Hello, reader! If you intend to post a link to this blog on Twitter, be aware that for utterly mysterious reasons, Twitter thinks this blog is spam, and will prevent you from linking to it. Here's a workaround: change the .com in the address to .ca. I call it the "Maple Leaf Loophole." And thanks for sharing!

Friday, December 7, 2012

What's Annoying

You know what's annoying? To integrate a computer (or whatever) effectively, I most often need it for one thing in a class. I need like five minutes for kids to

 - go to polleverywhere and vote on something
 - go to a link and drag a red dot somewhere
 - take a photo of their work and send it to a dropbox
 - open Geogebra to construct something and mess with it a minute and make a conjecture

I would like this to actually take five minutes. We have other things to do, here. We have to argue about what they voted on. We have to look at everyone's red dots and talk about what information we need to figure out where it should go with some more precision. We have to project someone's proof and tear it apart.

But for those 5 minutes we need every student to do something on a device, it takes one or more of the following:
 - a coherent school-wide tech plan maximizing the chances everyone will have basically constant access to a functioning, charged device
 - signing out a mobile cart, tracking it down, and wheeling it to my room
 - websites we planned to use being up and running
 - all students bringing their school-assigned tablet and having it charged OR
 - students who don't, having a smart device on their person that plays nicely with whatever website or app
 - all students powering up and getting logged into their device with no unexpected "I can't login"s

So using the devices for something that I would like to take 5 minutes usually takes 15-20, with the associated distractions of attention and loss of momentum. It seems like with all the preparation in the world, I can't get these interludes to take less than 15 minutes, and I can't ever, hardly ever, get it so every single student can participate. And mind you, I am not a noob at this stuff. At the risk of sounding hubristic, I'm probably one of the more experienced classroom-tech-deploying teachers you are likely to meet. And everytime I'm like, "Oooh, we need a device for this part," I'm also like, "Crap. Is there any way I can avoid this?"

Friday, November 30, 2012

My Centroids Lesson Keeps Stalling Out Right Here

and I don't know how to fix it.

The kids and I literally stared at each other for ten minutes over this. I wanted to take them all outside and drown them in the pool. (I know it's not their fault, though, obviously.)

I don't have any other good way to come at this, though. Other options for asking relevant questions seem too ambiguous for this age group. Applications of triangle centroid are thin on the ground, or at least I haven't thought of any yet.


Thursday, November 8, 2012

Benefit from My Hours of Frustration


There are some questions below to go with it that don't suck. No further comment. I am so sick of this lesson.

Open the Geogebra File Triangle Inequalities.ggb. (Follow the link from Edmodo, or go directly to You can use the sliders to change the lengths of two of the sides. You can also change the position of two of the segment endpoints. Side AB will always measure 10. Use the sliders to generate four different sets of side lengths: two that can form a triangle (you will know for sure if it turns purple,) and two that can not form a triangle.
Can a triangle be formed?




1 Using the given lengths of AB and BC below, find the shortest possible integer length of AC, and the longest possible length of BC.

Shortest possible AC
Longest possible AC







Answer this question without using Geogebra. I have three pieces of wood. The pieces measure 4 cm, 9 cm, and 11 cm. My friend has three other pieces that measure 5 inches, 8 inches, and 2 inches. Will we each be able to create a triangle? Why or why not?

Monday, November 5, 2012


So, one of my Geometry sections has 1:1 tablets. We have a set of twenty we are piloting this year, and I believe the intention is to go school-wide next year. I got chosen for this because, you know, I have a reputation.

I had become accustomed to the capabilities and limitations of the classroom tech available at old school. We regularly used a set of Dell notebooks on a mobile cart, and the TI-Nspire Navigator system. So I was at expert ninja level with those tools. I could use them inside and out, I had smooth ways of getting kids proficient with them pretty quickly, I was well-versed in what I could expect kids to figure out vs what I had to demonstrate carefully and repeatedly, and I could use them to actually you know make instruction better than it would be without them.

Starting with new-to-me hardware (Acer Iconia Tablets) and software (Windows 8) has been a frustrating exercise in back-to-novice levels of crippling ignorance. It's back to the first days with the Nspires, where it's impossible to anticipate where the tech will say "no," and no lesson plan survives first contact with the students. The simplest thing, "Take a picture of one of the proofs you just wrote and email it to me." turns into twenty minutes of troubleshooting cameras that don't work, and picture files we can't find in order to attach them, and how to login to your school email account. Meanwhile, my favorite smartass has already sent me an email with the subject GREETINGS FROM DEH OTER SIDE O DEH ROOM, and has spent the intervening twenty minutes taking selfies and is starting to get disruptive because I haven't given her something else to do.

But, shoot, I guess we just all have more things to learn here, che? I have been very consciously modeling what I like to think are productive behaviors, for example Cheerful Curiosity in the face of unexpected technology hiccups and also Not Throwing Any Tablets Out the Window nor Any Children Either for That Matter.

Having one section with tablets and two without, though, are some nice built-in experimental and control groups, don't you think? We're starting triangle centers this week, in conjunction with which I normally teach compass and straight-edge constructions. So, I'm thinking the tablet section will learn the constructions Geogebra-only, and the other two sections will learn them compass-ruler-pencil-paper-only, and we will see what we get. It begs the question if I can possibly fairly assess them all the same way, and if not, can I really draw any conclusions from this little mini-experiment. And I know it's not a real experiment, it's just like preliminary poking at experimentation. But whatever. I make my own fun.

Monday, October 29, 2012

How Bad Is Your Line?

This is ripped right off from PCMI 2011 Day 11. But I'm liking the Geogebra I made for it to calculate the sum of squares. Enjoy!

Regression Instructions on Nspire and 84

I have kids with both models of calculators, and I find that just giving them print instructions to work through at their own pace is the most efficient way for them to learn button-press procedures. It's either that or a live demonstration, and then you have to wait for everyone to keep up with you, and they don't have something they can look at later. On top of that, half the kids are not fluent English speakers, so I try not to make verbal instructions the only mode of communication, ever. The point of this is not for them to learn any math. We're doing other stuff for that. (So lay off about the inauthenticity of this task, please.) It's purely to learn the button presses. I spent way too much time making these, so please, take them so you don't have to duplicate my efforts. Also, disclaimer, these assume your handhelds have the latest operating systems. Which are way better than previous versions, so update yo' shit, people.

Nspire Regression Instructions (docx)

Nspire Regression Instructions (pdf)

84 Regression Instructions (docx)

84 Regression Instructions (pdf)

Monday, October 15, 2012

Why Algebra

I've been taking notice more this year with all the Why Algebra back-and-forth of how indispensable it is for learning Geometry. I know I'm not going to win any converts by answering "why Algebra?" with "because Geometry" but those about to rage quit this post are probably not going to be persuaded by a blog post anyway.

I don't mean the tepid "Algebra!" problems with the snazzy xy logo the textbook offers. I assign some of these, don't get me wrong, but if this is the sum total of the algebra used in your geometry course, you're doing it wrong.

I mean in the process of exploring how measurements on a plane relate to each other, algebra is a weapon the kids should be deploying like on the daily, in the cycle/ladder of examples, conjecture, prove, extend. Kids' resistance to this leads me to believe they aren't often asked to do this.

Expressing your conjecture. Here are some examples.

The resistance at first will be formidable. They will truck along obligingly until the last part, which they will leave blank and wait for someone to tell them what to put. I have to restate just what I want them to do a bunch of different ways, and ignore that they are pleading for me to just do it for them with their pleady little faces, and have the patience to wait them out. "Okay you saw examples of what results when angle B is 36, 48, 55 degrees. What about any angle of x degrees?" "5 sides 3 triangles, 6 sides 4 triangles, 7 sides 5 triangles. n sides ??? Triangles?" "how did you turn a 25 into a 130, and a 41 into a 98?" They will look at you like you are a crazy person. Meet this with incredulity. "You did take and pass an algebra course last year. Yes?" They will look at you with a face all dark clouds that says, "you bitch." Meet this with unrestrained confidence. "You, you can do this. Take a breath and focus on it for a minute. I wouldn't ask you to do something I didn't know you can do." They will. After the first few it gets easier.

Using Algebra to Prove Things
It's a major way we can know something is always true. "Is that always true? How do you know?" are sentences I probably utter in my sleep by now.

Here are some examples

The lovely part about using Algebra to make sense of Geometry is it offers context to hang your algebra on. In that last example, Mat originally ended up with e = -360 because he forgot to distribute the negative. He knew something was wrong, so I asked him to write it on the board so we could help. One of his classmates spotted the error in short order. Sometimes the stuff from the previous course doesn't gel until you have to use it in the next course.

I guess my point is, maybe "Why Algebra?" is the wrong question. If we agree that Mathematics (actual Mathematics involving logical, abstract ways of thinking about how quantities and measurements fit together, generalization, observing and using patterns, making predictions) is a valuable thing for an educated person to learn about, the question seems kind of silly. Of course Algebra. But, maybe we don't all agree with that. Or maybe we should talk about whether the content of Algebra 2 and beyond is valuable for everyone to learn about. Which the CCSS seems to have decided "yes" without consulting anybody. I guess I don't think the question has been very well defined.

Friday, October 12, 2012

Hours of Entertainment (Pew pew!)

Hey did you know underclassmen are almost as easy to entertain with laser pointers as kittens? It's true.

This challenge has had them going on and off for hours.

Hold this:

And move your body from one side of this board to the other:

while keeping the lasers on the stars. (There is a green Expo-marker star drawn on each side of the board.)

Other rules:
  • no changing the angle
  • hold the vertex against your sternum
  • always face the board, and no one stands between you and the board (safety, you know.)
A few of them are getting pretty good at it, so we appointed another kid to trace his path with chalk on the floor.

The children. They have some questions.

I know there are boring ways to get this point across with paper and pencil, but LASERS. THAT'S WHY.

Update: David Petersen made a Geogebra file to illustrate what is happening.

Wednesday, October 10, 2012

You Can Have My Compass and Straight Edge

when you pry them out of my cold, dead hands.

I apologize in advance that I'm going to get a little critical of people I don't know who are trying to do a good thing, and are probably very nice. This landed in my inbox today from someone who offhandedly described it as "cute" with no further commentary.

"How do we know something is true?" is a big, maybe The Big Question in Geometry. At least, in my course. I hope in yours, too. It's a big, bad, fun, important idea.

Don't get me wrong, the makers of this video did a very slick job with it. It is very, very well done. But I don't get the point of cutesy-ing up exposition on the topic. When is a learner supposed to watch it? Before or after they have looked at a bunch of examples of something and made a conjecture and paused to wonder if that thing always has to be true, and just how they can go about knowing that? Before or after they encounter a surprising consequence of a ho-hum construction? I really, really hope this isn't any learner's introduction to what proof is for. They need to get their brains in the weeds of puzzles they can't leave alone. They need to get their hands dirty. Please, teachers of Geometry. I am begging you, here.

I suppose maybe I'd show it after. Like, way after. Months from now. It is pretty cute. Maybe it will help snap into place some ideas they will have knocking around in their heads. But my prediction is it will not hold their attention.

Wednesday, September 19, 2012

On the Block All Things Are Possible

That was almost definitely the best class of the week.

Lucas walked in just before the bell wondering how long it would take to walk the length of the Great Wall of China.

Somehow, some way, my heart has not yet closed to hearing such questions.

"I wonder indeed, child! The floor is yours! Here, have this class of 12 rambunctious geniuses! Here, have some Internet! Have a projector! Let's rock this bitch out!"

You don't fiddle around with a class a little, you don't know what's possible.

Everybody looked a scosh alarmed. I perched up on a desk in the back and willed myself to not say much of anything. And good thing because dear God, these shoes.

They clarified the question on their own. They were riveted, every one. They were jumping up to open google maps. I suggested Google Earth and showed them how to measure distances. And the children, they were glowing. They were addicted. d=rt had its best day in a while. It's not explicitly part of this course, but let's not kid ourselves that all these cherubs have it on lockdown.

It took them all of 20 minutes to figure out, with satisfying certainty, how long it would take to walk the great wall of China. On periods, that would have been half the period, and there goes today. On the block, there were 70 minutes remaining, which if Miss Nowak can't adjust on the fly her treatment of parallel lines cut by a transversal to fit in 70 minutes, one should feel free to question her qualifications.

Tuesday, September 18, 2012

Fourth and Final Week of New Bloggers!

Here is our fourth installment of new bloggers! If you needed any evidence that our teachers are a national treasure, look no further. Passion, thoughtfulness, smarts - our weird and awesome little corner of the Internet is rocking it right now.

Sorry to pick favorites, but this is my personal favorite from this batch: Rachel Tabak @ray_emily has a blog named Writing to Learn to Teach. The fourth post for the Blogging Initiation is titled Error Analysis, Decimal Operations, and Being Less Lame and the author sums it up as follows: "Kids who would likely have been utterly lost received mini-lessons from peers. (Also, I could spot those kiddos and work with them fairly easily, given that I was NOT in front of the class blah-blah-blahing. Oh – in case it wasn’t clear: There was no blah-blah-blahing. I just let kids dive in.)" A memorable quotation from the post is: " Now that I’ve moved from moping to actually determining what in particular was not working—a necessary step that I’d pathetically avoided, previously—it’s time to get to work."

Amy Zimmer has a blog named Ms. Z Teaches in Mathland. The fourth post for the Blogging Initiation is titled Pictures! and the author sums it up as follows: "Looking at ways to engage students" A memorable quotation from the post is: "I love when math students get to shine using all their intelligences."

Sarah Miller has a blog named Proof in the City. The fourth post for the Blogging Initiation is titled Small change with a big payoff and the author sums it up as follows: "One thing I've realized this year is that I need to spend time at the beginning of my lessons reminding kids what we are working on and where we left off last class period. It helps get them focused, and makes it possible for me to move forward with the topic at hand." A memorable quotation from the post is: "They don't hang on my every word, they don't look forward to what new math knowledge they can get today, they don't take a moment to reflect on where we are and what we are learning before class starts."

vanvleettv @vanvleettv has a blog named Everything's Rational. The fourth post for the Blogging Initiation is titled New Blogger Initiation Week 4: Solving Equations Shout Out and the author sums it up as follows: "The post is about a post I came across by a fellow new blogger. It is a resource and insight as to how she teaches solving equations." A memorable quotation from the post is: "As I was cruising through the Mathblogotwittosphere, I came across a post by MathyMissC called reteaching solving equations and wanted to give some props to her."

Alex Freuman @freuman has a blog named Math Teachering. The fourth post for the Blogging Initiation is titled One way to get students to ask questions... and the author sums it up as follows: "For me, this is an effective way to get students thinking and asking questions. It targets quieter and more timid students." A memorable quotation from the post is: "It is very natural for me to pause during a lesson and say, "Any questions?" My feeling is that many students interpret this as, "If you're a little too slow to keep up with my pace, confess now.""

helen oehrlein has a blog named Bowditch's Apprentice. The fourth post for the Blogging Initiation is titled Wonderful Course for NYC/Long Island Teachers and the author sums it up as follows: "In my last post, I mentioned a great course I had taken that really moved me along s a math teacher. The coordinator of the program saw my post, and asked me to let teacher know that there are openings in the latest course, which starts on Oct. 3. It was the most valuable PD I have ever done." A memorable quotation from the post is: "Each class a different experienced teacher shared their best ideas and lessons. I learned so much, and wished that this had been part of my teacher training."

Thursday, September 13, 2012

Online Population Projection

For some reason, this came to my attention. Because, math was wrong? What?

Ben Foster anticipated Facebook's billionth user would login last month, in August 2012. He wasn't alone. Here was NBC News' technology blog, reporting on a prediction by iCrossing:

And Bloomberg Businessweek would only call it for "later this year:"

Which all seem to presume linear growth from here on out. Indefinitely? I don't know. Which just makes me wonder, to what extent can we apply usual population growth-type logic to online populations? If Facebook were growing within an environment with biological limiting factors, we would have expected what we've already seen, for example, exponential growth at first. For quite a while, Facebook was growing at a lovely exponential clip of approximately 10% a month. This shows their growth for December 2004 through December 2009, with an exponential regression to fit:

However, maintaining that growth rate was clearly unsustainable. If it were, Facebook's population would have reached seven billion In June of 2012. Obviously, that didn't happen.

In biological populations with finite space and resources, we expect growth that looks exponential at first, but due to limiting factors, levels off eventually. And, indeed, Facebook's growth did not continue exponentially.

And I suppose it has looked rather linear for a while, but I'm not sure that's the best model. The rate of increase has slightly decreased the past year or so (shout-out to the second derivative!) 

If we apply a logistic model to the data so far, we get:

Which has Facebook reaching a billion users in April of 2013, and predicts its eventual population will top out at less than 1.1 billion.

But this all raises more questions than it resolves. Facebook may be approaching its maximum realistic number of users within the United States. However, as far as I understand, it has lots of room to grow in other huge markets. So this logistic growth model is flawed as well. I'll cop to not understanding how graphing calculators come up with logistic regression equations, like, at all. At least not with nearly the depth that I understand how they calculate linear regression equations. I simply know how to apply it as a blunt instrument to a table of values. On the other hand, linear growth, as the news organizations have used, has not panned out - as we're past August 2012, and have not reached a billion users yet. Have worldwide, internet ecosystem limiting factors unavoidably kicked in already? Should we expect another period of exponential growth in the future, if it catches on in India? Are there reasons to think this linear-looking growth will continue for a long time? And for how long? I don't know if any of these are answerable! But I do love the questions.

Here is a Geogebra file, if you want to play.

Wednesday, September 12, 2012

We Got Tricks

So, I don't love tricks?  You know, the "don't worry about the why, kid, just remember this little song" variety. But we're in the weeds of finding areas and perimeters of composite shapes. Of the quarter-circle stuck on a rectangle stuck to a triangle variety. Yes I want them to have a intuitive grasp that the distance around a circle is a little more than three diameters, and yes I want them to see a circle deforming into a rectangle whose width is r and length is half a circumference. And yes we are mostly solving problems with tracks and whatnot.

Buuuut....I am not confident about how much of that they are going to be able to retrieve when they are sitting for their SAT's a year and a half from now. So, we are shamelessly using a trick, that a student heard somewhere else, for keeping circumference and area of a circle straight. "Chocolate pi is delicious, and Apple pis are, too." I'm storing it in the same dark place as "All Students Take Calculus," as in, it makes me feel a little dirty, but it seems to be a necessary evil.

Sunday, September 9, 2012

Week 3 of the New Bloggers

Katie Cook @kjgolickcook is my Real! Life! Colleague! She is very funny and very awesome and finally has a blog (yaaayaayaaay! (Kermit arms)) named Math Teacher by Day. Her post for this event is Why Do We Have to Learn This? and includes three very solid responses to that question. I'm looking forward to good things from Katie's blog - she's a long ball hitter, that one.

Chris Rime @chrisrime has a blog named Partially Derivative. The third post for the Blogging Initiation is titled NBI #3 — In which a student learns the truth about math class and the author sums it up as follows: "All about how I respond to that infamous, "When are we ever going to use this?" question. With super-bonus material related to the apparent difference between illiteracy and innumeracy." A memorable quotation from the post is: "This is as real as the world gets."

Sarah Miller has a blog named Proof in the City. The third post for the Blogging Initiation is titled Math Quotes and the author sums it up as follows: "I wrote about one math quote that I like, and how it has affected my teaching." A memorable quotation from the post is: "I even found a quote to explain why I love quotes."

Carl Edgren and Hannah Schuchhardt @hschuchhardt, @carledgren have a blog named Teaching Systematically. The third post for the Blogging Initiation is titled Get to the point. and the author sums it up as follows: "Students often just want to know the answer to problems - mathematics is the process of completing a problem for the correct answer. We need to show them that learning mathematics is about analyzing the world around us!" A memorable quotation from the post is: "The students simply want us to get to the point already."

helen oehrlein has a blog named Bowditch's Apprentice. The third post for the Blogging Initiation is titled A Hodgepodge of Ideas? and the author sums it up as follows: "I have come to believe that Precalculus is not a hodgepodge of ideas, but a study of the deeply related Mandala of the Functions (as Berlinski sees it). Furthermore, although these functions have much in common, their differences shine a light on why we really do need so many different functions." A memorable quotation from the post is: "Inverse functions are so useful that we truncate the trigonometric functions in order to create them, and we actually have a totally artificial, man-made inverse of the exponential function, namely the logarithmic function."

Mark Davis @graphpapershirt has a blog named Graph Paper Shirt. The third post for the Blogging Initiation is titled Where's All the Stuff Come From? and the author sums it up as follows: "This post is about how students come to class with misconceptions about photosynthesis and where plant material comes from. It's such an important concept to understand because it encompasses the fundamental idea of how the sun ultimately powers (almost) all life on earth." A memorable quotation from the post is: "To make a long post short, the students learn that even some of the brightest students in our country don’t know something as fundamental as where plant material comes from, and ultimately their food, and themselves!"

Jasmine has a blog named Jazmath. The third post for the Blogging Initiation is titled I Was Never Good at Math Either and the author sums it up as follows: "Parents night is an important time to show families how class really runs and the attitudes that we hope to instill in students. I try to run the ten minutes that I get with each set of parents as if it's a real class period." A memorable quotation from the post is: "I want to keep the focus on how we deal with discomfort and what we want to model for our children."

Kelly Berg @kmbergie has a blog named The M Stands for Math. The third post for the Blogging Initiation is titled Sharper questions and the author sums it up as follows: "I took a risk to teach material with meaning instead of with boring-ness. My risk paid off to the student's benefit. Students were involved and engaged. BAM!" A memorable quotation from the post is: "And right there I went from concrete to abstract AND they had better understanding of the concept because there was meaning attached to it."

Friday, August 31, 2012

Moar New Bloggers!!!

Week two apparently saw an almost equally enthusiastic output from our blogging-challenged! Pardon my lack of commentary, this weekend I have somehow managed to saddle myself with marking ~90 unit tests, ~50 notebook checks, and planning to teach an IB vector unit for the first time. Even still, I am going to go read at least three of these right now and leave a comment. Your assignment is to do the same!

Stephanie Macsata @MsMac622 has a blog named High Heels in the High School. The first post for the Blogging Initiation is titled 1st Days of School and the author sums it up as follows: "I wrote this post about something I wish had been part of my teacher training. I picked the book First Days of School by Harry Wong because it taught me about setting expectations and teaching procedures, which helped a lot in my second year (and beyond)." A memorable quotation from the post is: "After experiencing year one I knew what I DIDN'T want, but I still wasn't quite sure how to get what I DID want."

Heather Kohn @heather_kohn has a blog named Growing Exponentially. The first post for the Blogging Initiation is titled 10 years from now... and the author sums it up as follows: "This post is about what students will hopefully be saying at their 10 year reunion about our class, about me, and about what they learned. I summarize my end of year course evaluations and how that all I really want, is for the students to come home after 10 years and say hi." A memorable quotation from the post is: "It would mean the most to hear the students say they liked going to math class because it was fun, they learned a lot, and they know that even though I challenged them, I knew they could all succeed."

Allison Krasnow has a blog named Pi Crust. The first post for the Blogging Initiation is titled Cheating!! and the author sums it up as follows: "In addition to teaching middle school math, I am teaching an undergrad class at UC Berkeley this semester. It's a math methods class for students interested in being math teachers. So, sage blogging teachers...I'd love to hear from you what you believe should be taught in this course. I could blabber on and on about what I think is important, but I bet you can too." A memorable quotation from the post is: "Week 2 of new blogger initiation asks us to respond to the following question: “All new teachers should know about (blank) before entering the classroom,” and instead of answering it, I’m posing it to all of you."

Alex Freuman @freuman has a blog named Math Teachering. The first post for the Blogging Initiation is titled 5 Things I Wish I had Known when I Started Teaching and the author sums it up as follows: "If I could go back in time and give myself some advice, I would share these ideas with my old self. Hopefully, this will be helpful to some of the newer teachers out there." A memorable quotation from the post is: "I wish I had known that I didn’t have to hit every ball out of the park."

Brielliephant @Brielliephant has a blog named Thriving Not Just Surviving. The first post for the Blogging Initiation is titled My "Training" and the author sums it up as follows: "This is a list of a few of the first things that pop into my head when I think of all the millions of things I was never prepared for. Though, not to be a negative Nelly, I also have a short list of things I did learn and are thankful for about this year." A memorable quotation from the post is: "I was never taught that being the youngest, and one of the few, available young women teachers would mean that I should be set up with any and every available man by my fellow teachers."

Tad Snaith @TadSnaith has a blog named What Does Math Mean?. The first post for the Blogging Initiation is titled A Ten Year Reunion (Math Blogger Initiation Week 2) and the author sums it up as follows: "Another "student" added that they always felt that he made them think harder than any other teacher without them realizing. But in fact it wasn't that they "thought harder" but more so they felt comfortable to share ideas and thoughts in his classroom. They always felt trusted, respected, and worthwhile in Mr. Snaith's class." A memorable quotation from the post is: "it was a time in the day where students didn't have to worry about who was the best or who was the worst in math. It didn't matter. Everyone was treated equal."

Lee KT has a blog named Random Expected Value. The first post for the Blogging Initiation is titled Hokey Pokey for Functions and the author sums it up as follows: "I talk to my students a lot about how we think, how we learn. We remember if we connect new stuff to something already in our minds. So this is my hokey attempt at getting students ot understand and remember the duality between what they have learned previously as “y = ” and the function notation f(x)." A memorable quotation from the post is: "I make my thinking process explicit and visible to the students so that they can (perhaps) learn to think in better ways as a result."

Aaron C. @CarpGoesMoo has a blog named Random Teaching Tangents. The first post for the Blogging Initiation is titled New Blogger Initiation 2 and the author sums it up as follows: "This post was a rambling purge of the back to school blur ... with plenty of references to my inability to efficiently get 'flipped classroom' technology working for me instead of against me." A memorable quotation from the post is: "... and I don’t even care that this was an entire paragraph’s worth of run-on sentence."

Ben Owen @bahowen has a blog named Transformations. The first post for the Blogging Initiation is titled Two days down, 177 to go and the author sums it up as follows: "My post is about the challenges I'll be facing in my classes this year. Some challenges will come from my students, but other will come from the district offices." A memorable quotation from the post is: "It's hard to find the joy in teaching when my employer is trying to replace me with videos."

Jillian Paulen @jlpaulen has a blog named Laplace Transforms for Life. The first post for the Blogging Initiation is titled Calculus &; Cupcakes and the author sums it up as follows: "I wrote about the things I hope my calculus students remember in 10 years, as well as what I remember from my calculus class." A memorable quotation from the post is: "I won’t be so vainglorious as to proclaim that all my students will remember every skill I ever taught them, but I do hope for a few things."

Monday, August 27, 2012

Yet Another Love Letter to the Internet

Reason #9737465849 to get a blog, teachers. If you wait a few days, other people sometimes just do your work for you. :-) Thanks, Timon!

Act 1 - Moon Phases from Timon Piccini on Vimeo.

Saturday, August 25, 2012

Let's Hear It for New Bloggers!

It is common knowledge that I love Sam Shah as only one long time blogging buddy can love a blogging buddy. Basically I just love the Shah-ness of Shah, and I make no apologies. The other mastermind (mistressmind?) is Julie Reulbach whose Google Spreadsheet fu is downright scary - who knew? She is full of surprises, that one. They initiated this initiative to 1. give new bloggers a kick in the pants and 2. give the rest of us a way to see the new stuff out there. I was pleased to see that many of them took the advice to name their blog something that doesn't suck. This is long, so get yourself a bag of cheetos or a corn dog or something and settle in. If you read a post that you like - hey - leave a comment! It's free! And it will make their day.

vanvleettv @vanvleettv has a blog named Everything's Rational. The first post for the Blogging Initiation is titled Introducing Standards Based Grading and the author sums it up as follows: "I created a presentation to go through with students and their parents that gives a glimpse into the world of Standards Based Grading. I will use this sometime during the first week of school. Hopefully it will help ease the process of converting to standards based grading in my classroom. " A memorable quotation from the post is: "I wasn’t happy with the way I graded last year and want to do something about it."

Carl Edgren and Hannah Schuchhardt @carledgren, @hschuchhardt have a blog named Teaching Systematically. The first post for the Blogging Initiation is titled Helping Students Become Problem Solvers... and the author sums it up as follows: "We are really working to help kids become problem solvers, not just people who are good at completing math problems. There are 2 things we are starting this year: "Google Days" with an advanced class and more project based learning with all of our other courses." A memorable quotation from the post is: "Sometimes I think that recalling things you’ve learned is like recalling a memory – we are trying to get students to be able to put themselves back into the moment they learned a specific skill or idea."

MathNinjaTeacher @mathninjateach has a blog named The Education of Future Math Ninjas. The first post for the Blogging Initiation is titled Survival and the author sums it up as follows: "This post summarizes my pre-school worries about being a new teacher. Including the fact I am teaching a brand new curriculum." A memorable quotation from the post is: "At 7:05am Monday morning 25ish 9th graders will grace me with their presence and will forever be known as “My First Class Ever.”"

Ms. Philosoraptor has a blog named Normalcurvasaurus. The first post for the Blogging Initiation is titled What's with all the dinosaurs? and the author sums it up as follows: "The post I wrote for this week describes why I chose the screen name and blog name that I did (and my obsession with dinosaurs). I also briefly described what I hope to instill in my students as learners (and thinkers!) as a prospective teacher." A memorable quotation from the post is: "I want my students to become thinkers, and actually THINK about the mathematics they are doing."

mathtastrophe @mathtastrophe has a blog named mathtastrophe. The first post for the Blogging Initiation is titled Time Is Money - A Fresh Start and the author sums it up as follows: "It's a new year and I need a fresh start! I narrowed it down to two big things that I think will make all the difference in my classroom. A timer and an interactive notebook." A memorable quotation from the post is: "I want students to know that I value their time as well as my own, and I want them to know that in my class we use time wisely."

Beth Ferguson has a blog named in stillness the dancing. The first post for the Blogging Initiation is titled In stillness and the author sums it up as follows: "Blogging about my school experience is new to me and I’m enjoying the process. I began blogging a few years ago. At that time I blogged to help find my “center,” to quieten myself to recharge. Interestingly enough, I’m finding blogging to be a different experience this time around. " A memorable quotation from the post is: "It is in stillness that my soul finds delight."

Jennifer Kenney @jnnyknny has a blog named Algebra Awesomeness. The first post for the Blogging Initiation is titled Yakking Tracker and the author sums it up as follows: "I created stop lights to use in my junior high classroom to monitor noise level for my groupwork. They look fantastic and will help me to work on my behavior plan this year!" A memorable quotation from the post is: "I like to be able to control the volume on my own."

crazedmummy has a blog named crazed-mummy. The first post for the Blogging Initiation is titled Homework week 1 and the author sums it up as follows: "My post is about the blog name, the repetitive included pictures, and the reason for blogging." A memorable quotation from the post is: " I rarely leave a trail of slime behind me, but I do wear glasses."

loveteachingmaths has a blog named Love Teaching Maths. The first post for the Blogging Initiation is titled Back to school.. and the author sums it up as follows: "Analysing AS results for this year. Setting some personal targets." A memorable quotation from the post is: "If a student is not ‘good’ at a subject then why should we have to break our backs for them to just scrape a pass?"

Paul Gitchos has a blog named Second Thoughts. The first post for the Blogging Initiation is titled First Day Lesson Ideas and the author sums it up as follows: "I'm working on opening lessons to set the right tone in my math classes, which are Algebra 1, Geometry, Algebra 2, and Calculus. (Is that something like hitting for the cycle?)" A memorable quotation from the post is: "I am trying hard for an introduction to calculus that lets students understand why it was invented in the first place."

Kevin Krenz @kevin_krenz has a blog named Rational Limits. The first post for the Blogging Initiation is titled [NBI] Focus on culture and the author sums it up as follows: "I did focus on culture during my first year of teaching, but I did it wrong. I tried to build it, alone. This year I want to actively include my students in developing the culture of our classroom from day one." A memorable quotation from the post is: "I can help guide the development of our culture and be intentional about which values are emphasized, but I cannot create it on my own."

Nate Gildersleeve @Mrmacx has a blog named Hard Enough Problems. The first post for the Blogging Initiation is titled Blogger Initiative Pt 1 and the author sums it up as follows: "This post talks about implementing a flipped classroom and using google forms this year. I'm most excited about using google forms as a feedback tool to help foster a positive mathematical community." A memorable quotation from the post is: "So a student recognized that they were talking the most, but also recognized that they weren’t the ones with the best ideas."

MakingPaperAirplanes @MakingAirplanes has a blog named Making Paper Airplanes. The first post for the Blogging Initiation is titled New Year Goal and the author sums it up as follows: "Since this is my first year in my own classroom, I am having to set up and organize everything from scratch. It's been a challenge to decide what will work for me, and while I am not afraid to make changes, I want to have at least the basic bones settled before students show up!" A memorable quotation from the post is: "[Organization] has been a constant struggle for me, as I was working out of five different classrooms at two different schools last year."

Angie Eakland @aeakland has a blog named Coefficients of Determination. The first post for the Blogging Initiation is titled r squared equals 1 and the author sums it up as follows: "This is a post about the origin of my blog's name, but it's mostly about the synergy we all strive for." A memorable quotation from the post is: "To me, those 1's come with the synergy created between the art of teaching and the science of teaching."

Wednesday, August 22, 2012

Moon Safari

A whole bunch of juniors in high school just left my room, excited to go outside tonight and look up.

Update: Timon made a video that you could use to launch the lesson

I started by showing this:

Which is not all that exciting, granted. It's a table of the day in January 2012 vs how much of the moon was illuminated. The data comes from the US Naval Observatory. I explained what was in the columns and asked them to write down one thing they noticed, and one thing they wondered. Thank you, Math Forum. Their noticings were pretty good: the periodic nature, the numbers of full and new moons in January, the fact that few of the values are repeated. Their wonderings, though, were wallowing in lameness. I was hoping for anything, really, that hinted at making predications past January. But, no joy. This is a direct quote: "I don't really wonder anything about the moon."

Anyway, onward. It got better. I said by the end of class they would be able to predict what they would see when they looked up tonight, and know what the moon was doing on their birthday this year, and would know other days this year when there was a full moon.

They followed some instructions for entering values in a table and making a scatter plot on their calculator. Then sketched the scatterplot, and came up with a function to model it.

Then they were to use their calculator plot of the function to explore some questions:

 - Which days in January had a full moon? A new moon?
(This would seem obvious from the table, but once they have an equation graphed, they forget all about the table! It's kind of weird. I put this question in so they could get their heads around what x and y represented in their functions.)

 - How much of the moon is visible today? Discussion of how we'd have to change the calculator's viewing window to "see" today. Or what we'd have to plug in where in their function. Once we realized we needed to know today's Julian date, I gave them:

 - How much of the moon is/will be visible on your birthday this year?

 - On what days this month should we expect a full moon?

It might have started out slow, but by the end of class they were pretty animated. One girl noticed that there was a full moon on both of her parents' birthdays this year (before she noticed they were 30 days apart.) There were some different predictions for tonight based on the slightly different functions students came up with (some of them estimated a phase shift, some of them calculated it by various methods, and some of them pretended there wasn't one.) So, tonight they will look up and see if their model worked.

Open questions:
1. How to create a better hook/act one to prompt more and more interesting wondering questions? Or if anyone has ideas about realistic periodic functions that would be more grabbier, I'm all ears.

2. Would it be better to get an equation of the sinusoidal function by using the regression command on their calculator? More accuracy would take out some of the suspense "who was right?" but on the other hand, we'd have a more reliable prediction of what they would see tonight, and maybe if I was lucky a few kids would think that was kind of cool.

Saturday, August 18, 2012

Week 2 Odds and Ends

I don't have any dramatically awesome lessons to share or anything. I'm kind of reusing old stuff with tweaks, for the most part. I am feeling like a new professional challenge is in my near future. Because in class I'm kind of like: plan the lesson, teach the lesson, assess the lesson…and feeling like I have this shit on lockdown. Not to sound like an arrogant jerkface, but it's year eight and I'm sort of on top of it. Not that there aren't challenges, but I am ready for a new challenge. Seriously the challenges are like: this one kid doesn't try that hard, and so I have a talk with him, and then he shapes up. It's not that I don't love what I'm doing, I'm just temperamentally someone who enjoys a challenge and quickly tires of an insufficient level of difficulty. I am not that interested in administration, so. Either I will keep comfortably doing the same thing, or I will do otherwise. (Monumentally large disclaimer: I teach privileged kids who are very easy to teach in a school that makes my life very pleasant.)

Living overseas is pretty great and the bad parts are not all that bad. I mean honestly the worst of it is, you can't buy all the things you are used to buying, because you live in a third world economy. (Which, you know, get over it, princess. No one is going to die because they can't have a bagel.) It makes you notice how utterly, just, convenient every aspect of life is in the US. For example, you can't be like "I need clean underwear in two hours." It's more like, "I will need clean underwear on Tuesday." And, there are lots of things here that are way better. Dairy, wine, beef, pork, salads which turn out to be some shredded lettuce covered in beef, ham, and cheese, cafes with free wifi that will let you order a coffee and sit there for four hours. I did have a minor crisis in a large hardware store this morning over the lack of availability of telescoping curtain rods. They had 3 meters which were the exact width of the wall I was working with, or shorter ones which were far too short. I bought the 3m ones and am going to make it work. Somehow. I even got used already to using a 2-hole punch/binders instead of 3-hole punch/binders. I mean sure the 2-hole binder situation is floppier, but the 2-hole punch is like KAH-CHUNK-KAH-AH vs the 3-hole punch which makes complete holes through all the pages only when it is in the mood.

It will take me a while to get used to being on the block. I saw my A block last Tuesday, and due to my having to go in person to the bank Thursday morning for complicated Argentine banking reasons, and a holiday on Monday (dear Blessed Virgin: thank you for all the school holidays) I won't see them again until…Tuesday. I'm going to be like, "Hi, my name is Miss Nowak…" 

I did have some fun things happen in class that are probably worth talking about. Last Friday, all the freshmen went to freshmen orientation, leaving me with half-a-geometry classes for two blocks. So, I showed Flatland. I'd prefer to show it to everyone, but you know beggars choosers, and if I'm going to lose instructional time I'd rather spend it on something interesting and cool. This version is very, very well done, and I can attest that it holds the attention of teenagers the world over. At least in the Western hemisphere. It leaves them with the lingering question "what about the fourth dimension?" which is fun to seize upon. In periods, you barely have time to show the movie and that's it. But in blocks, you show the movie and then you still have 45 minutes to kill. So, best bet, start making you a table of vertices, edges, faces, cubes, etc in 0, 1, 2, 3, etc dimensions, and set them to looking for patterns, and wondering whether a fourth dimension exists and what we can infer about it. The verbiage about how you can see a 2D shadow of a 3D object, therefore if there is a fourth dimension we could see a 3D shadow of a 4D object, is very useful. They will have GREAT fun with this, and you will mostly have fun watching them.

Monday, July 2, 2012

#mtt2k and my own version

Here's both an entry to the #mtt2k contest, and a humble submission for a better video that provides instruction for this concept.

The target is the Coordinate Plane video. I used a tool called Popcorn Maker to add comments to it. I don't think this can be embedded, so please click here to go watch.

Before y'all get out your flamethrowers and head to the comments, I'd like to say a few things. I'm neither vitriolic, panicked, nor bitter about Khan Academy. I think it's a great resource and it's an excellent place to see a demonstration of procedures. I send my own students to it during exam review time, and they report that it is helpful.

Where Khan and the Gates Foundation overextend their claims, though, is when they suggest that the Khan Academy can serve as standalone instruction in Mathematics. Enduring learning requires productive struggle and time to noodle out unfamiliar problems, posed by a teacher who knows what you're ready for, and can provide expert scaffolding. Lecture-only instruction focused on mastering procedures is an impoverished substitute for doing Mathematics, and it doesn't matter if that lecture is in person or in a video.

Given that, I do think that the instruction provided in the Khan Academy could be improved with some better planning and basic pedagogical technique. It's already a good resource for some purposes, and I'd love to see it get even better. It's my hope that the key players involve will calm down, cut the drama, and work together to improve the available resources. It's math, people. Not the opera.

I made a video intended to instruct on the coordinate plane. Although I'm certain it could be improved since it hasn't been subjected to editing by anyone but me, I think it's better than the Khan Academy offering. First, it provides motivation for graphing quantities in two dimensions. Second, it asks questions of the viewer at key points, with the idea that the viewer would take a moment to think and respond before continuing. Here you go:

Friday, June 29, 2012

Are You Sure You Want to Do This?

(bit late to the party, sorry... been rather preocupado, although according to Dave Cox, I'm not allowed to complain unless I'm endeavoring to walk to Argentina, which I'm not, so I'll get on with it.)

Dear New Teacher:

Are you sure about this? I mean, I feel it's only fair to warn you. Older people in your life, parents, etc, have probably filled your head with silly notions about how teaching is a good job. It's rapidly becoming not that great a job.

Pension-wise, New York just went to Tier Six. SIX. I won't go into details, but Tier Six is pretty shitty. Granted, ten years from now, they will probably be on Tier Eight, and you will be feeling all smug to be on Tier Six. Tier Eight is going to be, like, a standard-issue leather jacket and spiky shoulder pads and lessons on shooting an automatic weapon out the back of a moving pickup truck.

Otherwise intelligent, nice people will assume you had to go into teaching because you are such a dimwit, you can't do anything else, or perhaps just misguided about what is important in life, namely having expensive stuff. You will hear some variation on the "If you are so smart, why are you a teacher?" question at least once every few months. From people it would be impolitic to offend with a smartass response, like your boyfriend's dad. Have an answer ready for that, one that is both diplomatic and speaks your truth.

You probably suspect the children will love you. They will not love you. Once you get decent at this, they will grudgingly respect you. That will take at least three years.

You will pour your every ounce of intellect and ability into teaching the Algebra 2 class of your life, and then the outside testing agency paid to test your kids and rate you based on their performance will write a lazy, error-ridden, confusingly-worded exam that only reflects about 75% of the standards they told you to teach. Some kids you really like, who you know learned a whole bunch in your class, will fail it. You will beat yourself up for the rest of the summer.

Your first year will be 50% drudgery, 45% heartache, and 5% awesomeness. After seven years I've gotten that down to about 40:40:20.

Okay, if you're still sure, understanding all that... you probably have a chance. And, given all that, this is the best job in the world. Getting someone else to understand something is HARD. But it's an intellectual puzzle that's worth building a career on.

I'm rooting for you.

But maybe open a 401k.

Update 30 Jun: Okay, to counteract the negativity above (even though all of it is totally true, and newbs need to hear it), here is a

List of Things That Are Awesome about Teaching that Politicians Probably Can't Screw Up:

1. You get to hang out with young people all day. Who are funny, idealistic, emotional, open-minded, and overall, a trip.

2. You get to learn all the new slang before other adults.

3. Office supplies.

4. You can propagandize for your favorite mathematicians TEAM LEIBNIZ!

5. You have the power to make a place where people have to spend 45 minutes a day into a joyful place of learning and safe risk-taking.

6. You get to play a part in what kind of people kids will turn into, hence what kind of world we live in.

7. Continuing to learn new things is a job requirement.

8. You will get to work with colleagues who are some of the kindest, smartest, most genuine people you have ever met.

9. That moment you find the key to that part of a person's brain that unlocks the thing you want her to understand.

10. That moment a class asks its own question and runs with it.

In a nutshell: you get to share the best of civilization with new humans. That will be enough to sustain you through a whole lot.