How I trained myself to drink black coffee

I stopped putting cream and sugar in it.

Dear AG Barr

Billy,

Can I call you Billy? AG sounds like what the 4H kids used to call themselves in high school, always followed by a head nod and hand gesture that has not aged well. And William makes you sound like a king, which, may I remind you, you are not. So Billy it is.

Look, Billy: We’ve got a situation on our hands here. At some point, people are going to read this damned thing, and they’re going to realize that there’s only one reasonable conclusion to be drawn from it. So I’m writing to help you with some of this damage control. You can’t change people’s opinion about what they read, but you can influence what they read. No, I’m not talking about redactions and the found poetry of your “summary” - those were cute tricks, but they leave behind a trail. What I’m talking about here is influencing not how they read it, but what they read. You’re going to leave several trails, so that the ensuing discourse will focus on which trail is real, not on the obvious implications of the one true report.

Have you seen the trick that TV villains use, where they stand in a hall of mirrors to confound the good guy? That’s your play. Release the report in ten different versions, with significant variations among them. Those prone to conspiracy, which at this point appears to be roughly half the country, will have everything they need. Some will argue that these are different drafts from Mueller’s team, others will argue that the version supporting their already-drawn conclusions is the one true report, and still others will (rightly) accuse you of trickery. But none of it will matter, because they’ll be talking about everything except what is, at this point, obvious to those of us whose brain has not yet been turned to mush. 

I think you can figure out what to put into those other versions, but just in case, here’s a starter list:

• Unnecessary, nonsensical editorializing by investigators, meant to confirm the worst fears of his constituents, coming out in not-so-subtle lines like, “The president, a white man, did not understand that his dealings with Klimnik were racially insensitive.”
• Salacious details about the president’s conduct, not just while in Russia, but also in places he could not possibly have been, such as Antarctica, the International Space Station, or inside a library
• “Accidental” inclusion of a report-within-the-report about Hillary Clinton’s role as a star witness

I could go on, but I think you’ve got it from here. I believe in you, and I believe in your ability to screw this up as badly as you need to.

Your Friend,

Plaidimir

PS Just in case, I have leaked ten different versions of this letter to the press.

What the hell is going on in Venezuela?

August 20, 2018: What the hell is going on in Venezuela?

This post is for my fellow gringos, and other interested parties, who might be reading about something happening in Venezuela and wondering what in the actual hell is going on there. 

From my first visit in 2002 to my most recent in 2012, Venezuela changed drastically, say, from a 5/10 on the Made-up Poverty Index to an 8/10. Venezuela went from a country with a lot of poverty to a country defined by it - evident in rampant inflation, severe shortages of household staples such as food and toilet paper, and in nationwide rationing that forced the majority of the populace to spend several hours per week in lines, hoping for a chance to buy eggs, flour, oil, or cornmeal. National homicide rates skyrocketed, eclipsing 500 per month in Caracas, the nation’s capital ¹. Medicine became scarce. There was growing unease. When our family visited, our primary fear was that we would be kidnapped - a fear that was not exactly allayed by the Barcelona airport’s wall-sized mural stating that it was everyone’s responsibility to report kidnappings², along with a kidnapping hotline to report any in the moment. 

From 2012 to today, the country has gotten exponentially worse, currently rating something like a 25/10 on the Made-up Poverty Index. 

Another clear indication that things in Venezuela were not going so hot? The currency situation. Here's a rundown of the past 16 years, with commentary:

2002: 

You could go to an official bank and exchange 1,500 bolívares for a dollar. This next part I’m only going to explain once, so read carefully: For foreigners like me, what a dollar could buy then is roughly what a dollar can buy now. The reason behind this is complicated, but essentially, it comes down to this: Even though dollars are scarce, everything about the Venezuelan economy is tied to the dollar. However, throughout all this time, most Venezuelans continued to earn the same salary, meaning their purchasing power declined dramatically.

2008: 

You can now go to the same official bank and exchange 2,500 bolívares for a dollar. Two other major developments: 

1. The government is getting tired of everything costing thousands and millions of bolívares, so they’re restructuring the national currency, effectively taking three zeroes off and calling the new currency the “bolívar fuerte.” So 5,000 bolívares are now 5 bolívares fuertes. 
2. As the government has kept the official exchange rate static, the bolívar has actually lost quite a bit of value in international markets, so now, on the black market, you can exchange one dollar for 7,000 bolívares (or, soon, for 7 bolívares fuertes.)

To give you a sense of what this means, over the course of six years, the price of everything has increased roughly five times what it cost in 2002. Your Starbucks latte that used to cost $5.00 is now $23.33. This price increase also applies to more basic supplies - a $2 loaf of bread is now over $9. You’d probably stop with the nonessential purchases, which is what happened in Venezuela at this time. 

2012

The official exchange rate is up to 4.13 bolívares fuertes to the dollar. The black market exchange rate is up to 35. That loaf of bread now costs over $45. 

2013

It’s only a year later, and you’re not planning on visiting for a while.

Regular, days-long power outages and water shortages become the norm. The Venezuelan government says, look, we recognize that what we’ve said our currency is worth isn’t actually accurate, so they move the official rate closer to the black market rate. By a little bit. 

The official exchange rate has risen to 6.3 bolívares fuertes to the dollar, while the black market rate has soared to 63. One loaf of bread: $84

2014-2015

Between September 2014 and September 2015, the black market exchange rate goes from 100 to 730 bolivares (fuertes) per dollar, and at this point, Venezuela is the country with the highest inflation rate in the world. 

One loaf of bread: $973

2016

It’s dishonest to give a single exchange rate for 2016, because at this point, things are spiraling really quickly:

February 2016: 1,000 bolivares fuertes to the dollar.

December 2016: 4,300 bolívares fuertes to the dollar.

This is when the US news starts to take notice of the enormous public health crisis that has been building for years. There is such a scarcity of food and medicines that visitors report that everybody looks to be in bad health - the most visible signs being that nearly everybody has lost weight, people’s skin is hanging from their bodies and badly burnt by the sun, eyes appear to be sunken, and there are numerous people eating from the trash. Almost everybody is doing far worse than before.

One loaf of bread: $5,733

2017:

July 2017: 10,000 bolívares fuertes to the dollar

September 2017: 20,000 bolívares fuertes to the dollar

December 2017: 100,000 bolívares fuertes to the dollar

One loaf of bread: $133,333

Here, you’re probably skeptical. “Wait a minute,” you’re saying, “if this is a country where people are living in extreme poverty, there’s no way people can afford this.

1. You’re right. People can’t afford it.
2. You’re also right that this isn’t exactly how it works. Yes, wages have increased some over this time (relative to to the 2002 dollar.) But they haven’t increased nearly enough to make anything really affordable. And besides, at this point, there is little medicine in the country, the nation’s hospitals are routinely without electricity (not to mention medical supplies), most of the nation’s professionals have fled the country, and colleges are closing their doors because professors refuse to work for wages that don’t allow them to buy even a loaf of bread per month.

2018

January 2018: 200,000 bolívares fuertes to the dollar

Up to this point, the “official” exchange rate has still been 10 bolívares fuertes to the dollar. You might say, “that’s meaningless!” And, for the most part, you’d be right. With one giant exception: If you’re part of the Venezuelan government, you can purchase dollars - actual US dollars! - at this rate. So, a government official (or, importantly, someone with government connections, go to an official government bank, pay 200,000 bolívares fuertes, and receive 20,000 US dollars. You take one of those US dollars (leaving $19,999 untouched), exchange it on the black market for 200,000 bolívares fuertes, return to the government bank, and exchange this for another $20,000 US dollars. Remember back in 2016, when I said almost everybody looked worse? Well, it turns out, she also noticed that there were a bunch of new restaurants opening, and that there was no shortage of brand-new automobiles on the road. People in the government, and people with government connections, are doing better than ever.

One loaf of bread: $266,666

One loaf of bread (with government connections): $2

Due to massive popular uprisings, the government makes a big show of stopping this practice of publicly allowing its friends to print free money, and changes the official exchange rate to 25,000 bolívares fuertes per dollar, and ends the de facto government loophole that allowed them to print dollars essentially for free. True, this 25,000 is a big jump from 10. But it’s also still far from the currency’s purchasing power within the country, and laughably far from the currency’s actual value in international markets³.

2018:

Now it’s August 2018, and you’re running out of clever expressions to show just how bad things have gotten. The black-market exchange rate is now at 5,900,000 (5.9 million) bolívares fuertes to the dollar. 

One loaf of bread: 7.86 million dollars

Minimum wage: 5.6 million bolívares fuertes per month (roughly $0.95/month)

You’re in charge of the country’s economy. What do you do?

Well, if you’re Nicolas Maduro, who is actually in charge of the economy, you look at a couple things:

1. Due to hyperinflation and rapid monetary devaluation, the minimum wage of your country is now 95 cents per month. That seems like a problem, particularly since your socialist revolution promised to redistribute wealth to the people.
2. People are really starting to notice this whole hyperinflation thing, like, every time they go to buy something and they have to pay some number of millions of bolívares fuertes, which reminds them of how bad things have gotten.
3. There’s still only one meaningful industry in your country - oil extraction and exportation. You have been unable to provide adequate food or medicine to your people. The New York times has recently reported that the average Venezuelan has lost 25 pounds in the past year. People are fleeing your country, building refugee camps on the Colombian and Brazilian borders and emigrating to Chile, Peru, and Ecuador like never before.

You decide to prioritize, and address #1 and #2, leaving #3 for another day.

Tomorrow, Venezuela will once again restructure its currency, much like the conversion from the bolívar to the bolívar fuerte, which removed three zeroes. This time, though, to go from the bolívar fuerte to the new bolívar soberano (the “sovereign bolívar”), you will remove five zeroes. So one million bolívares fuertes becomes 10 bolívares soberanos. 

In addition to this, you have decided to redistribute wealth by increasing the minimum wage by 3400 percent - from 5.6 million bolívares fuertes (56 bolívares soberanos) to 1,800 bolívares soberanos. 

At least, that’s what you had planned to do, until you were notified by your aides that this was an entirely untenable plan and that the country would essentially stop functioning, immediately. Sick, elderly people who have been relying on paying for their own home care (particularly since hospitals are currently out of order) and who have been saving for this, who had planned on their meager savings paying for six years of home care, would have been able to afford only two months before their savings dried up.

So instead, caught in bad policy-making, you say that it was simply a mistake, that you, like everybody else, were thrown off by the odd choice of five zeroes⁴, and that what you meant to say was that the minimum wage will be increased to 180 bolívares soberanos, not 1,800. So the minimum wage will increase only to about 3.5 times what it was (from $0.96/month to about $3/month.)

2019 and Beyond

Nobody knows what will happen. But there is almost no confidence that the August 2019 change will improve conditions for Venezuelans, and a sense of certainty that the country will continue to get worse in every possible way.

Meanwhile, many of us will continue to send bi-monthly 60-pound care packages of food, medicine, medical supplies, and toilet paper to our most trusted hospital and neighbors. We will continue to gather with other Venezuelan émigrés to sing música llanera , dance, remember old times, and worry together about our loved ones who have remained. Most will keep calling daily, hoping there is enough electricity to get through, and remind ourselves that the people we fear for are still there, living very real lives, fighting to survive. Most will encourage their parents and grandparents elders to leave, even though they most certainly won’t. This political and economic curse has ended the optimism of a country whose unofficial anthem for years hinged on these lines: “No hay mal que dure cien años, ni cuerpo que lo resista; yo me quedo en Venezuela, porque yo soy optimista.”⁵ 

––––––––––––––––––––––––––––––––

¹ This happened the same year that Chicago made headlines for surpassing the 500-homicide mark annually. Chicago and Caracas have roughly the same population.

² What a contrast to my hometown, Fresno, where the airport has an artificial redwood forest and an exhibit highlighting Sun-Maid raisins.

³ Just to be clear: The black market value is the best estimate of the bolívar’s value on international markets.

⁴ Note to future policymakers: Know the state of math education in your country before enacting policies that rely on people’s ability to mentally divide by 100,000 on a habitual basis.)

⁵ There is no evil that can last a hundred years, nor body that can take it; I’m staying in Venezuela, because I’m an optimist.”

A Restorative Conversation goes really well

May 28, 2015:

A restorative conversation stops a spiraling Tiara.

This morning, I walked into an SBAC testing room and saw that there was cereal on the floor around Tiara’s desk (Tiara is a 6th grade student at our school, and, of course, this name is a pseudonym.) Ms. Napoleon was texting the phone, and Tiara was sitting back at her desk and sulking.I said, “I’m going to pick up this cereal. Tiara, would you mind helping?” I started picking up the cereal, and Tiara started helping. When we were done, I said, “Tiara, can I check in with you?” and walked out of the room with her.

We walked to the dining hall, which was empty - I didn’t walk us upstairs (toward the reflection room) because I didn’t want Tiara to feel like she was being removed from the room. When we sat down, I said, “Tiara, I’m proud of you. A year ago, if I would have asked you to help pick up the cereal, I don’t know that you would have said yes. But just now, you chose to help. You’ve come such a long way.” Tiara smiled, a little bit. I paused for a few moments.

Me: “So what’s going on?”

Tiara started talking quickly, in a high-pitched voice. I couldn’t really understand what she was saying. This is how many of her meltdowns start. I said, “Tiara, I can’t understand you and I just want to hear what’s going on.” She was still mumbling somewhat, but I did my best to hear what she was saying and listen actively.

Tiara: “We were in class and they said we could talk but I was by myself in the back so I asked if I could move and he said no.”

Me: “Who is he?”

Tiara: “Mr. Landshark. So I got mad and that’s when I threw some cereal on the ground. Then Ms. Napoleon was texting for me to get removed and I was mad about that, too.”

I repeated the key facts, then asked, “what were you thinking about when that happened?”

Tiara: “I was mad because he didn’t let me move, and yesterday we already had an issue so it was already bad.”

Me: “Are you saying that part of your anger was carried over from yesterday?”

Tiara: “Yes.”

Me: “What have you thought about since this happened?”

Tiara: “I’m feeling a little better.”

Here, I decided to teach Tiara a little bit about how we, as humans, react to stress. This is where I was hoping most of the learning would take place, both from the perspective of Tiara understanding herself (personal growth) and from the perspective of Tiara understanding others (empathy.)

I explained what some call the “compass of shame”, which I instead called “the four stress responses”:

Whenever we go from a positive feeling to a negative feeling, it causes stress. This is something that happens to everybody: Our brains release a chemical, and whether we notice it or not, we tend to react in one or more of the following ways (I draw the compass):

• Withdraw: We actually leave the place we are.
• Avoid: We stay where we are, but we do everything we can to avoid the issue.
• Attack other: Usually not physically - often this looks like us saying mean things about the other person in our minds.
• Attack self: Also not physically - this is most often us putting ourselves down in our own minds.

Like I said, we all do these things. Sometimes we do more than one of them. Like when I trip on shoes that I left out and I get mad at my wife. I say in my head, “why didn’t she move those shoes!?” [points to “attack other”] But that’s absurd; it has nothing to do with her! It’s just my response to the stress of going from feeling good to feeling bad that happened when I tripped. Sometimes I’ll say something and somebody else will say something about what I said, and I have a stress response and say in my head, “that was so stupid. I can’t believe I said that. I’m so dumb/inconsiderate/mean.” But I don’t really believe those things about myself; it’s just a stress response.

I ask, which of these stress responses do you think you had today?

Tiara points to “attack other.”

Me: “What happened? Please know I’m not going to share any details of mean stuff you said in your head.” We both smile.

Tiara, “I was just thinking mean things about Mr. Landshark.”

Me: “Thanks for sharing. Again, that’s a normal stress reaction. It’s not what you chose to do; it’s just what happened...did you do any of these other things?

Tiara pauses and studies the compass. Finally, she points to “avoid.”

Me: “That’s what I was thinking. Say more about that.”

Tiara: “Well, when Ms. Napoleon was texting the phone, I was just kind of avoiding the problem, kind of in my own world, trying not to deal with it.”

Me: Sounds like a very normal stress response.

I explained the significance of knowing about this:

There are two reasons it’s important to know about stress responses: One, because it helps you recognize when you’re having one so you can stop it. You’ll notice that you are saying mean things about someone in your head and be able to say, “wait, this isn’t a choice I’m making; I’m just having a stress response.” And then you can give yourself a minute to let your body get rid of the stress chemicals. Because if you don’t notice it, often you’ll do something you didn’t mean, which will cause more stress, and then you’re stuck having a bunch of stress responses in a row.

The second reason is because another thing that causes us to get stuck is when we’re not right with someone else. That feeling is stressful and, if we don’t deal with it, it leads to even more stress responses.

Me: So you said you already felt like you weren’t right with Mr. Landshark. It sounds like that had something to do with what happened today.

Tiara: Yeah.

Me: So in these situations, the way to become right with somebody again is to figure out what harm was done, and then repair the harm.

Tiara: You mean apologize?

Me: Maybe. It probably depends on the harm. Let’s start with Ms. Napoleon. How was she impacted by what you did?

Tiara: She might have been confused because she had just come into the room.

Me: That’s a good start. How do you think she felt when she was texting?

Tiara: Maybe a little concerned, because she was trying to help me but I was avoiding it.

I wrote down: Ms. Napoleon - confused, concerned.

Tiara: And Mr. Landshark, I don’t think he cared because he didn’t notice what I did.

Me: That’s possible, but be careful with that. Just because somebody doesn’t say something doesn’t mean they didn’t notice. If he did notice, how do you think that affected him?

Tiara: He would have been mad...or maybe frustrated.

Me: Great. Is there anybody else affected by this?

Tiara: The kids around me, I don’t know if they saw it, but they might have been confused about what was going on.

Me: There’s one more person who I think has been affected by this, and it’s not me :) Who do you think that person is?

Tiara: Me.

Me: How were you affected by what happened?

Tiara: I was angry. But I’m feeling better now.

Me: What do you think was causing that anger? Were you embarrassed by the way you acted?

Tiara: I think that was it.

Me: Remember, that’s just a stress response. But it made you feel embarrassed, then you got angry. So - do you forgive yourself for having that stress response?

Tiara: Yes.

Me: OK; we’ve been talking for about 10 minutes. I’m curious - what have you learned?

Tiara explained the stress responses to me, fairly accurately. I asked why they matter, and she explained that they’re normal and we have to know they’re happening so we can stop them.

Me: How can you repair some of this other harm? What do you think you could do?

Tiara: I could tell Ms. Napoleon I’m sorry, that I didn’t mean to make her upset.

Me: That would probably help. What about with Mr. Landhsark?

Tiara: Same thing?

Me: What’s that?

Tiara: I think I should tell him I’m sorry, that I was just having a response to my anger and it wasn’t really about him.

Me: Do you think that will make the two of you right with each other again?

Tiara: I think so.

Me: Great! I’ve been learning about this stuff and I find it fascinating...it helps me to explain a lot of things that have happened in my life. Have you found this helpful?

Tiara: Yes.

Me: In what way?

Tiara: Because it helps me know why sometimes I start saying things about myself, but it’s just because I’m stressed.

Me: Thanks; that’s helpful to know. Let’s go back to class and crush this SBAC, OK?

Tiara: All right. [she smiles]

We walked back to class and, on the way, I said, “now, when you go back in there, know that you’re sitting next to some people that sometimes have their own stress reactions that sometimes affect you. Keep in mind when you see them having stress reactions, and notice when you’re having a stress reaction to what they’re doing.

Tiara came into the room, got right to work on her SBAC, called Ms. Napoleon over and said, “I’m sorry for what happened earlier. I didn’t mean to do it”

Ms. Napoleon asked me a minute later, dumbfounded, “what did you SAY to her!?”

Ten minutes later, Tiara and Mr. Landshark checked in outside. I asked her how it went afterward, and she said it went really well. “You’re all right with each other?” I asked. “We’re all right,” Tiara said, and she smiled and got back to work on her test.

Close Reading + Teacher Time Outs

Last week, I had the pleasure of working with one of our teachers for three days straight, trying to learn as much as we could about Close Reading.

Some background:

1. I wrote about Close Reading before. If you're into problem-based mathematics, you are probably the type who would like reading instruction centered on close reading.

2. Close reading is something that Achievement First has been taking fairly seriously for 2-3 years now. It is, at this point, central to our model. This is one of the areas in which I feel very lucky to have been at the right place at the right time, because I've been able to learn about something so powerful from people who really know what they're talking about.

3. Our school's "greenfield" model for next year has small-group close reading at the core of our humanities instruction, bolstered by a barrage of content knowledge, daily small-group writing with feedback, and twice-weekly seminars for students to discuss the big ideas of what they're learning, grounding everything in the myriad texts they've read.

4. The teacher I was working with, Tanesha, is a phenomenal teacher who is leading the close reading in our 5th grade next year, who has taught in a lot of ways and is eager to learn more about close reading. We've worked together in the past, and I'm ecstatic that she is joining our school community (and that she will be one of my own kids' teachers in the near future.)

5. Our close reading teaching cycle takes two days, and consists of

• A 45-minute intellectual prep meeting, in which teachers get to know the texts (together) and target outcomes deeply and prepare a hybrid script/menu that will allow them to help students draw out key findings from the text while ensuring that the teacher's mind is squarely on student thinking (i.e. listening to students, rather than listening for specific answers.)
• Day 1 of teaching (45 minutes), with real-time coaching
• Studying student work and intellectually preparing for day 2.
• Day 2 of teaching (45 minutes), with real-time coaching
• Studying student work to determine next steps

6. For what it's worth, our math teaching cycle is fairly similar, except that the two-day cycle doesn't always hold.

Here's what was great about this:

For these three days of "training" (training is in parentheses because it was more like co-exploring than a transfer of knowledge), we only worked with three students (all at the same time). We asked a teacher for a few kids with different levels of reading proficiency and ended up pulling Jordan, Marc, and Tina (pseudonyms, of course). There is something really special about getting to know a small group of kids as learners.

The text we selected, Because I Could not Stop for Death by Emily Dickinson, is simply a great poem. It's a lot of fun to read with kids of different ages. In this case, we were working with fourth graders...I'm not sure I would want to read the poem with kids younger than this, but I remembered the last time a teacher and I read it with a group of fifth graders, one of the kids, Jacob, said it was his new favorite poem OR song. There is a lot of joy in reading great texts with kids. There is also a lot of joy in reading great texts without kids - we did plenty of that, too, and it was exhilarating to dive deeper and deeper into each of these texts together.

By day two, Tanesha was getting far more out of the texts than I had gotten in my multiple reads. She was on fire, and bringing a close reading lens to everything she read at this point. I kinda expected this, because she's amazing, but it's nice to see your concept of someone validated so beautifully.

Probably the most fun we had was in teaching the kids, because of something I learned in a conversation with Elham Kazemi while at the NCTM national convention. I missed her talk at #shadowcon15, but you can catch the re-runs here. Tanesha and I had a lot of fun taking a liberal amount of time outs, asking each other things like:
* How about that line of questioning? Was I really having kids doing the thinking there?
* Should we ask for more evidence or push for more ideas?
* I want to ask this - is it too leading?
* Given what Jordan said, how do we figure out if he understands this? [points to anticipated response from planning page]

At one point, Marc called a "student time out", and the students started discussing the ideas in the poem on their own, without teacher intervention. This was great because it showed student ownership, it was a subtle way for Marc to make fun of us in a collegial way, and it gave us some necessary feedback that we probably weren't spending enough time sitting back and letting kids discuss.

All in all, the experience solidified my belief that reading great texts with great kids and great teachers is a pretty incredible way to spend my days. I'm looking forward to the next round, to seeing this in action with math and science lessons, and to continuing to grow through our school's collective wisdom and ongoing iteration!

An exhilarating conversation

Sebastian: Daddy, do you want to know what happened in school today?

Me: Of course I do.

Sebastian: My teacher was subtracting and said, we can't do 2 minus 8. So I raised my hand and said, "yes we can; it's negative 6." My teacher said, "you're ridiculously smart."*

I made a quick decision to ignore the fixed-mindset compliment and instead focus on the positive by focusing on the negative (so to speak):

How did you know 2 minus 8 was negative 6?

Not the best explanation, but the thinking is there.

At this point, you're likely thinking that I'm a math teacher, so I'm probably patting myself on the back for having taught Sebastian how to subtract in this case. I have not. About a month ago, he started asking me what negative numbers were, and I talked him through a conceptual explanation (something like counting down from three, then beyond zero). I was excited not because he was doing 'advanced math' but because he had applied his conceptual knowledge to this new situation.

So I thought to myself, I wonder what this kid can do. I remembered a story my parents told me (about asking about square numbers at an early age) and wrote this on a piece of paper:

0^2 = 0
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = ___

10^2 = 100

...and I read it aloud:"Zero squared equals zero; one squared equals one; two squared equals four," and so on, ending with "what do you think is the value of five squared?"

When I returned a minute later, this is what the paper looked like.

 Three things jumped off the page:
1. The kid got it. Nice!
2. His explanation focused on how he knew the answer was 25, not on how he knew what "squared" means. We call this a "what-how" explanation...not nearly as strong as a "what-why" explanation.
3. He decided to go one step further and write 20^2 = 200. I love everything about this, even though it's not correct.

I asked him about the 20^2=200. How did you figure that out? He explained: If 10 squared is 100, then 20 squared is 20 times 20, which is 200. I asked how he knew and he said that 20 was twice as much as 10 so it was 200 instead of 100. I asked him how he could check it and he said, "I could count by 20s." I stayed silent. He started counting by 20s and, when he finished ("...320, 340, 360, 380, 400. Four hundred!") he said, "I don't want to cross it out, so I'll just write 200 plus 200."

My heart sang. And then things got even better when I thought: Let's see if you can do these, too. These might look like your typical exercises, but, given where Sebastian is mathematically, they're at least one step above your average "now that you've seen one solution, try five identical problems."

Sebastian counted by 6 (aloud) to get an answer of 36. Then came 7^2, and he said, "I need to add 7 to 36." I asked why.

He tried it out. He got halfway through and stopped. "Wait," he said, "first I need to add six dots and then seven dots, so I need to add thirteen dots."

How did you get thirteen?

His response was somewhat messy. There was a lot of what-how talk thrown in there ("I need to add seven and six, so I need to add 13, so I know that four more gets us to 40, and then...") and a lot of false starts where he was trying to get to the answer while talking through his method, but his answer boiled down to this: "It was six groups of six but if I add six dots it will be six groups of seven. Then I need to add seven more dots so it will be seven groups of seven."

There are so many beautiful things about this response. The kid is seeing groups in his mind. He's understanding the nature of multiplication. He's using the concept of multiplication to make connections between two multiplication problems. He's using a pattern he discovered to determine that he even needs to multiply in the first place. He's up at 9:30 at night doing math because he (and his dad) just can't get enough.

He then spent about 10 minutes going down a rabbit hole, coming up with various answers that were not the actual value of 7 squared, partly because he was accidentally adding 13 to 30 (not 36) and partly because he was thinking really hard and his working memory was filled with a lot of things and he kept trying to decompose 13 different ways to make the addition easier.

The only helpful nudge I gave was to point to 43, point to 36, and say, "if it were 10 more than 36, what would it be?...but you added more than 10, so it should be more than that..."

At one point, I made what I consider a critical mistake. I said something like, "you're doing it right, but 36 plus 13 is not 43." The second half is fine, but the first half reinforces the idea that there is a 'right' strategy. I should have instead validated that his strategy made sense or that his strategy seemed like it was based on solid reasoning. That's OK. I like Sebastian's mistakes here, and I like my mistake too - if I had not said this, I don't know that I would have reflected on this idea.

He figured it out from there: He laughed at his handwriting-based mistake, used his tens and ones chart, and quickly got 49.

I asked him how he could check to see if he was right and he said, "I could count by sevens, but I don't know how to count by sevens." Then he counted by sevens anyway, and when he landed on 49, his face lit up.

Feeling confident, we strapped on some wax-and-feather wings and tried to see how high we could fly: 14^2. Here are some action shots:

That last picture is his sticks-and-dots representation of 14+14+14....+14 (14 times), and his tens-and-ones chart that he used to figure out what 14 tens and 56 ones added up to.

Here are a handful of brief takeaways from all of this:

1. Sebastian was able to do all of this math because he has been taught everything in a highly conceptual way. From the concept of subtraction to the concept of multiplication to the visual representation of multiplication that allowed him to find the link between 6x6 and 7x7, everything that he has been taught set him up for success here.
2. To take #2 a step further, I would argue that he was able to do math he hadn't yet learned explicitly precisely because he has not been taught a series of procedures. Teaching kids a bunch of procedures means they know those procedures but don't know how to approach procedures they have not been taught. "But his tens and ones are an example of a procedure!", you say. You're right, but this procedure is backed up by his conceptual understanding. When he learns the standard addition algorithm (with the corresponding conceptual understanding), it will be a natural extension of what he has already figured out.
3. To all you engineers out there complaining about how your child's common core math homework is far too complicated, a. in many cases, you're probably right, and b. you're looking at otherwise simple problems seemingly made complex by nonstandard strategies; it may be worth it to also check if your kids can do something you wouldn't have been able to do at their age because of their developing conceptual framework.
4. I'm grateful that Sebastian has teachers who have embraced the Common Core math standards and have committed themselves to teaching things conceptually.
5. Hearing and pushing kids' thinking is a lot of fun.
6. Kids, in general, are capable of more than we often give them credit for.
7. Notice how this "real-world" math was so engaging!
8. More than a handful.

Special thanks go to Sebastian for his hard work, to his teachers at Elm City College Prep Elementary for doing such a great job teaching him mathematical concepts, and to Joseph "Compadre" Yrigollen for his encouragement via text message while all of this was going down. Thanks also to you, loyal readers, for indulging me in a long-winded monologue about the virtues of talking math with your kids.


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*The use of "you're smart", while clearly well-intentioned here, is dangerous because it discourages mathematical risk-taking, particularly in relatively high performers who want to preserve their image of being "smart", and discourages relatively low performers from trying - if another kid is just "smart" then no amount of effort is going to get me there anyway. Beware the small phrases that reinforce fixed mindsets!

"We can't do X" is troublesome because it implies that, in math, there are things we can and can't do. The less arbitrary rules we impose on math, the better. After all, even the famous "can't divide by zero" edict really just means that dividing by zero is problematic. I mean, of course you can take a pile of money and try to split it equally among no people. Of course you can take a pack of M&Ms and put them into piles of zero M&Ms. It's just problematic, which is not always a bad thing. Every case of something you "can't" do in math seems to come down to constraints anyhow.

Seven for Sebastian

Hey everybody,

I haven't written in a long time because I've been spending most of my time listening. Also, I've got this quote stuck in my head from Jorge Luis Borges: No hables a menos que puedas mejorar el silencio. Don't speak unless you can improve the silence. I've been following what is happening in Ferguson (and, by extension, America) and have read a few great, thought-provoking books, and I spend most of my non-coaching working hours listening to different ideas about how to make our school better. I'm enjoying all of the listening and learning a lot; it just means I haven't gotten to write much.

But since I'm writing now, let me share a few stories about my son. Barbara often gets to be the star of this blog, but Sebastian gets to be the star today. Yesterday was my birthday, but I haven't written since his seventh birthday, so this one's for him. Here are seven stories so you can get to know him a bit:

1. He came to me one day and said, "I commented on a YouTube video." I was scared and asked him for the details, and he shared that he had commented on a video showing a 'time travel tunnel' that set people's cell phone times back a minute or two. He wrote that the electric lights probably created a magnetic field that interfered with the cell phones' operation.

2. He likes to climb up the walls and do pull-ups on the door frame, and every time he jumps onto my bed he jumps straight into a forward roll.

3. When I told him that I saw the Administrator of NASA Charlie Bolden at the train station, he later asked, "So Daddy, did you eavesdrop on NASA?" For the record, I did not, but I loved his choice of words.

4. He carries his older sister (age 8) on his shoulders and walks around the house. They are inseparable, to the point that he often says, "I'm going to go to Barbara's room now because I don't want her to be alone."

5. When we were at the zoo last week, he said, "Is that a bear?" and I replied, "Nope. Chuck Testa" and he thought it was the funniest thing in the world because he spends his time watching YouTube videos by a couple of lovable goofballs who taught him who Chuck Testa is.

6. He told me a story about how his teacher had him walk to the board to write something and he couldn't reach, so she picked him up so he could reach. He concluded with, "and that was my first time ever being picked up by my teacher." He is way small.

7. This summer, we visited my cousin Sarah's science lab, where she set up a sweet visit with demonstrations and the like, and after one of the experiments instead of a simple "good bye," Sebastian went up and gave the guy a big hug.

With all the good and bad in the world, I'm just happy I get to spend plenty of time with this little guy.