COVID-19 in Frankfurt am Main

 Some people have expressed interest in the numbers I've been copying down, from Robert Koch Institute, since April 2021.

I think this link will continue to update while the document is alive.

Vietnamese Food in München

Today we tried Oanh 65 for lunch. One order goi cuon, two orders hoanh thanh soup, one banh canh xao ga, and one curry. All were excellent.

Lindwurmstraße 65, about a block from the Goetheplatz U-bahn stop. Highly recommended.

Hohenschwangau

About two hours by train from Munich, the town of Füssen is the gateway to Hohenschwangau, home of two delightfully accessible Bavarian castles.

To

We got the Bahn Card 25 which gives 25% discount on train tickets, so we opted for first class. It turns out the first class sections of the RB68 trains amount to about 20 seats in a section of two cars. The consist seems to be three cars, with one married pair coupled with a single. As fate would have it we opted for the first class section in the single.

Also as fate would have it, there was some mechanical problem with that car about halfway to Füssen. They needed to uncouple the car and remove it from the train. That meant all passengers on that car had to move to the remaining part of the train.

Fortunately there were few first class passengers and we had no issue finding a new seat. There was a delay of about 15 minutes as they completed the work. The train made up some of the time during the rest of the journey.

From Füssen we took a taxi to our hotel in Hohenschwangau, the Hotel Müller.

Stay

Hotel Müller gives a good first impression. Friendly check in. Got our room ready early, as we arrived before check in time. Generous with advice without being pushy.

Our room had a balcony with view of Hohenschwangau Castle. Nicely appointed. But then we noticed odd things. The TV would not turn on. The phone did not work so we couldn't call the front desk. There was a safe in the room, but it was locked open with no means to unlock it. There were no racks to put suitcases on. Not horrible, but slightly off-putting.

Breakfast included, ordered from a wide variety of options and served by friendly staff dressed in dirndl. Recommend the fresh-squeezed orange juice.

Hohenschwangau Castle

A footpath from the left of the hotel leads up the mountain to the castle.

There are no guided tours, and the only option is audio guide. They are very strict enforcing COVID regulations. Must have "3G" proof. Small groups. Make at all times.

Ticket order came with harsh instructions demanding were arrive well in advance if the appointed time. If more than five minutes late no admittance and no refund. But in reality we did not need to arrive at all before the tour time, as all we could do was stand around and wait.

When our time arrived we scan or QR code at the entry gate, and the turnstile allowed us to proceed. If we don't move fast enough the turnstile whaps us on the backside.

Inside they check out vaccine status and hand out audio guides, burning 10 or do minutes. Guide walks with us from room to room, activating that room's content on the little audio device. Very robotic. This is a Castle that was actually used by Bavarian royals, and in that respect is interesting. The rooms are decorated not with things the people may have used, but with portraits and statues of former residents. I wonder if that was the actual decor at any point in time, or just to make it a museum.

A big deal is made of Ludwig II.

Overall impression is that it's a nice Castle and all, but I wish I knew more about German and Bavarian history.

Neuschwanstein Castle

This is a very pretty fantasy castle situated higher above the hamlet of Hohenschwangau. 

My hiking app, Gaia GPS, says the walk up from hamlet level was one mile with an elevation increase of 450 feet (2840 feet to 3290 feel above sea level). It took us just under 30 minutes.

Visitors are permitted into the outer courtyard from 15 minutes before their tour time. Again, why did they give instructions to arrive over an hour in advance? In the courtyard people are killing about waiting for the entry time. We were advised by the Steves book of a staircase over to the left which leads to an upper courtyard. This is worth the additional climb.

There are signboards at the upper level explaining that Ludwig intended this courtyard be blocked by a chapel, and the footprint of that intended chapel is visible in the paving stones.

Eventually the tour time comes. And you begin climbing stairs! OMG, so many stairs. Only a dozen or so rooms are completed, and those are the only rooms on the tour. As I saw rooms and heard more Ludwig II anecdotes I got the impression that Ludwig was not so much mad as her was eccentric. The castle send to have been a short of private themed park, where the theme was Richard Wagner.

So anyhow of you're going to the area definitely see both castles. But if I were forced to choose just one I would probably choose Hohenschwangau.

Other

We allowed waaaaaay too much time, guided by pre-COVID advice. We likely could have seen both castles in a single day. The guided portion of each tour was not more than 40 minutes.

But because we had so much time we had a very relaxed pace. We even made an unplanned side trip to a nearby thermal bath, Königlich Krystal Therme. Wow! 22€ well spent!

The region offer a transit pass for guests in the local hotels, so we were able to move around freely.  The hotel did not offer this on their own, but as soon as I asked it was quickly generated.

Füssen, the nearest train station town, is also worth spending some time walking in.

Palindromic Depth

 I tried a problem today in three classes, two 9th grade and on 7th grade, which I consider successful. I found the problem from Alicia Burdess (aliciaburdess.com) in a collection called Teaching Through Problem Solving. Also credited are Daniel Student, Geri Ann Lafleur, Dawn Morris Blackburn, Doris Duret, and Jonathan Scott.

The basic setup involves talking about number palindromes. I get into that with sentence palindromes, and my current favorite (which I first heard from my son) is, "No sir! Away! A papaya war is on!" I stretched this part more with the 7th graders, but eventually get into number palindromes, and then introduce an idea called palindrome depth.

If you take a number like 84, which clearly is not a palindrome and reverse the digits you get 48.
Add the two, 84 + 48 = 132, which is still not a palindrome. Reverse the digits and add again.
132 + 231 = 363, a palindrome.
Because it took us two operations to get a palindrome, we say that 84 has a palindrome depth of 2. Some numbers, like multiples of 11, have a depth of 0.

The task: find the palindrome depth of all two-digit numbers.

It was great that all students are able to access the problem. I definitely consider it low threshold. Students of all levels were excitedly exploring. I use visibly random groupings of three, and almost all groups were dividing labor and sharing results, and both making and testing conjectures.

One of the most interesting extensions a student with colored pencils came up with was to make a 9 x 10 table with each two-digit number, and they color-coded each number palindrome depth. Wow!

I will definitely use this one again.

Thinking Classroom Links

 In attempting to implement Thinking Classroom recommendations, I regularly run across ideas in twitter and (less often) in facebook. In order to find them again later, I will try to collect links here, in an updating list. At the start, at least, I will put newer entries on top. I doubt I will confirm any link stays alive beyond the time I paste here.

update 3 September 2021
tweeted by Dylan Wiliam -- Stella's Stunners
https://www.mathstunners.org/

update 27 August 2021
Teaching through problems worth solving. Alicia Burdess et alia
http://www.aliciaburdess.com/uploads/2/4/7/6/24763920/3.0_teaching_through_problems_worth_solving_grade_8.pdf

update 25 August 2021

Gleam Math
https://www.gleammath.com/blog

Initial links 21 August 2021

Peter Liljedahl's website
https://www.peterliljedahl.com/

Building Thinking Classrooms website (under construction?)
https://buildingthinkingclassrooms.com/

Big Wheel task (from Thinking Classrooms website)
You are standing in the living room of your ground floor apartment when a giant wheel rolls slowly past your window. The wheel is huge with a radius of 100 miles and when it passes the window it completely blocks out the light from outside. The question is, as the wheel begins to pass the window how will it appear to block out the light: (a) from the top of the window moving straight down, (b) from the side of the window moving straight across, or (c) from the top corner of the window moving diagonally down and across.

Video Game arbitrage (from Thinking Classrooms website)
I buy a video game for $10. I then sell it for $20. I buy it back for $30. Finally, I sell it again for $40. How much money did I make or lose?

Egg Timer task (from Thinking Classrooms website)
I have a 4-minute egg timer and a 7-minute egg timer—the kind that you turn over and let the sand run through. Can I use these to cook a 9-minute egg? If so, how long will someone have to wait for their egg?

Google Doc of tasks (owned by Kim Brown, I believe)
https://docs.google.com/spreadsheets/d/1rFKbmtaaSS_KiMr0jt9ZS8MQYp1Uxr5XINEDh9uycNA/edit?usp=sharing

Google Sheet of tasks (owned by Jeffrey C Hamilton, I believe)
https://docs.google.com/spreadsheets/d/1NSR8PlF2UaVT4tLTpCw-AYOfGkFz044lTkhHXb1-sH4/edit?usp=sharing

Orchestrating Discussions -- 5 practices per NCTM
https://t.co/RDeRdWMoPY?amp=1

Typing in German

 I have a US laptop (no surprises there).

But now, in Germany, I must at times type things in German. Here are the things I've learned so far.

First, I had to install the US International keyboard on my Windows system. I boot to my default US keyboard, but when I need international characters the key combination Shift+Ctrl toggles to and from the other keyboard. On the international keyboard there is a difference between the left and right Alt keys. The right one is sometimes called Strong Alt, or Alt Gr.

Important characters in German:

Germany still uses the character for some double-s instances which looks like a Greek lower-case beta - ß. I produce this character with AltGr+s.

Germany also sometimes uses two dots over the a, o, and u characters. There are two ways to produce these in US Intl mode.
1) press double quote " followed by the vowel. ä ö ü. This causes trouble when you want to start a quote with an A, O, or U word. In these cases, type a space once after the double quote, to produce a double quote. "As I show here."
2) the second method uses AltGr key combinations.
For ä hold AltGr+q
For ö hold AltGr+p
For ü hold AltGr+y

Currency here is the Euro. AltGr+5 gives € the Euro symbol.

The issue I don't have a good solution for yet is quotation marks. In Germany the most commonly used quotation style begins with a double quote at the base line curving towards the quote, and ends with a high double quote also curving towards the quote. For example: He said „You must learn German.‟

I have not yet found a key combination the produces these characters. I think that if I had a full keyboard with numeric keypad I could type the Unicode (Unicode 201E and 201F) but I'm using a laptop keyboard. For now I usually ignore the issue and use US style quotation marks. But, for extreme circumstances I've stored the correct quotes (double low 9 quotation marks and double high reversed 9 quotation marks) in a reference document, from which I can copy and paste.

In some MS Office applications I can automate this with autocorrect, but I'm not always in Office.

Learning German (Deutsch Lernen)

 In my imagination, one benefit of my move to Germany was the possibility of becoming a learner again. Not the learning from idle curiosity, as when I attend advance math seminars and workshops, but a learner of necessity. In reality many Germans have good communicative competence in English, but to really get by in this country and culture I need to learn German.

Why is becoming a learner of value to me as a teacher? I am reminded of some of the issues that learners face, and so can re-sensitize myself and, perhaps, adjust my teaching practice to become a better teacher.

I got two lessons yesterday. Lesson one; communications. My German teacher for some reason changed his Zoom information, and he posted a message with the new log in information in a Whatsapp group that most members of the class belong to. I suppose many people keep their phone by their side at all times and as soon as a message comes in to social media, they stop what they're doing and read it. I don't.

I have a full-time job as a teacher, and I don't interrupt class to stay up-to-date with the social media world. By the time I got to my phone, the message in question had been pushed far up the thread, buried in smiley faces and people chit-chatting about various uninteresting (to me) topics. It never occurred to me that my instructor had posted a vital piece of information 8 or 9 screens up the scroll, and I didn't look.

So when class time came, I attempted to log in. And I sat in the waiting room. I glanced at whatsapp to see if there was anything happening, and there was a note from the teacher saying, "sorry I have problems to login now. gimme a sec pls." So I waited. No idea he was talking about the new room number.

After a few minutes the chat in whatsapp stopped, but I still had not been admitted. So I waited. I checked my email to see if there were any notifications. And I waited. I sent an email asking if they're still having trouble. I checked whatsapp again and there was no information. So I posted there asking to be let in.

Only then did the teacher send a second message about the new room. So I switched and got into class a half hour late. To an empty room (it turned out that everybody was in Breakout Rooms working on some exercise). When breakout rooms closed and everyone came back, I was left to fend for myself with no briefing on what I had missed. Language classes are very fast-paced. I was allowed to experience in much greater depth than I ever hoped for the feeling of being completely lost in a class, where everyone else appears to understand, and not wanting to ask for additional explanations. Wow!

One of the ideas I've been increasingly convinced of is Cognitive Load Theory. I was 30 minutes behind, I struggled to leaf through the pages of the text book which were clued to me by the current topics in class, and tried and tried to catch up. To no avail, I believe because I was already so far behind that my "working memory" was stretched beyond capacity and I could not get enough additional information in to sort things out. Another excellent reminder, as this is so often the feel that students in Math class have.

What I wanted was for the teacher to pause, and bring me up to date. Even if not reteach everything, at least give a summary of what had passed.

I hope this experience helps make me a better teacher. While I'm not happy to have experienced it (it was extremely frustrating and irritating) I hope to use this to inform my own practice.