Teach 180: Amplifying Student Efforts (Day 1)

Although my school has less than 180 days in our school year, I have decided to try a "Teach 180" blog this year.  In the past, I have written blogs that are long and that I agonize over.  (It can easily take me 2-3 hours to write one blog post.) This year I will write shorter blogs and with that there will hopefully be less agony.

Today was the first day of school and I could talk about my classes and how they went.  Instead, I am going to focus on something that I read as I was registering for Math Madness.  (This is an online math competition that some of my students have participated in for the past four years.) The Math Madness website lists the following as its pedagogical foundation:

The idea behind Math Madness is to create a structure that motivates students throughout the entirety of a school semester, one of enough time duration and frequency that students can observe actual progress, and in turn, amplify their efforts to continue on that path. 

Math Madness has a structure that allows students to work toward improving in problem solving by beating their own personal best. This made me wonder, "Do I have a structure that allows students to work toward improving in my classroom?"  In the past, I would put a sticker on a "A" quiz or test.  However, for many students a "C" or a "B" is their "A" or personal best.  This doesn't mean that in my room "everyone will get a trophy" for simply showing up.  What is does mean is that I need to do a better job at recognizing not just the "A" students, but also recognizing those students who work with determination to "amplify their efforts" and ultimately, become more successful.

Post Desmos Fellows Weekend Reflections

I have just returned from San Francisco, where I had the opportunity to interact and collaborate with other amazing teachers over a technology tool that I love - Desmos.  It will likely take me quite a while to wrap my head around the ideas that were percolating at Desmos headquarters on Howard Street during that 48 hours.  After a nap on my first plane back east, I started to piece together ideas for an activity builder lesson.  But then that lesson morphed into some general ideas and half-formed thoughts related to teaching that I will share below.

When considering using technology for any lesson, we need to first ask ourselves "What is lacking in the current learning experience that technology can solve?"  As I worked on a Statistics lesson on interpreting the coefficient of determination with Bob (@bobloch) and Meghan (@mmcgovern04), I began to wonder are there lessons that don't lend themselves to using desmos and what do those lessons look like? Was the Statistics lesson we were creating truly better than the current hands-on lesson that I do in my classroom now?  Yes, I love Desmos, but I don't want to have an activity that looks like the stepsister's foot going into Cinderella's shoe.  Although the shoe (and lesson) looks great before we try it on, it just ends up being painful due to the poor fit.

  

So, now you may be wondering why use desmos at all?  If the shoe doesn't fit, why bother trying to wear it? When a lesson is constructed correctly, it gives students an opportunity to learn mathematics in the way mathematicians create mathematics.  Testing conjectures, making mistakes and failing is a natural part of the learning process.  We (many of the math classrooms in the United States) have put learning of mathematics in a sterile environment by removing the opportunity for students to experiment and learn from their mistakes.  Instead of giving students the opportunity to construct knowledge for themselves, we tell them the big idea and then drill them with repetition, expecting the repetition to somehow compensate for the sterile learning environment that was created.  With correctly constructed lessons, students can be given the opportunity to learn from each other and create understanding.  With a Desmos lesson, there is an added bonus - the dynamic structure of the learning environment allows students to see his or her mistakes immediately and the computer has the patience needed to let the student learn from the mistakes at his or her own pace.

Getting parents and administrators to understand the importance of constructing knowledge might be a challenge, because it is not the way they themselves learned mathematics.  At my school, if you ask what a parent wants for their child they would likely say something like, “Good grades to get into a good college to get into a good grad school to get good paying job.”  Although it is not bad to have these things – good grades, good college, good grad school, and a good paying job - I would rather have my child have learning experiences to help them deal with uncertainty, the willingness to be initially stumped by a question but willing to tackle the question, the ability to construct their own knowledge and understanding about whatever topics are presented to her.  

We have heard the phrase, “I hear I forget, I see I remember, I do I understand”.  This has been expounded upon by an American educator named Edgar Dale. His "Cone of Learning" shows what percentage of our learning is remembered after two weeks: 10% of what we read, 20% of what we hear, 30% of what we see, 50% of what we hear and see, 70% of what we say and write and 90% of what we actually participate in.  Basically, the more involved students are in the learning, the more they will remember and the deeper the understanding.  I find it very ironic that some very basic instructional design ideas for teaching in the 21st century are nearly fifty years old.

Image taken from:   

www.triton.edu/uploadedFiles/Content/Academics/Continuing_Education/Cone_of_Learning.pdf

As I finished my reflections on the plane, I thought about how my understanding of what it means to learn was influenced by memories of my early learning and how that has shaped the type of educator I am today.  I definitely don’t teach in the same way or have the exact same philosophy of teaching and learning that I had when I was new to teaching in my early twenties. Throughout the weekend at the Desmos training, I could feel my thoughts about teaching and learning – both teaching adults and teaching students – being molded, as if my views were made of malleable clay.  As tiring as it was to think and discuss and explore, it was also invigorating.  To know that there are other like-minded teachers who are a tweet or Slack post away for support and a collective effervescence on what it means to teach mathematics is comforting. To know that there are others like me who have taught for many, many years and still don’t know all the answers is quite freeing.

Over the next few weeks, I’ll be exploring the computational layer of desmos and looking at ways it can enhance my lessons.  My focus will not be on the bells and whistles of technology that have come to dominate the educational technology market; my focus will be on using the technology to appropriately enhance the student experience of learning through the construction of knowledge that happens when mistakes are made.

Special Shout Outs:
Suzanne (@von_Oy) for saving the day with Lyft to get us to the airport at 4:30 AM.
Jonathan (@rawrdimus) for keeping me company on the walk to the Desmos HQ on the arrival day.
Sarah (@mathteacheryork) for sharing her notes with me on Desmos PD.
Kristin (@Fouss) for telling me about her great Desmos PD day in Ohio.  I'll be picking your brain about this again in the future.
Stephanie (@welblair) for being a great roommate.

Nearing the End (#DITLife Post 11)

Note: The events in this blog entry happened about a week ago.  Prepping for finals, grading finals and items related to graduation took precedence over finishing this blog entry.  Finding time for reflection is one of the most challenging things about being a teacher.  (The second most challenging thing is finding time to workout.) There are days when I feel like I am bouncing from one item or activity to the next.  Like a ball in a pinball machine, I slow down only to be hit back into the crazy whirl of dancing multi-colored lights and deafening bells.

This week we have 3 classes and then final exams begin!  It is hard to believe that another year of school is almost over.  Students have signed up for classes for next year and the enrollment for AP Stat will warrant two classes next year!!  This has not happened in a long time (perhaps ever) at my school.

The day begins at 7:20 with me sending an email to a parent addressing a concern about a student's grades and the student's claim that they can't understand or learn from their teacher.  With three days of classes to remain, I wonder why the parent or student himself did not contact me sooner.  Although I have been told by my husband that it is not my responsibility to help students that are not my students, I list five different times that I could help the student before Friday. (It should be noted that the parent did not respond to my email in any way and the student never sought me out for help.)

Next, we have an awards assembly.  This takes about an hour and parents are invited to the assembly.  I am responsible for handing out the math awards and this year we had a ninth grade student qualify for the American Invitational Mathematics Exam (AIME); he was in the top 2% of over 53,000 students who took the AMC 10 contest.

Period A - The assembly runs a little long and the first period class of 40 minutes is more like 30 minutes.  Because I no longer have a class of AP students, I have chosen to co-teach with the AB Calculus teacher.  She has 9 of her 19 students left in the class. (Ten of the students in AB Calculus were seniors and are on senior-post term shadowing experiences.)  Over the past week, my colleague and I have had fun teaching a variety of topics that are not part of our traditional curriculum.

Last week, we looked at simulations of p-values in statistics.  We also gathered data on predicting when a minute has elapsed.  Students told a person that they would start a stopwatch and the participant was to call "STOP" when they thought a minute was up.  Do you think males are better or females are better at sensing when a minute has elapsed?  To see the lesson plan and sample results, click here.  This was a new lesson that I was trying.  It was nice to see that there was essentially no difference in the distribution of times for males and females.  So often in teaching statistics, we have data sets that show a difference.  The fact that there is no difference between the two groups is actually quite refreshing.

At the end of the week, my colleague used an activity from the NCTM Illuminations site on modular arithmetic.  We looked at how the idea of modular arithmetic and prime numbers was related to cryptography.  We also programmed our graphing calculators to list the prime factors of a number.  This helped us to see that although multiplication of two large numbers is easy (doesn't take long to compute) the factoring of a large number is hard (takes much longer to compute).  This led watching a video called Encryption and HUGE Numbers at Numberphile (see video on the left) and then a brief discussion of Euler's Totient function.

Period B - We have had a long-term sub in to teach Geoemtry and Geometry Honors.  Over the weekend I sent him an email offering to lead his class with a Kahoot review session.  We had students work in pairs rather than individually.  I have found that this increases communication about mathematics and students don't give up on a problem as quickly when they are working with a partner.

Period C - Next we played a review Kahoot on logarithms and trig in PreCalculus.  Again, I had students work in teams of 2 or 3.  I reminded students that there would be a more formal review time in class tomorrow when they could get help individually.

Period G - We currently have an opening for a part-time person in math to teach two sections of Algebra 2.  I conduct a phone interview with a candidate for about 45 minutes and then head to lunch. In my school teachers and students eat in the same lunch room and eat the same food.  I don't have to pay for lunch and that is a nice perk to teaching at an independent school. We talk about non-teaching topics, including tomato plants and pepper plants and the weather in Oregon.

Period D - We played the same review game as in Period C.  The second time I can anticipate where students will have difficulties and walk around the room as students work.  I give hints like, "Remember what the domain is for a log function." or "Be careful with the exponent."

Period E - My room has been inundated with students over the past few days as exams are looming.  For the next 40 minutes, I alternated between answering questions from a Geometry student and answering questions from a PreCalculus student.

Period F - For the last class of the day, we play the Kahoot review game in Geometry Honors.  By the end of the day, my students have a great amount of energy and they really enjoy something that allows them to be loud and a little rowdy.  I like that I can see the overall results later and I can see an analysis by question.  Usually, my students know what they did wrong before all students have answered the question.  Because of the competitive nature of the game, students will get questions wrong, because they answer very quickly and miss the detail of the question.  "What?!? We were supposed to find the total area of the prism?  We found the lateral area!"

Today I did something that I rarely do.  I left school at 3:30.  Of course later that night I spent an hour answering various emails and writing the answer key to a review packet.  But it still felt like I was ditching school by leaving at the time my contract says I may leave.

And now for the DITL questions:

1) Teachers make a lot of decisions throughout the day.  Sometimes we make so many it feels overwhelming.  When you think about today, what is a decision/teacher move you make that you are proud of?  What is one you are worried wasn't ideal?

Although it would be very easy to give the students in AB Calculus the "time off", I am proud of the work that my colleague and I did with our enriching activities.  Students would not have been exposed to these ideas (cryptography, modular arithmetic, simulations to estimate p-values, boxplots sampling, estimating population parameters, etc.) if we hadn't made the effort create the lessons.  Teaching based on student pacing and having students learn without a standardized test or grade at the end was very refreshing.

Although I enjoy the Kahoot games, I know not all students enjoy the Kahoot games.  Some students would have preferred to just work on the review materials and ask me questions.  Perhaps in the future I can find some way to have both happen in the same classroom at the same time.  I know there is a "ghost mode" in Kahoot and perhaps that would allow students to work on a Kahoot individually.

2) Every person's life is full of highs and lows.  Share with us some of what that is like for a teacher.  What are you looking forward to? What has been a challenge for you lately?

Although my summer will be extremely busy this year, I am looking forward to some down time.  That downtime will happen between the AP Reading and three workshops that I am leading this summer in AP Statistics.  Right now my main challenge is finding a part-time teacher to teach two sections of math for the fall and person to fill in for a twelve week maternity leave position at the beginning of the school year.  So far we have interviewed no candidates for the maternity leave position and only one candidate for the part-time position.  Both positions start in approximately 11 weeks.

3) We are reminded constantly of how relational teaching is.  As teachers we work to build relationships with our coworkers and students.  Describe a relational moment you had with someone recently.

My daughter is at the school where I teach and there are many teachers that have helped her to become the strong and confident young woman she is today.  One teacher in particular I found after baccalaureate, I thanked her and told her that she truly is a "rock star".  The students trust her and they go to her when frustrated or stressed.  She is more than just an academic support teacher.

4) Teachers are always working on improving, and often have specific goals for things to work on throughout the year.  What is a goal you have for the year?

My goal this year was to continue to build a classroom of collaboration and to visit other teachers' classrooms.  I met that goal and was able to blog once a month about teaching.  Next year, I would like to blog more often - focusing on a single lesson or event as opposed to a full day of teaching.

5) What else happened this month that you would like to share?

I applied to be a Desmos Teaching fellow and my application was accepted!  I will be going to San Francisco in July with other Desmos fellows to learn how to best use Desmos and Desmos Activity builder to create lessons that enhance student learning.  Although I have used Desmos a bit and have my students do a project in our coordinate Geometry chapter, I feel like I know very little about the power of this tool.  The image below is my favorite project from this year.  I'll get to check out the accuracy of this rendition of the Golden Gate Bridge in a few weeks!