’t separate a child from having the tools they need to do math. In his keynote he reinforced these ideals; his integrity and commitment are unparalleled, and honestly, have you ever met someone so humble who has done so much for so many?? Love hearing him speak.
- Michael Fenton led us through the Charge! activity and honestly, this presentation had a HUGE impact on my teaching methodology. Michael modeled how to run this activity and showcased Desmos’s pedagogy in creating rich mathematical activities for students.
- Do no harm * Trust Teachers * Design for real classrooms * Design for delight * Works every time One of the most moving moments for me was walking in and seeing these guiding principles on the walls. I do wish I had kept the video going two more seconds as you can just see Eli jumping into the last frame lol.
Fellowship, Fellowship, Fellowship. During the weekend we had breakout sessions (kudos to Julie Reulbach who gave a great session on using Activity Builder in Assessments). We spent time at food trucks and trivia, and learning you can only get an irish coffee to go if the irish part is in a sealed bottle, but I digress. The Fellowship was sooo much more than any one piece….it was the bonding with like minded educators, who share the same passion in making math accessible and fun for students.
BUT WAIT. THERE’s MORE. I left the weekend wanting more, and was thrilled to find that the Fellowship continues well past the weekend. Fellows share and collaborate on the Slack channel, seeking and giving support. There are online discussions and opportunities including presenting. I’m working on that piece now, and have been hosting webinars for our Department of Ed for other teachers. I’m going to continue my Fellowship journey and apply to be a Desmos Certified Presenter.
Are you passionate about math? About teaching? Want to experience incredible Fellowship with others that share that passion? Then apply today – it’s an experience unlike any other!
Foldables have been a staple in my classroom for years. The first foldable I made was on exponent rules for Algebra 1. Every year, my 8th graders seemed to do well when teaching the individual rules, but put them all together and 12 · 12 suddenly equaled four. I thought if they had a single resource they could refer to just maybe they could learn when to apply which rule. Having one piece of paper with all of the rules really seemed to help (although more than anything I think they just liked playing with the foldable and the cool way the paper folds :).
Since then I have compiled a lot of foldables, some created by me, and many others shared on the internet. A huge special thanks to Sarah Carter (@mathequalslove) who so freely shares her work. Many of the foldables I use with my Algebra2 and Algebra/Functions classes are from Sarah’s fantastic blog.
Students glue foldables into a black and white marble type notebook, putting the foldables on the right page with extra examples on the left. For the most part, students do really well with their foldable books, keeping them up-to-date and organized, and referring to them to help support their learning. Some students do struggle with organization, and occasionally someone will need an extra copy of a foldable. In addition, one of our support teachers sometimes asks if I have a foldable for her students on various topics. I started thinking about how I could create a digital file that would support both of these situations.
It’s definitely a work in progress, but I’ve created a Google Doc that resembles the Table of Contents for my Algebra 2 foldable books. In this document I’ve included links to the foldables we’ve done so far this year (I’ll continue to update as we progress through the curriculum). Some foldables were Microsoft Word/PowerPoint/Publisher files, so I have converted those to pdf files to upload into Google Docs. I will also try to provide links from the original sources for the files (this might take awhile!).
This school year I have been participating in a LITE Cohort (Leaders in Instructional Technology Exploration) through my district. This has been a great opportunity to learn about new technologies, connect with other colleagues, and improve my teaching practice by focusing on ways to enhance student engagement.
For our unit on parent functions, I wanted to give students some choice in how they could share what they had learned during our unit of study. As an avid fan of Desmos, I had already used Polygraph when we were building vocabulary in the quadratics unit. I also created an Activity Builder for teaching logarithmic and exponential parent functions, and students were very engaged. I decided I would make these two activities an option for the assignment.
Some students chose to create a Polygraph game for their project, and worked either with a partner or a group of three. I provided planning sheets so they could identify what graphs they would want to include, and some students drew them out by hand while others wrote the equations or typed them in a Google doc. I always love to see how differently students process when given the opportunity to choose. I heard a lot of great discussion about creating choices that would allow students to identify graphs based on yes or no questions. Some groups initially created graphs that were too similar, and it was interesting to see how they modified their graphs to provide a variety.
We played the polygraph games after students had finished the project and the students gave constructive feedback to the creators. One group created one sole graph in a different color than the others, and it was interesting how many “choosers” elected to choose this graph when playing this game. This option was a good choice for students who needed more structure, and many chose to work with a partner (creating one polygraph).
Several students chose to create an Activity Builder and WOW!!!! The results were just awesome! Students were incredibly creative, and the discussions were just SO RICH!!! Some students worked on their planning documents, and then we would conference and you could hear the wheels spinning, “wait, they won’t necessarily know how to do that yet – I need to add an instructional slide” or “Oooh – I could have them show what they know at this point by having them manipulate sliders!” It was truly one of those teaching moments where you just stand and smile in silence, knowing they are engaged, thinking critically and enjoying playing with math 🙂
Here is an example on Absolute Value Functions:
Here is a second example on Transforming Parabolas:
- CHOICE – why, oh why, do I not do more of this?
- Desmos – I was a little nervous about having students create Polygraph and Activity Builders. We did this shortly before Desmos updated their terms and conditions, and I’m worried from a standpoint of student privacy that perhaps I will need to rethink this. Since students worked in pairs/groups, there were only a handful created. It was such a rich experience that I want kids to have the opportunity but need to ask the powers that be at Desmos if it’s something I can allow kids to do. If not, I could always have them do all of the planning documents and then we could create it together?
- Understanding – parent function questions were included under a later assessment and the kids knocked it out of the park. Creating their own activity really helped drive home the transformation principals. Definitely need more student created assessments!
A while back I received an email from Josh Greesonbach, one of our district’s Instructional Technology Integrators, asking if I would be interested in helping with a Podcast on using Twitter. Our district is fairly large with over 60 schools, and they have created an EdTech Hub where they are showcasing some of the things we are doing in Chesterfield County.
I was immediately on board. I love Twitter and find it to be such a rich resource for teaching math. To me, it’s like the PLCs we have at school, but extended way past the limits of a physical school building. I have amazing colleagues not just in the classroom next to me, but in Oklahoma, Kentucky, Pennsylvania…..from all over. Resources are shared freely and so is support.
I love to share my experience with Twitter and the Math-Twitter-Blog-O-Sphere (#MtBos) because I feel so strongly that others can benefit if they are willing to try it. I’m not sure why, but I find that many teachers are just so resistant to Twitter. I think many still think it is just a place for celebrities to post every bit of minutia about their lives….I always compare it to television programming. If you leave your tv on E! that’s what you are going to get. But unlike television, Twitter offers math support! Come visit a faculty lounge where you can hang out, bounce ideas off of each other, laugh, cry, think about things from a different perspective and be challenged. I’m hoping this Podcast will reach others in our district (and beyond!) and encourage them to try Twitter and realize some of the benefits.
Check out Chesterfield County’s Podcast on Twitter & #MtBos here: CCPS Podcast
August is a time for professional development in our district. Sessions are held almost daily, with topics such as technology integration, working in a collaborative teaching environment, first aid/CPR training, and content specific training (ie. TI-Nspire training for math teachers). I attended several sessions this August, but two in particular really gave me pause.
One of the sessions had a LOT of important information. It was an all day session with structured breaks and a break for lunch, with many speakers addressing different topics. There was one activity that required attendees to get up and stand in a different part of the room for about 10 minutes, but other than that, we primarily sat and listened. The speakers were good – they were knowledgeable, had presentations to go along with their content, and most infused some humor along the way. Even though the content was very important, a casual glance around the room revealed very little engagement. Almost everyone had their laptops open. Some were a little more discreet flipping through email on their phones under the table. A few at each table were attentive, but as the day progressed, fewer and fewer people were really engaged.
A few days later, I attended a second session on a completely different topic. Again, we were at tables, and outlets were available for our laptops. Our introductory activity immediately had us up and moving. We were given name tags with pizza ingredients on a lanyard, but they were displayed hanging down our backs so we could not see our own ingredients. You had to find a group with other ingredients by asking yes or no questions about your ingredient until you formed a group of five making a complete pizza. After finding (and confirming) four other group members, the group set to work on a jigsaw activity. We came back to our original groups to share the information we had learned. The day continued in mostly this fashion. There were presentations broken up by group activities. We had think/share questions and discussed insights and opinions frequently. We took restroom breaks as needed (the group carried on while you were out of the room) and the inservice was over before I realized so much time had passed. I left the inservice energized, excited about the content and reflected over it long after I was home.
I know (most) of my students enjoy days that are more like the second in-service, with opportunities to get up and move, and activities involving collaborative groups. But some small part of me always thinks if the material is REALLY IMPORTANT, I need to structure the lesson more like the first session by telling them exactly what they need to know. Why is that? I can honestly say I remember the content from the second session because I was engaged 95% of the time. I’d have to refer back to the notes I took in the first session as I was not nearly as engaged. While both sessions offered new content, perhaps the biggest takeaway wasn’t the actual content of either session, but a reminder about the importance of engagement in the learning process. With the new school year beginning, this was the perfect catalyst to ensure more of my lessons are structured with engagement in mind 😀
Most of the activities in this review unit involve group work, and obviously, there are many ways to do this. Often in class I allow students to choose their own partners, and frequently this works really well as students tend to work with people they are comfortable with. Sometimes though, you end up with a group of three who are all stuck, and they spend a lot of time off task because they are not sure how to proceed. Since I had a limited amount of time to get through the review material, I opted to create groups for the students so each group had varying ability levels.
I sorted the students by their year long grade and made five groups (class of 25). I placed one of the top 5 students in each group to be the “leader.” Then I looked at the next five students and placed one in each group, and so forth. Then I looked at the bottom 5 students and placed them in the group where I thought they would be able to work best collaboratively. I had to tweak it a bit to ensure weak students had someone who was stronger AND would be someone they would feel comfortable enough with to ask and receive help. I also looked for possible conflicts, but for the most part, each group had a strong leader who could support others, and who would not be afraid to ask me for help if they needed it.
Before students got into their groups I role modeled how it feels to have someone say, “oh GREAT. Mary Williams is in my group – she is such a PAIN to work with,” and how that would hurt my feelings. Then the old, “your group is going to be GREAT because YOU are in it!” Yeah they’ve heard that before, but it warrants repeating.
I called out group member names one group at a time, and for the most part students found their group members without complaining. We rearranged the desks and this became the permanent arrangement for the next two weeks. I did tell students the groups were thoughtfully crafted based on their strength in math. I asked those who are super talented in math to realize some group members will need support. I reminded those who are not super talented in math YET that it is up to them to ASK for help, and then be willing to listen to that support.
This grouping strategy worked really well! I especially like the “Fish in the Reef” activity where all students have to be prepared to explain their group’s answer. The conversations that happen, and listening to students verbalize their thinking…it makes me realize I need to incorporate this element much more frequently.