# MTBos Mission #3 – Daily Desmos

So, the challenge this week was to pick a collaborative site and … collaborate! So, I chose DailyDesmos for a number of reasons. Years ago, when I was a student again for a glorious time, I fell in love with GeoGebra. For the past few years I have been preaching to my students and colleagues about the wonders of GeoGebra. I reached out to a colleague from Lawrenceville and had him come out and do a workshop for my school teammates. Fun has been had with GeoGebra. Recently, I was introduced through the wonderful blogger world to Desmos and I am in the process of falling in love with it as well. Recently, with my precalc honors class we had a triumph using Desmos. I blogged about it on Sept 10 and included this link ( https://www.desmos.com/calculator/nvinc8pwdh ) when my kiddos wrestled with creating a trig function to match the daily average temps of my old, beloved hometown of Gainesville, FL. This morning I dove in and took on challenge 201a ( http://dailydesmos.com/2013/09/23/daily-desmos-201a-advanced/ ) which was presented by the awesome Michael Fenton. Here is my crack at a solution to that one ( https://www.desmos.com/calculator/zmuvzpmvti ) and it is probably not as dynamic as it could be. I still need to learn about leaving traces behind rather than simply having the slider generated graph be new at each stage. I am imagining a sort of spirograph and I am certain that Desmos can handle that. I still love my GeoGebra – especially for individually rescaling axes as I go – but I am finding room in my heart for Desmos as well. As my school inches toward greater tech integration, I am seeing a day where my students would be spending time in class (on their own or in their pods) where they are tackling these daily challenges now and again. I am also dreaming of a time when I feel that I have time and energy on a regular basis to tackle these challenges.

I have thoughts about these graphs that I need to organize and make coherent. Another post for another day.

# New Challenge – Curriculum Development

Wish us luck and lend a hand where you can!

# Really Proud

So, in my BC classes we are wrapping up our tour of integration techniques. It’s pretty easy when you are convinced that integration by parts is the strategy to use, or when you know you are supposed to use a trig substitution, etc. Little parcels are easy enough to deal with. Throw them all in a bag at once and choose? Much much more challenging. Yesterday, in our 40 minute classes, each of my two sections of BC Calc made it through two problems and I could not be more proud of them. They fought, they tossed out ideas, they stuck through some thorny algebra. They critiqued each other’s ideas. They questioned mine. I tried – I really did – to give them space and let it unfold. Other than one idea that I knew would lead to pain, I did my best to let them run the conversation. It was the kind of day that justifies – at least in my mind – our decision to have BC as the second year calc class. In a one year track these kids would not have days like this where they could just play with ideas without regard for the clock. The problem that was the real winner is below (if my cut and paste graphic works right)

Edit – Image pasting is not my strength right now. Sigh.  The challenge at hand was to integrate the fraction dx/(x^(2/3) + 3x^(1/3) + 2)

One student in each class suggested completing the square and that was pretty thrilling. The first one even pushed a step or two through on a trig substitution involving secant. That’s where I intervened because I was pretty sure that this path would lead to pain. We looked at GeoGebra and tried to work backwards from its answer after we went down the partial fractions path. Man, what a good day and I was fortunate enough that one of my colleagues came to visit yesterday morning. She was their AB teacher last year so it’s possible that they stepped up their game for her. If that’s true, I’ll have to enlist her for future challenge days.

# Stepping Outside my Little Corner of the World

Our school had a day off on Friday (and a day off today as well) for a long fall weekend. We were asked by the powers that be to use Friday for professional development. I chose to drive a couple of hours in the morning to go visit another school. When I did my last job search in the early months of 2010 there were a number of schools that caught my eye and the school I visited on Friday was one of them. The chair there was remarkably kind and helpful in setting up a too short visit that morning. Since I had kid pick up duty that day AND we had agreed to house sit for some friends to look after their dog AND my boy had an ice skating birthday party to go to (there is a theme here about how life unfolds in the dardy household) I did not have quite the leisure I had hoped for. I arrived at 8:30 ish for a warm, quick chat with my host, I saw a Geometry class, then I saw a Precalculus class, then I saw an AP Stats class. A nice follow up chat and lunch with the chair, then I was off to home.

I always enjoy seeing classes – it is a part of my job as a chair that unfortunately gets buried under other tasks. It is fun to  pick up tricks from other teachers. In this case, the geometry teacher had a lovely way to highlight parts of the parallel line with transversals problems that they were working with that morning. She had spools of different color tape that looked like athletic trainer tape. She pulled off two of one color to highlight which lines in the diagram were parallel to each other and a different color for the transversal. It was SO COOL to see this way of making the relevant information in the diagram just pop out to the kids. It was also fun to see her improvise. The kids were checking their work from the night before and were having disagreements about measures they had taken. Out the window went the lesson plan for the day and out came a class set of protractors so that they could practice with their measuring skills. The teacher confided in me that some of her attitude about this was strongly influenced by her husband who is a woodworker. In the AP Stats class I was privileged to watch someone who was a real, honest to goodness statistician before entering the classroom. As a stats novice myself, it was great to chat with her beforehand and to watch her in action. I think that she convinced me to try an activity that has been previously pretty intimidating to me. The precalc class was fun to watch as well as the kids were hanging in there working through some complex polynomial graphing ideas.

I know that I have a tendency to look at my world and see the potential for excellence in the people around me. I know that I focus at times on what is not quite right instead of celebrating what is right. A visit like this worked wonders for me on a number of fronts.

1. It’s always great to reach out to more people to bounce ideas off of

2.  It’s fun to watch kids at work – especially when I have no preconceived notions of who they are or what they SHOULD be doing

3. It’s rewarding to talk to others who are working through some of the very same struggles. How do we accurately place test kids who are new to a school? How do we balance ambitions for kids with their abilities and previous track record of achievement? How do we find TIME in the school day/week/year for meaningful problem-solving while still serving an ever expanding curriculum? The chair I met with is thoughtful, experienced, and intelligent. The fact that she is struggling with these questions as well makes me feel better.

I’m proud of my school, our students, and my colleagues. I believe that we can all be better than we are but I want to try and focus on what we’re doing right and I think that this experience on Friday can help me with that.