Reflecting on using Desmos

I recently submitted a proposal to speak at NCTM on using Desmos to create opportunities for students to be right and wrong in different, interesting ways.  As I have used Desmos, this is the design principle that continues to stick out the most for me.  After seeing My Favorite No a few years back I have tried to use incorrect student responses to drive my instruction as much as possible.  Students see the teacher more interested in their thinking if they are wrong.  It validates all student thinking and encourages students to put their ideas out there.  Desmos activity builder is a tool that helps ask these types of questions.  It also easily collects, organizes, and displays student responses to help encourage whole-class discussions.

Taking the advice of Dan Meyer and Robert Kaplinsky, I proposed something that would inspire me to research it.  That research began today as I ran a Desmos activity that I created to introduce students to the equations of circles.  What follows are a few reflections on how things went.

                                     

Using Student Responses to Drive Instruction

In this activity students were to adjust sliders for different parts of the equation of a circle and observe what happens to the graph.  They would then apply what they observed to match different circles.  I also added a few error analysis questions and marble slides at the end for practice.

The first opportunity for students to be right and wrong in different, interesting ways is slide 2 where students were given the opportunity to see what part of the equation connects to the radius of the circle.  I used the variable a to represent "r^2" in the equation.   I did not want students to automatically think about the radius, and I also wanted them to notice the equation did not contain the direct value of the radius - it contains the radius squared.  I also left out the negatives for h and k because I wanted students to see the "opposite" movements.  After going over the activity, we derived the formula using the Pythagorean Theorem so that students could see why the center coordinates have the opposite sign of the values in the equation.

Below is the order in which I shared responses for slide 2 and a few notes on the discussion we had. By giving this assignment at the end of class, I was able to take my time reading the responses and organizing the progression I wanted to use in sharing them with the class.  Now that I have run this activity, I know what to look for so I would be more comfortable doing that on the fly during class.

Several students observed a change in the size and went no further. These responses speak to the accessibility of the question for all levels.  You don't need to know any math to make an observation.  It was not necessary to use any formal notation or vocabulary.  Students could just share what they saw.

The majority of students went further by identifying one of the above measurements as increasing or decreasing as the value of a increased or decreased.

There were multiple responses like the one above that mentioned the midpoint of the circle.  In my mind, this is a really interesting response.  As someone teaching geometry for the first time this year, I would not have planned to mention midpoint in a lesson on circles.  It makes perfect sense to see the center as a midpoint of the diameter of a circle though.  These students are using what they already know. Giving students the chance to play and make observations allowed me to center our class discussion on their prior knowledge and own language to develop new vocabulary.

A few students went even further and made the connection that the specific value of a was the same as the radius squared.  I found the first two responses above interesting because they did not directly say radius.  Once again, our discussion could start with those descriptions and work towards understanding exactly what they meant.  Allowing students to start the discussion created a need for a common language and vocabulary. 

Activity Design - Student Thinking

As I read through all the responses, I came across the following incorrect response on slide 16:

Once I saw this response, I went back and looked at slide 13 to find this response:

This student admits to "blindly" moving the a slider until he got the size of the circles to match.  He did not stop and notice the direct connection between the value of a and the measure of the radius.  These responses demonstrate the importance of adding slides to activities that force students to stop and explain their thinking.  Having students identify errors also encourages them to revisit previous slides to try and make connections that they might not have noticed the first time through he activity. 

Activity Design - Debriefing 

The first version of this activity had slides 16 and 17 as short answer slides.  I quickly realized that making it a multiple choice question with the option to have students explain would serve me better when debriefing the activity.  As a multiple choice question, the responses on the teacher dashboard would be organized based on the choice the student selected.  I am thankful for the design by Desmos that does not force me to choose multiple choice OR short answer.  I can easily have students select an answer from the given choices AND explain their thinking.

Reflecting on Professional Development

So this post started with me trying to answer a question posed by Dan Meyer on leading professional development: 

What is the point of opening a session on teaching and technology by asking the teachers to be students and do some math?

It has now turned into me rambling as I reflect on my experiences leading professional development sessions.

Before joining the Desmos fellowship I had only led 1 or 2 professional development sessions for teachers so my approach has evolved quite a bit over the last few months.  All of my limited experience has been leading sessions focused on Desmos. 

My number one goal used to be to give teachers something that was ready to use right away in their classrooms.  I know there were plenty of PD sessions I would attend in the past where I liked the ideas presented but would go back to my school and not have the time to implement what I took away.  I realize that goal is not realistic mainly due to two things:  time (I have yet to lead an all day session.  The sessions I have led range from 20 minutes to 90 minutes.) and the wide variety of experience/backgrounds of the teachers in any given session.  I now focus on having teachers leave with a new tool or new ideas but I understand that they most likely will not have a finished product ready to go.

My sessions then moved towards selling a tool to use in the classroom: Desmos.  I get overwhelmed trying to plan Desmos sessions because there are so many wonderful activities.  There are so many wonderful features.  There are so many subtle features that have huge impacts on teaching and learning.  I just want to show them everything!  There is no way to show everything during one session. 

It took a 20 minute session I led last week to teachers of all subjects to finally realize the most important goal of a session is to give teachers good instruction.  This is probably what the Desmos team has been telling me all along but I finally had my “Aha!” moment.  I was nervous about presenting to teachers of all subjects on a Friday after we had students for a half day.  The professional development on our half days is notorious for being a waste of time.  I knew I would have a tough crowd.  To my surprise, every session went well.  Teachers were engaged and having conversations.  My favorite moments were when we discussed feedback (When should you give it?  What should it look like? Etc…).  It was a lot of fun to listen to teachers share their perspectives across the curriculums, and all of it stemmed from a Desmos activity. 

The tool sells itself.  I don’t need to point out every little feature for them to be convinced.  They experienced an engaging lesson with great questions and wonderful opportunities to have class discussions.  I think this is why many of the Desmos fellows tend to start sessions by putting teachers in the role of students.  Teachers need to experience good instruction and see it modeled.  It doesn’t even need to necessarily be math instruction.  If they do, they will buy in and find the time to learn more about the tool you used.

As I start to plan my next session in March, the Desmos Guide to Building Great (Digital) Math Activities is where I will start and come back to throughout my presentation.  Those principles are ultimately what makes Desmos worth using.

Soft Skills

Soft skills for me includes every interaction you have with your students.  How you choose to phrase and deliver a question, correction, or request to your class as a whole or to an individual student can have a huge impact.  In some ways, I feel as though soft skills is one of my strengths.

Last week I overheard one student calling out another student for his horrible handwriting.  It was so bad that he couldn't even read it himself.  I calmly went over and mentioned how when I'm in a rush my handwriting can get pretty bad too.  One way I overcame that in school was to review my notes that night to make sure everything made sense while the material was still fresh in my head.  If I couldn't read something and figure out what it was based on the context within the notes I wrote, I could go in for help the next day.

The next day that student came to my Cav Morning (a morning study hall where students have a choice of what class to visit) having already started the homework and asked very specific and high level questions about the issues he was having with the material.  I'm not sure I can articulate how big of a deal this is.  This is a student who has not only struggled all year, but has embraced being "that student" who slacks off and just does enough to get by.  This is a class in which I have pleaded with all year to start the homework the night it is assigned instead of waiting over 24 hours to return to the new material from that class (we have block scheduling).

I believe this interaction and result shows how telling students to do something is not enough.  I have told students over and over what good study skills look like.  For this student, it didn't click until I was able to create a personal moment with him.  Instead of a lecture on what he should be doing, I made myself vulnerable by sharing my own struggles and the strategies I use to deal with those struggles.  As teachers we have to seek out those opportunities.

Another small thing I consider a soft skill is something I picked up during my student teaching.  I try to ask "Does this make sense?" instead of "Are there any questions?"  I'm not sure how much difference this makes but I like how it allows students to simply say no or even just shake their heads to keep our conversations going.  They don't have to formulate an entire question or get embarrassed by speaking up in front of everyone.  It also creates a culture where we aren't focused on the answer.  I'm not asking if students got the correct answer.  I'm asking if students understand where that answer came from.

When a student does ask a question, I make a point of praising that student.  A simple "Thanks for asking that question" or "That is a really great perspective to think about" goes a long way to encourage more questions.  I like to point out that student questions help me become a better teacher.  I share with students how they help me focus and adjust my teaching.  I also like to point out that questions show me that you are trying to make sense of the material.  You aren't just copying down information to memorize.  These small comments can help build up a safe and productive classroom environment over time.

There are other soft skills that I really have to work at though and that's why I appreciated Sam Shah's honesty in his post Not all of us have soft skills. I don't like talking about myself and usually won't do it unless prompted so it can be difficult for me to quickly form the necessary relationships with my students.  Sara Van Der Wer's post on name tents inspired me to try something similar this year.  It made a huge difference in how quickly I gained buy-in from my students.  I plan to use it again next year but spread it out over the first month of school.

Starting this calendar year I have also challenged myself to be more available and present for my students in the morning.  If I don't have any students asking me questions during our aforementioned Cav Monrning I tend to use that time to plan lessons or grade.  From now on, I will put my work aside and come out from behind my desk.  I do not want to isolate myself from my students during this time.  It's easy to get caught up with all the planning, grading, and other administrative tasks in teaching but those things will get done.  I need to prioritize taking advantage of this great opportunity to have casual conversations with my students and strengthen those relationships.

---Side note:  I'm going to continue to throw some love to Sam Shah as I highly recommend you read his recent post on Girls and Math.  It's a very timely post with the release of Hidden Figures and I felt as though I could really relate to a lot of what he had to say.  It has motivated me to try and organize either a viewing of the movie or reading of the book with my students.

My Favorite: The Desmos Guide to Building Great Math Activities

So this whole blog thing hasn't been very successful so far this school year, but thanks to the MTBoS 2017 Blogging Initiative I have reason and motivation to post throughout the month of January!  

The obvious choice for my favorite thing is Desmos.  What is not immediately as obvious is just how much Desmos influences my planning and instruction.  Its influence goes well beyond the specific graphs and activities I use in class.  Using Desmos and being part of the Desmos teaching fellowship has shifted my entire approach to planning and instruction.

The Desmos Guide to Building Great (Digital) Math Activities provides awesome recommendations for planning any math activity.  It does not matter if you are using Desmos or some other technology or no technology at all.  I have noticed myself creating lessons outside of Desmos that ask for informal before formal, create an intellectual need for new skills, give students opportunities to be right and wrong in different and interesting ways, delay feedback for reflection, and connect representations.  Many times Desmos helps me to accomplish these things more easily and more effectively but it's not a requirement.  

One of my favorite recommendations is to create an activity that is easy to start and difficult to finish.   I continue to focus on this recommendation as I look to improve my lessons.  One of the biggest challenges teachers face is the varied abilities and academic backgrounds that a single class can contain.  There are many Desmos activities that are not only great to use in the classroom but are also a great model of how to actually differentiate effectively.  Even if I don't use an activity in class, I can still take that model and apply it to a different topic or lesson that might not even use Desmos.

I have improved many of my lessons by incorporating Desmos, but I have improved an even larger amount by incorporating the recommendations made in the Desmos Guide to Building Great (Digital) Math Activities.  Desmos brings more than a tool to your classroom.  It brings a shift in your instructional approach.