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.  

Sunday, March 26, 2017

So Glad It Was Friday (#DITLife Post 9)

I knew Friday was going to be a challenge when I heard that one of the teachers in my department, Lia, would not be in school that day.  There was a voicemail left by her husband on my phone and a text and email from another teacher, Jane, about planning for Lia's classes.  I arrived at school around 7:20 AM to speak with Jane about the plans for class.  In two of the classes, a test was planned and since I happened to be giving that same test, I had the original to make copies.  Jane copied the test while I attended a student-led conference with one of my advisees.  At this conference, we discussed classes, academic challenges and college visits.  The student-led conference ended about 5 minutes before my 8 o'clock class.

8:00 - 8:40  AP Statistics
We began class with a quiz on chi-square goodness of fit tests. The quiz was designed to take 10-15 minutes, but some students needed 20 minutes.  I don't like rushing my students on assessments, because then I feel like I am assessing students ability to handle stress more than I am assessing their understanding of course content.  Timing of assessments is frequently challenging.

Next we worked through an old AP free-response question to understand how to do a chi-square test of association.  We had worked through chi-square tests of homogeneity the previous day and this test was very similar.  The only difference was in how the data was collected.  Prior to teaching AP Statistics, I did not even realize that there was a subtle difference in these two tests.

8:45 - 9:25  Substituting for Geometry Honors
Before I rush off to give the test in Geometry Honors, I send an email to a student that I was scheduled to meet with.  The email states that there was an emergency situation and that I won't be able to meet with her, because I will be filling in for another teacher.  While the students take the test, I look over the quizzes I just gave in AP Statistics.  Everyone gets an A on the quiz and shows their work in a detailed and organized way. (I have a great group of students this year - they all ask questions and do what is expected of them.  So, I am not surprised by these quiz results.)

Part way through the test, I notice that some of the pages of the test are missing!  Only the front pages of the test had been copied and not the back pages of the test.  Luckily there is another teacher in the room to proctor the students during the test.  I run down the hall to make the necessary copies and run back to class to distribute the pages.

9:30 - 10:10  PreCalculus
In this class we are doing our first trigonometry unit and some students are still confused by the unit circle.  We go over some questions from the homework, like "what is cosecant of 7 pi over 6" and "if cosine of an angle is equal to 1/2, what is the angle".  Next, I give them a blank unit circle to have them practice completing it.  This gives them a sense of how well they actually know the values of sin and cos around the unit circle.  Finally, we play a round of Kahoot in pairs to practice more with the six trig ratios around the unit circle.

10:15 - 11:10 Chapel
Chapel today was an invited speaker, a storyteller and author. Although the speaker was entertaining, I personally prefer when students or faculty give talks in chapel.  Getting to know other aspects of a student's life or a faculty member's life gives me a better understanding of who the person is, what they enjoy and what they value.

11:15 - 11:50 PreCalculus
Class starts late by about 10 minutes, because the junior class was detained in the auditorium.  There was a discussion about making a student an honorary class president so that he could speak at graduation.  When class begins we work through problems on the homework and the students complete a blank unit circle.

11:50 - 12:25  Lunch
I head to lunch after checking a few emails.  The faculty at my school eat in the dining room with the students.  We don't have lunch duty or hall duty, like in public schools.  The round tables in the dining room seat about 8 and we generally have 2 or 3 faculty tables in the room of 30 tables.  I had some sort of vegan rice dish that I thought was good, but a colleague at my table enthusiastically declared it "bleh".

12:25 - 1:00  PreCalculus
Students return to class and we do a Kahoot in pairs.  Students are doing well on most of the problems.  There are a few of them in this class (and in my other class) that were commonly missed. Luckily, I can look at past results in Kahoot and save the results to google drive or download them. The test on this unit is on Tuesday and I will be working over the weekend to make revisions to the test.  With 4 sections of PreCalculus, we will need 4 versions of the test and a make-up version.

1:05 - 1:45  Geometry Honors
This class takes the test that I gave earlier in the day.  While students take the test, I enter quiz and homework grades and respond to some more emails, including a survey about student-led conferences.  A few students finish early, but most wait to had in the test a minute or two after the bell rings to end class.  I'll be grading these tests over the weekend and writing a paragraph on each of my students in all of my classes.

At my school each teacher writes comments twice a year about their students.  This includes information about grades, homework completion, behavior in class, etc.  I only have 45 of them to write, but it will probably take me just under 4 hours to complete this task.  This is how I will spend some of my Sunday afternoon/evening.

1:45 - 3:30 Collaborating and Planning Although I am not usually in the mood to get work done on a Friday afternoon, I push through.  During period E, I work with another teacher on our test for PreCalculus.  We decide what types of problems to put on the test, how many problems to put on the test and point values.  We also look at what portion of the test will be calculator and what portion will be non-calculator.  (I took the test on Sunday and it took me about 13 minutes.  This means that it is probably too long for students to complete in 40 minutes.  This means I will spend time on Monday revising the test before working on the other versions of the test.)

The last period of the day I work on writing a problem to submit to Math Madness.  This submission is part of a contest and the idea for the problem came to me after a student suggested a generalization to a problem we were solving in class.  I wasn't sure if the generalization would always work.  So, initially we called it the generalization "Noel's conjecture".  The next day I went into class to show that I proved "Noel's conjecture" and that it was now "Noel's theorem".  This is an example of one of my favorite things about my job at Moravian Academy.  Students are always being creative and coming up with alternative strategies to solve problems.  Many of them get that this creativity is what it means to really do mathematics.

Although I did not get my tests graded, I know that I have the weekend to get them completed.  A typical weekend for me includes 4-6 hours of school-related work, sometimes more.

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?

I made the decision to quickly copy the other pages of the test.  Not all students completed all the questions.  Maybe I should have had them take the remainder of the test on Monday.  I will need to wait until the teacher grades the tests to see if we need to make some sort of adjustment or not.

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?

My presentation on prime numbers, RSA cryptography and programming the TI-84 went very well at the ATMOPAV (Association of Mathematics Teachers of Philadelphia and Vicinity) spring conference.  Although there were only 4 people in attendance (it was a small conference ), one of the participants sent me two emails including attachments related to the work he did that was inspired by my presentation.

My next presentation will be in San Antonio on April 6 at the National Council of Teachers of Mathematics annual conference.  I have the presentation ready to go except for the video clip that I would like us to discuss.  I had recorded some classes early this year using a swivl.  Unfortunately, the video quality was poor - you could not see what was written in the front of the room and you could only hear me and not my students.  Since the presentation is called "Revoicing: What Do Your Students Know", hearing the students is necessary.  I recorded some more last week and I hope I can find a 5-10 minute clip to use from those videos.

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.

Today I must have looked tired and worn out.  And to be honest, I am a bit tired and worn out. (Luckily spring break will be soon.)  A colleague asked me how I was doing, noting that I looked super tired.  I said that I was fine, but that I could use a hug.  She gave me a hug.  I am truly blessed to have teachers in my school who look out for each other and care for each other.

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? 

I have really been working on trying to improve classroom discourse.  Lately, I have been asking questions of students and when no one seems to know the answer, I tell the students to talk about it at their tables.  At first I am met with strange looks, until I say, "Go ahead and talk."  Then I walk around the room to listen in on the conversations and see what answers the groups get.  If not all the tables have the same answer, I invite them to defend their answer.  At this point, students are more confident and ready to talk about the question.  Although it takes more time to teach in this manner, more students are involved and more students get to contribute to class discussion without the feeling of being put on the spot.

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

We had three consecutive snow days and it was BLISS!  I got to read a book for enjoyment, get ahead on schoolwork, do some consulting work, prep for a conference, sleep more and I got some extra housework done!  It was incredible!!!

Monday, February 27, 2017

A Typical Day (#DITLife Post 8)

Although today is Monday, this blog is about what happened on Friday.  I can barely remember what I eat for lunch some days.  So, you may wonder "How can you remember what happened on Friday?" I anticipated not being able to complete my blog on Friday and made a few short notes on my laptop.

I typically arrive at school by 7:30.  Today, I have two students that sent me emails requesting to meet with me for some help.  One is in PreCalculus and has fallen behind due to multiple absences.  The other student is in Geometry Honors.  He is working on an review assignment about quadratic functions and parabolas.  He says that although he has had Algebra 1 and Algebra 2, he can't recall things like how to identify the vertex of the parabola from its equation.  I tell him that it is good he started working on this assignment early, because it will probably take an hour or so to complete it.

AP Statistics is from 8:00 - 8:40 and we begin our work with hypothesis testing for a single proportion by looking at an example about winners on American Idol.  At this point, I realize my once pop culture-relevant example has become dated.   But our test results lead us to conclude that there is not an advantage to going last.

Next it is B period (8:45 - 9:25) and I work with a Geometry Honors student who meets with me every Monday and Friday.  We complete much of the quadratic functions and parabola worksheet together.

Period D is PreCalculus and we spend the first 15 minutes of class looking at an example involving logistic growth and carrying capacity.  Students are given 25 minutes to work on an assignment and I warn them about an error I made when solving a problem on that very assignment.  The problem stated that amounts were given in thousands.  Therefore, the value 350 needed to be used for 350 thousand.  If students used 350,000, they end up having to take a log of a negative value.  Since negative values are not in the domain of the log function, this is a problem.  I always work through the homework that my students are assigned to make sure I can anticipate the types of questions they will have.  It also helps me to know if an assignment is too long.

Next is our weekly chapel and students are speaking about Art and Identity.  Chapel starts at 10:15, but I arrive about 10 minutes late.  A colleague has stopped in to see me about setting up her Sign-Up Genius account for the Student-Led Conferences that will be happening on March 17th.  She thinks it will be quick for me to show her what to do, but the process involves seven different steps.

During chapel, one of my students speaks about her identity as it relates to her ability to draw.  She does a wonderful job of weaving short stories about her work as an artist with the broader meaning of identity.  I asked her to share her chapel talk with me, because there were some things she said that I felt were worthy of being quoted.  Here is something she said in her talk:

"We’re always going to go back and fix what we don’t like and keep what we do, and later change that as well because it's getting old. But we have to stay flexible. Even when applying it to real life, if say you feel as though your current group of friends is unbreakable or you know exactly what you want to do after college, keep in mind that you advance and morph and change as a person, even without trying, both physically and mentally."

Next it is on to period C and my second section of PreCalculus.  This day is our lab day and we have 35 minutes of class followed by lunch for 35 minutes and then 35 minutes more of class.  For the first 35 minutes, I randomly assign students a partner to play Kahoot. Students are told that they must create a name using "&" in it.  The students are fairly creative and the room is buzzing with discussions about the problems.  If you are interested in the kahoot I used, here is the link to it: Kahoot on Logarithms   After lunch we do the same lesson that was done in my Period D class and most of the students get the homework completed before class ends at 12:50. 

My last class of the day is here!  It is Geometry Honors and it starts at 12:55 and ends at 1:35.  We are working on compass constructions.  Students work individually to create constructions involving copying lines, copying angles and bisecting angles.  After about 20 minutes, we look at two new constructions - drawing a perpendicular bisector and drawing a line perpendicular to a line through a point on the line.  We discuss why they work in terms of isosceles triangles and congruent triangles.  When I first started doing this unit in 2010, I learned how to use the compass on the smartboard.  However, standing at the front of the room doing this meant that I couldn't easily check to see if students were doing the constructions correctly for themselves.  

Compass Constructions Playlist at www.youtube.com/mathteacher24
So, I created short screencasts and posted them to my YouTube Channel - mathteacher24.  The constructions we do can be found in the Compass Constructions playlist.  This playlist has also been helpful when students are absent or simply want to review all of the constructions before a test.

At 1:40 I go to find a student in the freshmen lounge.  I have great news for him; he qualified for the AIME (American Invitational Mathematics Exam) by a large margin. (The qualifying score was 112.5 and he earned a score of 121.5.)  I also find two other students to remind them about the Muhlenberg College math competition that will be held the next day.  After about ten minutes, I return to my classroom to work with a student who is in Geometry.  He is not in my class, but his mom sent me an email asking if I could help her son with his math.  Since I was free during this time and his teacher was not, I gladly agreed to help.

After working with this student for about twenty minutes, the class period is over and he needs to go to his next class.  During the last period of the day (2:25 - 3:05), I make some copies for next week and begin on an answer key for a review assignment.  Then I post some math competition results on the bulletin board and go to visit our school chaplain.  She and I discuss items related to chapel and school life. 

I return to my classroom when the day is over to work with another student until about 3:50.  At this point, I have been at school over 8 hours, but I head out to have a slight break and spend time with some friends. I return to school around 5:45 for another 3+ hours of chaperoning an evening dinner and guest speaker event for a club called "Women's Awareness".  Around 7:45 my head started to nod off as I listen to the discussion of about 30 students.  The event was good and fairly well attended, but I leave school even more exhausted than my typical Friday afternoon.

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?

Having students work with a partner for the Kahoot activity was something that went well.  When students work by themselves, they are often overwhelmed by how quickly (and accurately) some of their peers can answer the questions.  This leaves them feeling defeated.  When students worked with a partner, everyone (including those who usually groan about Kahoot activities) was excited and worked on learning together.

A few weeks ago, I made a decision that was less than ideal.  I had created an activity in Desoms Activity Builder the previous year on asymptotes.  It was a big hit with my Calculus students.  I thought, "Great!  I can use that activity again!"  But it was a big flop.  In fact, the day after the Desmos lesson about 15 minutes into the lesson, a student raised her hand and asked, "What is an asymptote?"  You could immediately see the relief on the faces of the other students who had been too afraid to ask the question themselves.  I had to back up and reteach some ideas that I thought students understood.  So why did the lesson flop with that group?  I realized that the students in Calculus had seen the concept of asymptotes earlier.  The Desmos lesson reinforced what they already knew and allowed them to make connections among ideas.  The lesson contained too many concepts (vertical, horizontal and oblique) for an introduction to asymptotes and many students didn't quite finish the activity.

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?

Right now I am looking forward to two presentations that I will be giving - one is on prime numbers, RSA cryptography and programming the TI-84 to look for prime numbers.  This is not a talk I have given before and I will need to do some research to put it altogether.  The presentation date is March 16th.  The second presentation is about reflecting on teaching practice, specifically revoicing student responses in class.  I have made videos of several lessons and plan to have teachers identify the ideal and less than ideal teacher moves in the videos.  This presentation will happen at the NCTM conference in San Antonio at the beginning of April.

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.

Recently I applied for a job as the Director of my school.  Faculty were very supportive of my decision to apply for the role and several of them arrived at the conference room on the day of my interview to wish me well with a handshake or a hug.  

I found out about a week ago that I was not offered a second interview and my main concern was over the reaction of my colleagues.  So many of them wanted me to be hired in the new role.  My current hope is that they will support whoever ends up ultimately being hired for that position.

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? 

I finally read much of the book that I am referencing for my talk at NCTM in April.  The book is called "Promoting Purposeful Discourse" and I have about two chapters remaining.  Purposeful discourse in any classroom is important and I plan organizing Lunch Talks around topics related to teaching with my colleagues three times before the end of the school year.  (Be on the lookout for items related to the Lunch Talks in my next blog entry.)

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

My daughter and I did a college visit over President's Day weekend.  She is ready for college, but I am not so sure if I am ready for her to go to college.  She will be taking her driving test later this week.  She is ready to take the test, but I am not so sure I am ready for her to take the test.  Perhaps I need to remind myself of the words of my student's chapel talk - "keep in mind that you advance and morph and change as a person, even without trying".  Growing up and changing happened without my daughter trying.