Politics, math, and dog-whistles

In Frank Herbert's Dune, there is a cool idea of a military language with a flexible structure so that any pair of people can speak to each other in a way that they will understand, but which no listener will understand.

Modern politics and social media are moving closer to realizing this idea, through dog-whistles.

For example, I was really struck by this ad for a math curriculum package (see the second paragraph):

For the author and their intended audience, Common Core means something very particular and particularly bad.

Personally, I find the fragmentation of language very troublesome. Among other things, it contributes to a certain type of magical/fallacious thinking, nicely exemplified by the popularity of ObamaCare (according to some survey results):

1. The Affordable Care Act gets broader support than ObamaCare (they are two names for the same thing)
2. Individual provisions get significant majority (more than 50% of respondents) support, while ObamaCare does not only earns minority (less than 50%) support.

This first point is silly, and I don't see any logical way to redeem that combination of beliefs. For the second point, while it is possible to logically reconcile the two observations, the most likely explanation is that people surveyed were mis- or under-informed.

Teaching goals for English Language Arts

These are our current objectives for English language study with our children. These are very high level goals, but we feel it is important to write these down so that they can guide our detailed choices. Ultimately, our hope is to guide the kids to be independent learners.

Strong Readers (in-bound communication)

• Able to use reading as a tool for further learning. This means they must:
• Enjoy reading
• Have a large vocabulary and tools to build their vocabulary
• Good comprehension and tools to analyze what they are reading
• Familiarity with sources of information
• Read a wide variety of material: topics, authors, styles, forms

Writing (out-bound communication)

• Able to communicate ideas clearly and effectively (writing and speaking)
• Comfortable with the mechanics of writing: vocabulary, spelling, grammar, punctuation, physical writing and typing
• Learn a writing process: research, brainstorming, forming ideas, organizing ideas, drafting, revising

Conduit for other content

We will make use of language activities that also teach them:

• History: having data of history to learn from the past, ideas of historiography and perspective
• Science: technical jargon, tools to understand and develop scientific frameworks
• Philosophy and comparative religion: what are the great questions, different perspectives, forming their own values and understanding those of other people
• Current events: understanding the current context of their lives

Develop skills that support other language learning

• Grammar frameworks
• Methods for learning vocabulary
• Motivation

Math of Duolingo (100k Lingot Challenge)

Well, at least about the lingots . . .

During our recent long weekend, the two older J's and I were talking about lingot acquisition on Duolingo.  This is a summary of our conversations, plus a bit of background for Duolingo non-users.

What is the point of this post: opportunities for mathematical modeling are all around us!

Our streak obsession

Some of us have become heavy, frequent, users of Duolingo. While others debate whether it is the best tool for language learning, we've at least been finding it a good place to practice languages we already know and learn the basics of some new ones. And accumulating XP, experience levels, translation tiers, and lingots makes it into a fun game that tweaks our greedy instincts for more, more, more.

Especially those lingots:

Oooh, shiny, shiny!

You know our penchant for finding math in all things, so it won't surprise you to know that we've been thinking about the math of lingots. Especially when our curiosity took us to the Lingot Hall of Fame (Thousadaire's row) and we saw this:

There are people with over 100,000 lingots.  Hmm, how did they get so many? How long will it take us to get that many?

Some basic rules

Basically, we know 6 ways to earn lingots:

• Pass a skill: every skill passed earns 2 lingots (or 3 if you test out with a perfect test)
• Go up a language level: rise to level N and you earn N lingots.
• Extend your streak: consecutive days of play build a streak, every ten streak days, you earn S/10 lingots (where S is the length of your streak) 
• Wagers: you can bet on maintaining a streak and (net) earn 5 lingots every 7 days.
• Upload a widely liked document to immersion, more on this below
• Direct grants

Data on skills
Each language has a tree of skills that you complete to unlock the rest of the tree and earn lingots. Oh, yeah, to learn vocabulary and grammar skills, too, I guess:

A section of our German skills tree

There are 120 skills on the German tree. Assuming this is typical, that gives us a max of 360 lingots/language from completed skill trees. There are currently 50 live courses listed on Duolingo, so that means a user could earn 18,000 lingots by completing all the skill trees.

Not bad, but a huge amount of work. To give you a sense, over the past 150 days, I've managed to complete the German and Spanish skill trees, but those were both languages in which I was already quite proficient. Suffice it to say, my progress through the Russian tree has been much slower.

For our time estimate, we assumed 100 days to complete a tree with the possibility of working on 3 languages at a time, but we guessed this is a bit on the optimistic side. This gives us a lingot rate from skills of 10.8 lingots per day (3*360/100).

Also, our top L-tycoon, KcaJP is only studying 8 languages, so even with full trees (which seems unlikely, see below), that would be 2880 lingots from skills.

Advancing levels
The math on lingots from levels is pretty easy. If we have levels {n_i} for m different courses, then we received this many lingots for our level progression:

 n₁(n₁ + 1)/2 +...+ n_m(n_m + 1)/2 - m

The subtle -m comes from the fact that we start each course at level 1 and don't get a free lingot from that.

I've seen one claim that the max level per course is 25, so that would be 324 lingots/course, or 16,200 total lingots. Making similar assumptions to that for the skill trees, we estimated 150 days to get to level 25, 3 languages running in parallel, for 6.48 lingots per day from this source.

Based on the KcaJP's levels in the 8 courses, I think this source only provided 514 lingots. Also, because many of these 8 courses have very low levels, it is unlikely KcaJP has completed many of the skill trees.

Extend your streak and wagers
This is very similar to the language levels, but is open-ended. In this case, lingots accumulated are S(S+10)/200.

Betting on keeping mini-streaks (each of 7 days) gives us 5 lingots every 7 days, so we will accumulate 5*S/7 from this source.

Data on likes
The last two ways to get lingots are to be loved. If you are loved for yourself, people can give you lingots directly. The most extreme case we've seen was a user who was gifted about 4000 lingots. However, even gifts of 100 lingots are extremely rare. Because of this, we aren't counting on donations and think it lingot gifts can be ignored for understanding lingot tycoonhood.

One other way is to be loved, indirectly, is to upload a document to Immersion that then gets upvoted. Typically, this earns the uploader 0-5 lingots. There is one extreme example (a Harry Potter page) that got about 1500 upvotes. Again, we think this source can be safely ignored for our analysis.

How long for our 100k badge?

So, in summary, we have the following as the key factors for earning lingots:

• Pass a skill: estimate 10.8 lingots per day, source of 2880 lingots for KcaJP
• Go up a language level: estimate 6.48 lingots per day, source of 524 lingots for KcaJP
• Extend your streak and wagers: 5*S/7 + S*(S+10)/200
• Total forecast lingots on day S: S²/200 + 18 S

We rounded the coefficient of S since our estimates for passing skills and level increases weren't precise to that level anyway.

Solving this quadratic for 100,000, gives is about 3020 days for us to reach 100,000 lingots, or 8.3 years. Assuming we keep our streak every day for that whole time, our assumptions mean we would have:

1. Earned about 32k lingots by completed 90 skill trees (40 more than duolingo currently has, but there are another 29 at different stages of development and we're gonna take 8 years, so, maybe?)
2. Earned about 20k lingots having gotten to level 25 on 60 courses (not sure how this links with 90 completed trees, but, oh well)
3. Earned about 48k lingots from sheer persistence

An obvious conclusion

Having explored our estimates of how long it would take us to get 100,000 lingots, we want to turn back to our favorite Ltycoon, KcaJP. While we can't guess about how many lingots KcaJP has been gifted or upvoted, the visible sources of income are:

1. less than 2880 from skills
2. 514 from levels
3. less than 12000 from streak and wagers (this is the max available since Duolingo launched on 30 November 2011)

In total, that would still be an impressive 15k lingots, but we've still got 100k unexplained!

So, how did this lingot tycoon reach this pinnacle of virtual wealth? Frankly, we don't know, but can conclude that there must be/have been other ways to earn lingots. We have found parchment fragments suggesting a distant time when it was easy to earn loads of lingots from translating on immersion. Is that the key?

Freeform tangrams: an imagination game by J1

Who: J1, J2, and J3 (a late appearance)
When: just before bedtime
What did we use: two sets of tangram pieces

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J1 came up with a new game this evening. The rules:

• number of players: 1 or more
• playing pieces: 1 or more sets of tangram pieces
• designer: each round, one player takes the role of the designer, putting the tangram pieces into a configuration. This could be a random arrangement or intentional
• Taking a turn: in a clockwise order starting with the person to the left of the designer, players say what they think the tangram looks like from their perspective. After everyone has taken a turn, the players shift 90 degrees to their left and repeat the cycle, but this time they are looking at the tangram from a different orientation.
• Once everyone has had a go from all 4 orientations, the next player becomes the designer
• Advanced play: once someone has said what they think the tangram looks like from their perspective, the experienced players can add a comment to start building a story based on that object.
• Winner: everyone!

We played with J1, J2, and J0 taking turns as the designer. To give you a feel for it, here is one of our designs from 3 different orientations:

Here are some of the ideas for what we saw: person jumping out of a box, a wheelbarrow, an army officer, a flower, an 8th note in a mirror, a catapult, a road grader, a knife cutting an apple, the sword in the stone, I was surprised that no one said "poop," which just shows how engaging the two of them found this activity. I doubt it would have been as successful if I introduced these rules and asked them to play!

Our own puzzle book

How a hacker gets started?

who: J1
when: early afternoon
where: online

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J1 came up with a fun and surprising word game.

You know those promotions where you eat/buy something, then get a code to enter online for a game or drawing? Recently, one of J1's favorite snacks has been doing a treasure/pirate themed contest. Each "serving" comes with a code that, once entered, gives him 1-5 plays of a little game.

Pre-processed form of fav snack

Three interesting tidbits:

1. We know there are 20 code words and we don't have all of them
2. Only one valid code can be entered each day, but it seems an unlimited number of attempts can be made
3. The codes are all related to treasure

What has this inspired? J1's first hacking attempts (to my knowledge).

Hacking + Pirates ≅ Win! (mod LittleBoy)

He has been thinking of treasure words and trying them in the system.  He was successful today and that's sure to encourage him for tomorrow.

DIY: Madlibs

who: J1 and J2
where: lounging around the house
when: 10 minutes before violin lessons
what: a language game
*warning* this episode contains some little boy humor that not everyone will find appropriate.

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A picture of something that is not yet, but will eventually become,
an example of my sons' current favorite double duty noun/verb.

Mad Libs - the background
I enjoyed MadLibs as a kid, so I introduced them to the family. Instead of taking the easy route (buying some) or the easier route (downloading from the web) or the easiest route (getting an app), I had the great idea to make my own!  The idea was to take basic sentences, whatever their original context, take out some of the key words, then ask for substitutes from the same parts of speech.

Of course, this also required teaching a little grammar along the way:
Nouns: person, place or thing (also animal or idea, according to wikipedia).
Verbs: action words (also occurrence or state of being, again, wiki)
Adjectives: words that describe nouns (ha, I got this one!)

I decided these three were enough to get us started.

Our Libs
The first try, this came from the literary classic, Spot's Treasure Hunt:

Daddy has planned a thin event for Mommy.  Run and jump with the pillows in every temple to help Mommy and her playdough search for hidden earth.

If you guessed that the yellow highlight is for the words (or phrases) we added, then give yourself a gold star.

The next one, direct from the back of Origami Paper Planes:

The poop and snails are happy to run you on board. The fleet consists of 126 testicles and other mad kidneys.

Finally, from the front page of the BBC news webpage:

Feces are running near the south-eastern Ukrainian city of London.  Earlier, the blue and sad presidents shook as the saliva was pooping.

You can see there is a bit of a theme to the word selection...

Did they love it?
After our third round, J1 asked suspiciously: "Daddy, is this the game?"

P thought that was hilarious.

Oh well.

Pattern replication

who: J1 and J2
when: just after breakfast and mid-afternoon, in between rounds of Sleeping Queens
where: in our play room and in my office at home
what did we use: pattern blocks and an oversize book (and play Sleeping Queens)

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With J1 out of school all week, I've plenty of opportunity to use the activities that I'd listed in advance of our math party. I particularly wanted to try the second of my pattern blocks challenges:

Pattern Blocks Activity B: needs pattern blocks and a large pillow to block the view.  With a friend, take turns making a secret design and verbally describe it to the friend to tell them how to replicate it.

J1 was reluctant to humor me, since he wanted to play Sleeping Queens (all day long, as it turned out). However, when I explained what I wanted to do, he got more interested, saying, "ah, we've done this at school before, it's easy." I was about to set up half a pillow fort to use as  screen to block his design when I realized we had inherited a gigantic (roughly 1 meter tall) book about mummies that was perfect.

J1 set up a design and then started describing it to me and I asked questions when I didn't understand.  Here are the two patterns,

So we got pretty close, thanks primarily to his use of the word "tessellate" to describe shapes that fit snugly together. You can see that we each took for granted the orientation of the top green triangle. J1 didn't tell me which way to point it and I didn't think to ask.

Then, I went behind the screen and put together a fish about to chomp some square orange food, but our communication was really poor and J1 made the design on the bottom:

We got interrupted, otherwise I would have liked to try a couple more times in each role.  In the afternoon, I got a chance to do it again with J3. Not surprisingly, he went for a more complex design than he could describe, including a slightly innovative orientation for the orange squares. He was having trouble giving me instructions, so we ended up with him just rebuilding the original in front of me. In any case, he'd used more than half our orange squares, so we couldn't do a faithful reproduction.

Incidentally, the second design above is what he put together when he was playing with the blocks on his own afterward.

My lessons:
I really liked this pattern activity.  First, it gives a semi-natural reason why they might care about some basic elements of math such as number and shape. Those form some of the basics for explaining what pattern they've created.  Similarly, it is a natural place to start introducing angle measures and concepts like parallel and perpendicular.  When I am describing my designs, I try to use a full range of vocabulary and encourage them to ask about any words they don't know.

Second, like the flexagons, it is a mixed math, art, and language activity.

Third, this was something the kids found engaging but challenging, so it seems like the right level for their current abilities.  In general, it is hard to find things that fit like this.

Sleeping Queens

Finally, the game Sleeping Queens loomed over our day.  One of the friends had brought and left it yesterday for the math party. J1 had played it at school and was really excited; left to his own devices, he would have played continuously and it really was the last thing he did before going to sleep. By the end of the day, J2 was also playing along (and winning). I have to give it a positive endorsement on their enthusiasm alone, but I do have two caveats: for our small children, they feel they are being attacked when someone steals their points (a standard part of the game play) but the game seems to simple to suit older children (and certainly won't be much of a mathematical experience for them).

Baby pictures
Just for amusement, here are some snaps by J3:

Does the Pharaoh approve our pattern design?

Our future coconut crop?

activities for a math party

Who: 6 classmates of J1 + J1 + J3
When: all morning + lunch
Where: our house
What will we be using: see below

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Some planning notes for a math (and English language) party at our house next week.

Misc:
- Brief explanation of basic rules of the house as everyone arrives: be kind, be respectful, be safe, persevere
- Explain schedule, particularly if there are going to be full group activities (reading a story, making food, eating food, change to 100 board pattern)

- have water, fruits and cut vegetables available for snacking throughout the day

- activities set up in stations around the house with some printed guidelines. Tidy up after you finish each activity (to make it appealing for the next people)!

- Kids will go through the activities in pairs, may depend on attendance.  

- Maybe J1 allowed to join whichever pair he wants? Otherwise, create group of 3 to deal with odd number?

- Do we need a map so that the kids have some idea of what is available? How many activities do we really need for 4 hours (which will include lunch)?

Passport
To start, everyone gets a passport book and decorates the back cover with their name, partner's name and own design. The book is to record which activities the children have done through the day.

100 Board
Guess my pattern: needs 100 board and 2 colours of tiles (5-10 minutes total time)
3 or 4x through the event, J0 will set up some patterns on the 100 board.  Kids guess what the pattern is each time. Pattern ideas:
- odds and evens
- multiples of 5
- squares
- Fibonacci sequence
- Primes

Pattern Blocks
Activity A: needs pattern blocks, design cards, and a camera
- Copy some pre-made designs
- Make your own design and take a picture (adult will help with the picture?)
Activity B: needs pattern blocks and a large pillow to block the view
With a friend, take turns making a secret design and verbally describe it to the friend to tell them how to replicate it.

Stacking blocks 
Tallest tower: needs collection of building materials (we will use duplo, stacking blocks, trio blocks, polydrons and magnatiles), measuring tape and camera.
- build the tallest tower you can
- estimate the height
- measure the height
- take a picture

Origami
Ninja stars: needs paper cut into squares (or even better, 1x2 rectangles)
- take apart some pre-made stars and investigate
- think about how to make them and ask questions
- try to make your own
- decorate
- throw them at designated targets (maybe this is too risky to encourage?)

Hexaflexagons: needs paper cut into strips
- with help, make a trihexaflexagon
- decorate the sides
- explore
- make more if interested
- make a hexahexaflexagon (advanced, gets an extra stamp)

Other origami: can be added according to interest of children
- animals
- polyhedra
- etc

Story
Reading: needs a selection of books
- Select a book with your friend
- read and discuss with an adult (depending on preference, kids can read themselves, adult can read to them, take turns, etc)
- Should this be done all together or pairs?

Writing: needs paper, pencils, some coloring pencils/crayons
- modelled on the story we have read
- insert yourself and make some additional change to the structure
- write your story
- illustrate/decorate

Games
Pick a game and play with your friend
- Sum swamp
- Chess
- Chinese checkers
- Chinese chess
- Uno

Programming
Pencilcode intro
- Adult shows them basic intro to pencilcode set-up
- let them explore the gym, other people's code and play

Food: I'm inclined to drop these ideas for the first trial run of this event; mini-pizza is the strongest contender to keep
Mini-pizzas: needs pizza dough (shaped), tomato paste, cheese, cut veg
-  each pair gets a blank dough to top and decorate as they desire
- bake
- eat

Coconut faces: needs coconuts and craft material
- Ask an adult to open a coconut for you
- Make a face on the top
- drink it and pretend the face is making silly noises at your friends

Mini-bread experiments: needs water, flour, yeast, salt, eggs, sugar, milk, oil, honey, seeds, cheese
to be done with J0 supervision, have everyone do this all at one time?
- each pair gets to measure out 150 gr flour, 2.5 ml salt (1/2 tsp)
- measure optional wet ingredients (egg, milk, honey, sugar, oil) up to 80 ml total
- add water to top up wet ingredients to 80 ml
- mix wet and dry
- knead and shape
- rise
- bake
Note: generic ingredient ratio should be checked against some sample recipes