Reporting to parents, continued

A while back, I wrote about information that Dreambox and XtraMath send to parents about their child’s progress. Now I’d like to share some more actual feedback, but with a different contrast, brought to my attention by an alert reader.

I will keep the source anonymous by request.

Consider these two year-end summaries, both for the same child. One is by the child’s regular classroom teacher, and the other is by the child’s math teacher. This is a school where children are shuffled for math instruction.

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Literacy

[Child] has worked hard in third grade to increase her literacy skills in becoming a life-long reader and writer. She’s a mindful reader when choosing books of personal interest and challenge level. She reads with superb confidence and stamina. As a reader and writer of nonfiction, [Child] researched an animal of interest and published a book that demonstrated expertise of the topic. She crafted nonfiction text features that reflected her individual voice. She read and analyzed poetry—then applied the tools of a poet to craft individual poems. Wow! You’re an amazing reader and writer! Way to go, [Child]!

Math

[Child] has made progress in math this year. She should work on learning her basic subtraction and multiplication facts over the summer. I have enjoyed having her as a student! Have a wonderful summer, [Child]!

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I understand that these are different teachers, and I understand that [Child] probably spent quite a few more hours with the literacy/home teacher than the math teacher. But I don’t think those are the major things at play here.

The difference in the richness of the description of [Child]’s current literacy and growth from the description of [Child]’s mathematical knowledge and growth reflects the ways we view these two subjects in American schooling.

Throughout my own children’s elementary schooling, I have seen deep and rich attention paid to their learning to read and write, and surface, fact-based attention paid to their learning math.

Literacy is about power and beauty and self-actualization. Math is about memorization and speed. These are the ways we represent these subjects to parents, teachers, and children.

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Summertime (or anytime) reading recommendations

A friend asked for tips on getting started understanding some new domains in mathematics teaching the other day. An experienced high school teacher, he wants to know more about  elementary and middle school topics, especially fractions, place value and multiplication and division algorithms.

For obvious reasons (mainly that I won’t shut up about these topics), I was on his short list to ask for recommendations.

It occurred to me that others might be interested in this particular brain dump. So here it is, lightly edited. Enjoy.

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Fractions. Entry level stuff on this is Connected Mathematics. In particular, Bits and Pieces 1, Bits and Pieces 2, and Comparing and Scaling. Any version of these units is fine. Work the problems from the student edition; have the teacher edition there for guidance.

I made major progress on understanding student thinking when I constrained myself to using only ideas that must have come earlier (i.e. in elementary school) and to those that had been previously developed. When I tried to appreciate the problems on their mathematical merit, or to build connections to my undergraduate mathematics knowledge, I didn’t make much progress that was useful to working with kids.

Then turn to Extending Children’s Mathematics (written by the Cognitively Guided Instruction team—CGI—and published by Heinemann). There is a lovely research perspective that should give you new ways to think about the CMP stuff.

More advanced perspectives are to be found in the work of the Rational Number Project (RNP), and there’s Susan Lamon’s book, Teaching Fractions and Ratios for Understanding. For contrast, read Hung Hsi Wu’s Math for Teachers curriculum. For extra credit, write a comparative analysis paper reconciling Wu’s work with CGI and with RNP; argue which has the greater influence on the Common Core fractions development.

Conspicuously absent from these recommendations is the “Essential Understandings” series from NCTM, published relatively recently. I find the writing style of these texts hard to process. Others may recommend them, and if so, perhaps you ought to take them more seriously than I have been able to.

Place value. There is an oldish JRME piece by Karen Fuson, the CGI folks and another research team about place value. It’s a seminal piece and totally worth your time. There is no one book I can recommend; my exploration of the conceptual landscape of place value has been idiosyncratic and informed more by small pieces of others’ research work combined with my own classroom experience and experiments. Most of that is documented on this blog.

The “Orpda” number system that Cady and Hopkins wrote about (and which I bastardized as “Ordpa”) was foundational to these explorations. Short, short article but the ideas opened a whole new space for me in thinking about what it means to learn place value.

The Young Mathematicians at Work book on number sense, addition and subtraction is pretty good. But those articles and the blog are better starting points.

Multiplication and division algorithms. I am trying to recall how I came to know the algorithms I know. I have to say that these steps I cannot really retrace.  I am loathe to recommend digging through Everyday Math for them, because things are so diffuse; it’s hard to get the right book in your hand in that curriculum to learn any one particular thing.

The Kamii piece I recommended a while back is good. It was published in the 1998 NCTM Yearbook on algorithms. Sybilla Beckmann’s Mathematics for Elementary Teachers book is good, too.

But looking back at my standard algorithm diatribe last week and trying to think about what small set of resources would prep someone else to build a similar case (or to counter it), I am less clear than I am about fractions or place value. I do not know what this says about my knowledge, nor about the topic.

10-minute reading time

A few weeks back, bedtime was spiraling out of control. The kids share a room; they would be wound up at bedtime and the transition to sleep was not happening smoothly. We had a big, big problem on our hands.

We solved the problem with 10-minute reading time. The kids have to be in their beds. We dim the lights. We set a timer for 10 minutes. It has to be quiet during that time. Then we turn out the lights, do the picture (remember the elephants?) and sleep comes more easily.

Complete transformation. It is awesome.

Tabitha, the other night, wanted to color. We talked and agreed that she could do it sometimes. As is the nature of 5-year olds, she soon wanted to know the limits.

The following conversation took place on Wednesday night this week.

Tabitha (five years old): I know I can’t color every night but can I tonight?

Me: Yes.

T: Then read, then color the next night?

Me: I don’t know. I think reading twice before the next color is better.

To be clear. It was not my intention to get into a math conversation at this point. I just wanted her to go to bed.

No, this move on my part was truly about literacy, not math. I don’t want 10-minute reading time to turn into 10-minute coloring time. I really, really like the idea that books will become part of my kids’ independent bedtime routines.

But Tabitha loves to know the rules she’s playing by. And when those rules are based on numbers, they’re going to lead to math every time.

T: So read-read-color-read-read-color…like that?

Me: Right. That sounds like a good ratio.

T: Or read-read-read-read-color-color?

Whoa.

Couple things.

First of all, I used the term ratio with absolutely no expectation that she would process it, and I am quite sure that she did not. I have long been an advocate of using good vocabulary with my children—there is no shame in not knowing the meaning of a word, but also no sheltering them from the fact that these words exist. This is at least partly the source of their substantial vocabularies. But I do not believe she knows the word ratio.

Secondly, Tabitha’s reformulation of the 2:1 ratio as 4:2 blew me away. It nearly slipped past me without notice. I was focused on getting them to bed; we were in the truly final phase of that process. I had pretty much tuned her out.

But when I looked at her, I could see she was expecting a reply. She needed to know whether she could get two coloring nights in a row by doing four reading nights in a row.

So I replayed her question in my mind, counting the reads.

Me: Yes. That would be fine. You may do that.

 

Just sayin’ (literacy and numeracy)

It now seems to be widely accepted in literacy circles that kids should be encouraged to read. And that it does not matter very much what they read, they should be encouraged to read. Fiction, non-fiction, classics, graphic novels. It doesn’t matter as long as they’re encountering new vocabulary, important narrative structures, etc. They just need to read. In school or out of school, they just need to read.

We’re not there yet in mathematics.

In math, we think they need to work on these number facts at this grade level, and those number facts at that grade level. Identify this shape at this grade and sort those shapes at that grade.

We have free reading time in class every day in elementary school. But free math time?

I’m just sayin’.