A fantastic end to teacher appreciation week!

So last night I gave homework, like I sometimes do.  But I flat-out told one of the sections – “I’m not going to put a grade in the gradebook.  So as far as the grade goes, there will be no difference whether or not you do it.  If you do, turn it in tomorrow and I just want to see where we need to spend more time, and where we can move a little faster.”**

To be honest, I wasn’t expecting much.  A solid amount of the students I have is (are?  Am I talking about the students (are) or the group (is)?) taking geometry for the second time.  Not by choice.  Across the board, I can usually count about about a third of my students doing any given assignment on time.

But my smallest class (only 13 students) was the section to which I revealed my secret.  TEN OUT THE THIRTEEN students! And! Yesterday, two people were absent.  So out of the eleven people who knew I gave an option assignment, actually did it.  And we had a really good class about it.

And it was on proving characteristics of quadrilaterals using coordinates of the vertices.  Usually not a topic for which I have a great response.  Fluke?  Or is optional homework really a good route to take?

#MTBoS, what do you think?

**These may not have been my exact words.  It was about 29 hours ago, I may have lost some detail.  But you get the idea…

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May the fourth be with you…always

From a student today:

“I’d like to thank you for being a awesome educator, advisor, and comedian. At first I thought Geometry was just going to be some boring class where I would just sleep all period. But you changed my perspective now I find geometry to be quite the fun and education class.  Also, no matter how the class acts you still treat us respectfully. Another thing is that you can break down the most difficult lessons into something a 3rd grader could understand.  So I want to say thank you.

Sincerely, __________”**

All the above was written to me.  I’m sure it was part of another class assignment or something, but he still had to choose me out of his seven teachers.  And I got three of them!

Not very mathy today, but I was super-glad to see it and wanted to share.


If you have been, thanks for reading!

**Typed as written.  All spelling, grammar, and punctuation was typed as the student wrote it.

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7000% tip! Or is it?

Otherwise I wouldn’t have anything to write about!  A slow day as far as math teaching goes.  PARCC testing all morning, a shortened schedule due to a pep rally in the afternoon, and covering for a teacher who had pep rally stuff to do came together in the perfect storm of: the only class I saw outside of the standardized testing room I was in was a tenth grade honors English class.  Made for a pretty uneventful day in regards to my own classroom action.

I probably should have been more on my toes about doing mathy things with battle of the classes at the pep rally, but I was more concerned with watching the festivities.  Anyway, on my way home (shh, I took the screenshots in the car) I saw a headline with a number in it.  THREE THOUSAND DOLLAR TIP!

6800 percent

6800 percent

When I got into the parking lot I was curious, “Is  this a normal tip at a crazy expensive restaurant, or did the patron do something really nice?”

Then I saw 6800%.  Holy crap.  If my server is good, I may sport for 25%, maybe 30?  Wow.  Anyway, then the “related headlines” section came up and I saw this:

7000 percent

7000 percent

Did a DIFFERENT person leave a huge tip?  Nope.  Same person.  So which reporter has the better pre-algebra percent skillz?  Stefanie Tuder or Sammy Nickalis?  It’s difficult to see through the “play” icon, but the bill was $43.50 and the tip was $3,000.

This is going to lead to one of my favorite discussions with my class…turns out that the tip was actually almost right in the middle.  6,896.55…%  Here’s the discussion topic:

When is it OK to round our answers?  How far is it appropriate to round?

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4 + 2 + 9 = 2^0 * 15.  

Holy moly.  A lot has changed since last time I posted (last June).  I was super excited because I was within a month of marrying the most amazing woman in the world.  We lived in Pennsylvania.  She was ending a long-term substitute position and I was excited to start the next school year with the same school that I was with.

We’re married.  We got the news that I was not returning to the school where I was located (a hard piece of news to hear at the time, but in hindsight it was great).  We packed up and moved about 200 miles south to southern Maryland and we both got contracts to teach in the same county.  We live with our cat and we both have a commute that is shorter than 15 minutes in duration.  Yes, a lot has changed.  And yes, a lot has improved.  Anyway, to the math!

For a long time now, math has interested me.  Abstract thought was the thing to which I could always turn to relax me.  Even in times of complete frustration with whatever it is I am thinking about, I knew at the end of it all, progress didn’t matter.  I was exercising my mind, and it made me happy.  I stand up and talk to my students about the benefits of being passionate about something, and for the past few years I thought that my passion for math was a facade.  It was something that I was supposed to have as a math teacher; how can I teach my students about math if I’m not passionate about it?  So we roll camera starting at 7:30 and cut at 2:15, my acting day is done.  But it wasn’t an act!  I don’t know if I am such a good actor that I became the character I was playing, or if I just never had the stage on which to show my true colors.  Even though the cameras stop rolling* when the school day is done, I find myself talking to myself, my wife, my parents, my sister, my friends…anyone who will listen, and sometimes even those who don’t listen, about math.  The cast of characters in the long and rich history; intriguing problems that I can’t figure out (which is, unfortunately, a large set.  But it keeps me busy; I’m never bored).  How to teach math, how NOT to teach math, how to learn math, how not to learn math. You name it, I’ve had discussions about it. I think my cat even has some opinions on it by this point in time.  But anyway, I am trying once again to start writing about my passion.  But now more than ever, I realize it is my passion.  I’m not just blogging about math because it’s what a math teacher in 2015 is supposed to do.  I’m doing it because the person I am, who also happens to be a math teacher, is truly interested in sharing knowledge, in learning something, it hearing critiques, in finding out what works for some people and what doesn’t.

So, ladies and gentlemen of the blogosphere, today’s the day.  @MisterATHomas has a twitter and a blog and will try to increase his presence and his passion, one post at a time.

If you have been, thanks for reading!

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June Bugs

The punchline to an old (I think) joke…”If April flowers bring May flowers, what do May flowers bring?”  To the people who answer, “pilgrims!” and smile smugly at you — say, “no! June Bugs!”

But really this June, nothing is bugging me.  Quite the contrary, actually. On a good, very good, amazing, wonderful, etc…note, I can now start counting the days until our wedding by simple subtraction as long as I know the date.  June 28 – June 1 = 27 days until the wedding.

Previously, I had to make an equation (which I would actually do) by setting up variables for each month.  There were S, M, L for short months (28 days: February), medium months (30 days hath April, September, June, and November), and L for long months (31 days).  My equation would look something like 28S + 30M + 31L + 28 = Days until wedding.  In 4-dimensional space with S, M, L, and Days axes, my Days-Intercept would be 28.  Now instead of racking my brain to picture 4 dimensional space with some sort of curve whose shape models the timeline of my life, I can simply think back to elementary school when I learned the number line.  28 – today’s date?  Sweet.  I can handle that.

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It’s been a while. I’ve been thinking…

After a PD about VAAS – Value-Added Assessment Systems – after the school day today, I was thinking a lot about adding value to things.  Not necessarily mathematical value; just value in general.

Now, as I’m sitting here planning a way to attempt a mass success for my upcoming midterm test, I am having a bit of trouble deciding what kind of value I want to add to my students.

I could throw little tidbits at them.  FOIL!  Factor using an ‘X’ to do ‘diamond problems!’ ‘PEMDAS!’  But then, as soon as there is a trinomial multiplied by a binomial, what do I do?  (First, Middle, Last?  FML?)  “Yes, you HAVE seen it before.  It’s just a distributive property problem.”

I could try to teach them the distributive property well.  Then it gets dry for the kids who get it because there is surely going to be a group that is lagging behind and uninterested (or worse yet, disinterested because I keep introducing “new rules.”)  I would love love LOVE everyone to appreciate math as much as me and want to understand its fundamentals and play and experiment and explore.  But alas, by the time they get to me in 9th (or higher) grade, generally an attitude towards math is already fairly solidly formed one way or another.  Am I wrong?  Am I just not doing something right?

If I’m speaking to the highest percentage of the audience, I guess the answer is to use mnemonics.  Use little memory devices that trivialize deeper meaning and will do enough to have a student pass a test.  If I’m speaking to my morals and everything that I know is right, I guess the answer is to teach the subject, “Failures be damned!”  I know there are always these quotes and these people that say things about doing what you know is right and the outcome will always be better than it would have been otherwise.  In this environment though, if I teach to those who care about it and  teach the subject deeply, I can almost hear the administration’s response to, “Yes I know only 5 of the 30 people I have passed.  But holy crap, they REALLY passed!”  and it, in my head, sounds something like this:  “Enjoy your summer.  Don’t come back in the fall.”

I think back to the original topic of this post.  It’s been long lost.  I don’t even really know where I’m going with this.  I know a goal of standards is so that everyone knows virtually the same material coming out of high school so it’s a “level playing field” of sorts.

If standards work, truly work, sure, there are people that may otherwise not have known how to factor a quadratic that will remember for a little bit longer how to factor a quadratic.  But at what cost?  Did Picasso know how to factor quadratics?  Who knows!  And that’s my point.  The world got along just peachy (peachily) before everyone knew what everyone else knew.  If a kid passes grade school, middle school, and high school, there have been (probably) more than 20 professionals that have said s/he has gotten enough out of the class to move on to the next grade.

People, after hearing from 20 professional doctors that your child is healthy, do you make your child then go to the state board of health and take one last physical, just to be sure?

After hearing from 20 professional financial advisors that you are going to be OK to retire, do you go to one last state-run agency to see for sure?

After seeing 20 dentists and hearing you don’t have a cavity, do you go to the state board of dentistry and have one last person check, just to be sure?

Ugh.  From “How do I get my kids to pass a midterm?” to “Hey Standardized Expectations – I hate you.”


PS – A bit ironic that the smarter-than-I-am people making the decisions about what is best for the education of our children grew up in an education system before standardized test were…the norm (get it?)  If these tests really produce the brightest “products” to graduate high school, then everyone should feel incredibly confident with the future of the country — one run by our standardized products.  My guess?  When the kids now are in power enough to change a whole paradigm of education, they will.  “No more standardized tests.  We had to go through it for our whole academic careers; no way in HELL we’re making our kids go through that.”


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Gee, I’m a Tree!

So, good news!  And it’s two-fold.  Or several fold?  Or just crumpled up in a little ball…

First, it’s August!  My birth month.  Not really unexpected good news, I have come to be pretty good at predicting when this good news will arrive from year to year.

Second, I found out that I will be teaching two sections of Algebra and one section of Honors Geometry.  Yay, yay, and yay!  Though I am admittedly a little nervous about being the only Algebra teacher.  Why?  Well, it’s nothing major.  The set of Algebra Keystone scores is a big focus to a lot of people (internally and externally).  Not that this is a big deal, I’m very confident in what I can do.  I just know that when my learners, at least the ones who have Algebra this coming semester, take the Algebra Keystones, I will feel somewhat (totally?) responsible for the outcome.  I know this is not totally the case — they’ve had years of math before me that led to who knows what, but it’s still something that I think about.  Part of me is very nervous for this, and another part of me is super excited because if the scores improve, I also like to believe I can take at least some of the credit.

Third!  (is that really like saying sixth? [because 3! = 6] ) One of the things that will make it significantly easier for me to teach is (get this!) I  won’t be travelling among classrooms.  That’s fantastic! Though, I was looking forward to presenting the “travelling facilitator” problem to my learners.  At this point I’m pretty sure, but not 100% sure, which room will be mine, but that’s just a small detail that will work itself out.  I can’t wait!  We’ll see if my excitement holds up but I’m pretty confident.  

PS – maybe I should ask to teach statistics?  I’m throwing in words like significant and confident.  The parameters of the school year are August 12 until June 20.  There we go again!  

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So I was just watching a show on the Panama Canal…it said that a staggering 14,000 ships go through the canal each year.  I started thinking about the numbers a little bit and knew that meant between 35 and 40 per day, on average.  


Then it was talking about a ship, the Zim New York, that could navigate the trickiest part of the canal in only 3 hours…

THEN…it said that this tricky part was only wide enough for 1 ship to fit through at a time – so one ship going from Caribbean to Pacific meant that no ship could go through it from Pacific to Caribbean simultaneously.  

I was wondering if that meant there are certain days on which only east-to-west travel is allowed, and some days on which west-to-east travel is allowed.  Is there a long caravan of Fishyback container ships travelling in one direction, or is it like yielding over a one-way bridge?  

OR were they only talking about the enormous ships that make up the Panamac class to which the Zim New York belongs?  I have more pressing things to do, but my curiosity is getting the better of me.  (Watch out, River! [she’s my cat])

If you have been, thanks for reading!

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A new month already?  July-in to me?!  Nope.  Couple of things I’ve been thinking about this morning/early afternoon:

1: 6 months are done, 6 months to go.  That should mean the halfway point of 2013?  31 + 28 + 31 + 30 + 31 + 30 = 181.  Half of 365 is 182.5.  So today’s the 181st day. Tomorrow’s the 182nd. Wednesday, the 3rd, at noon – we are halfway done with the year.  July 4th I will set off fireworks not (only) in celebration of Independence Day, but the beginning of the second half of the year.  This also just got me thinking — is there exactly half a year between equinoxes?  Solstices?  Is this a proof that the orbit around the sun is an ellipse and not a circle?  

2: I’m charged (sort of) with making the school more “mathy.” Simple things — factoring the date, making little equations, math vocabulary. 

     2a: Should I make equations out of the dates ahead of time so I know one will work, or make them up on the fly because I like a challenge?

     2b: Any other ideas how to “math up” the school?


Thanks for your help!  And if you have been, thanks for reading. 

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Not a post about measuring things.  A post about the book Measurement by Paul Lockhart.  I love this page…it’s from page 15 of the edition I own.

  This is the kind of thing you have to do as a mathematician: try things. Will they work? Will they yield useful information? Usually not. But you can’t just sit there staring at some shapes or numbers.  Try anything and everything. As you do more math, your intuition and your instincts will sharpen, and your ideas will get better. How do you know which ideas to try? You don’t. You just have to guess. Experienced mathematicians have a great deal of sensitivity to structure, and so our guesses are more likely to be right, but we still have to guess. So guess.

I wish for this to be an idea that my (and all) students would have about maths.

“If you want to paint a picture from your heart, there is no ‘answer painting’ on the back of the canvas.”

I had a discussion with my mother the other day, and it went something like this:

Mother: How would you fix math in school?

Me: I don’t know.  But I think it’s reversed.  Kids learn the boring and mundane stuff like memorizing multiplication algorithms and how to do long division and do worksheets and worksheets during “math time” in elementary school.  They learn that all math is, is manually doing the work that a calculator can do; and when they realize this, they feel like they don’t need or don’t like math because it’s not a subject on its own. It’s useful for other things, they are told.  But who cares?  When the students get curious, they are told there’s more interesting parts of math, but they need a foundation first.  Learn the boring stuff now. Gain a hatred for math now. Think that math is all about doing arithmetic now.  The interesting stuff will come later, when the kids will all already discount it as something for nerds.  Then laugh and ask “when will I use this in real life?” Then laugh again as the teacher struggles.  There are a lot of ways to answer this question…I’ve gone with:

You won’t.  But you need to pass this class to get through high school.

(incidentally realized this was not the best option. Never used that more than once or twice.  That’s it Andrew, feed the hatred…)

Well it depends what you want to do.

Ok — leading to further questions and further digression.

You’re right, maybe you won’t. But when will you need to know the sonnets of Shakespeare or know the states and capitals?  You can look them up just as easily as you can use a calculator.

Fantastic.  Lets get into a war of school subjects….

Does it HAVE to be useful? Can’t math just be a subject for the sake of being a subject?  Interesting to learn?

My personal favorite there.  That’s what I generally stick to.  Maybe this isn’t the most interesting to the students, but it is the most personally satisfying to me.

Mother:  okay, so what can be done about that?

Me:  I don’t know.  Don’t hand kids multiplication tables to memorize.  Hand them pictures. Hand them basic word problems. Read to them and ask them questions.  Give them calculators.  If they keep pressing 6 times 4 long enough, they’ll realize that it’s 24 and memorize because it’s convenient for them, not because there’s a test on it on Tuesday.

Mother: How do you measure how well they’re doing?

Me: (again) I don’t know. Give a project. Ask questions. Assess on the quality of the work, not the quality of the answer. On the descriptions they give you. On how well they communicate their thoughts to you.

Mother: Would that really be a math teacher’s job?

Me: Maybe we need to rethink what a math teacher is.

**end discussion (which I now realize was more of a soliloquy.) 

So that’s it.  Sure, I made it a bit more formal for the sake of typing instead of just conversation while driving to get batteries for a loupe.  I don’t know if it was useful for me to think about or not, or if I just got frustrated because by the time the students are in high school, they have such a concrete attitude towards math that I have to spend my time convincing them it’s useful when in reality I just want to show them it’s interesting.  As the year comes to an end, maybe I’ll focus my energies on getting ready for next year.  Stop asking the “how much paint will she need to buy to cover this…” questions, and abstract it to “we have a rectangle.  What’s the area? You want to know why anyone would ever want to know this? Here’s a computer. Figure it out. Then write a paragraph telling me why or when area is useful.”

Ugh…frustrating, stressful, time-consuming?  Yes.

Thought-provoking? Absolutely. So I wouldn’t trade it for anything.


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