## Wednesday, December 28, 2016

### 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 275th 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.

## Monday, November 21, 2016

### Running on the Hamster Wheel (#DITLife Post 6)

Around this time of year I feel like this...

Except this little hamster is at least taking a few seconds to breath on occasion.  My goal was to post on October 25th, but that date came and went.  Two weeks ago I was getting by teaching on a day-to-day basis.  I knew my content and how I wanted to teach it, but this was what my lesson plan book looked like for that week - at the end of the week!

Now it is November 21st and I have had enough.  I actually need to stop for a moment and reflect.

 Today was Grandparents' Day at school and I had my lessons planned for interactivity between grandparents and their grandkids.  I arrive at school ready to tackle the day when I see a note on my desk to myself.  (Notes like this one litter my desk throughout the year.) Julia took the test on Friday.  "Oh no!" (Actually, I said something other than "no".) I was to write a Probability & Statistics test over the weekend so that Anya could take it early.  E period was at 2:00.  Surely, I would have time to write a test by then.  Let me check my schedule...
8:00 - 8:40 Period A Prob/Stats

8:45 - 9:25 Period C PreCalculus

9:35 - 10:45 Chapel
Perhaps 10 minutes to work on it?? No, I need to check on a colleague to make sure he is set to do Desmos Marbleslides after chapel. And I need to get to chapel early to be sure I am seated near the front.  I am leading a responsive reading in chapel.

10:50 - 11:25 Period B
Super!  I don't teach period B.  But wait, I need to pick up my daughter at the orthodontist.  She is getting her braces off today.

11:30 - 12:05 Period F Geometry Honors
12:05 - 12: 40 Lunch
12:40 - 1:15 Period F Geometry Honors

1:20 - 1:55 Period D PreCalculus

2:00 - 2:35 Period E - Anya's taking the test!
Looks like I need to get this done in the next 15 minutes or get a box lunch and finish it over lunch.

I use the online teacher resources for The Practice of Statistics (5th edition) to quickly cull questions for a test - eight multiple choice, one free response from an old AP Stat exam and two other short answer questions that look good.  Normally, I would take two or three days to put the test together, create an answer key under timed conditions, revise the test and then copy it for my students. (If it takes me 8-10 minutes to complete, students should be able to take the test in 40 minutes or less.)  Rather than copying and pasting into a word document, I use the "old school" method - scotch tape and scissors.  Working between class periods, the test is ready around 1:15.

While Anya takes the test, I create the answer key for the test and then create a homework answer key.  I scan this as a pdf and then email it to my stat students with a reminder to show up at 7:50 for the test. (Classes are 30 minutes tomorrow due to a half-day of school.  Rather than waiting until the Tuesday after Thanksgiving Break to take the test, my students voted to come into school 10 minutes early to take the test before Thanksgiving.)

At 2:40, I quickly scan some emails and comment on a google doc about potential changes to the bell schedule for next year.  After about 10 minutes, I decide that I have had enough for today.  I grab my coat and music folder for my walk over to Snyder House.  There I get to be a part of 100 students, singing songs to prepare for the Vespers service in a few weeks.  When I leave the room around 3:20, one of the college counselors sees me and asks if I was singing with chorale.  When I respond affirmatively, she says something like, "Good for you.  Taking time to care for the soul."  That is also what this blog is doing for me right now.  I am getting off the hamster wheel for at least an hour or so.

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?

The move I am proud of happened in Geometry Honors.  We had a triangle drawn with two sides being trisected.  This created three parallel segments.  One student asked if the longest segment was three times the shortest segment.  Rather than saying "Yes" or "No" outright, I called this idea "Angelica's conjecture".  We looked at several numerical examples to see if it was true and eventually saw that algebraically the conjecture would always be true.  I need to remember to pull this example back out when we begin to talk about similar triangles.

The move that wasn't ideal was creating the test at the last minute rather than spending more time thoughtfully planning it. In addition, the student only had 35 minutes for the test due to shortened class periods.  It may not seem like 5 minutes is a large difference, but it is 12.5% of class time.  When she handed in the test, I asked if she could stick around for 5 more minutes, but she said that she couldn't because of something going on in her next class.  ***

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?

A recent high was parent teacher conferences. They happened about 2 weeks ago. All the parents were receptive to suggestions to help their child improve. The challenge will be finding the time to get lessons ready and grading done over the next few weeks. After the parent teacher conferences, I noted 11 different meeting times I had set with students each week. Each of those meetings will be 30-40 minutes long. Another challenge will be finding the time to visit colleagues as part of the peer observation #observeme challenge. I have observed four peers this year, but my goal is to observe eighteen before the school year ends.

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.

I have been having more relational moments with colleagues this year.  It has been a rough time for many people around me at school for a variety of reasons.  I like to solve problems and want to help, but I don't have the experience or answers needed to take on many of my colleagues' personal challenges.  My only tools are perception, empathy and being a sounding board.

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 has been to read a book on questioning skills and then apply what I learn to my classroom.  I was to read most of the book before the end of November.  I have not opened the book yet.  Perhaps I will have time to read a chapter or two over Thanksgiving break.

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

One of my most fun moments in the past month happened on Saturday night.  We have a Guatemalan exchange student staying with us for about 8 weeks.  She had never seen snow before.  We got just enough snow on Saturday night to stick to the window and hood of my husband's car.  My daughter, Cassie, and I took María Inés outside to show her the snow.  As she grabbed some snow with her bare hands, her excitement and joy was fun to watch. We ended up having an impromptu snowball fight and Cassie recorded us as we squealed and laughed between pelts of snow.

*** Postscript: December 7th - I allowed the student to do a retest after reviewing the questions with me.  She admitted that she rushed through the last few problems and after we had a discussion about the questions she missed, I wanted her to have a chance to prove herself again.  There is one other student in the class that I am giving this same opportunity to.  Doing re-tests is not something I do with everyone or something that I do often.

Allowing students to do retests for all tests would mean an additional hour per test re-written, 2 hours for grading, 1 day of missed class time (or spending time before school, after school or during planning periods to proctor the tests).  That equates to at least 3 hours per test x 4 classes x 12 tests per year or 144 hours of additional work.  The equivalent of extending my school year by 3.5 weeks. (Assuming a workweek is 40 hours/week.)  In life you can re-take tests as much as you want.  You can take your driver's exam as much as you want, but you pay each time.  There is a monetary incentive to passing your exam on the first try.  Offering retakes for every test all the time would mean that there would be no incentive for students to do their best the first time.

(I know what I have stated goes contrary to Standards-Based Grading.  I would love to hear how some teachers manage the paperwork and minimize the "I don't have to try on the first test" attitude.)

## Saturday, October 1, 2016

### Damage Control: The Day After a Sub (#DITLIfe Post 5)

Although I was officially supposed to post on Sunday, September 25th, I thought it made much more sense to talk about a school day than a day off from school.  This post will be about Monday, September 26th, or as I like to call the day after being out, "Damage Control Day".  Experience has taught me that sometimes only a portion of what is listed is done.  Creating plans based on the assumption that the sub would know math is usually not a good idea.

I arrive at school at 7:30 and quickly review the notes left by my sub.  Damage control averted!  My sub was a retired math teacher from my school and she wrote notes for me like "Great class!" and "Wonderful group of young people!" and "I am fascinated by this blue pen that writes in pink ink!!"  Everything was done according to the plans I had left.

Next I make copies for my first period class and copies of a test for later in the day.  I also quickly check my school email.

A Period - Probability and Statistics (40 minutes)
This class consists of ten seniors and we are beginning a unit on data analysis.  We already completed a unit on how to gather data from observational studies, surveys and experiments.  We create a dotplot for sleep times of my students in my Geometry Honors class.  (One of the survey questions I ask my students on the first day of school is "How many hours of sleep did you get last night?")
Here is a dotplot from Fathom for all of my students.  Whenever possible, I use data gathered from my students or data in the news that is relevant to my students.

We also watch an Against All Odds Insides Statistics video on displaying quantitative data with stemplots.

As the class ends, one student asks me for a letter of recommendation. This is my 5th such request.  I give students this list of questions to students to answer prior to writing their letter.  I have done this several times now and it works well.  The idea is not my own, but based on the recommendation of an AP Statistics teacher I know. (I am a part of an email group of 30+ other Statistics teachers, but I can't recall who I stole this idea from. Carl, perhaps??)

B Period - Planning Period (40 minutes)
I spend the next 40 minutes organizing papers, emailing a student, trying to fix the grades that are entered in my online gradebook.  I also have a few minutes to speak to a colleague about presentations we are giving at the PAIS biennial conference in two weeks.
·
C Period - PreCalculus (40 minutes)
Today is the first test of the year in PreCalculus.  There are 4 sections of PreCalc and we have created 4 versions of the test.  As I write my answer key as the students take the test, I notice that there is an error on one of the 4 versions of the test!  The problem can still be solved, but it isn't a comparable question in terms of difficulty.  Ugh!  Even working together with a colleague on the test over a period of two days, we didn't catch this glitch.

Assembly Period (40 minutes)
Every Monday we have an assembly period where students, teachers or outside faculty give presentations.  The speaker today is Mr. Eckman, a history teacher.  Last year he and his family lived in Argentina, where his wife did research related to a book she is writing.  His talk is informative and entertaining.

F period (70 minutes) (Our class periods are never in alphabetical order. Long story.)
Today is the lab period day for this class.  That means we have 35 minutes of class and then lunch for 35 minutes and then another 35 minutes of class.  Usually we have a quiz on Monday in this class, but we are preparing for a test that will be given on Wednesday.  This will be the first test for the Honors Geometry students and their first work with proofs on a test.  Before we go to lunch we work on a proof that has two main methods of solution - a shorter way using more recently learned theorems and a longer way with a more algebraic approach.

I tell students that either approach is acceptable and give the analogy of driving from home to school.  They can get to school multiple ways - a more efficient way or a scenic way.  Right now, I just care that they take an appropriate route to get to their final destination - what we want to prove.  Eventually, they will find the more efficient routes when writing solutions to proofs.

When we return from lunch, we work on an activity to help students realize that they can't assume certain things are true when they are given a diagram.  Students work individually and then in groups to make a list of what they notice (know is true) and wonder (think may be true) about the diagram I have on the board.  We then gather the ideas and make a class list of what has been noticed and wondered.  Here, you can the initial diagram.  We are only given that lines AB and BE are perpendicular.

This second diagram shows our class list.  You will notice that some things are circled in red in the "Wonder" list and arrows are drawn to the "Notice" list. These are the items that we decided could be moved to the "Notice" list after I told them that BD was perpendicular to BF and angle 2 was congruent to angle 3.  One of the things I really like about this activity is that all students can create the initial lists.  Plus this activity helps me to figure out which students are likely to make assumptions and jump to conclusions without supporting evidence.

D Period - PreCalculus (40 minutes)
This is my other class of test-takers today.  While they take the test, I organize some papers on my desk and then walk around answering questions.  Most students are fine, but a few ask questions out of a need for reassurance that they are doing things right.  When one of those students asks me a question, I usually say something like, "It's always a good idea to go back and check your work", or "If you are stuck, skip it and move on".

E Period - Planning Period (40 minutes)
During this time, I work with PreCalc teacher to discuss a project we are going to give in PreCalculus.  Then, I begin to grade a homework set for Prob/Stat over google docs.  I also check my email, deleting old ones to get my inbox down to under 30 active emails!!

G Period - Planning Period (40 minutes)
I enter grades for two classes for a report that is due tomorrow at 9 AM. I begin to grade the PreCalculus tests, because I want to include that grade in their reports.  At the end of the period, the other Geometry teacher comes to my classroom.  I forgot to go meet with her during the second half of the period.  We have a test we are giving in 2 days!!

Later that evening, I work for 2.5 hours on grading and finishing the grade reports that are due the next day.

(Note: The rest of my week was extremely busy and today - Saturday - is the first opportunity I have had to reflect and finish this blog post.)

And now for the 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?

The decision I was most proud of today was using the Notice/Wonder activity as a way to think about assumptions and proving ideas to be true.  Time will tell if this will help them on the upcoming test. The teacher decision that was not ideal was forgetting to meet with my colleague.  I should have worked on the test over the weekend, but I had spent the time at the Jersey shore with my family in celebration of my mother's 70th birthday.

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?

I am looking forward to developing my presentation on questioning and discourse for my presentation at the NCTM conference in April.  This week I was able to get a hotel for \$179/night.  That's very reasonable for 4 teachers sharing the same hotel room for 3 nights!

My challenge lately is that there are a few students in my PreCalculus class that don't seem to be getting some concepts.  I need to spend time to work with them individually outside of class. (I looked at my notebook for student help on Friday and I have had 29 individual meetings with students so far this school year.  Those have ranged from 10 minutes in length to 40 minutes.)

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.

Students are willing to put more effort into their work, if you show you care about them.  Prior to working with one of my students recently, I asked him which colleges he would be visiting in the south and what he was planning on studying.  He also told me he was excited about seeing some relatives he had not seen in a long time.

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 had my goal meeting on Friday.  Every faculty member is to write two goals - one related to curriculum/teaching and one related to technology.  Here are my goals: 1) Work on improving questioning strategies to encourage more classroom discourse and higher-order thinking.  2) Help other colleagues to develop technology skills, specifically Plickers.

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

I gave back tests to my Geometry Honors students on Friday (September 30).  Often the first test grade is lower than what these students typically get.  One such student sent me an email on Friday evening.  He said that he was disappointed in how he did and that he expects more from himself.  He asked if I could help him understand the material better so he doesn't get another grade like the first one.  This is the type of request I would like to see from all of my students when they don't quite get something.  Of course the grade on a test matters.  But if it was only the grade that mattered to this student, he would have asked, "Is there any way I can do some extra credit to bring my grade up?"

## Friday, September 9, 2016

### The Longest Day Ever (#DITLife Post 4)

The Longest Day Ever for a teacher is most likely "Back-to-School Night" or "Open House".  It is the day where parents follow their son's or daughter's schedule to meet the teachers.  It is also a time where teachers probably talk more than they should, modeling one of the worst ways to teach.  I did not talk to the parents about grading and homework policy and classroom minutiae.  To see what I did, skip to the end of my blog post at the End Detour Sign or read on about my school day.

 The Morning: My day began at 7:30 with a meeting with a student who had missed class the previous day due to being released early for a golf match.  Then, I quickly made some copies of quizzes that I would be giving later that day and the next day. First period began at 8:00. (Or it would have under normal circumstances.) But today is far from a normal day, because not only is it "Back-to-School" night, it is Picture Day!!  This means math classes are interrupted by 10 minutes so students can get their school picture taken.  When my Probability and Statistics students return, they take a quiz on sampling methods and then they work in groups to discuss short news clips related to observational studies and experimental design.  In years past, we have had a whole class discussion that I led.  This year, I had students discuss the articles in small groups and let them lead the discussions.

I hoped to get the quizzes I just gave graded during my Period B class, but I had some emails to attend to, plus a student dropped in to review for a quiz.  In addition, I made copies for a meeting I was to have later that day with the Headmaster, spoke to our academic dean about a student and grabbed some coffee. Caffeine 1, Grading 0

(Note: As I am writing now, I am realizing English teachers would be cringing and for now, I am declaring consistency in verb tense to be optional.  Remember, it is "The Longest Day Ever".)

During period C, we make some discoveries about the discriminant as it relates to roots of a parabola.  This is based off a desmos activity builder lesson written by Shelley C called "Discriminants of Quadratics and Cubics".  Due to the choppy nature of class today ("It's picture day.  Say Cheese!"), I end up leading too much and not asking the necessary questions for students to discover what they are to discover.  Class ends with all of the students successfully completing a summary chart, but I vow to do better the next time with period D.

Lunchtime and The Afternoon:
Now it is period D.  Today this class is 35 minutes followed by lunch and then another 35 minutes of class.  During the first 35 minutes, there is a quiz.  Some students finish in 15 minutes and others finish in 30 minutes.  When we return from lunch, we work through the desmos discriminant activity.  Vowing to do better than I did in C period, I use the thumbnail and overlay features better.  As students do the first slide, I say things like "I can see Emilie has a negative discriminant.  Does anyone else have a negative discriminant? What quadrants is Emilie's graph in?  Does the graph need to be in those quadrants to have a negative discriminant?"

By the end of this class, all students have successfully completed the summary chart and they have also successfully submitted answers to the following slides. (Note: I don't have these mathematicians as students, but desmos has a feature of changing student names to "Incognito" names.  It's pretty cool that these are names of mathematicians.)

Now it is period G, a.k.a. the fifth class of the day on a Thursday.  During this time I almost get both sets of quizzes graded.  However, I also meet briefly with Lia (a teacher who teaches Geometry Honors) and Marilyn (a teacher who teaches PreCalculus.)  Lia shares a unique way her students solved on of the homework problems.  Marilyn and I discuss how the desmos activity went and I shared with her how I modified the activity the second time I did it.

Finally, it is my last class of the day, Geometry Honors.  We are starting to develop a culture of trust as students share their answers.  As we review the one question, I use Lia's idea as an alternative solution after two other solutions are shared.  I tell students that even though I have taught this course for over 10 years at Moravian Academy students continue to surprise me with new ways to solve or approach problems.  I want them to surprise me and share their ideas!!!

It is now 2 PM and I have a meeting with our new Headmaster.  When I arrive, he is meeting with a colleague and I wait until 2:15 PM.  We share ideas on several topics and I leave the meeting feeling like my ideas have been heard, understood and valued.  However, I also leave feeling exhausted at the thought of returning to school for the evening.  I finally pull out of the parking lot at 3:15 PM.

The Evening:
 After eating dinner at home, I head back into school at 6:30. I meet with four different groups of parents for 10 minutes each.  I did not talk to the parents about grading and homework policies and classroom minutiae. Parents had received that information on a handout that they signed at the beginning of the school year. Instead I wanted to see parent perspectives on mathematics learning and I wanted to share my views on mathematics learning. I displayed a statement on the Smartboard and the parents would use plickers to share their responses.  I scanned their plicker cards with an app on my phone and then we looked at a summary of the results.

For example, we looked at the question shown below.  After parents shared their answers, I told them that I did not agree with this statement.  All students are capable of learning math and some find some topics to be easier for them than others.  It was interesting that the parent responses were split almost equally between Agree, Disagree and Neutral. (Note: The Woordle comes from words my students put in a google form on the first day of class.  These words were what they used to describe math for themselves personally.  Challenging is the biggest word, because the students used that word the most.)

As parents left, I encouraged them to take the handout on "Glory in the Struggle".  (Excerpts and synopsis by Audrey Weeks from an article by Suzanne Sutton in “Bulletin” (Feb. 1997) – a periodical for the National Association of Secondary School Principals) Once students start doing courses near the end of their high school career, they can struggle even if they haven't struggled before.  We need to recognize that struggle isn't bad, but a part of learning something that is new and challenging.  There is value in learning something that takes time and this handout is designed to give parents ideas about how to support their child as they learn and sometimes struggle.

Finally, the longest day is over and I go home at 9 PM after finishing the grade entry of the quizzes.

#DITLife Blog 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?

On this particular day, I was proud of making the decision to approach the delivery of the desmos lesson differently and it worked better!  One decision that was not ideal was not taking enough time to get a student to communicate her answer to a Geometry problem.  I thought she was on the right track and asked for clarification once.  I still wasn't quite sure what she was saying.  As is often the case, I say something like "You seem to have the right idea."  But then, I don't work to get the student to fully communicate his or her idea.  This kind of interaction takes time and practice.  I can practice more, but the time crunch (40 minute classes) will always be a challenge.

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?

This year has begun with cautious hope and optimism due to some system-wide changes.  Students and faculty are saying "Thank you" and showing appreciation for each other.  I am especially looking forward to our math competition, Math Madness.  Students love trying to beat their previous best and beat whatever school we are going against. (If you aren't familiar with Math Madness, it is an online competition and students who enjoy challenges like the AMC contests will enjoy Math Madness.)  Right now my biggest challenge is balancing time and getting enough sleep! As I write this, I am so glad it is Friday.

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.Building relationships takes time.  Recently I was speaking with our theater director about the upcoming play for the spring, Arcadia.  As he spoke it was clear that the play was very rich and meaningful to him.  I can’t wait to see it to support him and our students. 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 is to be better at asking questions and teasing out answers from students.  Specifically, I would like to incorporate some of the ideas from a chapter from the NCTM publication "Promoting Purposeful Discourse". The article I have not had time to read just yet is called "Revoicing: The Good, the Bad and the Questions" by Jean Krusi from Ames Middle School in Ames, Iowa.  I'll be posting more on this in future blogs. 5) What else happened this month that you would like to share? I posted the following sign for the #observeme challenge and sent the following email to my colleagues.

Many of us agree that we enjoy learning from our colleagues when we see them teach.  We also like it when colleagues visit our classes and give us informal feedback.  This type of collaboration doesn't happen nearly enough.  My status quo has been to stay in my room, getting papers graded and lessons planned.  I don't visit many classrooms and I don't have many visitors.   This year I am going to (in the words of what I said today at "Chassembly") say "No, No, No to the Status Quo".  This year I am formally extending an open invitation to all of you to visit my classroom.  I hope some of you will welcome me into yours.

Should you come to visit, attached is the welcome sign you will see hanging on my door.  I teach Probability/Statistics Period A, PreCalculus Periods C and D and Geometry Honors Period F.

Today is day 8 of school and there have been 22 teachers who have responded to the email with open door invitations to their own classrooms.  I have also had two faculty visit me and I have visited one faculty member.  Time will be the biggest challenge to seeing all 22 teachers who have sent me invitations.