Desmos: Your Smart Graphing Calculator

“Do I have to buy a graphing calculator?”

This was the first question asked by a student in a grade 10 math class during my final practicum. A very honest question. I know when I start reading any course syllabus, the first question on my mind is, do I have to buy a textbook?

And so came the introduction of Desmos —a free online graphing calculator.  But far from the fact that it’s free and doesn’t need any fancy equipment to use in class (students can access it from any personal device), Desmos has a lot more to offer. Think of the smartphone you’re using now, and then think of what you were using before that. That’s Desmos. It’s a smart graphing calculator, and graphing is just one of its features.

What I found to be most helpful before using it; however, was observing an experienced teacher put it into action. This is definitely something I would recommend when it comes to integrating new technology in the classroom. Reading about it or watching tutorials online on how to use it is extremely helpful, but watching someone put it into action or even having the opportunity to engage with it offers you a full view of that desired outcome.

The big picture; what does Desmos offer you:

  1. Online graphing calculator —no account needed; if you have internet access, simply go to desmos.com and start graphing from any personal device. If you want to save your work; however, you need to be signed in under your account (free). You can also download it as an App on your device.
  2. Pre-made Classroom Activities that you can use as-is or adapt/edit to fit your own classroom needs —simply sign up for a free account to access them.
  3. Custom activities via Desmos Activity Builder —design and create your own digital math activity online to integrate into your lesson.

Classroom activities or custom activities are simply a series of interactive slides that students can work their way through either at their own pace, while still engaged with their peers (see below), or using teacher pacing (whole class working on the same slide).

Here is a screenshot of a classroom activity offered by Desmos that I tried with my students during practicum.digital-activites Some features you can add into your digital activities include; text, notes, hidden folders (from students), student input, multiple-choice questions, images, videos, and graphs. Students can also interact with their graphs, sketch their thoughts, type their response, or have their work carried forward from a previous slide to continue solving.

What does it offer your classroom:

  • Allows you to focus on the math in an engaging way
  • Allows students to see how their graph changes in real-time depending on their input
  • Supports social interaction in and out of the classroom
    • Students are able to see peer responses and provide them with instant feedback or critique their work
    • Teachers can build a strong PLN with other educators using Desmos to share/discuss ideas and/or collect feedback
  • Safe learning environment: you can choose to anonymize student names when sharing responses and have them take on famous mathematician’s names instead
  •  Teacher/student pacing: have the whole class working on the same slide together while facilitating a discussion or allow them to work at their own pace while still getting that feedback and support from their peers -students can also continue to work on the activity from home
  • Pause the class: grab your students’ attention at once by pausing their work to showcase a solution or start a discussion that can help them carry forward
  • Formative assessment: check-in on responses while your students are working to provide them with instant feedback or use it to guide your next move.

Here are some screenshots of what the teacher can see as students are working. These responses can also be shared with the class as a focus on discussions. Activity link.

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Breaking it down; how to use it:

Note: One of the best things I like about Desmos is that it’s not just designed with students in mind, but teachers as well. The instructions and support offered for this tool are unlike any I have seen; albeit I’m still starting off my career in teaching, but I’m sure experienced teachers who have used it would argue the same.

Team Desmos offers video tutorials on its graphing calculator features and classroom activities. A full PD package is also ready for download if you’re looking to share the learning with others. You can access them here or you can also check out their user guide loaded with visuals.

Classroom Example:

Here is an example of a lesson I adapted from my intermediate mathematics course at uOttawa that integrated Desmos into Pear Deck into hands-on.

Task: What is the maximum number of pieces you could get using 20 straight cuts?

pizza-problem

First, we experimented with this:

Then, after noting the quadratic relation, we used Desmos to find our solution:screen-shot-2017-01-29-at-3-24-16-pm

In this lesson, I integrated Desmos online graphing calculator into my original plan and provided a link on Pear Deck for students to easily access it. Overall, I think they enjoyed the activity in itself and going through that productive struggle in trying to figure out the solution really paved the way for Desmos as a math tool to help us solve problems. I think what students like most about using Desmos is that it’s easy to use; you don’t spend the majority of the time explaining how to use it, but in actually using it.

With time management in consideration, I think next time I try this lesson, I will use Desmos Activity Builder for the graphing portion. Linking it to Pear Deck for students to access on their own doesn’t allow you to see their work once finished to be able to assess/offer feedback.

I still have a lot of learning and experimenting to do in integrating Desmos into the classroom, but it’s definitely a tool I would recommend to try and introduce to your students.  

Waiting for that ‘someday’

Ten years from now, guaranteed I’ll be a great teacher. My lessons will unfold exactly as I hope, no more mistakes, classroom management will never present me with any new challenges, and I will be an expert at designing truly authentic learning experiences and orchestrating deep—very deep—discussions that truly capture and elicit my students’ curiosity.

Of course, that’s a lie. But a lie that as a beginning teacher you tend to believe is true. That today is about making mistakes and tomorrow—that someday—is about becoming an expert teacher. But then, as you begin to emerge yourself in the practice, this image starts to fade away. Bit-by-bit you start to realize that that ‘someday’ doesn’t even exist and this image is serving more as a justification for making mistakes. As if somewhere down the line mistakes will no longer be valid or acceptable. As if teaching, the art of tapping into another human’s brain, influencing the shape of neural pathways and continually trying to make learning relevant to the changing world around us is something that is finite.

How could I have believed that this is true while holding on to the idea that teachers are researchers? When does research ever stop? When does the learning ever stop?

I had five goals written out before walking into my final practicum and it was time to reflect on them. Did I meet my goals? Can I place a checkmark now beside all these areas?

No, I didn’t meet all my goals. I didn’t even know what the criteria for that even means. Sure, I developed in some areas, but in others, I barely touched the surface. In fact, the more I reflected and the more reading I was doing online to find out what other great teachers are doing in these areas, the more I realized how much more learning lies ahead of me. I could only think of this quote in that moment:

knowledge-quote

But I was perfectly satisfied with that and instead of feeling disappointed, I continued to read with a smile on my face. I was exactly where I wanted to be because as Dan Meyer once placed it, “I need a job that has me learning everyday.”  Not to say that learning only occurs in the field of teaching, but rather, it’s the type of knowledge seeking that excites your neurons, whether it be about education, arts, sports, fashion –whatever makes you curious to learn more.

Today, my fixed mindset image about ‘someday’ mastering the art of teaching no longer exists. Instead, it’s reflected more in a truly authentic yet unfinished painting with only one purpose —to keep you curious.

In a previous post, I made a sketchnote reflection about my top 10 What Went Well during practicum with the intention of following up with an Even Better If one, but the list was simply too long. I ended up writing this instead, but as a final Even Better If statement: aim to be an expert in the content of your subject, but know that the art of transferring that knowledge will always be a work in progress –enjoy the painting more!

Final Practicum Refleciton: What Went Well

Here are my top 10 What Went Well sketchnote reflection during my final practicum (i.e., what mattered/what I feel much more developed or comfortable at).

reflectins_www

This form of reflection turned out to be extremely beneficial because not only was I taking the time to express and breakdown my thoughts in writing, but actually delving deeper while trying to find the right visual to capture them.

3-Act Math: Super-Sized Coffee

This was the first lesson I did to start off my practicum. It’s entirely based on a 3-Act Task by Dan Meyer. Originally, I had my lesson set-up inline with the task to target the question: How many gallons of coffee would it take to fill up the super-sized cup? 

Walking through the plan with my mentor, however, she noticed that the students might be quick to solve this one—given that they had some similar practice before—and suggested that we start with the extension question instead: How many regular-sized cups of coffee would it take to fill up the super-sized cup? This would also offer them a new challenge during the conversion process.

dimensions

What I appreciate the most about great mentors is that feedback is always offered with choice. Even though my plan was fully written-out and I was now playing around with my slides on Pear Deck 20-minutes before I walk into my lesson, the decision to change the plan was still mine to make. Of course knowing that your mentor will be there to back you up when you need the support makes risk-taking much easier.

Moving on, I presented the entire task via Pear Deck here (full credit to my AT, for showing me how to properly set-up a 3-Act Math Task on Pear Deck and choice of wording).

ACT 1: Gourmet Gift Baskets Video (making/filling-up the super-sized cup) followed by: wonder

So, “why are they wasting coffee?” To try and set a new world record! But before finding out if they were successful or not, we focused on, “how many average cups could fill the large cup?” We estimated numbers that are too high, too low, made a best guess, and then it was time to solve.

ACT 2: What information do we need to help us solve?

I presented the image of the super-sized cup along with its dimensions on the screen, and acting on another pro-tip, I simply placed my Starbucks coffee cup on a high table—front and center—and left it up to the students to get their own measurements. Most measured in centimetres, but one group went with inches instead. They worked on this task in VRG on VNPS.solving

All groups applied the right formula to find the volume of the super-sized cup and average cup but ended-up with different numbers. With support from my AT, here’s what we discussed:

small-cup-dimensions

1. The top diameter of the Starbucks coffee cup is 8cm and the base diameter is 6cm. We had to take this into consideration to get a more accurate sense of how much coffee can actually fit inside the small cup. One of the students suggested that we take their average and so we did.

2. Most students aimed to convert the volume of the large cup into centimetres, but did a length conversion instead. My AT highlighted the difference and then we talked a little about the method of operation they used to solve (subtraction vs. division). It was then time to wrap-up the lesson. error-conversion

The following day I asked two of the students to use the portable keyboard available in the classroom to explain and model the steps for converting volume before sending them back to their boards to finish solving.

Here are some of the answers we got:answer_coffee20161108_115943

ACT 3: Video result (available in Pear Deck link): were they able to set a new world record/how many gallons of coffee is that?

We didn’t actually get around to watching the video result mainly because it took me sometime to get a good handle on time management during practicum, but we worked on a consolidation handout to allow for individual reflection/practice on conversion—which is the area I found they struggled with the most.

Overall, I really enjoyed this task and one that I would definitely try again. I felt it was really rich in its content and offered students a nice visual to develop their conceptual understanding of volume and conversion. Time management and better preparation to be able to offer strategic support during productive struggle will be my areas of improvement for next time.

Thank You For …

Reading a simple Thank You card from my students reminded me why reflection is such an important part of teaching.

Practicum is over and naturally what follows is that you finally start to take in all the new learning you got and zoom in on some of the moments or experiences that you were simply too busy to take note of during that time.

There is a lot to reflect on but what I didn’t expect is that a simple thank-you card will prioritize this list. My plan was to start off by reflecting on some of the lessons I did for future reference but as I was reading the card (over and over again), I realized that what mattered most to my students weren’t the activities we did together or how engaging they were, but the time I dedicated to individually helping them one-on-one. I’m sure  they still enjoyed some of the activities we did together, but when it came to expressing their appreciation, the first thing they remembered was that one-on-one time.

Here’s a sketchnote reflection capturing some of those thoughts:

reflection_thank-you-card

So many times I underestimated the value of practice time in class for catching up on some skills or consolidating ideas, but looking back on it, it was during those times that I got to know my students, get a close-up of their actual thought-process, and gather real-time assessment.

~Another valuable lesson from my students.

 

Flipping Bottles

Today, for our intermediate level math course at uOttawa, Cassandra Mclean and I took our first shot at designing/presenting an activity station. Ok, it’s not really our first shot, we kind of did it last year as well for another course, but I think building off from previous experiences, it definitely felt a bit more developed this time.

The activity itself targeted Grade 9 linear relations. We had our ideas down but then two days before our presentation we came across Dan Meyer‘s  #BottleFlipping lesson and Jon Orr‘s successful implementation of it via Twitter and decided to scrap our original plans.

We modelled our (15-20 minute) activity around Jon Orr’s lesson design.

Set-up the table with an instruction sheet, “contest” sheet, an iPad to watch a quick video, some devices for Desmos, and of course …the water bottles!

Each group started off with watching this quick video, then they logged onto Desmos for the first part of our activity. Here’s a sample from some of their responses:

screen-shot-2016-10-11-at-8-06-52-pmscreen-shot-2016-10-11-at-8-07-20-pm

Next, was the actual contest:

screen-shot-2016-10-11-at-8-24-17-pmscreen-shot-2016-10-11-at-8-23-19-pmbe6c9a7e-6dcc-4c63-acbf-0d0df48dbf74-1

Some groups got a little bit more competitive than others and started to have conversations about slight differences in the bottle design 🙂

Our timing was a little off because most of the groups didn’t get around to the final step (which is kind of important) and we also had to change it into only 2-3 one-minute trials. But, overall, I think it went pretty good and we even got some nice feedback.

Full credit goes to Jon Orr and Dan Meyer.

Planning for a 15-20 minute activity station was definitely a nice experience, kind of allows you to regroup your thoughts around lesson planning and your strategy for picking out main ideas/activities. It was nice to participate in them as well, felt like a mini in-class PD session on lesson ideas .

My final thought –if only all my lessons went this smooth 🙂  

Technology in the Classroom: Defining its Purpose

Technology use in the classroom largely depends on how teachers choose to incorporate it, but that’s not all.  One of the biggest takeaways from my first two weeks of practicum was reflecting on the purpose behind integrating technology in the classroom. On thought, I came to ask myself, why is it possible that one could walk into two different classrooms using the same tech tools, but see different results in terms of student engagement?

Having the fortunate opportunity to be able to observe how an experienced teacher capitalizes on their benefits allowed me to highlight the difference and dig deeper into thought about what makes their success vary from one classroom to the other.

From my personal observation and reflection, the key factor that stood out for me was the reason behind choosing to integrate technology –the one beyond learning that “special” skill. It’s first and foremost about taking the time to define the purpose I want it to serve in my classroom. Asking myself as a designer/facilitator the most important question when lesson planning—why? Why is this important for my students? Is it just about being tech-savvy, or can I further define its purpose and allow it to help me create a more meaningful and enjoyable learning experience? If my goal is to improve student engagement in the learning process, then how will they be able to engage in conversations with their peers, showcase their thoughts, share different strategies, and collectively engage in group discussions as they use this technology?

Walking into my placement two weeks ago, I was already curious to learn how technology can be integrated into a Grade 10 Math class. From previous experiences, I still had the idea in my head that when it came to technology vs. group-based activities, student engagement wouldn’t be as high.

Having that expectation and the imbedded image of students sitting on separate devices totally disengaged from the environment around them (only talking to their peers or teacher when they have a question or answer) definitely paved the way for one of my favourite experiences so far. For the first time I had the chance to experience what it truly felt like to be a facilitator/designer in the classroom. Albeit I was just an observer and active participant, but having that opportunity to experience the deep meaning of the former mentioned terms was truly inspiring.

For the entire 75-minutes students were leaders of their own learning. From the design of different activities that triggered curiosity, to the use of Visibly Random Groups (VRGs) and Vertical Non-Permanent Surfaces (VNPS), and the idea of showcasing and extending the learning with Pear Deck and Desmos, students were engaged and stimulated throughout the entire process. What struck me the most was that at no point was the technology isolated from the hands-on activities students were working on. They both served the purpose of complimenting each other. More specifically, the tools selected:

  • Created a safe space for students to communicate their individual thoughts, collectively;
  • Provided an extension to the hands-on learning with the added feature of personal/group reflection;
  • Provided students with a platform to analyze and present their own learning;
  • Offered room for feedback vs. direct teaching
    • Instead of highlighting key ideas by writing them on the board or reading them off a slide developed by the teacher, key concepts were conveyed through feedback on student work/thoughts projected through Pear Deck or displayed across the room (VNPS). The content of the “teaching” material was derived directly from student work.

Overall, more than just a tool to help students learn a new skill, technology served a much bigger purpose of creating an interactive community of thoughts.