Jan 152017
 

One question that comes ups often with math majors in the program is “Why do I have to take a computer science class?”

I am not sure where the official requirement comes from, but I can say that I am extremely thankful I had a computer programming class in college. It was over 20 years ago, and it was Pascal programming, but I am very happy that I still remember the skills I learned. I don’t remember anything about Pascal, but over the last 20 years, and especially the last three weeks, I have used the heck out of those skills.

When I was in business, the programming skills allowed me do some serious Excel sheets and data crunching that got me noticed and promoted.

As a teacher, those Excel skills allowed me to strip data from the PDF reports and turn those into useful files that we could actually mine for relevant data on our learners and their learning. Those skills also allowed me to learn basic HTML and CSS coding to build websites over a Christmas break and create multiple websites.

Now, as a master teacher I have spent several weeks building a very complex database in Access to manage our check in and check out process with the hundreds (soon to be thousands) of items in our teaching supply store room. To do this, I have had to teach myself Visual Basic, Access structure, as well as some basic SQL database language.

Now don’t get me wrong.I do not have anywhere near the skills to be paid to program in any of these languages, and it is taking me 5 times longer than a real programmer would take. But, because of that Pascal programming class 26 years ago I have the ability to learn the new skills, new languages, and troubleshoot the really bad code I am writing and make it better.

Why should today’s learners learn coding? Because if this dinosaur can reap these benefits out of the class over my career, then imagine what benefits our learners today will reap over the next 25 years! It only gets more important and more essential from here.

May 282016
 

I have been searching for a bulletproof, simple, and efficient backup solution for my PC for about two years now. I have tried several different tools, online versions, software versions, and nothing really worked for me. Maybe I was too picky. More like too lazy, really.

image of safe

First off, my requirements:

I have read repeatedly about the 3-2-1 policy of backups. Backblaze has a good explanation of it. 3 copies, 2 onsite in different devices, 1 offsite for security.

I believe this is a minimum backup requirement, and everything I do is to attain it. However, attaining it is a pain in the rear, which is why so few people really do it, I believe. It has taken me about two years before I found something really simple and easy that allows me to reach this goal.

I have two networked hard drives on my desk. One is a 4 terabyte drive, and the other is an older 500 GB drive. The 4 TB is the main drive, and the older one is a redundant backup.

I also have a 128 GB micro SD card in my Surface Pro. Finally, I have two 80 GB iPod Classics.

I require the software to be single purchase, and less than $30.00. That is the limit I placed on the purchasing. I do not want to pay monthly for backups, because I believe it will be a continuous expense over the PhD process and beyond. I also use Dropbox, (and have 76 GB of free storage on it) so I do not need a cloud service backup.

After using CrashPlan, and about 10 other softwares for a couple of months at a time, I have finally found a backup solution that works for my lazy self.

I purchased BVCKUP 2.  Cost for home use is $19.95. Here is why I purchased it.

It’s backups are not encrypted, just simply backed up. The software is TINY! I mean really small. It sits in the system tray, monitoring the computer, and does incremental (delta) backups on my schedule. Currently I have it backing up every 2 hours to the 4 TB drive.

It saves deleted files in a “deleted files” folder. This way, when a file is deleted, it removes it from the folder on the backup, but does not delete it.

Once a week (currently Saturday mornings) it backs up from the 4 TB drive to the 500GB drive.

Finally, the 128 GB micro SD card in the computer has second by second backups. The reason I am not relying on it at all, is that this chip is with my computer. It is encrypted, with my computer. If my Surface is stolen, the chip and the computer are useless because my password is brutal. If my computer breaks, I have it as a backup. However, the category of “stolen” negates this as a reliable backup system.

Last but not least, I have the two 80 GB iPods. These work fabulously as external hard drives. I reformatted them, and use them as backups. I backup to them and take it to work with me. One is always at work, one is in my bag. I swap them out at work.

Finally, I do nothing once this is set up. BVCKUP monitors the computer looking for the drives and the time. Bvckup recognizes when one of the iPods is plugged in and does the backup then and there. It is fast and small enough that there is virtually no hit to using the computer. I don’t notice it at all.

All I have to do is plug in the iPod, and Bvckup does its thing.

I turn on the 500 GB hard drive once a week. Bvckup recognizes it is on, and backups the 4 TB drive immediately.

I spent 15 minutes setting up the program, and now I do nothing but plug the drives in. I have complete peace of mind for all of my PhD files, my teaching files, my program’s files, the grants I am writing, the articles I am writing, etc.

I can break my computer over my knee, it could be stolen tomorrow, and I can have 100% of my files replaced on a new computer in less than an hour after getting home.

This is pretty powerful, and I thought that peace of mind is worth writing about. After two years of working on coursework for the PhD and knowing all along that I could lose everything if I wasn’t careful, I no longer have to worry.

Try it. I think you will like it too. It is completely free for two weeks, no strings attached. That is what sold me, to be honest. After two weeks with dead simple backups, I realized that one little worry was taken off my shoulders.

That is worth $19.95.

 Posted by at 9:05 pm  Tagged with:
Jun 082015
 

My learners have been using Plot.ly for a week, and have asked me a ton of questions on how to do certain things with their data. I wanted to add details to my last post on Plot.ly v. JMP and tell you the decision I made regarding the issue. All of the questions I have below are actual questions / issues  my learners ran into using Plot.ly.

Issue 1. How to add % totals to the columns of data in a graph?

One group of learners had a beautiful graph made in Plot.ly. It was nice, communicated well, but had lots of information in it. They wanted to put the % of each column in the graph to make it more informative.

In other words, they had this ……….and wanted this. (the reason for the arrow in a sec)

graph1 graph2

Yes, these are JMP graphs. Why? Because after an hour of looking, I could not find a way to have Plot.ly do it. Their help is silent on this issue, and I looked through a whole bunch of graphs shared on their website and found not a single one to do that.

As far as JMP, it took two clicks. I can’t show the menu because it is a drop down and as I tried to screen cap, it went away. You click the red triangle I pointed to, hover over to “Histogram Options,” and click on “Show percents.” If you want to “Show counts,” you can do that too. One or both! Two clicks. This was incredibly simple to do in JMP, incredibly difficult in Plot.ly.

Issue 2: Chi-Square test

I already dealt with the fact that Plot.ly calls graphs that use categorical information histograms in my last post. This has caused so. much. confusion.

But now my learners are trying to do the statistics for their data and see if there are significant differences in their samples. They are trying to DO statistical inferences. If their data is quantitative, they can do a t-test easily. Well, they can do a two sample t-test easily. They cannot do a one sample t-test or a matched pair t-test. They cannot do a z-test in Plot.ly, and as it turns out, you cannot do a Chi-Square test in Plot.ly unless you already have the summary counts.

Really? I can do the “histogram” to get the counts, but I cannot import those counts into the table to do the Chi-square? It won’t count the instances of words to count them for the test?

For example, if the learners data looks like this:

data1  Plot.ly will do a histogram for it and tell me what percent or what counts there are for Gender and AP/Honors.

If I want a Chi-Square test for these two columns, the only way I could make it work was to look at the graph of counts, write down the information into a two-way table, and enter the counts as a matrix in the graphing calculator.

To do the same thing in JMP, we do the following steps:

1.  Go to Analyze, Fit y by x JMP1

 

2. Click on OK. That’s it. The output contains the following:

JMP2  A mosaic plot of the graph which is nothing more than a stacked bar chart, except the width of each column is proportional to the total number of things in the column.

Next, we get the contingency table. If I click the red triangle, I can choose other values to include or exclude from the table.

Finally, the Chi-Square test p-value.

That was around 6 clicks, instead of making the graph, counting from the graph and writing a table, and then inputting the table to the calculator.

Issue 3: separating data by a response

The group who was doing the AP/Honors and work in Issue 2 had another problem. They asked for GPA and the number of hours you worked. But they needed the mean GPA of only those in AP/Honors and those not in AP/Honors, as well as the number of hours worked.

Plot.ly will give us the total 1 variable stats for the column of hours worked, but it will not give it to us in two groups of Y/N based on type of classes taken. It will not do it.

Enter JMP. 6 clicks. Analyze, Distribution, put the variable where you want them, OK.

JMP5

That’s it. You get a 1 variable stats for those who are in AP/Honors, and a separate 1 variable stats for those not in AP/Honors. Doing a two sample t-test is simple and easy once this information is obtained. This is not information Plot.ly can give us.

Issue 4: Linear Regression t-test

Last issue, and then I will stop. I have several learners doing quantitative projects that lend themselves to linear regressions and linear regression t-tests.

Plot.ly makes beautiful scatterplots. You can adjust the axis, overlay the regression line, insert the equation into the graph, etc. They are pretty.

But, if you want a residual plot. No go. If you want to reinforce the statistics of y=a + bx. No go.

This is what it looks like in Plot.ly.

plotly1 You have y=mx + b from algebra, you cannot do residuals, and you CANNOT do a linreg t-test.

In JMP, it looks like this:

JMP4 5 clicks, Analyze, Fit Y by X, put the variables in the correct spots, and hit OK. Notice this is the exact same dialogue box you use for categorical data. JMP uses the same path for different types of data, but tells you in the bottom left corner HOW it will act on your data.

You get output that looks like this:

JMP3 If you want the residual plot, hit the red triangle next to “Linear Fit” and show residual plot. That easy.

Bottom line

Although I fully understand that every single complaint I have had with Plot.ly can be solved by learning the programming language and learning to program the software, I don’t think I can ask high school learners, in the last 4 weeks of class, to learn it so they can do a project on statistics. Honestly, I don’t want to take the time to learn the programming language of Plot.ly so that I can do it for them, either.

Plot.ly makes BEAUTIFUL graphs. It is a powerful platform to show connections between quantitative data sets. But, it does a so-so to bad job on statistics.

JMP makes graphs that may not be beautiful, but the statistics is primary to the operation of the program and makes doing the statistics easy. I think without some major changes to Plot.ly to work towards the statistics side instead of the data representation side I will go back to using JMP next year.

It was just too difficult to teach the way Plot.ly handles or mishandles the stats.

 

Sep 112014
 

Today was my quiet day, only two classes. But, I was busy all lunch upgrading my learners calculators!

2014-09-11 12.28.03  Yes, that is the pile I have done today at lunch. About 5 learners have already come in and picked their calculator up, thank goodness. I am a bit nervous having $1200 of calculators sitting on my shelf, especially when they are not mine!

This is one of the things that we don’t often realize takes up a ton of time. The learners don’t realize that these things have operating systems, and that the operating systems change from time to time. When learners are buying calcs on eBay (which I always encourage because TI=ripoff) the calcs often come with out of date OS’s and are lacking functions that truly make the calc useful.

For example, look at the following two prompts, both come directly off of the TI-84:

TI-84NEWvs.  TI-84OLD

 

Which one of these screens would you rather see when typing in information?  Me too. The left one is much more friendly.  I say at the beginning of my class, every day for the next two weeks, “You want me to make sure your calculator is updated. Please come see me.” We had a 2 minute discussion of what the current versions were the other day when we were talking calculators too.

I think this is the biggest change so far this year on the calculator front. Last year, I had 5% of my learners ask me to update their calcs. This year, I am up to around 40% already. That is worth it. I am really annoyed in May when someone says, “Yea, I knew there was something about updating, but I never bothered.” That person probably is not trying for a 5.

How to make this process easy? For the NSpires, have 2 4 port hubs with cables plugged in. This allows you to shove out updates to 8 similar calcs all at once using the Teacher Software.

For the TI-83 and 84’s you have to update one at a time, but it is fairly quick using TI-Connect.

Oh, and it helps if you have a directory that looks like this: calc directory

All the current OS update files, old update files (bcs the NSpire must be updated to 1.7 before you can take it to 3.9), 83, 84, 84C images, etc. I download all the new files when they update (2 times a year for the NSpires, really TI?)

What a pain in the butt. But it helps my learners.

—————-

AP Stats:

Not much happened today. It was a continuation of yesterday (same content, different period). Tomorrow is my 3 in a row stats day.  I am going to challenge them with some bad graphs and another short relay card race on contingency tables. Then, moving on to 1 variable quantitative stats. Yay!

Alg 2 Honors:

It was an AMAZEBALLS Day.  We did this exercise with one quadratic function. Just one. But the conversation we had was so amazing. I gave then one, factorable function in Vertex form. Then we started going to town. The “wow, look at the connection here” and “oh, I get it why it was this!” and “wow, this is all the same stuff!” was terrific.

The homework was to do one more.  The future of this looks like doing another one. Then, I will give one in standard form, and we will have to teach completing the square. And they will get one that has imaginary roots, and I will discuss imaginary numbers. This one page will get used 200 times throughout the year to deeply understand the functions and the connections between functions.

functionfun  File can be downloaded too.

And the day was awesome because I said about 20 words, and my learners said about 200. I am shooting for a 5% ratio tomorrow.

Sep 092014
 

fire-142514_640 via

With three sections of 32, 34 and 35 in AP Stats  I am trying something different this year with teaching calculator skills. Instead of teaching the skills as I go like I did in previous years I switched it up and burned a day. It was not wasted though, it was highly productive. I have learners with Nspire’s, TI-83’s, TI-84’s, TI-89 Titaniums, and  Casio’s in my class. This variety is killer with a large class. If I had to teach how to do a 1 variable stats on all platforms as I go, class would grind to a halt pretty quickly.

With that in mind, I decided to do something radically different. I burned the day of content, and instead focused on “can you find these commands on your calculator don’t worry about what it means just find them.”

Calculator fill in blank instructions DOCX format

Calculator fill in blank instructions PDF format

I am okay with burning the day because I promised the class when one of them said, “But wait, I forgot how to do a 1 var stats!” my response would be, “Then I am here at lunch for you to show you.”  I will not spend any time in class teaching how to use the calculator, we will spend time in class USING the calculator.

In addition, I added some materials to my site for AP Stats: http://www.mrwaddell.net/apstats/  for calculator help:  http://www.mrwaddell.net/apstats/learner-resources/calculator-instructions 

There are links to video playlists, video searching, as well as some good resources for using the different calculators.

Will it work? Only some time will tell.

I know that I will be busy updating calcs over the next few weeks. That is super important.

 

 

Aug 042014
 

2014-07-25 12.48.04

My Favorites are some of the best part of the TwitterMathCamp experience, and this year was no different. I know one favorite I had was walking into this building and seeing that even a public high school could afford to build a dedicated Science & Math Center!

But inside the building, we were offering our own My Favorites. I had one my favorite that I offered, which is a cheap (free) way to record your class so you can observe yourself.

Take an old smartphone and remove all the apps. It is best to use a phone that has a SD card, but if you can clean enough space off of an internal memory phone that works too. Once you have at least 4 gig free, then you have enough space to record 45 minutes of video at 720p or 30 minutes at 1080p. Ideally you would want at least 8 gigs so there is extra space.

Once you have this phone ready, you can use whatever you have on hand to construct your own stand. Lego’s work great, a coffee cup, or even a paperclip. Learners will freak out at a tripod and video camera set up in the back of the room (I know, take it from personal experience) while they will not even think of the phone sitting on a shelf recording them.

Two other My Favorites that were offered by others that I really liked are Plickers and a very interesting and annoying problem that has incredible extensions.

Plickers are “Paper Clickers” and it is genius. Using a cell phone or tablet with camera and the paper funky symbols you can poll the class on a question and have the responses immediately tracked and recorded. You can show the class results in bar graphs, and later can use the results for data tracking and demonstrating what you are doing for your admin. Great discussion and engagement in class and  data tracking for later. It is a win-win.

Finally is this problem. IT is tricky, fun, amazing, and all around a well designed problem.

triangles

What proportion of the triangles is shaded?

That is it, just find the shaded area. The solution has extensions all over the place and is a great problem to try and work through.

I hope you Enjoy!

Jul 012013
 

clip_image002 via

I want to begin with an apology for the length of this post. It is long, but the payoff is huge (especially since it was hinted at that there may be a question on a future AP exam that follows this idea closely).

So, I will kick it off with great way of writing Null and Alternative Hypothesis statements that is very understandable and fits with the ideas written about in the first post in this series.

There are only 2 conclusions you can write when you are doing inference testing and ONLY these two which mirror the types of errors:

1. Because the pvalue of (__) is less than alpha = (__) we reject the Ho. There is convincing evidence that (Ha – write out).

2. Because the pvalue of (__) is greater than alpha = (__) we fail to reject the Ho. There is not convincing evidence that (Ha – write out).

Type I Error: Finding convincing evidence that Ha is true when, when it really isn’t.

Type II Error: Not finding convincing evidence that Ha is true, when it really is.

This is the format / structure of Null and Alternative answers and formulation for type I and type II errors that Josh Tabor uses in class. It is aligned with the two statements he uses at the beginning of the year, as well as the evidence / convincing evidence questions he asks.

But it doesn’t really explain power, yet.

To do that, let’s look at a story that can be used in class.

A particular high school batter, Johnny, hit .250 last year’s season, and was not very happy with that average. Over the summer Johnny attended several batting and baseball camps and feels he improved. Not just improved a little, but improved dramatically! Johnny now feels he can hit .333 based on his performance at camps, and he is ready to take a larger role on the team. However, the coach still believes Johnny is a .250 hitter. The coach, however, has a good grounding in stats, so he sets up a good batting experiment for Johnny. He is going to take a sample of 20 pitches, average the number of hits, and make the decision based on that sample.

At the end of the practice, Johnny hit 9/20 or .450! Johnny says this means he is way better than .333, but the coach disagrees and says the .333 is reasonable.

So what is going on here? At the beginning of the year, we would have two options:

A. Johnny achieved that number of hits through random chance

B. Johnny is actually better than the coach thought

Do we have evidence for one or the other? Do we have convincing evidence?

At this point of the year we would have a Null and Alternative:

Ho: Johnny is not a .333 batting average batter

HA: Johnny is a .333 batting average batter

We could use the p-value and the alpha level we choose to make a decision, and we are finished. Right?

Not so fast. What about the power of the test created by the coach?

clip_image004

Well, let’s start with what we know about power. What 4 things can change, or have an effect on the power of a test?

1. Make alpha bigger. Not requiring as much convincing evidence.

2. Increase sample size. More information makes making a decision easier. The curves become narrower, which makes beta smaller.

3. Make SD smaller by better experimental design, think the Rania problem earlier.

4. Have the means of the two curves further apart, which is also called the Effect Size.

There is a handy applet from Rossman/Chance that will help us out tremendously in this question. The one we specifically want is on Power (and oddly enough has a baseball set-up J).

I will post some screen captures here to help explain.

clip_image005

The top distribution with the red little end is the Null Hypothesis. The red dots (all three of them) are the number of samples of size 20 that our simulation had 9/20 hits. We did a hundred samples, so we should be confident that the curve is reasonably distributed. The p-value associated with Johnny having 9 hits out of 20 is .03, so we have an answer to our question. The coach should believe that Johnny improved from a .250 batting average.

But here is the payoff.

The bottom distribution with the green end is the Alternative hypothesis. The number of green samples, 21/100 is the POWER of the test. The coach has a 21% probability of not making a type II error here! The black part of the distribution is the beta, 79/100 or 79%.

Notice the mean of the top, Null, distribution is approximately 5, while the mean of the bottom distribution, Alternative, is approximately 6. The difference between them is the Effect Size. How can we increase the power of this test? We can take increase the sample size from 20 to 80. That will reduce the spread by half. That would give us this picture:

clip_image006

That increased the power to 37%. Of course, we would have to know how many hits Johnny had on the test with 80 at bats. I would think he would be one tired baseball player by that point.

Josh hinted strongly that a “calculate power” problem is coming on the AP exam, and this is similar to the format that would be used. It isn’t that hard when you are looking at it like this. In fact, power makes a lot more sense.

Sep 212012
 

It has been a while since I did a #MyFavFriday post, but I have to share this because it has been making my life so much easier this school year.

Dropbox.  Yes, that service. I know, so many other people have written about it in the past, and so have I, but this year I made the move to put 100% of my teaching files* into dropbox and I haven’t looked back.

All dropbox is, is a small program on your machine that monitors a particular folder, named “Dropbox”. Anything in that folder is synced with the web portal and any other computer that is signed in. It is a folder, nothing more. If you can save a file in “My Documents” you can use dropbox. Just save it to “Dropbox/Algebra 1” instead of “My Documents/Algebra 1”.

These are some of the things I no longer have to carry around with me when I leave and return to school because of dropbox.

  1. Laptop
  2. power cords
  3. flashdrives

That just removed 7 lbs from my backpack, and turned my motorcycle commute into a much more pleasant experience. In fact, I only take my backpack home when I have to take dead tree materials home or to school.

But that is not all I use it for. I have dropbox installed on 6 different computers. 2 at school, 4 at home. Dropbox allows me to streamline my workflow and be more efficient. Let me explain.

At school, one computer is in the front of the room attached to an LCD projector and a smartpanel, the second computer is at the back of the room at my desk.  I will work on a document for class at my desk, and immediately upon saving it will be updated on the front computer. This means I can pull something out of my email at the back of the room, walk to the front, and show it to the class. I can have software installed on the back computer, do a screen shot and save, then show. No flash drives, no futzing with anything.

At home, I have it on all my computers. When I am working on a project at school, I can save the document and go home. When I arrive home, boot my computer, and my full project is sitting there ready for me. It is on all my computers, even the old clunker that I boot once a week. That old clunker downloads and syncs all the files, so I have a weekly backup of everything.

My wife also has dropbox, and we have a shared folder between us. That allows us to connect our dropboxes and have files shared between our computers. We now have 1 shared, encrypted password file instead of 2.

If you want dropbox and don’t have it yet, you get 2 Gigs of storage for free. If you sign up with this link you get and extra 500 megs and I get an extra 500 megs for free. Because of that I have 13.4 Gigs of free storage right now.

When you include picture uploading automatically (through the smartphone app) which saves you from needing to connect your phone to your computer or emailing the pics, the accessibility of dropbox on the internet through the web portal, and the seamless syncing of the docs, it is a win win win for teachers.

If you are on the fence, do it. It takes the process of managing your files and turns it into a non-entity.

Aug 202012
 

Well, this is new to me, at least. I have used powerpoints in class, but this add-on allows you to do some different things with the software. I hate to compare this to Prezi, but clearly that is the only comparison to be made.

It is called pptPlex, and is a free add-on from Microsoft. Below is a video of my first use of pptPlex.

If you want some better introductions / helper videos on how to use pptPlex, I have some links below for you.

An introduction to pptPlex

Using pptPlex for infographics

Another pptPlex demo

A teacher who is really ‘excited’ about pptPlex!

Creating cool powerpoints using pptPlex

Official Microsoft videos for pptPlex below

Making Backgrounds with pptPlex

This on is just called “pptPlex”

Aug 022012
 

I am rather late to the gate with these thoughts, in large part because I drove (well, rode my motorcycle) to St. Louis from Reno, which took 4 days to get home. More on that in a different post when I do the math from the trip video.

If you ask one of the teachers from my department about me, one thing almost all of them will say or agree with is that I hate paper. I hate paper note, paper suggestions, paper anything. I ask my department to submit everything to me through email, because I lose paper notes, throw away binders, and just downright hate keeping track of paper.

With that said, I admit I took 11 pages of notes, kept track of them through 4 days of a conference, and 2000 miles of motorcycle riding. This event meant that much to me, and that is saying a lot.

I am going to start on day 1 and work through all my notes. I am composing this more for myself than anyone else. Like all of my reflective posts, it really doesn’t matter if anyone else ever reads them. This is the place where I reflect and compose my thoughts for my future self (because if I do it on paper, it gets thrown away!)

Wednesday – A personal exploration:

To say I was nervous on Wednesday would be an understatement. I had just ridden 1900 miles over three days to meet with a group of people I had never met and only talked to through twitter, emails and blogs. Yea, I was nervous. You see, I am an incredible introvert. I attended a NCTM conference my first year as a teacher with 2 other teachers from my school. At the end of the conference, I had spoken with exactly 3 people in a meaningful way, 2 of which came with me. I attended sessions and sat in the back. I wandered the floor and just kind of nodded and said the minimum I had to.

At that point I realized that if I was going to become a half way decent teacher, I had to overcome this fear of putting myself out there. Even riding my motorcycle to the event is a sign of my hesitance to talk to people. I was riding alone, where the only conversation going on was inside my helmet. If I flew I might have to actually talk to someone (although I usually don’t when I fly, either.) This has been my most difficult challenge as a teacher, because it is so incredibly easy to just stay in my room and never reach out. I used to actually have it on my to do list every week, “Make contact with other teachers.” I don’t any more, but the tendencies remain.

So I walked into the hotel dirty and sweaty from riding in the heat and the first thing that happens is Lisa H. tries to give me a hug! Okay, ice broken, I can deal and grow.

After a shower so I was feeling like a human being again, a group of us walked up to the nearby mall and had a nice dinner at a southwestern restaurant and chatted. It was nice, and it gave me a chance to get to know people in a very casual way. It definitely was the right thing to do. I did think about staying in the hotel and sleeping, but decided otherwise. I am glad I did.

The actual events of the week after the break (warning it is long & detailed):

Continue reading »