Even Numbers #hashtag

The problem with even numbers is that they are divisible by two. I've never been one for making resolutions, but I have tried to set goals for the year. At the end of last year, I set two goals. Therein lies the problem. For one of them, I was completely successful. Although I still haven't checked my grades, school seems to be going well. For the other, I was a complete failure (there is still a lingering, albeit completely irrational hope). I still haven't figured out if I would trade one success for the other, not that I have the option. So this year, I am going to set an odd number of goals. That at the end of the year, I will know how well I did. I will be able to tell whether I am a failure or a success.

Ignorance is Bliss #hashtag

This weekend while watching football, one the announcers talked about the team "matriculating down the field." I am not sure what he meant to say. Matriculate means to gain acceptance to a college or a university. I know what the word means because I got an e-mail talking about matriculation at U-M and I had no clue what the word meant; I had to look it up. It got me thinking about sort of ignorance is socially acceptable.

In some blog post, I have mentioned how people will brag about being bad at math. In a similar matter, we had a guest speaker brag about how he was completely ignorant of the basic rules of football, as if it was some sign of sophistication. At the opposite end of the spectrum, I have never heard anyone use the same tone to say that they "couldn't find Canada on a map" or "never managed to master tic-tac-toe." What is worth knowing? What sort of knowledge helps us interact and communicate with other people? Aside from math, what things ought people know?  

Priorities #hashtag

This is the desk that I sat in for my geometry class. It was kind of broken, but we didn't have a lot of options. Luckily, the desk wasn't that nice to begin with. The writing area was too small to hold an 8.5x11 piece of paper. So the fact that it wobbled didn't make it much worse than the non-broken desks.
On an unrelated note, earlier this year there was a hundred million dollar gift to improve the athletic facilities at U-M. If only math was as profitable as real estate or as entertaining as college sports (Let's be honest, algebra is much more interesting than college basketball). 

Data #hashtag

People would rather travel through time than read peoples’ minds. Time travel seems full of potential problems. Let’s say that you could travel back in time and change history. So, you hop in your DeLorean (or take a trip in your Klingon Bird of Prey around the sun) and you travel back in time and do something cliché like kill Hitler. When you travel back to the present, you would return to a world that you would not recognize. Everything would be different. So, even if the world was better from a geopolitical perspective, the life you left behind would most likely be gone.

Over the Thanksgiving Break (Which it seems like people really enjoyed) I had a conversation with a friend of mine about the percentage of people that like pumpkin pie. I guessed less than half. He guessed about 90%. It turns out he was right. Also, I included the pumpkin pie chart.

Richard Lavoie yelled at people, but the vast majority of us would rather hang out with him than Nel Noddings.

There was more crying this semester than last semester. Perhaps other people had a less stressful summer than I. Perhaps during the fall there were the same number of cries per day, but there were just twice as many days during the fall over which to shed them. I was surprised that three-quarters of recipients cried more this semester than during the summer term.

We would rather study alone than with someone else. It’s strange given the social constructivist view of education that we have all been exposed to, we would still rather study by ourselves than in a group.

Very Pretty #hashtag

Artifact 1: Google Calendar from a random week in October

Explanation. This is a screenshot of my Google calendar. It is from the third week in October. It includes 17 credits of 400+ level classes at, arguably, the most prestigious public university in the Western Hemisphere. It also includes a total of 7 hours of work tutoring a Differential Equations class.

Evaluation. This was the typical week. Eventually, ED 504 dropped of the schedule, but was replaced by meetings for INS videos and the Geometry project.

Application. I, somehow, survived. If I can survive this, I should be in pretty good shape for the rest of my life.

Artifact 2: Google Calendar for next week

Explanation. This is a screenshot of my Google calendar for next week. It includes nothing.

Evaluation. This is identical to my schedule for the following week, too. Number of drives to Ann Arbor over that two week time span? Zero, 0, naught, nil, nada, none, ничего... 

Application. I will now have time to clean the mess that has become of the inside of my car. I might, if I get really motivated, watch a movie. I am going to sleep a lot. I am going to take a day and not touch my laptop. I am going to read on my Kindle and be happy.

Math 498 #hashtag

We got assigned a very similar problem. Given a jug of size A and a jug of size B, what sort of different measurements can you get? It turns out a lot. I have to go write my RWT otherwise I would write more about this. Instead, I'll just post the video and let my reader ponder the possibilities. I will be back in about 11 days.

Now Trending #hashtag

Google N-gram: Love, Joy, Peace, Hope

In the process of searching the internet for a book, I came across Google's N-gram. Google has scanned millions books (about six million books). The N-gram site lets you search for the frequency of words used. I searched for love, joy, peace and hope. Unfortunately, all of these words are on the downturn. Love has rebounded from a low in the 1970's. Peace had an interesting trend line with peaks near the end of the First and Second World Wars. There is still not a lot of joy out there.

More Poetry #hashtag

I created this poem while thinking about my teaching philosophy. One of my classmates liked it, so I thought I would share. I think it needs a few more stanzas. Feel free to make comments on additional lines.

Teaching
The goal of a teacher is to make oneself obsolete
to help young minds to become complete
to help young students meet their ambition
and to show them the value of metacognition.

Other poetic posts: Poetry 1, Poetry 2, Poetry 3, Poetry 4

On a related note, I am a poetaster. Now, poetaster is not one of those neologism that I so despise. According to Merriam and Webster, it has been in use since the 16th Century. It seems like a more modern compilation of "poet" mashed with "disaster", but apparently people have been adding the suffix "aster" to denote poor quality for hundreds of years. There are the words "medicaster" (quack doctor), "philosophaster" (bad philosopher) and "politicaster" (redundant word for petty politician) out there, too.

While trying to type in politicaster to the dictionary, I stumbled badly and typed in a jumble of words that lead to a suggestion of "Are you looking for poliodystrophy?" I was not looking for poliodystrophy intentionally, but I did find that it was an interesting word. It is the "atrophy of the gray matter especially of the cerebrum." Hopefully, by being a poetaster I am avoiding poliodystrophy; even writing bad poetry requires a fair amount of cognition.

Just a few observations #hashtag

+ Much as with people, numbers can be are irrational, perfect, complex.
+ Consider 12+3-4+5+67+8+9 = 100 There exists at least one other representation of 100 with 9 digits in the right order and math operations in between.
I found this on this Pen.io page.

Given the dimensions of a grocery cart, you could probably fit 60 cantaloupes into it. However, it might be really heavy to push. I will have to do more data collection on the dimensions and weight of cantaloupes before I move into a more formal calculations. (See this previous post). I am working on this, and I wanted to update any of you who might be worried that I had forgotten this important problem.

The metal desk that I sit at is frozen. Similarly, the laptop sitting in front of me is frozen. It is funny to think of things that way. While the desk usually feels cold, my laptop is warm to the touch. Yet, it is still frozen. It was sort of mind-blowing when Chuck D. shared the observation about frozen desks with us during the summer. This must be how students feel when I tell them that if X is a negative number, then -X is positive. Also, the square root of a 1/4 is 1/2 and 1/2 is greater than 1/4 (Taking the square root of a number between 0 and 1 yields a number that is bigger than what you started with!). The edges of Koch's snowflake contains an infinite length within a finite area (Ok, that is probably too advanced).

On a related note, regarding things that might make my head explode, the semester is almost done. Wow.

Closing Quotes: 
"I have often been surprised, that Mathematics, the quintessence of Truth, should have found admirers so few..." - Samuel Taylor Collridge


"Whoever thinks a faultless piece to see, Thinks what ne'er was, nor is, nor e'er shall be." - Alexander Pope

"The investigation of the meaning of words is the beginning of education." -Antisthenes

Bass and Ball (2008) #hashtag

"Mathematics rests on shared definitions, meanings, and ways of establishing conclusions. In this way, mathematics differs from arenas of human activity where individuals are free - even encouraged - to develop their own ideas, interpretations and ways of working. The importance of the collective in mathematics is a special educational resource. This confusing problem they [the students in the article] are debating is one which they must all agree. They must move from their different perspectives to a common one, and they must do so using the rules and tools of mathematical practice rather than personal or idiosyncratic ones whose effectiveness would depend on power or personal persuasion. Mathematics both requires and depends on common ideas and practices; it does not submit to individual domination or privilege."

I have no idea how to properly cite this article. I'm not sure where it came from or if it was ever published. I'm not sure whether Prof. Bass wrote the selected text or Dean Ball wrote it, but I feel better in life knowing that run my school understand math. No offense to another other teachers out there, but math is the only subject where we actually know things. I'll sleep better tonight knowing that someone else out there understands math.

Stories of a Stranger Track 2, by OAR #hashtag

I particularly enjoy coming up with cryptic titles. I wonder if anyone will figure this title out.

I read this article about memory. There were a few things that seemed worth writing about. The first was that memories are still malleable. Every time that we remember something, it changes just a little bit. That is why it helps to keep a journal or perhaps a blog. It reminds us of what really was, rather than how we see things from a distance. It is a bit sad to think that the way we remember things isn't exactly how they really happened. Perhaps the happiest moments in my life weren't all that great. Hopefully some of my happy memories are real.

The other point, was a description of the someone with a 'superior autobiographical memory' (a really good memory). The authors describes the subject: "As Healy got older, he realized that painful events that happened 20 or 30 years ago would come back to him with the same emotional intensity, as if he were reliving those moments again, like when he pledged a fraternity in college but did not get in because he was heavyset and shy. Or when he was let go from his first job out of college after just two months."

Although I am far from having a superior autobiographical memory, I find that my above average memory is still a pain as often as a benefit. Whereas people with below average memories tend to forget the things that they would rather remember, I have the tendency to remember the things that I would rather forget. With spaced repetition, it becomes much easier to remember things. If only there were an effective strategy for forgetting.

Wish list #hashtag

Christmas is coming...

Ok. I wonder if I could make one of these for less than what Steelcase sells them.

Analogies #hashtag

Christmas : Thanksgiving :: Nazi Germany : Czechoslovakia

This post makes me feel sad. It's really funny, but no one will ever read it. The great thing about the internet is that there is a low barrier to entry. At least in the developed work, almost anyone can get online and publish something. The downside is there is so much noise. Most of what I write is just noise, too. It's my venting of frustration, repeating something that someone has already said more clearly and concisely than I have, a hastily scribbled assignment or just me reposting cartoons. Still, today I felt like I had something really funny that I could share with the world, but it will be lost among the millions of blog posts, tweets and status updates that are being uploaded at this very nanosecond. So, yet again, the internet makes it easier for us to speak, but harder for us to hear.

Aside: Originally, the end of the analogy was Poland instead of Czechoslovakia. I thought that the analogy was a better fit with Czechoslovakia. With Poland, the invasion was quick and dramatic whereas Czechoslovakia was slowly annexed (first with the Sudetenland and then with the rest of the country). That better describes the slowly devouring growth that Christmas has become.

Violet Update #hashtag

I've been using Capzles.com to record the flower on my desk; I wrote about creating a Capzles page earlier in the blog. You can check out my flower using this link. Scanning through the slideshow, you can watch my flower go from mostly-dead to its current happy state. It makes me wonder how my violet's twin is doing.

I'm really happy that I've been able to make good use of Capzles.

Kings of the Wergs (ED504) #hashtag

For our Webinar Tool, we decided to go with Pen.io. However, one of the other contestants was Storybird. Storybird is a publishing site that provides students with a set of images and then asked them to create a story about them. It allows for students to quickly create aesthetically pleasing stories. If you make it easier for kids to excel, I think you are more likely to get students to buy-in. The stock set of images was very pretty and I think having that in the background would encourage students to create something that they could really be proud of.

One of the books I liked most was 26 Homegrown Words. I really hate it when I am reading an article and the writer makes up a new word (the type that they put in quotation marks). The English language is full of words; why do we need more? Then I read an alphabet book and realized that sometimes I feel jwift (You'll have to read the book to find out what the word means). So, perhaps it's ok to make up new words. It got me thinking about how cool it would be if one of my students created a new word. Think about it: if you were middle-schooler and you took some feeling, object, action or thought and picked a combination of letters to describe it. Then, later, you found that someone you had never met was using the word that you had created. . .  well . . . wow. . . wouldn't that be empowering?

In my mind, creative writing is disrespected. Consider Jules Verne. Some people consider Verne to possess a prophet-like status because of the way his novels describe technology that wasn't invented until decades later. Verne didn't have visions of the future, he created it. Generations of engineers and scientists grew up reading his books and then went forward and built the world that he had inspired. It takes creativity to find solutions to the world's problems. We need more people who are able to see a world, a better world, that does not yet exist. Math can solve a lot of the world's problems, but mathematicians need something to inspire us. That inspiration is likely to come from language and, in particular, from creative writing.

Related reading: Neil Gaiman and reading fiction.

Completely unrelated aside: You can't write poems about 'poetry' in iambic pentameter. Poetry is dactyl; that means it has one stressed syllable followed by two unstressed syllables. The consecutive unstressed syllables will never fit into an iambic line. At least that is what I think, given my limited knowledge of the English language. My goal for the next week is to use the phrase "They go together like dactyl words and iambic pentameter" and see the confused look on people's face.

Moustaches #hashtag

In previous classes, we have talked about trying to make a more just world. I'm not sure that I want to spend my time trying to make a more just world. It's not that I have anything against justice. It is only that I am not sure what justice is. If justice is people getting what they deserve, what are the chances that I know what they ought to get? So, justice becomes something that I can talk about, write about and think about, but something that I am completely incapable of identifying in the real world. I can create scenarios where I ponder the implications of what justice is, but I will never have the kind of detailed information in real life that I would have in a scenario.

So, I intend to spend my time trying to make a more merciful world. It is a world where we give everyone our best, whether or not they deserve it. It is a world where there is more fun and more laughter and perhaps a little bit more whimsy. I'll leave matters of justice to people who are wiser than I. Today, I am just going to try to make a world where other people smile a little bit more often.

Webinar Reminder #hashtag

Greetings Citizens of the Internet.
This is a friendly reminder that our Pen.io Webinar is tonight. Mr. Lemoyne, Miss Strait and I will be hosting the webinar today at 5:30pm. Just click on the link sometime after 5:00pm on tonight and be prepared to learn.

Webinar #hashtag

Greetings Citizens of the Internet.
This is a friendly inviation to our Pen.io Webinar. Mr. Lemoyne, Miss Strait and I will be hosting the webinar on November 14 at 5:30pm. Just click on the link sometime after 5:00pm on Thursday night and be prepared to learn.

Quicktime #hashtag

Sometimes I feel like being asked to turn in a video in the Quicktime format is like being asked to retype my paper into Portuguese.

Being a Teacher is #hashtag

A large portion of the time we spend is dedicated to learning how to teach. There are methods and strategies and practices to be deployed. I took a few minutes today to think about how to be a teacher. Being a teacher is being a professional optimist. It is seeing the best in people. It is seeing the potential in our students. No matter how difficult they make it, we always want to be looking toward what they could do. Being a professional optimist means seeing the best out of every bad situation. Every failure is a learning experience. Every wrong answer has a bit of truth that we can build around. Every time we get knocked down is an opportunity to practice picking ourselves back up. 

Poetry #hashtag

Classic Folk Verse:

Remember, remember!
The fifth of November,
The Gunpowder treason and plot;
I know of no reason
Why the Gunpowder treason
Should ever be forgot!

Guy Fawkes and his companions
Did the scheme contrive,
To blow the King and Parliament
All up alive.

Threescore barrels, laid below,
To prove old England's overthrow.
But, by God's providence, him they catch,
With a dark lantern, lighting a match!

A stick and a stake
For King James's sake!
If you won't give me one,
I'll take two,
The better for me,
And the worse for you.

A rope, a rope, to hang the Pope,
A penn'orth of cheese to choke him,
A pint of beer to wash it down,
And a jolly good fire to burn him.

Holloa, boys! holloa, boys! make the bells ring!
Holloa, boys! holloa boys! God save the King!
Hip, hip, hooor-r-r-ray!

Thoughts:
4:05pm is 1605 in 24-hour/military time. It was interesting to read how Guy Fawkes Day transformed from an Anti-Catholic Holiday [Fawkes was a Catholic trying to overthrow the Protestant monarchy] to something more patriotic. I am trying to think of something similar among American Holidays, but I have yet to find one. Perhaps Halloween is as close as we've come from completely repurposing a holiday.

Other poetic posts: Poetry 1, Poetry 2, Poetry 3

Remember to Vote #hashtag

This Tuesday remember to vote. . . . for Michigan's Mr. Football.
I'm not going to tell you who to vote for. However, if you are going to vote, remember that this is the Mr. "Football" Award. So, you might want to consider a player who excels in many facets of the game: running, passing, kicking and punting, perhaps.

On a completely unrelated note, here is an article about high school football players.

Beyond digital footprints #hashtag

In a previous posting I wrote about my digital footprint. This XKCD: What if post got me thinking about digital tombstones. Think about it, given the ever shrinking cost of data storage the things we post on the internet will likely be there forever. FOR-EV-ER. My friends grandkids will be able to read this. It got me thinking about the stuff we leave behind.

I am going to write a story, to my friends' grandchildren. Your dad was born on March 21. I always found it easy to remember because it was the same day of the month as my birthday. I remember getting an early morning text the day of your dad's birthday. I had moved into you grandma and grandpa's house to look after the dogs when your grandma went into the hospital. They were great dogs. You may have seen them in pictures. Max was a bit neurotic, but he and I were friends. Cleo was dumb as rocks, but so sweet. We had a tradition of lighting up numerical candles for birthdays. I had a zero in my car waiting for the day your was born (technically his zero-th birthday), but it melted so we never used it.

Thirty-some years from now, when I am dead and gone, you'll be able to read this post in some Google/NSA archive and get a glimpse of what the past was like for your family. I hope this blog-posting was more interesting than anything written by Samuel Pepys, if they still make you read that terrible diary in your French-Chinese class [I'm assuming that the French-Chinese have taken over most of the world by now, and we are all forced to learn to read and write in French-Chinese. So, in the same way that we might read Tolstoy in 'English' class, you'll reading literature in 'French-Chinese'].

Also, if time travel exists when you are reading this. Please come back and tell me about sports outcomes so that I can win lots of money gambling [insert a description to the rest of the plot from 'Back to the Future: Part II" here].

All joking aside, the persistent nature of information on the internet is something that our generation will be the first to live with and learn from. What we do today matters, not just because it affects the people around us, but because there will be a digital record of it for (potentially) the rest of human history. John Donne wrote about how each of us are just one chapter in a big long book. Now that book is available for everyone to read. So, this weekend, when you are playing games at the U-M/MSU tailgate, remember this: your grandkids might read whatever you post on Facebook this weekend. Stay classy, Ann Arbor.

Comics of Literacy (ED402) #hashtag

The following cartoons came from or were inspired by my literacy class. 

It is interesting how the numbers we use in a math class are different from the numbers we encounter in real life. Over the summer, we were working with calculating the sales tax on a jacket that cost $60. In real life, nothing costs $60. The calculation for sales taxes is identical for something that is $59.99 or $60. I wonder if we used more realistic numbers, if students would be terrified by the slightly more complex calculations or it would help them feel more empowered in the real world.

XKCD Original (I cropped to 'keep it rated G')

Also related to literacy is number sense. We spend a lot of time in my placement working to help students develop number sense. It is one of those skills that I take for granted. I had a nice discussion today about what 21/29 was 'close to.' Just at a glance, I could tell that it was between .7 and .75, but some of the students struggled with making that same estimation. I wonder how long it took me to be able to develop the skill to be able at a problems and get a feeling for what a reasonable answer would look like.

Now, just for a bit of math before I go. What does 21/29 actually look like? Well, I started doing the long division to figure out what it was as a repeating decimal. After I got the 11th digit after the decimal point, without seeing a pattern, I stopped. I looked on my calculator (which only goes to 9 digits after the decimal point) to double-check my work. I was right, I still had to wait on the pattern. I used Wolfram to get a solution...
0.7241379310344827586206896551 (repeating)
It goes for 28 digits before it starts to repeat! It got me thinking: I wonder what two-digit denominator would lead to the longest period/repeating part of a decimal. I would ask one of my professors, but I am afraid he would put the question on our next test. Back to math homework. Good night inter-web.

Bad Math (MAT498) #hashtag

I really enjoyed this video about "bad" math and it inspired the rest of this post.

If a student wrote down 1+1=10, most of us would mark it wrong. However, there is the possibility that the student could be right, if he is writing the answer in base-2. In fact, for any two digits, a+b=10 would be a mathematically correct answer, just in base-(a+b). So, 9+9=10 in base-18 and 2+2=10 in base-4.

What about speaking in more general terms?
23+47=72 in base-8

Changing the base makes this simple addition problem look like solving a linear polynomial.
[2(x)+3]+[4(x)+7]=[7(x)+2]
6x+10=7x+2
So x = 8 (makes sense, 8 is a our base.

Looking at bigger numbers, for what base is 123 + 256 = 412?
Now, you could cheat and just look at the unit digit. I notice that 3+6=9 on the left side of the equations, and from the right side I notice that 2 is congruent mod 7 to 9, therefore 7 must be our base. But, if I was not so crafty, I could consider the equation [x^2+2x+3]+[2x^2+5x+6]=[4x^2+x+2]
That works down to 3x^2+7x+9=4x^2+x+2
or 0=x^2-6x-7
So, 0=(x-7)(x+1)
Since we can't have a negative base we will ignore x=-1, Therefore x = 7.
So, in base-7, 123 + 256 = 412.

Geometry / Edublogger (MAT431) (ED504) #hashtag

(I try to include information in the title about which class, if any, this post is related to. Also, if it is at all related to a specific ED504 assignment. Sorry that this title is so jammed full of meta-data)

Hierarchy of Hexagons
When I first read the blog post, I didn't like it. Why would you call a hexagon made up of only right angles "Bob"? That doesn't make sense. What does "Bob" have to do with math? Then, I started thinking about rhombi. Yes, that is the plural of a rhombus. For a freshman in geometry class, is the word "Bob" or "rhombus" more familiar? Does either of them really communicate any information? It really depends on the student's prior knowledge. If a student has a heard of a rhombus before, then they can benefit from the image in their head and the definition that they might remember. Not all students have that.

So, the more I read, the more I liked the Hierarchy of Hexagons activity. It gets students thinking about how to create definitions of their own, how to recognize patterns and how to classify different objects. That's math. That's geometry. That's topology. That's cool. Even if calling a shape "Stacy", seems silly, I shouldn't be too critical. After all, I named my first car "Stacy" and my current auto is affectionately named "Hailey". Speaking of her, I need to go vacuum her before it starts raining.

Disciplinary Differences #hashtag

Poetry #Hashtag

From one of the Harold and Kumar Movies, apparently.

I fear that I will always be
A lonely number like root three.
A three is all that's good and right,
Why must my three keep out of sight.
Beneath a vicious square root sign
I wish instead I were a nine.
For nine could thwart this evil trick,
With just some quick arithmetic.
I know I'll never see the sun, as 1.7321
Such is my reality, a sad irrationality,
When hark! What is this I see,
Another square root of a three
Has quietly come waltzing by,
Together now we multiply
To form a number we prefer,
Rejoicing as an integer.
We break from our mortal bonds,
And with a wave of magic wands.
Our square root signs become unglued,
And love for me has been renewed.

Graphs #hashtag

This is just on observation I had the other day on my way to class. I walked by four cars parked on the sidewalk, which was roughly equal to the number of people I encountered over that same walk. I should probably posts this on Greg's Graphs.

For the Movies #hashtag

Freep: With need for nuclear weapons questioned, builders find a new target - errant asteroids
So we have all these scientists who know how to build bombs that would be used to fight an unwinnable war against a country that no longer exists and we need to find something to do to keep them busy. Basically, we're having them Fact Check "Armageddon"/"Deep Impact". I can't figure out if I think this is awesome or ridiculous.

Fakebook: Everything on the internet isn't real (ED504) #hashtag

I created this awesome Fakebook Profile.
Take a look: Seven

Digital Footprints #hashtag

I got my first e-mail address on May 16, 1997. I used it through high school and college until I finally got my current Gmail account. I recently tried to delete the account and was unsuccessful. I signed in and searched but could not find instructions about how to delete the account. So, somewhere on the internet, there is a Juno e-mail address with an embarrassing username that will send e-mails to me (for the next sixty days until the account goes inactive again). 

So I started searching for what other items I have left hanging around the internet. I found a Yahoo! account and deleted that. I found my webpage and I'm working on deleting that. I found my LiveJournal account and I am saving a personal copy of that and then deleting the account. It is just a matter of going out there and making that digital footprint a little smaller.

If you are interested in searching for someone, check into Spokeo or Pipl. It is also good for finding out accounts that you might still have floating around.

Learning with Technology/ EduBlogger (ED504)

So I stopped by my old work today to work on my RWT. I spread out everything that I was using for the task. I had my laptop (on which I was writing the document), the Kindle Fire (which I was using for a as a web browser/second screen), the Kindle (which is where my "Intellectual Character" text lives) and my Camcorder (which I used to redo my mentor interview).

Behind this pretty picture is my backpack. It has a couple of binders, two Geometry books, a teaching Middle/High School Mathematics books and a Diff Eq book. It makes my back hurt. I can't wait for the day when all textbooks are digital. Dan Meyer writes about his disappointment with digital textbooks. For Dan, the difference between conventional textbooks and e-books is not different enough. Both just present the information with little interaction between the reader and the text. In Dan's world, textbooks would include social networking. Students would be able to modify the text and offer alternate examples and explanations. Rather than reading a problem that said to "draw an octagon" students would be prompted to take a picture of an octagon (e.g. a stop-sign or MMA ring). The textbook would include basic quizzes and integrated formative assessment tasks. He sees the current world of digital textbooks and looks longingly to a future of interactive learning applications.

For me, I have much lower expectations. For the $150 or so a Kindle Fire retails for, I already get a lot. I can search documents. Documents can be automatically updated and can include hyperlinks. I can watch videos and listen to podcasts. From a literature perspective, I have thousands of free classics available within a click. With digital textbooks, I have the option of carrying one device and bringing along every textbook my school owns. So, if I am in Calculus and struggling with partial fractions, I can check out the digital copy of the Pre-calc book to look over some extra examples. For me, the added costs of going digital is worth the pristine shape and clear text of a digital textbook. Digital texts aren't all that different from printed texts, but they are still significantly better.

Capzles (ED504) #hashtag

I am not entirely sure if this counts as "One posting on a 504-inspired or related topic of your choosing" so that is why I gave the double label. I'm sure I'll write another posting that is a better example of something related to 504, but just I've given this one the (ED504) designation just in case I only post distracting content.

I made a Capzles!

Given the bugs that cropped up during the Capzles presentation, I was thinking that perhaps Capzles wasn't useful for educational purposes. My attempts to sign up for Capzles were foiled for the entire week after the presentation. Eventually, it worked and I was able to create my Capzles.

Every day that I bring my camcorder to school, I take a picture of my flower. Over the course of the first few weeks, I saw her slowly start to die. However, she was only mostly dead and since I have adjusted the watering system, she looks much better. She has lost all of her flowers, but, for the first time in a while, I am optimistic that she might survive the school year.

Horticulture aside, how did Capzles work? It was a little bit slow. Every click seemed to take a while to respond. However, I was able to upload my pictures all at once and they were arranged by date; that part went really quickly. It was just when I had to go in and label the pieces and write a description that things bogged down again. Also, the spell-checker in Chrome did not work while I was writing in the description box, so I am sure that everything I wrote is probably only partially legible.

After being able to play around with the tool, I could see a few applications. In science class, if students had to do a long term project that involved watching something grow, Capzles offers an easy way to automatically arrange files by date. Also, it was easy to scroll through the photos and see my plant get worse and then get better. If students were working on a history project and they could get a collection of photographs of the same place over time, then Capzles would offer a powerful way of presenting that information. The strength of Capzles is that it sorts items by date and it allows for an easy side-by-side comparison of images. There are some things that Capzles does well, even if integrating file types besides pictures and music doesn't seem to work.

Google Autocomplete of the Day #hashtag

I am not sure how I feel about people searching for "Who invented electricity." On the one hand, I am happy that people don't know who invented electricity. On the other hand, I am a little bit disappointed in the English-speaking world for asking who invented a natural phenomenon.

It is interesting to think that people are searching for who invented electricity, but they aren't searching for who invented sound, heat or gravity.

The Power of Pink/My placement #hashtag

NFL Network: Power of Pink
The NFL Network is going to show this video segment over the weekend about my placement school. So, we're kind of famous.

Math and Truth #hashtag

from "Beyond Being Told Not to Tell"  by Daniel Chazan and Deborah Ball on page 6.

XKCD.com

Love and Mathematics / EduBlogger (ED504)

Dan Meyer's Blog (dy/dan) is the center of my blogosphere. He not only brings in his own content, but he is great about aggregating other posts that he has read. On my latest visit to, dy/dan, I came across a link to Sarah Hagan's blog and a couple of posts that she had written. 

The first post I came across was about Relations and Functions. In the example she used in class, she stated that if Bob is dating Jill and Sue, then he's not in a functional relationship. If you wanted to see the relationship described as ordered pairs, it would look like {(Bob, Jill), (Bob, Sue)} -> Not a function. The example made me laugh and apparently made her students laugh, too. It activated existing schema surrounding the phrase "functional relationship", even if the example was based upon the social norms of rural Oklahoma. The use of example instantly got me thinking about XKCD.

XKCD: Greatest Comic Ever

We can always make use of humor as a way of gaining students attention and the the use of familiar language to convey mathematical meaning, even if it is built around puns.

Another recent posting was titled Good Things is a Great thing. In the attempt to build a positive classroom environment, Ms. Hagan takes a few minutes each Monday morning to have students share one good thing that has happened to them. Originally, the Okie thought it was a bit hokey, but the students have latched onto it. The post got me thinking about the importance of building relationships between students and the teachers. We are teaching math to people. The emphasis is on the students, not the content. Getting the students to talk about themselves and their interests is going to be a necessary condition before they are likely to engage in a conversation about mathematics. Starting off with good things helps to make students comfortable in the classroom.

In the year 2000 / Tech in my placement (ED504)

I have a very short commute most mornings to my placement because, as I have previously mentioned, my placement school is the very high school that I graduated from a decade ago. This has given me the ability to compare how the use of technology has changed in the school since I attended.

We have added two more computer labs since I attended. One computer lab is new, while one of the "new" computer labs came from dividing an oversized computer lab into two smaller labs. Each classroom features the same 27 inch TV mounted to the wall from when I was walking down the halls. Nowadays the morning announcements feature much better graphics, including green screen backgrounds for the students/anchors sitting at their mock news desks. Clearly, the TV and communication classrooms have upgraded their equipment. A wireless network spans the entire school and a handful of new routers were installed over the summer to help make the coverage more reliable.

Inside the math classroom, little has changed in terms of technology. The overhead projector has been replaced by a Doc-Cam, LCD projector and a laptop combination. Every classroom I have seen has a similar setup for the projector. We can contrast that with the blackboards that hang next to the projector screen; we still use chalk in most of the classrooms. We have a classroom set of TI-81 calculators (The TI-81 was discontinued in 1996). My mentor teacher has a pair of Windows ME laptops set up in the corner of the room in case we ever need to use them for student projects. The technology insides the classroom itself has not changed much.

One noticeable addition is the use of Skyward for managing attendance and grades. I have already heard from a few students who monitor their grades and assignments on a daily basis. Skyward also features a calendar with students homework in them. If a student misses a day they can download any handouts that they missed in class. The teachers and the students are connected. Another feature of technology in my placement is our use of the flipped classroom. Ten years ago, most students had dial-up or nothing. Now there is an expectation that all students will be able to watch videos online at home.

The ubiquity of students' cell phones is another technological change that I have noticed in my placement. Most of the students have a smartphone. Most of their smart phones have cracked screens. Many students wear earbuds like a piece of clothing. Most of my students think that if they put their cell phone under their desk that they can text and I won't notice.

There are a few things missing from my placement. We do not have a full time media specialist. The doors to the library are locked before lunch. Also, as I previously noted, we have a wireless network in the school. On the other hand, we don't have laptops. The teachers have laptops, but students do not. We don't have a one-to-one technology policy. We don't even have a laptop cart. We have WiFi throughout the school so that teachers don't have to bother about plugging in an ethernet cord to their computer and so that students don't have to use their cell phone data plan when are watching videos on the internet. I see technology in my placement, but I am not sure we use technology to further student learning any better than we did a decade ago.

Google Autocomplete of the Day 10/6/13 #hashtag

I was expecting "how can i get help with algebra" to be in the top four. I was totally wrong.

Google Autocomplete of the Day 10/5/13 #hashtag

I always find these amusing. Apparently, people on the internet really want to get iOS 7, grow taller and get rid of bugs. I might have to make this a recurring item on the blog.

Podmaster /Tech Tools (ED504)

"You can call me at my new New York phone number" is going to be a Facebook post of mine one of these days, just so I can trick my friends into thinking that I'm moving to a different country (New York is practically a different country).

How did I get a phone number in New York? I got it through the magic of Google Voice. Google Voice is an internet phone service. It is free for domestic calls and can be added onto an existing Google/Gmail account. Not only does Google Voice let me make phone calls from my computer, but it will forward calls to my cell phone. In fact, I can have Google Voice forward calls to six different phones.

Another magical feature about Google Voice is the recording features. Voice mails are recorded, transcribed and e-mailed to my Gmail account. The quality of the transcription varies from call to call, but at the very least I can usually pick out the name and some of the details. For example, the other night I got a voicemail that read "Hello Mr. Nickel. If you can give me a call back. I really need that money and I'll Albert 30 caps okay. Have a good day..." I could see the caller's number and got the basics of the call; someone was calling to remind me that I owed them money, although the part about "Albert 30 caps okay" was actually about breaking my knee caps. The transcriptions still need a little work.

Probably the most interesting feature is the call recording option. With the push of a button, a lovely female voice will tell my caller that the conversation is now being recorded. It gives me the option of recording interviews, saving my best explanations or keeping track of a conference call so that I could back and later listen to what we were talking about. So, now, not only will the NSA be recording my phone calls, but I can, too.

Here are some possible uses for Google Voice in Education

• Create a hotline. Because the phone number can be forwarded to six different phones, it could be shared with six different teachers or six different coaches. The JV football coaches could have one number that a player could call and reach the next available coach. Similarly a group of math teachers could set up a call line for math help. Users can automatically set up a schedule so that the phone won't ring at four in the morning, too.
• Student interviews. Anytime a student needs to interview someone for a project, they can do it over the phone and have a recording of the process.
• Leave a message. Teachers could have the phone number and just always leave it in Do Not Disturb mode. They could post a daily outgoing voicemail to pass information onto students or they could have students call in and leave a message requesting the homework problems they wanted to go over on the next day.

The other audio tool that I explored was Audacity. If using Google Voice was like playing checkers, then using Audacity was like playing chess. Anyone can play chess, but it it hard to be good at chess. Similarly, I had no problem using Audacity. I was able to record audio files, import some background music and cut some of my "Ummms", "Okays" and silence from an interview I recorded via Google Voice (Thank you Dr. Taylor). I even played around with some of the effects by having the music fade out. If you need to edit audio, Audacity is free and users can easily combine clips from multiple files into one audio file. If you want to master how to use Audacity, on the other hand, get working. It's going to take a while.

While working with podcasts, I came across two that were particularly interesting. NPR's Planet Money is something that I have listened to for years. When I tutored economics, I would make copies of some of the episodes and give them to students so that they could hear about the concepts they were reading about in their text. In the process of researching Math Podcasts, I found very little in terms of useful audio podcasts. However, I did come across the BBC's "More or Less". It is loosely related to math. They talk about making sense of statistics in the news. While it might not be directly related to solving linear equations or completing the square, listening to the stories they talk about could be an exercise in developing quantitative reasoning skills for students.

Redheads #hashtag

Are 19% of the redheads living in Scotland?Someone made up the fact that 19% of the world's redheaded population lives in Scotland and it showed up in a BBC News report. It turns out that only 1% of the world's redheaded population live in Scotland. There is an evolutionary advantage to having light skin/red hair for people living outside of the tropics; pale skin is much more efficient at using limited amounts of sunlight to produce vitamin D.

Also, Left-handed people do not die 9 years later. Also surprisingly, left-handed are on average younger than right-handed people.

Game on Wayne (ED504)

It's good to be back to blogging.

One of the takeaways from Peter Pasque Prezi presentations was a sort discussion he had about the difference between games and puzzles. Puzzles are something that we only solve once. Having worked on quite a few jigsaw puzzles in my life, I could not agree more. Those 1000 piece puzzles are essentially disposable items. I have never met anyone who solves a puzzles, then mixes up all the pieces and immediately tries again. On the other hand, I have spent hours playing the same game only to go to sleep thinking about the next time I will get to play. In fact, I am forbidden myself from playing any Sid Meier game until I have completed the MAC program. I do not have the self-control to stop playing.

Games and puzzles are different in what they give us and what they asks of us. A puzzle asks one questions, "How does this fit together?" A game gives us a couple of answers and then asks us to find our own questions. The rules for "Axis and Allies" are extensive, but they offer no insight into whether invading Australia is a good idea or not. As paradoxical as they sound, the rules to games tell us "how to play", but they do not tell us "how to play" a game. They set up boundaries, but we are free to explore anywhere inside those boundaries. It gives us infinitely more options to try and to evaluate than a puzzle.

In terms of evaluation, I am not entirely sure how badging would work. On the one hand, the older I get, the less value I see in grading courses. As a high school student, I was always excited to get my report card. I can contrast that with the MAC Program, where I have yet to check on my final grades from the summer term. Looking over returned assignments gives me an idea of what I know and where I could improve. Reading through my notes from last semester will give me an idea of what I know and what I still have questions about. Looking at a letter A through F is such an inaccurate measure of knowledge. If I get an A, assuming accurate measurements, it tells me I have displayed knowledge and skill of all the required material. If I get a B or a C, the grade tells me that I am missing something. At this point, the advantage of badging becomes apparent. Instead of getting a grade in Geometry at the end of the semester, my students would collect a badge for Trig-o-Mastery, a badge for Constructions, and a badge for Proofiness. Students and I would both have a better idea of what skills they had demonstrated.

The problems start to creep up when comparing students. Both Usain Bolt and I could run 40 meters without falling over, but one of us is clearly better at it than the other. The problem with badges becomes one of setting standards. If we want to create a meaningful badge for running 40 meters, what becomes the dividing line between an acceptable performance and unacceptable performance? If a student just barely meets the requirements for Trig-o-Mastery badge, then they might struggle when they start in a trigonometry class the following year. Two students could earn the same badge but still have huge differences in their current ability level. Another problem with a badging system is that the binary nature of the system makes it difficult for students to see progress. A student who improves might still not improve enough to earn a badge and feel an undeserved feeling of failure. Finally, there is the permanent nature of badges. Badges should operate like CPR certification or driver's license, they should expire at some point. Just because one of my students can consistently solve a quadratic equation in grade nine does not mean that the knowledge will be retained.

Well, there we are. This is blog posts #50. I should get a Blogger badge.

Master of Blogging

My Desk #hashtag

I took a picture of a few items around my desk at my school. I know it is illegal to post pictures of students. It might be of questionable legality to post pictures of my classroom. I feel pretty safe showing pictures of these closeups.

I have a few quotes on my bulletin board behind my desk. They are mostly from Winston Churchill. There are also some math cartoons. I also have a picture of CUJO on my bulletin board. The content really isn't for the students. It's more for me. It's my six square-feet of sanctuary. 

On my desk, I have a coffee mug with pens in it. I have to fix the three-hole punch (it is currently broken). I have a power cord and extra monitor for my laptop, although I rarely use my laptop at school. You can also see my window.

Also, I have my African violet. I'm not sure she is going to make it. I have to go do some research and figure out what it means when the leaves start to curl up. I'm not sure if she gets enough sun/too much sun or enough water/too much water. The note on the pot is a lotto ticket. It says, "Don't be afraid to fail." Even if failure is likely, it might still worth a shot, if the prize is worthwhile.

Come up with a great idea, then go home and get things done #hashtag

Read WIRED: Balance Creativity and Productivity

Is letting employees telecommute a good idea? It turns out that the answer is maybe. Studies show that employees are more creative when they have opportunities to serendipitously interact with one another. On the other hand, they tend to be more productive when they are allowed to work from home. Why does this matter?

If the same is true for office workers and students, then it gives us an idea about what type of work should be done in class and at home. If students are more creative when they are with a group, then students should be assigned problems (new tasks) during class time. Homework should focus on exercise (repeated tasks designed to develop mastery) or other assignments that the student needs to get done.

The article also gives us ideas about how to study. When it comes to writing a paper, we should work with others long enough get a set of good ideas. Then we should go home and write the paper.

Read/Write and Math (ED402) & #hashtag

Our discussion in ED402/Literacy got me thinking about the differences between reading and writing. Originally, I thought of reading and writing as two distinct activities. Reading was inputting information and writing was outputting information. Then I thought more about the topic. Reading is much more complex than that. When we read, we are taking some sort of external stimulus and thinking about it. However, the information is not all new. What we often do is read something and relate it to something that we already know. At no point while reading this paragraph has the reader encountered a new word. Instead, a series of words in this text is being rearranged to communicate ideas. So, reading is less about input and more about arranging ideas and making connections.

What is writing? Well, writing is arranging ideas and making connections. In that way, reading and writing are the same cognitive task. The biggest difference is medium. When we read, it is a cognitive task. Physical manifestations like the movement of the eyes along the text or the mouthing of words might occur, but what is really going on is in the brain. Similarly, when we write, we are still arranging ideas and searching for the right word. It is the same activity as reading, it is just that there is a different, more overt, set of physical manifestations. Whether I am thinking about what sentence I am going to write next or evaluating the sentence I just wrote, I am doing the same thing.

Related to literacy, I gained a new idea of the components of literacy. Being literate means knowing how to navigate, understand context and extract meaning. I think that the part about being able to extract meaning is the part that most people understand as being literate. If I can take this jumble of stick figures and curves and turn into sounds or ideas, that is the basic aspect of literacy. The idea of navigating was something completely new for me. It is about knowing where to look for information. Part of that concept is related to syntactic literacy, the ability to understand grammar and sentence structure. If I write that "Alruk is welderl", then English speakers will be slightly confused. They will have no idea what "Alruk" is, but they will still know that it is a person, place, thing or idea. More specifically, they will know that "Alruk" is not just any noun but also the subject of the sentence. Furthermore, they might not know what "welderl" means, but they will have a good idea that is is an adjective.

Literacy has the potential to be a rather complex topic. We'll see how the semester goes.

Education in the News #hashtag

Greetings Mr. Ross. Last time it rained really hard, it started raining inside the second floor hallway in the School of Education. I'm not sure if they fixed the roof or if next time it rains really hard, we're going to have a similar leak. I am just saying... in case you hadn't noticed.

In unrelated news, I like Arne Duncan. He's talking about how high schools should start later in the day because the science indicates that students learn better when they have been able to sleep a full night. What Arne is talking about matches up with what I read in Brain Rules. In Chapter 7, Medina writes "When sleep was restricted to six hours or less per night for just five nights, for example, cognitive performance matched that of a person suffering from 48 hours of continual sleep deprivation." So, that means that means that by the time Friday rolls around, students are hardly functioning.

It makes me wonder if giving a test on a Friday is a good idea. How accurate would the results be? If I give students a test on Monday, then I might see lower scores because students would forget things in between the previous class's review session and the exam. However, the lower scores might be a more accurate gauge of their long term retention. If I give a test to a sleep-deprived adolescent on Friday afternoon, then the lower score might be the results of the environmental stresses from a lack of sleep rather measuring diminished cognitive functioning.

Starting school an hour later seems like a great idea. The only problem is that it would mean that school ends an hour later. That means football practice runs an hour later. The practice for the musical runs later. Students work an hour less at their part-time job. In the end students might just end up sleeping in an hour later but staying up an hour later, too. There is a simple fix. Make the school day shorter. Now, a new problem has arises. How do you fit in the necessary number of instructional hours? Simple. Make the school year longer. Summer vacation suddenly becomes a month shorter. It sounds inconvenient for teachers, but it is important to remember the purpose of schooling. A school system should be focused on educating children, not making life easier for it's employees.

I wonder how much more expensive it would be to have a longer school year.

Moving on to the next topic, one Arkansas school district is arming teachers. This just seems like an awful idea. I can imagine why large schools might want to have an armed security guard. I can even fathom rural school districts, where police response time might be slow, arming certain administrators. I cannot begin to understand how a school with dozens of guns is going to create a safe environment for schools.