(Not-Quite-Sunday) Catechism: Escape


Q: What is the reason for the third commandment?

A: The reason for the third commandment is that the Lord our God will not allow those who break this commandment to escape His righteous judgement, although they may escape punishment from men.

I have been having difficulty with this question of the catechism and continue to wrestle with it. We have reflected on the profundity of the third commandment and seen how it echoes throughout the rest of the law, especially in the prior two commandments. It is, in many ways, the commandment that we most readily and thoughtlessly break. What does it mean, then, that its existential purpose rests on the surety of God’s judgment?

One thing that has helped me is Pastor Jimmy’s reminder at this past church retreat of the notion of progressive revelation. What may seem at first glance to be a shifting in standards or doctrine at different snapshots of the Old Testament resolves itself when we look at the overall narrative of that history. From this scope we see that there is a deliberate vector of revelation that both broadens and deepens our understanding of God’s perfection over time. His character expands in facets and levels of virtue while humanity’s notability is correspondingly eclipsed in its diminishment and failure. Just as we may allow a certain latitude with our very youngest children and expect them over time to get old enough to know better, so God has gradually let us adjust to seeing His glory. In our case, however, our dawning understanding of the Name we inherit leads us to a simultaneous conclusion of our ultimate and undeniable unworthiness.

Jesus, then, is a kind of metaphysical singularity. He is the endgame of this revelation, and a new beginning. The Alpha and the Omega. A single bloody door of Passover, the threshold between us and God, through which is both forgiveness and the freedom to finally do right and grasp at a holy identity. A single name above all others.

If we stay stuck in the muck of our present reality, obsessed with the world of man, we will never see Him. We may never know, until it is too late, the full cost of our sin, of our mockery of God, His will, His word, and His created order. We will never know how little we measure up in the full extent of the scale since, instead, we only compare ourselves to each other.

When we consider, though, God in His glory, His name in reverence, we have to face with sobriety how we have no rightful place in that schema. We are utterly and justly effaced, laid low to annihilation.

At the end of our despair comes a savior. A still, small invitation to connect despite everything, at the cost of personal sacrifice. Do we dare scoff His name then?



Incredibly, I was asked to be part of a brief church panel discussion on lessons from marriage. A lot of good spiritual advice was given, but I felt bad that there wasn’t much in the way of practical wisdom that was discussed. Rick did bring up communication (of a sort), however; he put it as, “listening to what she’s saying instead of what you’re hearing.”

listen up: ears really are strange looking if you think about it

This calls to mind the first episode of a new podcast I’ve subscribed to–The Hidden Brain. It’s an NPR podcast about “the unconscious patterns that drive human behavior, the biases that shape our choices, and the triggers that direct the course of our relationships.”

The first episode begins with the concept of switch tracking, consciously or unconsciously changing the subject of conversation. It’s an important social concept to understand, and one that would have made me a lot wiser in a lot of difficult conversations.

You can listen to it here:

or go to the episode page.

There’s also lots of good advice in this series of Youtube videos about how to give and receive feedback. (Lesson 5: Don’t Switchtrack)

Having said all this, I used to be very concerned with upping my game in terms of relationships. (“As a young man” — do I have to say that now?!) I know better now that with a relationship as serious, as involving, as contentious and covenantal as marriage, tools, tactics, and techniques have serious limitations. It’s fine to try to learn as much as you can to try to better serve your spouse, but in the end, what I found I had was fool’s gold.

Real love comes from a higher power. Meet the numinous, and you’ll find he’s been switching tracks on you all along.

Railroad Wye Switch

A Good Day for a Shopping Marathon


Yesterday, I got it in my head to go on the Old Town Boutique District Scavenger Hunt. One of the advantages of homeschooling I’m finding is that I can actually follow through on the “I’ve always meant to…” items that get shelved into the dark recesses of intention. Well, I’ve always meant to stroll around the shops on King Street, and this gave me an excuse to do just that.

So, apparently, you can pick up a scavenger hunt “passport” at any number of participating stores and use that as a guide and excuse to casually browse through a number of stores. This was great for me because I’m not much of a shopper, and I psychologically need some sort of goal or directive to be in a store and, honestly, I’m a little intimidated to be in some of the chi-chi places.

I didn’t realize you could get the passports free (I was skimming), so I signed up for a BAGGU bag experience at $10, which you pay for online and pick up at the Visitor’s Center in Alexandria. Turns out, worth it. In addition to getting the opportunity to have your passport ticked off, you get a nice little freebie at each store you visit.

Being as confused as I normally am, I didn’t realize that stores wouldn’t dig out the freebie unless they saw you had the bright neon bag with you. I spent half the day with the bag stashed in the stroller, so I missed a lot of freebies. Oh well. As luck would have it, someone involved in promoting the Boutique District noticed me shlepping my kids around and gave me a nice little gift card to Union Street Public House for taking our picture for publicity. I probably look bedraggled.

(There’s also an Instagram game/contest, but too much for me. I do wish now I had some pics to share; you should check the link out to peruse all the fun other people had.)

Yes, of course, the kids were with me. Didn’t I just say that homeschooling gave me an excuse to do these things? I mean, truthfully, I just thought we could use the day to take a nice stroll out of doors, but there were some hidden opportunities in the scavenger hunt.

For one, it was easy for me to hand the passport over to Biggie and tell him to go to the counter and get the passport stamped at each store. I actually got him to accost people and say “Please” and “Thank you.”

We also got to see a lot of neat stuff. Wonder of wonders, King Street has some pretty cool stores! There was a lot of sensory enrichment; we got to smell soaps and spices, taste olive oils, touch yarns, and just take in lots of wonderful curiosities. JB’s favorite was probably eating a yellow watermelon mini-popsicle at Whimsy Pops. Or maybe eating half a caramel-salt donut at Sugar Shack. (Did you know Sugar Shack posts daily freebies on their Facebook page?)

Biggie bought a few little things, like some rocks at Potomac Bead Company, so there was a little math practice in there, too.

And the exercise. We started at 11 at the eastern end of King Street, and we marched through the highways and byways of commerce all the way up to the Metro Station, three hours later, just in time for a playground playdate with the Alexandria Homeschoolers group. JB was in a stroller, and Biggie did not complain once.

This was not really my original plan; I didn’t really have any expectation to accomplish anything other than have some time outside and see a couple of stores, but Biggie made it a mission. Even after our time at Blue Park Playground, he insisted that we go back and hit the last few stores that we missed on our passport. So we finished, which qualifies us for an entry into a drawing for a gift card.

Prize, no prize, we got home with a bunch of stories and a free bath bomb from Ladyburg, which made my kids smell nice again.

And now she’s fine



Yesterday we went to the pediatrician’s office. We’ve been growing increasingly concerned with JB (our two-year-old); she’s had a cold for a while, but recently she’s been having some strange symptoms. Her nasal drainage has gotten dark, she’s had a mild fever, she’ll scream bloody murder every time we try to wipe her nose, and there’s been a weird dank smell emanating from that area. Dana urges me to make an appointment for her.

Doctor: “Oh. There’s something up there. I think your daughter stuffed something up there.”

And now everything makes sense.

Fortunately, we were able to make an appointment to see an Ear-Nose-and-Throat specialist that afternoon. So we make a day of it. I’m trying to peel through all the coupons Elijah and Evangeline scored from summer reading, so we go visit the Treasure Trove thrift store (which benefits Inova) and have lunch at Bob Evans. We then browse in a nearby library while waiting for our appointment — I pick up a Def Leppard CD to listen to in the car.

Popcorn kernel. JB had stuffed a popcorn kernel up her right nostril. It came out in two pieces, probably because it was softening up and rotting up there.

She’s a lot happier now, thanks.

Out of touch, out of reach, yeah
You could try to get closer to me
I'm in love, I'm in deep, yeah
Hypnotized, I'm shakin' to my knees

I gotta know tonight
If you're alone tonight
Can't stop this feelin'
Can't stop this fire

Oh, I get hysterical, hysteria
Oh can you feel it?
Do you believe it?

Watership Down, Phantom Tollbooth To Go


I’ve written before about how I use bedtime reading to seed Biggie’s reading with more challenging material. Nowadays we don’t do it as consistently; some nights we make exceptions because we’re watching (as a family) a show on PBS or, as we did last night, Penn & Teller’s Fool Us (Biggie’s really into magic right now).

We just finished Watership Down by Richard Adams, one of my personal favorites and, I’m happy to report, now one of Biggie’s. Often called “Lord of the Rings with rabbits,” it is a good stepping-stone into Tolkien but immensely charming on its own merits. It brings wonderful attention and heightens awareness about the natural world since most of the book is told from the rabbits’ point-of-view. Richard Adams conceived of it as tales he improvised for his daughters on long car journeys, and there’s a real masterful yarn-spinning aspect to it—it’s full of imagined folklore and strange societies and dangerous heists and other derring-do. The language can be advanced but Biggie had no trouble going along with it, and its rhythms are perfect for evening readings. Truth be told, I sometimes rued that my son would sneak off to read chapters on his own, depriving me a little of the delight of reliving the story once again.

Bright eyes

Next on the slate is The Phantom Tollbooth, which came to mind because I’ve recently been considering dragging Biggie into a youth bookclub at a local library. There’s one in Sherwood that read Tollbooth last month. A little easier than Watership Down but breaking some new territory in the kind of books Biggie reads. And it’s another book with a map in it.

Milo navigates The Kingdom of Wisdom

Building Math: Making Math Midichlorians


Again, what follows are largely notes and excerpts from What’s Math Got to Do With It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success (2015 revised and updated) by Jo Boaler.

Yesterday I posted about how Boaler argues that math instruction in the United States promotes a kind of passive learning that does disservice to the actual nature of real mathematics. Efforts to provide reforms or alternatives, including Common Core, have roundly been met with resistance, often organized and political.

Putting that aside, what’s a parent to do? Boaler herself helped create a summer camp designed to give a sort of Jedi training in math to math-averse students.

One of the goals… was to give students opportunities to use mathematics flexibly and to learn to decompose and recompose numbers. We also wanted students to learn to ask mathematical questions, to explore patterns and relationships, and to think, generalize, and problem solve…. We decided to focus… on algebraic thinking, as we thought that would be most helpful to the students in future years, and to focus upon critical ways of working including asking questions, using mathematics flexibly, reasoning, and representing ideas. (146)

As you can see from what I’ve put in bold, Boaler suggests a couple of major objectives that will make our kids stronger mathematicians: (1) getting the confidence and curiosity to ask good math questions, (2) playing with numbers and using concepts flexibly, (3) being able to articulate, discuss, and defend their reasoning and problem-solving, (4) having multiple ways to mathematically represent ideas and processes.

What are some things that can be done at home, with or without school?

There are many books filled with great mathematical problems for children to do, but it is my belief that the best sort of encouragement that can be given at home does not involve sitting children down and giving them extra math work, or even buying them mathematical books to work on. It is about providing settings in which children’s own mathematical ideas and questions can emerge and in which children’s mathematical thinking is validated and encouraged. (169)

Any sort of play with building blocks, interlocking cubes, or kits for making objects is fantastically helpful in the development of spatial reasoning, which is fundamental to mathematical understanding.
In addition to building blocks, other puzzles that encourage spatial awareness include jigsaw puzzles, tangrams, Rubik’s Cubes, and anything else that involves moving objects around, fitting objects together, or rotating objects. Mathematical settings need not be sets of objects. They can be simple arrangements of patterns and numbers in the world around us. If you take a walk with your child, you will stumble upon all sorts of items that can be mathematically interesting, from house numbers to gate posts. (170-171)

Research on learning tells us that when children are working on their own ideas, their work is enriched with cognitive complexity and enhanced by greater motivation. Duckworth proposes that having wonderful ideas is the “essence of intellectual development” and that the very best teaching that a parent or teacher can do is to provide settings in which children have their most wonderful ideas. All children start their lives motivated to come up with their own ideas—about mathematics and other things—and one of the most important things a parent can do is to nurture this motivation. (172)

❑ Buy more Legos.

[Sarah] Flannery says: “…almost without our knowing we’ve been getting help since we were very young—out-of-the-ordinary help of a subtle and playful kind which I think has made us self-confident in problem solving. Ever since I can remember, my father has given us little problems and puzzles…. These puzzles challenged us and encouraged our curiosity, and many of them made math interesting and tangible. More fundamentally they taught us how to reason and think for ourselves. This is how puzzles have been far more beneficial to me than years of learning formulae and ‘proofs.'” (173)

❑ Tell dinner time stumpers.

No matter how outrageous a student’s contribution or question, he could respond: “Oh, I see what you are thinking. You’re looking at it as if…” This is a very important act in mathematics teaching because it is true that unless a child has taken a wild guess, then there will be some sense in what they are thinking—the role of the teacher is to find out what it is that makes sense and build from there. (176)

❑ Try to figure out what the heck your kid is doing.

Math conversations should be relaxed and free from pressure. Fear and pressure impede learning, and children should always feel comfortable when offering their ideas in math…. When students know that I am not judging them harshly and that I genuinely value errors, they are able to think more productively and learn more. (178)

❑ Don’t talk about grades.

One of the very best methods I know for encouraging number flexibility is that of number talks…. The aim of number talks is to get children to think of all the different ways that numbers can be calculated, decomposing and recomposing as they work. (178)

Some good prompts to use while you are working with children are:
* How did you think about the problem?
* What was the first step?
* What did you do next?
* Why did you do it that way?
* Can you think of a different way to do the problem?
* How do the two ways relate?
* What could you change about the problem to make it easier or simpler?

❑ Talk about numbers.

I’m being facetious in an impoverished attempt at levity, but I actually think Boaler’s advice is excellent. In the ninth chapter of her book she has a list summarizing her practical takeaways for parents. She uses a lot of absolutes in this list, each of which I can think of numerous exceptions, but the gist of it is good.

  1. Never praise children by telling them they are smart. This may seem like it is encouraging but it is a fixed-ability message that is damaging.
  2. Never share stories of math failure or even dislike.
  3. Always praise mistakes and say that you are really pleased that your child is making them.
  4. Encourage children to work on problems that are challenging. We know that it is really important for students to take risks, engage in “productive struggle,” and make mistakes.
  5. When you help students, do not lead them through work step-by-step. Doing this takes away important learning opportunities for them.
  6. Encourage drawing whenever you can…. Both drawing and restating problems help children understand what questions are asking and how the mathematics fits within them.
  7. Encourage students to make sense of mathematics at all times…. If children seem to be guessing, say, “Is that a guess? Because this is something we can make sense of and do not need to guess about.” Mathematics is a conceptual subject, and students should be thinking conceptually at all times.
  8. Encourage students to think flexibly about numbers.
  9. Never time children or encourage faster work. Don’t use flash cards or timed tests.
  10. When children answer questions and get them wrong, try and find the logic in their answers—as they have usually used some logical thinking.
  11. Give children mathematics puzzles.
  12. Play games, which are similarly helpful for children’s mathematical development.

Minion Jedi

Next: What I do, as a homeschooler

Breaking Math: What’s Real, What’s Not, What’s Math Got To Do With It?


One of the anxieties that often come up in schooling in general and homeschooling in particular is math. At every school I’ve been to there has always been endlessly handwringing over what kind of math instruction is most effective, and once I’ve started homeschooling, I’ve noticed that there is constant, persistent discussion about the pros and cons of various math curricula.

I touched upon the Common Core last week, and some of the most frequent and strident complaints about these standards are the proposed changes they make to math education. Families can’t seem to make heads or tails about the “new new math” and there’s a lot of grousing—some of it understandable, some of it histrionic—about how it seems both overly complicated and infantile. Turns out that if you hate math as a parent, you’re probably better off not helping your kid with his or her homework. Little wonder you have frustrated parents posting their kids’ “ridiculous” homework on Facebook as a way to tell Common Core to suck it.

I love math. I’ve had some very, very good teachers in middle school and high school, starting with Ms. Counihan in 6th grade, who coached my first math team. I was always a little too stolid to ever be a starter on the teams, or a professional mathematician, but I’ve always been fascinated and appreciative of mathematical concepts and puzzles. I’m, therefore, fairly at ease about handling math instruction for my kids.

Nevertheless, I’ve been reading What’s Math Got to Do With It?: How Teachers and Parents Can Transform Mathematics Learning and Inspire Success (2015 revised and updated) by Jo Boaler, and I couldn’t help bookmarking pages and taking notes.

As for Common Core, she says this:

The Common Core math curriculum is not the curriculum I would have designed if I had had the chance. It still has far too much content that is not relevant for the modern world and that turns students off mathematics, particularly in the high school years, but it is a step in the right direction—for a number of reasons. The most important improvement is the inclusion of a set of standards called the “mathematical practices.” The practice standards do not set out knowledge to be learned, as the other standards do, but ways of being mathematical. They describe aspects of mathematics such as problem solving, sense making, persevering, and reasoning. (xxvi)

NOTE: Much of what follows are just excerpts from the book, as I find it well-written, and I’m too lazy to synthesize it all into my own thoughts.

She starts with some of the common misconceptions of mathematics as a discipline and its true nature as practiced by mathematicians.

…mathematics as a learning subject, not a performance subject. Most students when asked what they think their role is in math classrooms say it is to answer questions correctly. They don’t think they are in math classrooms to appreciate the beauty of mathematics, to explore the rich set of connections that make up the subject, or even to learn about the applicability of the subject. They think they are in math classrooms to perform. (xviii)

Ask most school students what math is and they will tell you it is a list of rules and procedures that need to be remembered. Their descriptions are frequently focused on calculations. Yet as Keith Devlin, mathematician and writer of several books about math, points out, mathematicians are often not even very good at calculations as they do not feature centrally in their work. As I had mentioned before, ask mathematicians what math is and they are more likely to describe it as the study of patterns. (19)

Imre Lakatos, mathematician and philosopher, describes mathematical work as “a process of ‘conscious guessing’ about relationships among quantities and shapes. Those who have sat in traditional math classrooms are probably surprised to read that mathematicians highlight the role of guessing, as I doubt whether they have ever experienced any encouragement to guess in their math classes. When an official report in the UK was commissioned to examine the mathematics needed in the workplace, the investigator found that estimation was the most useful mathematical activity. Yet when children who have experienced traditional math classes are asked to estimate, they are often completely flummoxed and try to work out exact answers, then round them off to look like an estimate. This is because they have not developed a good feel for numbers, which would allow them to estimate instead of calculate, and also because they have learned, wrongly, that mathematics is all about precision, not about making estimates or guesses. Yet both are at the heart of mathematical problem solving. (25)

After making a guess, mathematicians engage in a zigzagging process of conjecturing, refining with counterexamples, and then proving. Such work is exploratory and creative, and many writers draw parallels between mathematical work and art or music. (25)

Another interesting feature of the work of mathematicians is its collaboratory nature. Many people think of mathematicians as people who work in isolation, but this is far from the truth…. The mathematicians interviewed gave many reasons for collaboration, including the advantage of learning from one another’s work, increasing the quality of ideas, and sharing the “euphoria” of problem solving. (26)

People commonly think of mathematicians as solving problems, but as Peter Hilton, an algebraic topologist, has said: “Computation involves going from a question to an answer. Mathematics involves going from an answer to a question.”… All the mathematical methods and relationships that are now known and taught to schoolchildren started as questions, yet students do not see the questions. Instead, they are taught content that often appears as a long list of answers to questions that nobody has ever asked. (27)

Another important part of the work of mathematicians that enables successful problem solving is the use of a range of representations such as symbols, words, pictures, tables, and diagrams, all used with precision. The precision required in mathematics has become something of a hallmark for the subject and it is an aspect of mathematics that both attracts and repels. For some schoolchildren it is comforting to be working in an area where there are clear rules for ways of writing and communicating. But for others it is just too hard to separate the precision of mathematical language with the uninspiring drill-and-kill methods that they experience in their math classrooms. There is no reason that precision and drilled teaching methods need to go together, and the need for precision with terms and notation does not mean that mathematical work precludes open and creative exploration. On the contrary, it is the fact that mathematicians can rely on the precise use of language, symbols, and diagrams that allows them to freely explore the ideas that such communicative tools produce…. As Keith Devlin reflects: “Mathematical notation no more is mathematics than musical notation is music.” (29)

So why is it so many don’t understand math as this “music of the spheres”? Passive learning.

The type of traditional teaching that concerns me greatly and that I have identified from decades of research as highly ineffective is a version that encourages passive learning. In many mathematics classrooms across America the same ritual unfolds: teachers stand at the front of class demonstrating methods for twenty to thirty minutes of class time each day while students copy the methods down in their books, then students work through sets of near-identical questions, practicing the methods. Students in such classrooms quickly learn that thought is not required in math class and that the way to be successful is to watch the teachers carefully and copy what they do. … Students who are taught using passive approaches do not engage in sense making, reasoning, or thought (acts that are critical to an effective use of mathematics), and they do not view themselves as active problem solvers. This passive approach, which characterizes math teaching in America, is widespread and ineffective. (40)

One of the major downsides of this kind of instruction is the kind of inequity it tends to engender very early on:

When the researchers looked at ten-year-olds, they found that the below-average group used the same number of known facts as the above-average eight-year-olds, so you could think of them as having learned more facts over the years but, noticeably, they were still not using number sense. Instead, they were counting. What we learn from this, and from other research, is that the high-achieving students don’t just know more, but they work in very different ways—and, critically, they engage in flexible thinking when they work with numbers, decomposing and recomposing numbers.
The researchers drew to important conclusions from their findings. One was that low achievers are often thought of as slow learners, when in fact they are not learning the same things slowly. Rather, they are learning a different mathematics. The second is that the mathematics that low achievers are learning is a more difficult subject. (141, emphasis mine)

Not surprisingly, the researchers found that the lower-achieving students who were not using numbers flexibly were also missing out on other important mathematical activities. For example, one of the important things that people do as they learn mathematics is compress ideas. What this means is, when we are learning a new area of math, such as multiplication, we may initially struggle with the methods and the ideas and have to practice and use it in different ways, but at some point things become clearer, at which time we compress what we know, and move on to harder ideas. At a later stage when we need to use multiplication, we can use it fairly automatically, without thinking about the process in depth. (142)

Nevertheless, people are still very married to the kind of traditional math instruction they are familiar with. Chapter 2 of the book delineates the “math wars” have taken place for and against reforms. If you’re someone who feel conflicted about this controversy, I’d recommend you read this chapter to get a sense of the politics behind the rhetoric.

Anyhoo, what’s the alternative? She gives two examples. One, a “communicative approach” pioneered by Railside High School in California:

The focus of the Railside approach was “multiple representations,” which is why I have described it as communicative—the students learned about the different ways that mathematics could be communicated through words, diagrams, tables, symbols, objects, and graphs. As they worked, the students would frequently be asked to explain work to each other, moving between different representations and communicative forms. When we interviewed students… they told us that math was a form of communication, or a language. (59)

… the teachers enacted an expanded conception of mathematics and “smartness.” The teachers at Railside knew that being good at mathematics involves many different ways of working, as mathematicians’ accounts tell us. It involves asking questions, drawing pictures and graphs, rephrasing problems, justifying methods, and representing ideas, in addition to calculating with procedures. Instead of just rewarding the correct use of procedures, the teachers encouraged and rewarded all of these different ways of being mathematical. (67)

The other, a project-based approach at Phoenix Park School in England:

Instead of teaching procedures that students would practice, the teachers [at Phoenix Park] gave the students projects to work on that needed mathematical methods…. At the start of different projects, the teachers would introduce students to a problem or theme that the students explored, using their own ideas and the mathematical methods that they were learning. The problems were usually very open so that students could take the work in directions that interested them…. Sometimes, before the students started a new project, teachers taught them mathematical content that could be useful to them. More typically though, the teachers would introduce methods to individuals or small groups when they encountered a need for them within the particular project on which they were working. (69-70)

Again, if this interests you at all—or if you have doubts about the efficacy of such an approach—I would recommend you pick up the book and at least read the third chapter, especially the part where the results of the Phoenix Park program is compared to a more traditional approach at the Amber Hill school. There’s a lot to chew on.

Next: Some guidelines for parents