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!!!

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.

End of 2016 Reflection (#DITLife Post 7)

Our last day of school was Friday, December 16th and although I could have written a blog about that day, I needed a break.  See exhibit A below for proof.  Note: The pink "awake" time was when I got up to feed the cat.

Exhibit A

Then, I succumbed to a little-known corollary of one of Newton's Laws.  The actual law is "A body at rest tends to stay at rest."  The corollary is "An unwritten blog tends to stay unwritten."  Today, I got some momentum going by spending the last hour working on a teaching and leading philosophy statement.  Before my daughter and her four friends emerge from the basement (there was a sleepover last night), I thought I would use Newton's Law to my advantage.

Although not ideal for a #DITLife blog post, what I am about to write is being pieced together from memory.  Friday, December 16th was the last day of classes before Christmas break.

Period A - This forty-minute class started at 8 AM and was devoted to students working in pairs on the German Tank activity.  We began the activity the previous day.  The goal of the activity is to introduce students to sampling distributions and what makes one statistic better at making an estimate of a population parameter than another statistic.  Ideally we want an unbiased statistic with small variability.

Each pair of students gets a bag with slips of paper numbered consecutively from 1 to N.  They are to mix the numbers in the bag and then pull out seven slips of paper.  From the seven numbers on those slips of paper, they are to determine a way to estimate N.  Popular statistics are based on doubling the mean, doubling the median, or finding the mean plus three standard deviations.  This year two girls came up with a statistic that I had never seen before. (This is probably my eighth year of using this activity.)  They calculated the average difference between consecutive pairs of numbers and then added it to the highest number.  A sample calculation is shown here based on the numbers:

Here is the calculation:

Note that many of the terms in the numerator sum to 0 and the resulting calculation is:

It is interesting to note that this statistic really only uses the highest and lowest numbers and all of the other numbers are inconsequential.

I was curious as to how this statistic stacked up against the Partition method that was developed by statisticians during World War II.  The Partition method assumes that the values are approximately equally spaced from low to high among the tank numbers.  Drawing seven tank numbers essentially splits the number line from 1 to N into 8 partitions.  The highest number is about 7/8th of the way when counting from 1 to N.  Multiplying the highest number drawn by 8/7 would yield the number N. Based on the seven numbers used above, we would have 337(8/7) or about 385.1.

The actual number of tanks is 344.  So, for this sample the "RedfernFerrari" method (named after the girls who created this statistic) produced a statistic that was closer to the population parameter than the Partition statistic.   But how does it do in the long run?  The screenshot below is from Fathom and shows 100 sample statistics based on samples of size 7.  Which statistic would be better to use to estimate N - Partition or RedfernFerrari?  This is the question that I will be posing to my students on January 3, our first day back from break.

Period B - During my forty-minute planning period, I started to plan for January 3rd by making copies and organizing papers.  I can't recall the number of cookies I ate from the faculty room, but I know it was too many.

Period D - For the first fifteen minutes of class, I returned a test that students had taken the previous day.  Many students had problems on the first page - matching polynomial equations to graphs with a focus on end behavior.  So, I had the students work together in groups on a fresh copy of this page of the test before they saw their own test.  As they did this, I learned that some students thought that to find the degree of the polynomial that you needed to add all of the exponents.  This is true for f(x) = x(x - 1)²(x + 8)³, where the degree is 6. But it is not true for f(x) = x⁴ + x³, where the degree is 4.  Had I not reviewed the first page in this way, I would have not discovered this misconception.

Next, I gave students time to work on their Birthday Polynomial project. (I had discovered this project during a twitter chat several years ago.  I don't have the original link now, but there are many versions of this project online if you search "Birthday Polynomial".  Here is Mr. Reed's version of the project.)  The project is not due until Friday, January 6th and many of the students did not want to work on it.  As it was the last day before break and there were Christmas movies showing in the dining room to celebrate meeting a school-wide service goal (students and faculty brought in over 275 items to donate to a home for a refugee family), I allowed students to go to view the movie for the last twenty minutes of class.

Chapel - Many students and faculty participate in our weekly chapel and today was no exception.  The theme of the chapel was light and dark.  I was surprised by the variety of photos students and faculty had contributed to make the opening slide show.

Period C/Lunch - This period was similar to my D period PreCalculus class, but I had about 1/3 of the class choose to come back after lunch to work on their birthday polynomial projects.  We also sang two math-themed holiday songs - "Oh, Number Pi" (to the tune of "Oh, Christmas Tree") and "The Famous Four-Sided Shape" (to the tune of "Rudolph the Red-Nosed Reindeer").

Period F - In Honors Geometry, we had just finished a unit on similar figures and I decided to spend our last day before break doing a problem called "The Two Telephone Poles".  Initially, I gave my students a blank diagram devoid of numbers or context and had them individually list what they noticed and what they wondered.  In other words, what they knew was true and what they thought was true.  They had about 2 minutes to do this.

Students came up with many ideas for "Notice" including vertical angles, BE + EC = BC, and there are five triangles in the diagram".  The ideas for "Wonder" included statements about similar triangles, perpendicular lines, congruent angles and parallel lines.  After I had students compare their lists at their tables, we created a class list from their individual lists.

Next, I added right angle symbols at B and D to show segment AB was perpendicular to segment BD and segment CD was perpendicular to segment BD.  As a class, we decided which "wonder" statements could be moved to the "notice" column.  When a student would give me a statement to move, they had to justify their answer.  

Finally, I added some numbers to the diagram and gave them the context of the problem.  Two telephone poles are erected perpendicular to the ground and 40 meters apart, as shown in the diagram below. The poles are 30 meters and 20 meters tall, respectively. Two of the supporting wires are shown, each running from the top of one post to the bottom of the other.  How high is the crossing point of the wires off the ground?

Because students had already spent time thinking about the diagram and what was true, they quickly solved the problem by using similar triangles and creating a system of two equations.  After each group had the answer, I showed how coordinate geometry could be used.  By setting AB on the y-axis and BD on the x-axis and having B be the origin, we could easily write equations for lines BC and AD and then solve the system of equations to find the point of intersection of the two lines.

At this point we only had about 8 minutes of class time left.  I asked the students the following follow-up question. The public service commission has stipulated that the meeting point of the wires must be 15 meters off the ground. With the given conditions, would it be possible to position the poles either closer together or further apart so that this requirement could be met? Explain your answer.  

Ideally, we would have had about 15 more minutes of class time for exploration of this follow-up question.  I had some students say to move the poles closer together, and others said farther apart. Very few said that it wasn't possible, which is the correct answer.  Instead of having time for exploration, I showed the following video to dynamically demonstrate that it was not possible.

Period E - I was done teaching for the day at 1:40, but I still had work to do.  My day was definitely not over. First, I talked to a colleague about plans for PreCalculus for after break.  She shared with me information about the midterm exam, including review materials.  Then, I had to finalize and print the line-ups for the home swim meet.  As swim team statistician,  I enter the swimmers into the twenty-two events for the meet, run the computer at the meet and generate reports for the coaches.

I leave school around 2:40 and arrive at the pool shortly before 3 o'clock.  We are missing some students who normally record times at the scorers table and I recruit some swim alumni for the task.  After making many changes in the line-up for the away team, I print off the meet line up and the meet starts.  I realize that the computer is no longer communicating with the timing panel.  I try some fixes with the computer and the cable, but to no avail.  All times must be entered by hand into the computer.  This also means there are no split times.  The meet ends around 6 PM and I let the coach know that I will come in during break to work on the panel to try to figure out what went wrong.  (Note: I went in today, December 27th and after about 30 minutes realized that a pin in the cable was bent.  Using a paperclip to bend it back, it seems to be working for now.)

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 am most proud about recognizing the alternative statistic presented for the German Tank problem.  I am very excited to show the class that the "RedfernFerrari" statistic is comparable to the one created by statisticians during World War II.

The decision that was not ideal was rushing through the paradox of the two telephone poles problem in geometry.  If I only had 40 minutes in the future for this lesson, I might not have students create individual lists of "Notice and Wonder".  However, this would only save me about 3 minutes of class time.  A better option would be to do this lesson during a 65 minute class on a lab day.

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 on a general high relative to teaching this school year.   Even though this is my twenty-fourth year of teaching, I have been trying more new teaching strategies and most are working well.  I have been asking more open-ended questions, like "In what ways is this like or different than what we just did?"  And even if I ask a question with a single right answer, I am working on following that with a "Can you describe your thinking?" or "How can you be sure your answer is reasonable?"

A low happened on December 9th when our Guatemalan exchange student returned to Guatemala.  It was sad to see her go.  We had so much fun - visiting New York City, going to ice hockey games, carving pumpkins and having a mini snowball fight.  My whole family misses María Inés.

On December 16th, I was looking forward to break.  But now I am feeling re-energized and I am looking forward to returning to school.  We have two weeks of classes and then a week of midterm exams.  With swimming thrown in there and some other professional growth opportunities (more in future posts), I know the next few months will fly by.

The biggest challenge lately is a lack of substitute teachers.  This often leads to full-time teachers filling in during their planning periods without any compensation in terms of time or money.  Teachers at my school fill in because they want to help their colleagues and do what is best for students.  The absent teacher is always grateful to the teacher who filled in.  However, there is an underlying sense that the administration is not grateful, or at the very least, does not express that gratitude outwardly.  In an ideal world, we would increase the substitute teacher pool and be more aware of time as a valuable commodity.

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.

On December 18th, I had the opportunity to see the Santaland Diaries with some of coworkers from school.  The theater teacher was the sole performer in the show.  The show was very funny with a few poignant moments.  However, the best part of the day was having time to talk to the college counselor on the car ride to and from the show.

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? 

My goal is to finally get around to reading the book that I am referencing for a talk in April.  The book is called "Promoting Purposeful Discourse" and I know once I start reading it, I will be hooked.  It the starting part that is getting to me.

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

It was announced in November that our current director (in public schools, that would be a principal) is not returning for the fall of 2017.  We were in this same situation as a school three years earlier and at that time I briefly thought about applying for the position, but did not for a variety of reasons.  After many hours of thinking and having discussions with trusted colleagues, I have decided to apply for the position.  

At the opening chapel of school this year, I gave a birthday wish for the school.  I stated, "In our 275^th birthday year, I offer the following wish for our school, our community, our students and my colleagues.  No, no, no. Don’t stick to the status quo.  Be true to who you really are.  Thoughtfully, not impulsively, let us stretch out of our comfort zones and reach beyond our status quo."   As I apply for this position, I will be stretching out of my comfort zone and even if I don't get the position, I will have learned more about myself as an educator and leader.