Monday, December 28, 2020

Queen's Gambit comments

Putting this hear for no particular reason.

Queen's Gambit: B+/B. Entertaining, with some issues.



The ending was too perfect, but we knew something like that would happen from nearly the first scene (as soon as we knew Borgov's name). I wonder if it would have been better with a slight twist: if the final game had been a legitimate draw. Probably the general audience doesn't know this, but it is (now) very common for top level chess matches to end with a draw.  I'm not sure how common that was in the 60s.

To support that result, they probably would have had to lay a bunch of groundwork earlier.  maybe a game with Shaibel that ends with a drawn position and he has to explain why it isn't worth continuing to play? As it is presented in the show, a draw is just a trick, when one player thinks they have lost, but they think the other player doesn't see how to win, then they offer a draw as a psychological play on the lack of confidence.


They did, eventually, address all my major issues (drugs, genius). Also, the way they set up the team support was well done.  First, they show us that the soviet players are collaborating.  The audience  probably thinks that's cheating, but it serves to legitimize the support from the US players (which, as depicted, is pretty implausible, since it involves exactly the 6 serious male players who have appeared more than once).  Then, during play, Borgov deviates from the ideas the team had considered, so we see that Beth actually does win "on her own."


By coincidence, I just read The Big Bounce, a novel from the 60s.  One theme of that book was "women are bored and unsatisfied with life, have to turn to substances or craziness to occupy themselves." It is very condescending.  Unfortunately, there were also echoes of that in TQG: Beth herself, the society girl from high school, Beth's bio and adoptive mothers, Cleo.  Jolene and Packer(? the woman from the first chess tournament) are exceptions, but they don't get much screen time in those roles.

Perhaps would have been nice to see more of her bio mother. I didn't really understand what was going on with her, so maybe she was trapped. Didn't seem that there was anyone trapping Alma, the adoptive mother. There were nods to the idea of some generalized social pressure (the first Life interview, the society club high school student, the two women getting paired in the first tournament), but it was all pretty diffuse.  For example, we didn't ever see any US Chess Federation opposition to Beth playing in the open division for the US championship.


Other misc thoughts: 

(1) Beth's affection for Townes doesn't really ring true.  Fine that she had a crush on him for a while, but I didn't buy that it was a deep love simmering for years and years. 

(2) I didn't understand the lack of consistency in the post-sex scenes between Beltik and Benny. In the first, Beth is shown to be cold because she is immediately thinking about chess, but, in the second, she is shown not comprehending that Benny would immediately think of chess afterwards.  

(3) Cleo says (and Beth seems to agree) that Benny is only in love with himself. While we definitely see that he thinks highly of himself, he has clearly gone out of his way to help Beth, for no discernible benefit to himself.

(4) The Cleo sabotage evening had several things that didn't sit well.  First, Cleo knows that Beth has a big day ahead and completely undermines her. It was such an extreme degree that I almost thought there would be a reveal of Cleo getting paid off by the Russians or some other group opposed to Beth. Second, it shows Beth waking up in the bath. Could that possibly be a thing? If she were so unaware that she wouldn't notice the discomfort, wouldn't she drown?

Saturday, May 16, 2020

Chinese and Weiqi (go) videos

A collection of videos for studying go and chinese together, for J1:

— Beginning level tutorial, this series is made almost 20 years ago, classic but outdated (

— Beginning to mid-level life-death problems (

— Bad moves analysis (in Chinese literally translate to ‘smelly’ or ‘stinky’ moves) (

 — Ancient complicated life-death problems from the 1700s, some are doable, some are so massive and even challenging for pros (

  Ke Jie’s 15 best games voted by fans

— Pro game, commented by Ke Jie (

— AlphaGo VS AlphaGo 50 games (

— CCTV (China Central Televison) ‘s documentary about weiqi (

Tuesday, February 11, 2020

What is 8?

I've had a chance to spend more time doing math with the kids again and am hoping to write up our activities more consistently.  Let's see how this works out!

Graham Fletcher created a set of  Progressions videos for various elementary school themes. J3 and I recently went back to his page and found he had a new(er than we knew) progression on early number and counting.  Even for this simple topic, the video highlights some points we hadn't considered explicitly, for example distinguishing producers (of a number) and counters. Also, the cardinality point that smaller natural numbers are nested within larger numbers wasn't something we had talked about, but we soon realized it was part of many examples in how we understand numbers.

With that as inspiration, J3 and I decided to search for a range of examples of a single number, we chose 8, in different forms.  There is at least one obvious version we're missing.

Add a comment (with picture, if you can) to show other forms of the number 8!

Marking 8 on the 100 board, an easy place to start:

8 beads on the abacus shows the relationships 3+5 = 8 and 10-2 = 8 (also 100- 92 = 8)

8 can hide in plain sight. Without labeling the three lengths, it would have been hard to recognize the longer one as 8 cm and, for you at home, impossible to know without reference to show the scale.

It happened that, within the precision of our scale, two chocolate wrapped chocolate bars were 8 oz (2x3.5 oz of chocolate + about half an ounce of wrapping for each):

8 cups of water ended up being a lot, so this version unintentionally revealed a relationship 4 + 2 + 2 = 8

Though I'm not sure I can articulate why or show supporting research, I feel it is very valuable to build experience with physical models of numbers to create familiarity and intuition about what they are/mean. In particular, I hope this helped J3 anchor the importance of units of measure and scale in the interpretation of numbers.

Finally, this construction has nothing to do with the number 8 (or does it???)

Thursday, May 30, 2019

Quick 2019 resources for parents

A quick list of resources for an elementary school parent

Resources depending on prep time:
  • Grab-and-go

  • More prep time, in increasing order of advanced time required
    • the puzzles and games are very good. 
    • Math Teachers at Play blog carnivals:  Variable amounts of prep time, but usually there’s at least one activity that is ripe for exploration, may take a bit of reading through the carnival to find a suitable one.
    • Mike's Lawler's blog: wonderful collection of (mostly) videos of his family working through problems, puzzles and mathematical explorations. Because his kids are older, it will take a little time to find something you think is suited for your son and then a bit to organize the activity.
    • Georgia State math standards: Despite the name "standards," these documents have a full curriculum with a collection of really great activities. As with any full curriculum, not everything is a complete winner, but there are enough gems. Also, this is probably the best resource for finding material to complement a kid's weaknesses.
This page is still the most comprehensive list of our favorite resources:
Unfortunately, it is a little dated as I haven’t really been maintaining this blog in the last 2 years.

Friday, August 3, 2018

A context investigation

Note: I drafted this a while ago and never finalized the post. Reading it again, it seems fine and maybe interesting without additional work, so I'm publishing it.

Fake Math Models

Robert Kaplinsky wrote a note recently discussing fake math models and unnecessary context. This prompted an activity with the kids.

This issue seems to have come up a lot recently, so I've noticed a pattern: I really hate bad contexts.

Robert wrote: "it looks like the context is completely unnecessary to do all of the problems."
I would go farther: this context is harmful. The context creates a conflict between the specific new material (rational vs irrational numbers) and other important concepts (measurement and measurement error). Subtly, we are discouraging students from
(a) forming connections across topics. For my taste, surprising connections has to be one of the most beautiful and delightful aspects of math.
(b) using all of their ideas and creativity to understand a challenge.
(c) putting new mathematical ideas into a broader mathematical context (maybe I'm just repeating point a?)

I admit that the example only touches on these points lightly, but I suspect the accumulated weight over the course of a school math education is substantial.

If I were full-time in a classroom with a textbook, I'd be tempted to use it as follows:
1. create censored versions of all problems and examples (as you did)
2. work through the questions with the kids
3. Ask them what context they think the publishers originally included and why
4. show the published version
5. discuss (does the published version relate to the math, does it help them understand, does it add confusion, does it conflict with something they know, etc)

Tuesday, July 24, 2018

Playful Math Education Carnival #119

Welcome to Playful Math Education Carnival #119! Just to be clear, that exclamation is to express excitement, not factorial. Fortunately, you will have a bit of time before there's any danger of confusing this post with the edition (119 factorial).

Anyway, only the very coolest folks get to handle a MTaP edition that can be written with a factorial. And I just realized how close (and yet how far) I was to such glory.

119 Fun facts

  • 119 is the number to call for emergency services... in parts of Asia (wiki reference).
  • Of course, 119 backwards is 911 which is the US emergency services phone number
  • 119 is aspiring, the sequence formed by summing proper factors ends with a perfect number.
  • 119 isn't prime, but it almost feels like it
  • 119 = 7 x 17. I don't think products of consecutive primes ending in 7 has a name, but maybe it should?
Do you have other fun facts about 119? Please? Please?


I'm saddened to note the passing of  Alexander Bogomolny this month, and I dedicate the edition of the  carnival to him. The material he developed and made available on his site is truly amazing and remains with us for our benefit.


Aperiodical has an article from Benjamin Leis on the Big Internet Math-off.
Something James Propp wrote as part of the Big Internet Math-off: A pair of shorts


I was reminded of the game of Chomp! in Shecky Riemann's linkfest (most of which isn't elementary level, but worth investigating).

Cathy O'Neil tells her mathematician origin story. I hope all our kids can have an empowering math experience like this.

Discussion of a "square dancing" puzzle from Mike Lawler: part 1 and part 2. I think there is a lot more to explore here and hope some of you will write parts 3 and beyond... 

I always love game discussions. Set is a game you probably all know, but in case you don't here's an intro and a deeper analysis in the Aperiodical.

Pat Ballew writes about divisibility rules. Pat also discusses a fun XKCD in prime time fun.
I'm delighted at how this starts with something many take for granted (12 hour vs 24 hour time of day conventions) and then builds a fun exploration.

Middle school

Have you been waiting for someone to write the perfect post giving you an introduction to tons of Desmos activities? Well, Mary Bourrasa has done it for you.

Michael Pershan tweeted a pointer to a nice collection of logic puzzles on puzzling stackexchange.

Denise Gaskins pointed out a past note about factor trees and some cute wordplay from Danica McKellar's book: prime numbers are like monkeys.

This segues directly into a review of two number theory books by Ben Leis (also the author of the Big Internet Math off post above) in which he discusses some other visualizations beyond factor trees: 

High school

Ben Orlin invents and illustrates a new adage that there are no puddles in mathematics, only oceans in disguise

More advanced

Mathematical theorems you had no idea existed because they are false:
Have fun finding counterexamples. Also, link disproves the conjecture that there is nothing worthwhile on facebook.

The Scientific American Blog has been running these columns on "my favorite theorem." Go back and take a look (I think this was their first one): Amie Wilkinson's favorite theorem.

A fascinating discussion of the Fields' Medal and some ideas about what it should be supporting. 

What was the score? Maybe the sum of scores was 119?

Wednesday, May 30, 2018

Ambiguity in math class

Math class is a special place. We've talked before about some of the special assumptions that are based into that context: teachers pose questions, students answer questions, all questions have answers, questions include all the necessary information, answers are usually "nice," problems can be answered with the tools students have (just been) taught, diagrams are indicative while the underlying true forms are perfect, etc.

Of course, not all math classes make these assumptions or leave them implicit, or are constant about which ones are in force, etc.

In this post, I want to pick up a thread related to the "one true answer" myth: problems that have multiple interpretations.

You are driving from your house to a soccer tournament. The distance is 120 miles. For half of the trip, you drive 60 mph. For the other half, you drive 30 mph. What is your average speed over the whole drive?

Where's the ambiguity?
For the teacher who poses this problem, there is no confusion. Obviously, students are meant to calculate that it takes 1 hour to drive the first 60 miles and 2 hours for the second 60 miles. That means it took 3 hours for 120 miles, or 40 mph average speed.

The catch: what does "half of the trip" mean? As an alternative, it could mean half the time of the drive. If that feels contrived, consider the following natural statements about travel measured in time instead of distance:

  • "The drive took 3 hours; we stopped for a snack half-way." In this case, time and distance are equally natural in normal conversation.
  • "The flight took 6 hours;  I read half the time and slept the rest." In this case, time is the more common metric, but it wouldn't be considered unusual for someone to talk about the distance they flew.
  • "We were gone for 2 weeks, half at the beach, half visiting our cousins." Here, time is the natural metric, while it would seem strange to focus on distance. However, a vacation spent hiking the Appalachian trail or cycling across country would shift the balance back to distance.

Sources of ambiguity

I came up with four potential sources of ambiguity in math questions:

Things that can be measured in multiple ways. 

This extends the idea from “half a trip” ambiguity about distance or time. J1 and I had a discussion a couple of weeks ago where we measured chocolate bars and cookies using three different metrics: mass, cost, utils. For example, which is more:

  • 100 grams of chocolate that costs $2.00 and you value at 100 utils
  • 80 grams of fresh baked sugar cookie that costs $2.50 and you value at 90 utils

In business, it is common to have to deal with the ambiguity of whether “stuff” is measured in physical amounts or monetary value.

Pronoun ambiguity

For example: Ellis had 10 strawberries. Ellis gave 4 to his father and he ate 2. How many does he have now?

Who is meant by each occurrence of "he"? In each case, it could mean either Ellis or the father which leads to 3 distinct answers: 6, 4, or 2.

I accept that this is an example of bad English, but we're in math class and never claimed to be masters of language (did we?)

Tense ambiguity

In the prior story it could be that giving the strawberries away and eating them happened before the state where Ellis had 10. Let's add some extra story context to make this alternative more clear:
Ellis still had 10 strawberries. He bought a pack of 16, but Ellis gave 4 to his father and he ate 2.

I think this alternative interpretation is more of a stretch, but I've seen cases where the uncertainty about when things were happening is more natural.   

Assumption of scalability

Joe can bake 2 cookies in 20 minutes. How long does it take him to bake 4 cookies? 400 cookies? 4 million cookies? 4 quadrillion cookies?

I saw one math class question that involved writing books, a task which is very unlikely to happen at a constant rate.

Your challenges

  1. Find other sources of ambiguity that can infect (or add spice to) math class problems.
  2. For N a positive integer, create a puzzle that has N distinct solutions based on (reasonable) alternative interpretations.