Norway 2025 part 1 -- Hadeland

For this time we decided to spend the first few days close to Oslo, our arrival airport. Searches raised our interest in the Kistefos Museum and so we decided we'd start there.

First our flight was scheduled to arrive just before 7 in the morning. I didn't think much of it but when I got to the car rental area the door was locked and they had posted a sign saying they don't open until 8. Uh-oh. Would have been nice if they mentioned that when I reserved the car.

Okay, not really a big deal. I reserved a small EV (they described it as like a VW ID3, a car not sold in the US so I wasn't sure what to expect). What I got was a Toyota bZ4X, another car not sold in the US but much larger than the expected VW.

I'm familiar with the instrument layout in Toyota so it was an easy car for my first EV.

The built-in navigation, similar to our Lexus, had an annoying quirk of announcing turns after they had passed. "Take the next left turn" when it should have said "turn left now!" There also was no android auto capability. I missed several turns trying to get accustomed to it. 

I had thought to bring my Flight Flap, which is a small sheet of silicone-coated aluminum which can be bent into a shape to support a cell phone and found appropriate positioning to give me the equivalent of a heads-up display for Google Maps.

We arrived at the hotel, the Granavolden Gjæstgiveri at roughly 9 AM and asked reception if we could check our bags, but they noticed that had a room available for us to check in. Lucky break. So we checked in, and even had plenty of time for the breakfast buffet. Then we set to exploring our surroundings.

I did not know when I booked, but the hotel is on a significant pilgrimage path in Norway, the Gudbrandsdalsleden going from Oslo to Trondheim. It is close to an old church (currently not photogenic due to construction scaffolding) and some other sights, including the Steinhuset from the 13th century. This is the oldest remaining stone building from that period that isn't of religious origin or in a city.

There were nice walking paths nearby, and we had a pleasant couple days and were able to mostly recover from our jetlag.

We did accomplish our primary objective at the Kistefos Museum. Many notable artworks. Below is a hodgepodge of images that I captured.

Community Gardens Germany

 http://www.cityfarmer.org/german99.html

https://www.treehugger.com/german-allotment-gardens-kleingarten-4859448

https://www.dw.com/en/a-brief-guide-to-german-garden-colonies/a-39133787

Birds

Updating list of birds sighted.
Page references are, unless specified otherwise, to Lars Svensson et alia Birds of Europe Second Edition, Princeton Field Guides

Grey Heron (Ardea cinerea) (P p.84) before I bought the bird book in April 2021. Seen in the KGV behind my apartment.

Tree Sparrow (Passer montanus) (P p.372) on my kitchen window ledge April 2021. Perhaps house sparrow. Flew away before I could fully confirm. But seemed too small for house sparrow, and crisper, higher contrast markings than the illustrations on page 373 for house - more like tree.

Pigeon

Egyptian Goose (Alopochan aegyptica) May 2021 banks of Nidda River. Brown eye circle.

Common Swift (Apus apus) June 6 2021 by bird call along Lorscher Strasse.

give up and publish.

Frame the Cards

 Task: create a rectangle with playing cards of any one suit from A through 10 such that the total count of pips on each edge is the same. Here is an example that does not meet that restriction.

The total across the top is 20, bottom is 19, left side is 23, and right side is 22.

Here is an example that does meet that restriction.

All edges in this example total 20.

According to the source where I found this problem, Teaching Through Problems Worth Solving version 3.0 by Alicia Burdess and a few others, problem #27, Frame the Cards, there are 10 unique solutions to this problem. By unique I assume simple rotations and reflections are out, as would be a solution that simply swaps the position of two inner cards on the sides with four cards. I wanted to find solutions and, if possible, figure out an easily articulated rule for generating solutions.

First thing I realized was that only certain totals for each side are possible. The total of all numbers from one to ten is 55 (cue the standard math teacher story about a young Gauss). But each corner card would be counted twice in a total. The highest the corner cards could be is 10, 9, 8, and 7, totaling 34. But 55+34 is 89, and 89 isn't evenly divisible by 4, so that can't be a solution. The highest possible corner card total is 33, which would make the total on each edge 22, if we can work it out right.

Similarly the lowest total for corners is 10 (1+2+3+4), but that also gives a total count of 65 which isn't divisible by four; same problem as above. So the lowest workable corner total is 13, making each edge 17, if we can work it.

Because we need a total that is divisible by four, the total for the corners can only be 13, 17, 21, 25, 29, and 33. This significantly narrows down the possibilities if I want to try brute force solving.

If we start at the high end, the only way to make 88 is with corners 10, 9, 8, 6. I know I am aiming for a total of 22 to an edge, I know if I try 10, 3, 9 across the top that leaves 8 and 6 in the bottom corners. I would need another 8 to make that 22, so this isn't possible. It also starts me thinking about what corners are possible. What if the top were 10, 4, 8 and the bottom is 9, 7, 6. That would force the left edge to be 10, A, 2, 9 and the right edge 8, 3, 5, 6.

Great! I know it is possible to find a solution. Is there any other solution with these corner values? The only grouping I didn't try is 10, 6, which needs another 6, so that isn't possible. This must be the only solution with 22 to an edge.

So I realize that I can filter possibilities for appropriate corner combinations. Once I filter for the corner there must be a way to filter for the corner placements as well. If I consider the low corner total of 13 there are only three combinations to make this total; {1,2,3,7}, {1,2,4,6}, and{1,3,4,5}. Remember that a corner total of 13 forces an edge total of 17.

Since there are two edges (which I'm putting on top and bottom) composed of three cards, I need to be able to make the edge total two ways with the grouping of cards. There are a low finite number of distinct corner placements. In the first case, of {1,2,3,7} I can only have 1,2 and 3,7, or 1,3 and 2,7, or 1,7 and 2,3. There is no third card to bring 1,2 up to the target 17. Same for 1,3. Same for 2,3. So I can conclude it is not possible to work this puzzle with an edge total of 17.

The analysis for the 17 edge case was fairly quick, because there are so few combinations of cards for the corners. But the number quickly increases with higher numbers. I need a better way to analyze this.

Next higher than the 17 edge is an 18 edge. This requires corner cards totaling 17, which can be made in nine ways, with {1,2,4,10}, {1,2,5,9}, {1,2,6,8}, {1,3,4,9}, {1,3,5,8}, {1,3,6,7}, {1,4,5,7}, {2,3,4,8}, and {2,3,5,7}. As before there is no third card to bring 1,2 or 1,4 or 2,4 up to the required 18, so the first combo is out. On the other hand, at first glance {1,2,5,9} looks like a possibility.

I'm not thinking of a good way to do this analytically, so I will use a Python script (running on my TI-84 Python Edition) to identify quintuples of interest. I will use for loops to run through all quintuples, and test for possibility of generating the desired edge total. I won't brute-force for all solutions this way, but rather will narrow down the possible corner combinations to look at. I'm hoping I will see some pattern in those numbers.

Weimar Food Memories April 2022

Food on Weimar trip, April 2022.

Tuesday 19 April

36 Pho 

Kaufstraße 5 order pho nam and a Saigon beer

I liked. Portion seemed small (is that possible for a bowl of noodle soup?) so I supplemented with their baked spring rolls and dessert of a tapioca/sweet potato/banana/and a few other ingredients. Perfect. 

Wednesday 20 April

Bratwurst stand

Formosa

Tofu with hundred year eggs. Beef soup with noodles. Buns with bean paste.

Thursday 21 April

Erbenhof breakfast buffet good variety.

Scharf Ecke

Rinder gulasche (Seiko schweine schnitzel)

Creperie du Palais

Adventures in Disability

 On Wednesday 4th of May while bicycling to work I had a mishap which toppled me. In the fall I apparently twisted my leg to the point that I was unable to walk. I immediately notified my employer that I would not be in due to a accident on my commute (I had been told several times over my stay in Germany that an accident during a commute is considered a workplace accident and has more extensive insurance coverage than any other routine mishap).

My wife had visited an orthopedist not far from the accident location, so using my (damaged) bicycle as a support I hobbled over there without an appointment. It's not their fault that my German is so weak, but the people in that office have minimal English, so communication was not free-flowing. At any rate, the doctor saw me.

At each stage I emphasized this happened during my commute to work. They took x-rays (which are called Röntgen, corresponding to the Japanese word for x-rays, so I understood) and after a while the doctor told me - the good news is no bones are broken; the bad news is there is damage to the medial collateral ligament (MCL) and perhaps the cruciate ligaments as well.

He prescribed an analgesic called Novalgin, had a nearby orthosis shop bring a pair of crutches, told me to get an MRI (called MRT in German, the T being for tomography), and said he would see me again after the MRT.

First problem. I tried to arrange the MRT, and the facility he suggested had no openings until early June. So I searched and found they had other branches, and one had an appointment the next day. Booked online, because that allows me to compensate for my language failings and translate things. But when I went for my appointment, it turned out I had booked a different branch. Yikes! But the receptionist was VERY friendly and rebooked me for that facility on Saturday. This place was relatively nice because it is so accessible by public transportation (my ability to walk was severely limited), so I went ahead.

Saturday the MRT went mostly as expected. Check in, and go to one waiting room. Later be ushered to another waiting room closer to the MRT machines. Dump all metal-containing objects in a locker and lay down on the MRT platform. They did not fully support my leg, so once the procedure started I could feel that I was trembling a little bit. After about ten minutes, done.

Tuesday I saw my orthopedist again. No surgery needed. Prescription for a knee brace orthosis. Instructions to put limited weight on the leg, if I don't feel pain.

This has been draft for three years. I'm fully healed. I may edit this later. I had to switch to an Unfal doctor (accident) because it was a work related injury. Found a good doctor in Bockenheim (not far from me) who was teach doctor for a few professional teams, and same building had a PT guy, Schmidt. They were good. Back in USA, not much from PT people, but on my own began regular Pilates and TRX work, and my knee is back as good (or better?) than before.

Calculus Problem From OpenStax

 I was trying to explain to someone how I got a solution to OpenStax Calculus Vol 1 section 4.1 (related rates) exercise 43, so first I did a google search to see if there was a posted answer. I found two answers posted, and I disagreed with both of them, and they also disagreed with the OpenStax solutions (which only had a numerical answer and not an explanation).

So I worked it again, and my work agrees numerically with the OpenStax answer and I'm satisfied. If anyone else is searching for the supporting work, this post is an attempt to document that.

First, the problem: A batter hits a ball toward second base at 80 ft/sec and runs toward first base at a rate of 30 ft/sec. At what rate does the distance between the ball and the batter change when the runner has covered one-third of the distance to first base? (Hint: Recall the law of cosines.)

Whatever triangle we construct to visualize this set up has sides along the line from home to 1st base, and from home to 2nd base. The third side of the triangle is from the runner's position to the ball's position. Since a baseball "diamond" is actually a square, we can say the angle between the 1st baseline and the line passing through home and 2nd base is 45 degrees (or Pi/4).

If r is the runner's distance from home and b is the ball's distance from home then Law of Cosines tells us the relationship to d, the distance between runner and ball, is d²=r²+b²-2r*b*Cos(π/4). At the instant the runner is 1/3 the distance to 1st base r=30 (1/3 of 90 feet). This implies time t=1. This tells us b=80. We can calculate d=62.497

If we differentiate that equation relating d, r, and b (with respect to time, as r, b, and d are functions of time) we get d*d' = r*r' + b*b' - Cos(π/4)*(r*b' +b*r'). The problem statement tells us r'=30 and b'=80. Substituting in known values and solving for d' we get d'=62.497.

The solutions manual gives 62.50, which is the same answer to two decimal places precision.

Berlin Food Memories April 2022

Notes on most of our restaurant experiences during a one week trip to Berlin. 

Sunday 10 April

Mogg, Auguststr. 11-13, is a limited-menu sandwich shop in the Old Jewish Quarter. They're located in a building which was formerly the Jewish Girls School (Ehemalige Jüdische Mädchenschule). The building dates to 1927, That, of course, was closed down as Jews were deported to be murdered under National Socialist policies. After the war the building saw a number of uses. More recently it was refurbed and now houses a number of small restaurants and art galleries. 

We went back a few times over six days. We had both Rubens and Pastrami. Both are on a German rye bread, square loaf, sliced thickly (about 2 cm). Generous portion of meat, nice balance of cheese, dressing, and sauerkraut. Side of cole slaw and half of a small pickle. Seats were in demand, and we were lucky to get in when we went. If you can, I recommend you make a reservation.

On the way back to our hotel we noticed Wiener Brot Holzofenbäckerei at Tucholskystraße 31. The shop window is only a couple meters wide, but we liked the look of what we saw and went in. Good choice! The pastries are, not as is common in US bakeries, overly sweet. This allows the flavors of the fillings (fruit, cinnamon, chocolate, poppyseed) to come through clearly. Over several visits we tried strudels, struesels, and rolls. Hard to say a favorite, but I'll give my top three as the sour cherry streusel, and the cinnamon and chocolate rolls. This place is well worth going out of your way for a treat. They have a cute logo of a fox (with long eyelashes) carrying a baguette in its mouth. I would have bought one, but they don't sell t-shirts.

Monday 11 April

Jewish Museum cafeteria inside the Berlin Jewish Museum (Jüdische Museum Berlin) there is a well-reviewed cafeteria. The offerings seems to change, and the day we visited the items on the printed menu were not available. They did have daily specials, and we tried the cauliflower curry soup, and tandoori chicken. The soup was good, the chicken not so much. Although I would go back for the soup, I don't know how to be certain what offerings they have on any given day. Hit or miss.

Tuesday 12 April

There is a big deal in Berlin popular culture (maybe in German popular culture) for a dish called curry wurst. The legend is that it was invented in Berlin, and now there is a lot of buzz about various curry wurst shops. We went to one of the famous ones Konnopke's Diner. They are convenient by public transit, located underneath the U-Bahn tracks at Schönhauser Allee.

Okay, so now I've eaten official (East) German currywurst. And I don't see what the big deal is. It's a boiled bratwurst, cut into chunks, smothered in ketchup, and sprinkled with what seems to be canned curry powder. Some people claim, quite passionately, that this one was the best, but I can't see why any boiled bratwurst smothered in ketchup wouldn't serve just as well.

Rausch Schocoladehause is a fine chocolatier located at Charlottenstraße 60. They have three stories open, with the first devoted to sale of chocolate goods, the second where you can custom order a particular blend of ingredients at a particular "darkness" level. The third level (in European numbering, the second floor) has a cafe. We ordered coffee and cake. Quite delicious. Quite pricey. Nice for a splurge, but I wouldn't eat here on a regular basis. The store is decorated with a number of sculptures made of milk chocolate. Prominently displayed in the cafe is a chocolate Titanic. Wow! I hope their air conditioning system never breaks down.

Down the street from the New Synagogue we noticed a wall decoration characteristic of Thailand. On investigation it turned out to be the front of a Thai restaurant, Kamala at Oranienburger Str. 69. Their menu looked authentic enough (many of the Asian restaurant menus we had been seeing had odd combinations of offerings that left us unsure of what cuisine the chef actually knows how to make) so we gave it a try. From the street you take a few steps down to the restaurant door. Inside the restaurant is in three or four levels, with a few tables on each. Still concerned about COVID we liked that we could be mostly isolated in our own room (it was not crowded on our visit). Although the menu has many offerings, it seems that for the most part they have a few sauces which you can order with a few different proteins. We both ordered a Phanäng curry, mine with chicken and my wife's with duck. We were both satisfied. It had just enough spiciness to leave a little tingle in the mouth, and good balance of flavor. 

Wednesday 13 April

After touring the Pergamon we felt we needed a snack, so we went to their cafeteria. It was a warm day and they were only seating outside on the terrace. This was nice because it overlooks the Spree River, and was quite pleasant surroundings. We ordered a Flamkuchen, a thin-crust German version of pizza. It was good enough. This was the only place where the waiter solicited a tip, and I gave them none.

For dinner I went to Pho at Linienstraße 134, a moderate walk from our hotel. I chose outdoor seating, and soon realized that many other people in outdoor seating are smokers. Oh well. Their menu adopts the conceit of an airline ticket. Cute. I ordered the summer rolls and a bowl of pho. The summer rolls were mostly okay, but in making them there were too many layers of the rice wrapper, making an unchewable chunk at one end. The pho was okay. I would have liked more vegetables in the broth. It had a good level of spiciness for my taste.

Thursday 14 April

After touring the Memorial to Murdered European Jews, we went to Noodles Plus at  Hannah-Arendt-Straße 1. The menu had a mix of Chinese-looking items, and some with atypical ingredients, like peanut sauce. We ordered a dim sum assortment (four each of 3 different dumplings) and I tried their mapo dofu. Both were good.

Friday 15 April

Encouraged by favorable online reviews, we tried Bentokado at Eberswalder Str. 5. When we got there, we saw the sushi fish did not look particularly fresh, so opted against any of the sushi offerings. I ordered the miso ramen, which was okay. My wife ordered the shiitake vegan udon, which she said was very strange. She was very unhappy with her choice. She had been looking forward to ordering a Japanese cake for dessert based on the photos on the website, but on seeing the actual options changed her mind. Essentially, the name (which could translate from Japanese as "lunch box corner") is not at all what their menu is about.

Another Wasted PD Day

 I just survived another wasted two days of what passes for "Professional Development" at my school.

Thursday session 1: Toxic positivity 101. This is not to warn us of the perils of toxic positivity, but to encourage us to gaslight each other. Session started with that classic red-flag warning, "Studies show that ..." without bothering to cite any study.

Session 2: Visioning exercise. I am sorry, but I literally have absolutely no recall of what we did during this session. Sessions are named in ways which are not helpful in remembering content. This may have been the session where our principal described Hattie's work as "doing a bunch of math" on research to show that an "effect size" of 0.4 is the minimum for one year's growth. There was no mention that the "bunch of math" which underlies much of Hattie's work is statistically invalid. I often mentally check out when material depends on belief in Hattie.

Session 3: Dictate to teachers how school trips (towards the end of the school year) will be handled.

Session 4: How to write letters of recommendation. Geared exclusively  to Gr 11 and 12 teachers, but all teachers must attend.

Session 5: For advisory teachers, and I was excused, as I do not teach an advisory.

Session 6: Read through the IB evaluation received, note the areas that were highlighted for improvement, and explain to us that the school won't really address those areas despite giving lip service to the changes.

Friday session 1: Calisthenics.

Session 2: Read and summarize an article of entry-level undergrad educational psychology. I would have expected anyone who is a certified teacher had already read this material.

Session 3: Share "Best Practices." Require everybody to write up a "best practice" and then walk around reading what everybody has written. This session used the vocabulary word "plenary" in a way I had never heard before. That is, in this session "plenary" means a summary of what happened during the previous period.

Session 4: Follow up on school trips. Staff are to decide what activities students will engage in on school trip, based on student survey results that are unrelated to school trip activities. Note that during this session the facilitator sat reading their email.

Session 5: So-called Pub Quiz about social studies topics and movie titles.

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.

Immigration Office

I went for my interview with the Immigration Officials. Several people at work assured me it is no big deal, and mostly a formality, but perhaps unconscious bias left over from a Cold War childhood had me nervous about dealing with a German bureaucracy.

Fortunately most of my transition to Germany has been shepherded by Relocation Agency, hired by my school, and they have overall done a very good job of taking care of me. My agent, Cathy, met my wife and me at West Banhof Station, and drove us to the Immigration Office in downtown Frankfurt. Frankfurt is not really that big a city, but it seemed to take a long time to get there. Maybe there were one way roads the forced a circuitous route. Although I usually have a very good sense of direction, I lost track of the turns until we pulled alongside a long building that had the feel of "government offices."

As we pulled into a parking spot I noted a long line of people waiting to get into the building. We exited the car and joined the line. The line did not move at all. I assumed we were all there for appointments with an immigration official, although the building itself seemed to be a generic government office building, with a variety of departments.

At some point the guard began letting people in. He'd check their proof of having an appointment, and let them in by ones or twos. I didn't worry about it at the time, but I suppose we were the only trio in line.

When we got to the guard, our Relocation Agent showed the letter confirming our appointment and told the guard, "we have an appointment." He indicated she can go ahead, and my wife an I tried to follow. He stopped us. I tried to pantomime that I'm with her, pointing at the Relo Agent, and he seemed to accept that. But he wouldn't let my wife through. It was as though he couldn't conceive that there might be a grouping of three. We stopped, tried to explain, the Relo Agent noticed and came back, waved the appointment letter. The guard wasn't buying it.

Finally he let us through, but as his parting shot, scolded my wife for having her mask a bit too low on her nose.

Into the building. Down a hallway. Up a stairway. And from that point on, all frames of reference disappeared. It was a loooooong hallway, uniformly grey, with doors on both sides. The only markings were generic office numbers -- 1.073, 1.074, 1.075, and so on, door after door, down the almost featureless hallway. Finally we got to the end of the hallway and turned left. To another long featureless hallway. How long can this continue? I felt as though I was in a Kafka story. The hallway ended in a doorway to the outside, which I saw led to a bridge to the next building. Where I found yet another long hallway.

Eventually we got to a waiting room, where we were to wait to be called. The appointment was just for the two of us - the Relo Agent could not go in with us - so she prepped us for what to expect, but still reassured us that it was essentially a formality.

And it was mostly a formality, except I got scolded for working prior to getting a work visa. For a few moments they had me sweating. Then the interviewer said it would be okay since it was only a few weeks, so she'd ignore it.

From there it was bureaucracy. She filled out forms. She glued my ID photo to one of the forms. She scanned four of my fingerprints (both index fingers and both thumbs). She gave me a voucher and told me to go down to the payment office to pay the registration fee. I did so and brought back the receipt. She put an official-looking stamp on one of the papers and handed it to me, and said that was my temporary permit, and I should receive the actual permit in the mail. She repeated the process for my wife. And we were on our way.

And thus went my interaction with German bureaucracy. I have legal permission to work here, as does my wife. and we continue to adjust to our life.

Norway 2019

Visited Norway again this summer. This time we decided to rent a car and drive the various places we wanted to go, rather than try to deal with public transportation and suitcases. So we flew to Oslo to start.

Stayed at the Thon Rosenkrantz Hotel. Thon has dozens of hotels in Norway, Holland, and Belgium, but most Americans have likely never heard of the chain. Their HQ is in Oslo, and the Rosenkrantz is one of their nicer offerings. They told me their breakfast won a competition for "best breakfast in Oslo," and I would agree it seems deserving.

It is named Rosenkrantz because its address is on Rosenkrantz Gate ("gate" is Norwegian for "street") not far from the theater. It is a convenient location to reach many sites in Oslo. Our first day included a trip to the Munch Museum. *sigh* disappointing.

We had seen the various Munch paintings at the National Gallery last year, as well as the holdings on display at KODE in Bergen. The organization and quality of the works on display at the museum bearing his name just didn't measure up. So much of their display seemed geared towards self-promotional PR. The works on the wall, to my untrained eye, didn't seem so important. There was no exposition, explaining how Munch developed his style into the characteristic that almost all Westerners recognize from The Scream.

If I understood the story correctly, the current museum will be closing, and they will move to a new location closer to the National Theater.

Following Munch, we decided to head over to Bygdøy to walk through the Norsk Folkemuseum. The peninsula is a pleasant ferry ride from the docks by City Hall. On our trip last year we had already seen the Fram Museum (about arctic explorers -- recommended) and the Kon-Tiki Museum (ho-hum), but had missed the open-air museum with its collection of buildings.

I was intrigued by the style of fencing they had on display. Over our trip I found that this style is very common in Norway.

Scandinavia seems to have many of these open-air folk museums. On our trip last year we went to Skansen in Stockholm, which is part of why we skipped the Norsk on that trip. But for this trip we went to several. The idea doesn't make much sense in the USA, where our pre-industrial history was rather short, but many places in Norway have over 1000 years of cultural history. The museums try to gather the actual buildings from various parts of the country, and then reproduce in an actual landscape setting how people lived and worked in those areas and those days.

Lots of intricate metalwork.

A scarecrow. I doubt this is actually a historical design, but very photogenic nonetheless.

Detailed woodcarving at the entrance-ways to buildings.

A mangle, for flattening wrinkles out of linen cloth.

A container.

The Gol Stave Church, likely from the first half of the 13th century. The key architectural element that makes it a stave church are the vertical bearing posts (staves) in the wall structures.

Some shots of the church interior.

Hmmm. I think it's another modern design element.

We ended the day by heading to the outskirts of town and to the Vigeland Park inside Frogner Park. We had become much more comfortable with public transit, and so took a trolley to the park. This entails a ride through several neighborhoods of Oslo, getting a view we might not otherwise have seen.

Gustav Vigeland has a very distinct style, and he convinced Oslo to let him place some 200 sculptures in this portion of Frogner Park. 

Walking around center city Oslo there is a very prominent Freia sign.

Freia is a large confectionery company. I believe they are now owned my Kraft. Much of the chocolate candy sold in Norway is marketed under Freia branding. One of their products is the Kvikk Lunsj (pronounced so it almost sounds like "quick lunch"), which is almost indistinguishable from a Kit Kat bar.

The next morning we checked out of the Rosenkrantz, picked up a rental car, and drove to Lillehammer, host city of the 1994 Winter Olympics. 25 years later, there isn't a big imprint of the Olympics, but one very visible site is the ski-jump, still looming over the city high up the mountainside. The Olympic torch from 1994 is also at the same location, flame extinguished.

During the daytime it's possible to ride the chair lift up to the top of the jump hill. At any time the park is open it's possible to physically climb the stairs of the viewing stands, which a number of people were doing, apparently for exercise.

We stayed overnight at a hotel that was in a building that had been a grain mill until the 1990s. They retained much of the feel of the old building, leaving some of the milling machinery in place in what became the restaurant. A stream ran right by the building, not surprising for a mill. It was a charming place to stay.

We had wanted to stop at another open-air museum in Lillehammer, called Maihaugen, but arrived shortly before closing time and taking the advice of the hotel clerk did not go up there. In retrospect, we realized we should have gone directly to Maihaugen, and checked in to the hotel later.

Maihaugen is described as Norway's largest open-air folk museum outside Oslo. I'll not be able to confirm that, as I did not get there this trip.

**** this is where the draft ended****