words, numbers, and the culture of offering

This is sort of another plug for Ed Zaccaro, but also an observation about language and dignity in the context of math.

I posted a while back about Ed Zaccaro’s Challenge Math series, which I think was written for kids who needed more than the classroom could provide, but also seems to work well with kids with all sorts of different relationships with math.

This week I was surprised when one of the eight year-olds I work with asked specifically if we could work in the Zaccaro book.  I’d done a quick bit of one page with her once before, and she was OK with it, but tends to balk at anything she has to stop and think about, anything that requires reading as the Zaccaro problems do.  This is not because she doesn’t like to read or isn’t a good reader. She is.  But as a math student, she tends to balk at reading. We’d mostly been working on quick little problems I’d chosen for the purpose of letting her see that she is more capable when it comes to math than she has learned to believe.

She leaned right in as soon as I opened the book in front of her.  She remarked on the illustration of the large sweating ants and then started reading the first problem on the page.  She sped through three in a row, understanding exactly what the problems were asking for and doing much of the computation in her head.  This is exactly what she doesn’t do when she’s interacting with her Pearson pages from school (which, as far as I can tell, were written and issued very quickly after the Common Core standards went into effect).  She’s constantly choosing operations that don’t fit the situations in the word problems.

I’ve been frustrated with the language of many of these problems ever since the materials were issued, but in watching this child with the Zaccaro problems, I realized something new about how they are tripping kids up.  The Pearson word problem language is often ambiguous, which is terribly troublesome in the context of math, but it’s also just plain dull.  For kids who are readers, accustomed to sentences written with care and intention, poorly written problems are not just potentially confusing.  They’re an insult to the sensibilities of the literate child.  The literate person.

I realized that what this student has been doing with her classroom math work is to scan each word problem and attempt to match it with a procedure.  If it looks like the kind of problem for which one should divide, she’ll divide.  If it looks like you have to trace your finger across the table shown and fill in a number according to a pattern, she’ll do that.  No matter that often the problem is asking for something slightly different.  In order to notice that, she’d have to subject herself to the agony of reading the dull text slowly. As a result, her actual ability and number sense is obscured. In a situation in which the reading is in and of itself engaging, she is freed up to think fluidly and flexibly about what there is to do with the numbers.

What the Zaccaro book does for her (that the Pearson book does not) is offer something.  That sounds too simple to matter, but I don’t think it is. An offering concerns itself with presentation and connection, free of attachment to result. It is the fundamental unit of authentic human exchange. It says “Here.  This is for you to have and use if you choose.” It grants dignity, agency, autonomy. In the course of our deep but desperate commitment to educate, we’ve moved away from offering toward mandate and decree, often undermining our ability to pass on what there is of useful knowledge and skill to our young.
The good news is we can resume a culture of offering any time we want.