Monday, October 30, 2017

Books 2017: Quarter 3

Friends, it is fall. And fall is definitely the best time for talking about books.

As you probably already know, I've been reading a classic a month for the last two years. It started as a one-year project in 2014, but I've enjoyed it enough to keep going with it & will probably continue until it starts to feel like a chore. You can find my past reviews by clicking on the "books" tag at the end of this post, or be my friend on Goodreads. (You can also just go to the site & hunt down my review feed without being my friend, if that's more your speed.)

ICYMI, the classics I selected to read in 2017 are here.

On to the reviews!

Wednesday, October 4, 2017

SMPs for Parents and Other Civilians: MP 1 (Part 2)



This is the second follow-up post to a previous one aimed at parents and other non-math teachers, The Real Power of Studying Mathematics, about the significance of the Standards for Mathematical practice.

For the first follow-up post, see MP 1, Part 1: Making Sense of Problems.
* * *

In our last post, we talked about the first chunk of MP 1--what it means to make sense of a mathematics problem. Today, we'll continue with the second chunk of Practice 1: Persevering in solving problems. What does it mean to persevere in the context of a mathematics problem? What does perseverance look like? What does it not look like? And what can parents do to support students?

At the most literal level, perseverance just means to keep going and not give up. Sounds simple, right? Alas, for many students, especially as they begin to experience rich, challenging mathematics for the first time, it's not always so simple.

Wednesday, September 27, 2017

SMPs for Parents and Other Civilians: MP 1 (Part 1)

This is the first follow-up post to a previous one aimed at parents and other non-math teachers, The Real Power of Studying Mathematics, about the significance of the Standards for Mathematical practice.

I was talking to someone once about this practice (MP 1, "Make sense of problems and persevere in solving them") and she asked me, "Isn't that just, like, doing math?"

Well, yes and no.

Yes, in that if you can't make sense of a problem, you're probably not going to get very far toward solving it. And if you can't persevere, you probably won't get to a solution even if you can make sense of the problem. In some ways, MP 1 is a kind of "Gateway Practice"; if you struggle to make sense and persevere, it's difficult to get much of any math done at all.

No, in that MP 1 is more of a starting point, a 'necessary' condition for doing powerful mathematics, but it is far from sufficient. You made sense of a problem enough to get started? Great! You're hanging in there and persevering? Also great! But there is a lot more to be said regarding how students are able to make sense of problems, and a lot to be said about how effective and efficient our perseverance is, and more yet to be said about what we do once we have solved a problem. All of that is what we get from the other seven practices.

Let us break MP 1 down into its two constituent parts:

    1) Make sense of problems.

    2) Persevere in solving problems.

Today we'll focus on what it means to make sense of problems; in the next post we'll come back to what it means to persevere in solving them.

So...what does it mean to make sense of a problem?

Ask any math teacher; if s/he had a nickel for every time a kid read a problem and threw up their hand to proclaim "I don't get it!," s/he'd have a whole lot of nickels.

To make sense of a problem means to read or look at a problem, comprehend the information that's being communicated, and be able to ask yourself, "What mathematics is involved in solving this problem? How will I know when I have an answer, and what will the answer mean?"

Wednesday, September 20, 2017

The Real Power of Studying Mathematics

Hint: It's not knowing 17 different ways to solve a quadratic equation.

As the wee progeny of many of my friends and family began to wind their way through elementary (and middle???) school, I've had a number of conversations lately with adults who work outside of education about what it means to have a "good" math education and/or a "good" math teacher and in particular what should they look for in a school or classroom to know that their child is going to get a decent mathematical education.

It's a very tricky, very loaded question that I always struggle to answer in any helpful way. I mean, I can certainly list any number of elements I would hope to see in any math classroom my child were going to spend time in. For example:

  • A focused, coherent, and rigorous curriculum that aligns at least pretty well with the Common Core
  • A balance of procedural, conceptual, and problem solving/application elements
  • A focus on making sense of mathematics rather than on "answer-getting"
  • Rich, open-ended opportunities for tinkering, discovery, and general "mathematical play"
  • Procedural fluency that is built on conceptual understanding and robust number sense rather than rote memorization
  • De-emphasizing speed, but without altogether abandoning the idea of "mathematical efficiency"
  • Explicit discussion of the myriad ways of accessing and making sense of mathematics (multiple representations, multiple solutions, etc.)
  • Explicit discussion of the brain science that underlies fixed vs. growth mindsets
  • Celebration of mistakes as a necessary part of the learning process that enriches and enhances our understanding
  • Opportunities for collaboration with diverse peers (and I mean diverse in every sense of the word)

...Etc.

...Etc.

...Etc.

Wednesday, July 12, 2017

Books 2017: Quarter 2

Guys. Where is the year going. July?? Crazy pants.

As you probably already know, I've been reading a classic a month for the last two years. It started as a one-year project in 2014, but I've enjoyed it enough to keep going with it & will probably continue until it starts to feel like a chore. You can find my past reviews by clicking on the "books" tag at the end of this post, or be my friend on Goodreads. (You can also just go to the site & hunt down my review feed without being my friend, if that's more your speed.)

ICYMI, the classics I selected to read in 2017 are here.

On to the reviews!

Friday, May 5, 2017

Dividing small by big (fraction division & pattern blocks, part 2)

Last time, I related the tale of how, with a single fifth grade arithmetic problem, Cathy Humphreys shook my confidence in my math abilities to the core and then rebuilt it again from the rubble, better, faster, stronger, because that's how she rolls.

(Do you know why 1 ÷ 2/3 = 3/2? Are you sure?

Are you?

ARE

YOU

?)

1 ÷ 2/3 is tricky because, unlike, for example, 3/2 ÷ 1/4, the divisor does not fit evenly into the dividend. But once you understand the nature of the problem--what fraction of the unit in question comprises the leftover bit?--you can probably more or less make your way through most problems where the divisor is at least smaller than the dividend.

So hold onto your pantaloons, mateys; we're about to go off the map a bit. Here there be dragons, ie, problems where we are asked to divide a SMALL fraction by a BIGGER fraction.


CRAZY TALK.

Tuesday, May 2, 2017

That time Cathy Humphreys taught me to divide fractions

Despite my background as a high school teacher, I've gotten deeply interested in grade 3-5 math in the past few years, particularly all the bits related to number, operations, & algebraic thinking and how they weave together to create the ramp that ultimately gives kids access to formal algebra.

But it was not always this way! As a college math major filling out applications to masters & secondary credential programs, I definitely saw myself as a high school teacher, much more interested in the complexity and rich structure of Algebra II and trigonometry and calculus than in the usual middle school topics. And I *certainly* had never gone back to closely examine my own conceptual understanding of the foundational mathematics we learn in elementary school. Who wants to teach fractions and decimals when you could be initiating kids into the wonders of trigonometric functions??

BO.

RING.

So, I got into a secondary program, started student teaching Algebra I, & learning all the magical things they teach you in Curriculum & Instruction (ie, "methods") class about how kids make sense of ideas like variables and functions and data analysis over time and what it really means to understand all these things anyway. It was mystifying and terrifying and amazing, and in addition to learning how to teach, those experiences also unlocked for me an entirely new dimension of understanding. It was exhilarating ("Who knew math could be even MORE AMAZING??) but also a bit panic-inducing ("How the HECK am I supposed to get kids to understand it THIS way?!?"). All in all, though, I was starting to feel pretty darn good about my content knowledge.

And then, one day, Cathy Humphreys came to class.

She came to teach us about fractions.

Wednesday, April 12, 2017

My NCSM & NCTM 2017 Highlights

Hi friends,

I spent this past week in San Antonio attending the annual conferences of the National Council of Supervisors of Mathematics and the National Council of Teachers of Mathematics as I do most years, and as always, I had a fantastic time and learned a ton.

Just a quick overview of some of the highlights:

Learning, Planning, and Teaching Together: Facilitating Job-Embedded Professional Development, Kendra Lomax and Becca Lewis (University of Washington). I feel incredibly strongly about practice-based PD, and since I also happened to know that Kendra got rave reviews from a group of K-2 teachers she'd recently been doing some practice-based/job-embedded PD with, I was excited to hear what she and her colleague had to say on the topic. We heard about how they've been exploring the idea of rehearsal as a way of teachers preparing to teach a lesson, where the rehearsing involves very focused and thoughtful real-time coaching from a teacher educator. They shared some interesting videos, and I look forward to exploring more of their work on on the TEDD (Teacher Education by Design) website.

Tuesday, April 4, 2017

Books: 2017 Quarter 1

As you probably already know, I've been reading a classic a month for the last two years. It started as a one-year project in 2014, but I've enjoyed it enough to keep going with it & will probably continue until it starts to feel like a chore. You can find my past reviews by clicking on the "books" tag at the end of this post, or be my friend on Goodreads. (You can also just go to the site & hunt down my review feed without being my friend, if that's more your speed.)

ICYMI, the classics I selected to read in 2017 are here.

On to the reviews!

Tuesday, January 10, 2017

Books: The 2017 Classics

BEHOLD! The classic novels I'll be reading in 2017:

JANUARY: The Forever War, by Joe Haldeman. "The Earth's leaders have drawn a line in the interstellar sand, despite the fact that the fierce alien enemy that they would oppose is inscrutable, unconquerable, and very far away. Private William Mandella has been propelled through space and time to fight in the distant thousand-year conflict; to perform his duties without rancor and even rise up through military ranks. He's willing to do whatever it takes to survive the ordeal and return home. But 'home' may be even more terrifying than battle, because, thanks to the time dilation caused by space travel, Mandella is aging months while the Earth he left behind is aging centuries." I like to do one true sci fi classic each year & this one got a lot of votes.

FEBRUARY: Midnight in the Garden of Good and Evil, by John Berendt. "Voodoo. Decadent socialites packing Lugars. Cotillions. With towns like Savannah, Georgia, who needs Fellini? Midnight in the Garden of Good and Evil takes two narrative strands--each worthy of its own book--and weaves them together to make a single fascinating tale. The first is author John Berendt's loving depiction of the characters and rascals that prowled Savannah in the eight years it was his home-away-from-home. Then, on May 2, 1981, the book's second story line commences, when Jim Williams, a wealthy antique dealer and Savannah's host with the most, kills his "friend" Danny Hansford. (If those quotes make you suspect something, you should.) Was it self-defense, as Williams claimed--or murder? The book sketches four separate trials, during which the dark side of this genteel party town is well and truly plumbed."