Tuesday, July 18, 2017

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:   

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.

Tuesday, June 6, 2017

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!

Saturday, April 29, 2017

Another Very Busy Day (#DITLife Post 10)

(Note: Today is Friday, April 28th and the day I am blogging about happened on Tuesday,
April 25th. Although I wanted to write this blog entry sooner, I did not have a full hour to do so until 5:45 PM on Friday.)

I arrive at school at 7:30 AM to help two students.  One needs to review for a quiz that took place on Friday, April 7th (before spring break). The other has questions on a homework assignment.  They leave the room a few minutes before first period is scheduled to start.

Here is an abridged version of my day.  The items that are bold I will discuss in more detail.

8:00 - 8:40 AP Statistics - discuss two investigative tasks from previous AP exams

8:40 - 9:00 Make copies needed for the afternoon and respond to emails

9:05 - 9:50 Visit a 9th grade World History I class

9:55 - 10:35 PreCalculus lesson on graphs of cos, sec, tan and cot

10:40 - 11:00 Work with student on course registration for following year

11:05 - 11:15 Speak with Academic Dean about student concerns

11:15 - 11:40 Interview with three Lafayette students for their college education course

11:40 - 12:15 Give make-up quiz to a student, answer questions about AP review for another student

12:15 - 12:25 Answer emails and make copies of trig graphs for PreCalculus

12:25 - 12:50 Eat lunch

12:55 - 1:35 PreCalculus lesson on graphs of cos, sec, tan and cot with Lafayette students observing

1:40 - 2:20 Work with 2 students with questions on Geometry, talk to colleague about letter of recommendation

2:25 - 3:05 Geometry Honors lesson on volume of sphere involving world's largest twine ball

3:05 - 3:30 Talk to a student about summer acceleration plans and gather items to create a test

3:30 - 4:30 Spanish class

4:30 - 6:00 Write test for Geometry Honors

Visit a 9th grade World History I class

This year I have been trying to visit many teacher's classrooms to observe their teaching.  It's not part of my job description to do this, but I decided to do this at the beginning of the school year for several reasons.  First, I want to have a broader perspective of the student experience at my school - the courses they take, the interactions with their peers in other classes, the teachers they have.  Knowing about my students' experiences helps me to see them as more than just "math students".  Second, I want to get ideas on how to teach and manage classrooms from my teaching peers.  Third, I want to provide the teachers I visit with constructive feedback - feedback that I feel has been poor or missing for many of my colleagues over the past several years.

On this day, I visited Mrs. Burd's World History I class and the students are discussing concepts around the development of Islam.  Students answer questions and ask questions with some students more engaged than others.

Morning PreCalculus Lesson on Graphs of Cos, Sec, Tan and Cot

We are a little behind in this class and I have to finish the graphs of cos and secant from the previous day.  As we complete the graphs together, I have the students discuss the properties of the graphs at their table.  (Note: It takes a while into the school year for students to realize that I actually want them to talk to each other during class and work together to learn from each other.) The graphs of sin and csc look ok together on the same graph.  You can distinguish each of them and determine their properties. The graphs of cos and sec look ok together on the same graph. You can distinguish each of them and determine their properties. But...the tan and cot tan graphs...You decide.

We were getting near the end of the period and as I added the cot graph to the tan graph, I could tell that the students were thinking the same thing I was thinking.  Brain overload!! There is too much here!!  What do I focus on?  Which asymptotes go with which function.  Immediately after class I did a google search and found this nice graph of All Six Trig Functions and their properties. You can click on the link to download it for yourself, but here is a screenshot of it.

Because class was over, I emailed the PDF to the students in this class.  But I also made copies to give them the next day and to give to my other class later in the day.  I always feel bad for the first class I have when teaching a lesson to multiple sections.  When something doesn't go as planned, it happens in the first section of that class and then the second section gets the benefit of my reflection on the lesson and subsequent improvement upon it.

Afternoon Spanish Class
Last fall it was announced that there would be conversational Spanish classes offered for 8 weeks by two of my colleagues.  I chose the Tuesday class to fit my schedule, but it has been a challenge to budget my time to get to class.  The class is actually a break in my day.  It gives me a chance understand what it is like to be a student again - to be confused and then feel success - to be tired and work to focus - to interact in a learning setting with my peers.  An added benefit is I get to observe another colleague in action and gain some more ideas relative to the art of teaching.

Write Test for Geometry Honors
It is now 4:30 and I am spent and want to go home.  However, I need to write a test for Geometry Honors.  Although the test is scheduled for Monday of next week and I had planned on writing it over Thursday and Friday, there is a student that wants to take it on Wednesday morning.  Every year I write new tests for my classes.  This allows me to make sure that my test accurately reflects what has happened in class.  In addition, I let students keep their tests after I have graded them.  If I used the same test from year to year, it would be very easy for students to get copies of the test from their siblings and friends who had me the previous year.  

I make some copies of some pages from a teacher resource and use what I find to craft a four page test which covers the concepts of volume and surface area for prisms, pyramids, cylinders, cones and spheres.  I'll work on making a second version of the test later in the week. (I distribute different versions to students seated next to each other.  This has allowed me to catch students who cheat by copying off of their neighbor's paper.) After I make the test, I take the test.  It takes me about 10 minutes to create the answer key.  This is a sign that the test can be completed by all students in 40 minutes.  If it took 13 or 14 minutes, the test would be too long and I would need to revise it.  As I take the test, I notice a typo and fix it.  Finally, I print off one copy of the test for the student.

It is now 6 PM and I can get my daughter from the baseball game (she is the team manager this year) and go home.

And now for the #DITLife reflection 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 made that you are proud of? What is one you are worried wasn’t ideal?

Today I met with six different students when I wasn't teaching.  Although I focused on each student while they were with me, I was feeling rushed.  When I am rushed, I talk more and students talk less.  I do more explaining and less asking of questions.  When I ask at the end of our meeting if they understand the material, students always say "Yes".  But on a day like today, when I had no time to breathe, I am uncertain.

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?

Last month I spoke at the National Council of Teachers of Mathematics annual conference.  My presentation was called "Revoicing: What Do Your Students Know" and the focus was on classroom discourse.  Unfortunately, I was up against a well known speaker for that time slot and only had 5 people in attendance at my session.  However, they seemed to enjoy my session and we had a lively discussion on the topic of classroom discourse based on the video clips we viewed from my classroom.

Since the end of March one of the teachers in my department has been on extended leave.  This has been a challenge for many reasons - finding a qualified substitute, grading student assessments and ensuring continuity of the curriculum.  I have been fortunate to have very supportive colleagues within my department who have helped to make the transition to the extended leave smoother.  I am especially grateful for Jane Cook and the work she has done with the long-term substitute teacher.

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.

Over the past several years, I have become known as a "go to" person for advice.  Some people seek me out, but other times I know a person is in need of a friendly sounding board and I approach them.  The end of spring break was one of those times.  I had a two-hour conversation with a colleague and I hope listening and discussing ideas related to the situation was helpful.

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

One of my goals for this year was to visit classrooms of my colleagues.  Although I have not been in as many classrooms as I would have liked, I have visited thirteen classrooms to date.  In addition, I have worked on building a classroom to encourage more discourse.  This has been challenging at times with sports dismissals and 40-minute classes.  I look forward to having longer classes next year to be able to teach the way I should be teaching more often, using more student discourse and hands-on activities.

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

During spring break, I was able to take my daughter to visit four colleges in Texas. (Note: We live in Pennsylvania.)  She and I shared many of the same views about the schools we visited and we were able to cross some off the list.  Driving across Texas with limited cell phone reception and no GPS to guide us reminded me of the days of traveling with my parents.