Anchors, close reading, and a case for problem-based mathematics

Think of the following:

1. What is/was your grandfather like? (If you are or were lucky enough to have known two, pick one.)
2. Who was your best friend in college?
3. Where did you go on your last trip? What was it like?

Sometimes you have an epiphany that seems to connect to so many different parts of your life that you can't wait to share it with the world...and then you realize that - precisely because the epiphany was so tailored to your own experiences, almost designed to fit snugly into your brain - maybe the world won't appreciate how you felt discovering it.

That's not what worries me about this post. What worries me is that the idea behind this is probably something you have all thought of already, and I'm simply late to the party.

Here's the gist: In your life, there are a very few anchor experiences that define key eras of your life. Maybe these moments number in the tens, maybe in the hundreds - but compared to the gargantuan number of memories that we can call to mind when remembering, say, middle school (or the first year of marriage, or your first job, or that house on Garland Avenue, or ages 3-9, or that summer in Argentina, or your maternal grandfather, ...) the number of memories that have come to define the experience is pretty manageable.

These anchors are largely a function of how the mind works. In Funes el memorioso, author Jorge Luis Borges illustrates brilliantly that memory is more about forgetting than about excessive remembering - through a main character who is incapable of forgetting details and is thus entirely unable to generalize (for example, the word "dog" has little meaning to Funes, as there is no unique set of characteristics that all "dogs" share.) As Borges points out, if we actually remembered everything equally, it would be difficult to make sense of anything.

I would guess these anchors are somewhat universal and, over time, become somewhat arbitrary. They're not always the most important memories, and they're not always the most representative of the experience they have, in some cases, come to supplant. When Iyouthought of your responses to the initial questions above, I imagine the same image of your grandfather came to mind that usually comes to mind. To me, the house on Garland always begins with a specific snapshot: Bamboo curtains against a mango-colored accent wall, with the punishing Fresno heat coming through the large sliding glass door. My grandfather always introduces himself to my working memory by blowing a low note on a trombone just above a small child's flapping hair, or leaning back and smiling on a couch in a beach house. Niagara Falls is a view of the falls on my right with my kids playing in the bath to my right. From there, sure, we can imagine a handful of other memories, and push ourselves to remember many more, but the important highlight here is that this one memory often serves as the entry point to all the others.

If possible, think of something new you've learned recently, as we're all famously bad at remembering what it was like to learn something that we now know without thinking. I'll focus on something I started learning long ago (over half my life ago, at this point), so there's a good chance I'll get at least some of this wrong:

Most of my anchors for Spanish vocabulary and grammar came from popular (or once-popular) songs...our teacher enlisted Juan Luis Guerra to teach us about the subjunctive, Joan Baez and Mercedes Sosa for the present perfect tense. In college, I had a professor who emphasized analyzing and memorizing poetry, and for a time I would remember lines of these poems when trying to recall whether a certain object was a masculine or femenine noun. I still remember the line "y caliente...como agua de la fuente" when hesitating for an instant to recall whether to say "el fuente" or "la fuente." What I didn't realize until today was that all of these times when we spent two days on the lyrics to one song, analyzing what the songs meant, we were doing a form of close reading. We were determining the main ideas presented in the song, but we were also internalizing a boatload of vocabulary and grammar in context.

Two weeks ago, my epiphany came during a one-hour discussion about close reading with our instructional leadership team - Rebecca, our principal; Nick, our ELA dean; Chris, our math dean; Dacia, our regional superintendent; and me, our historian (as in history coach, but also as in high school club member who was voted neither president nor treasurer and thus goes home to blog about it on everyone else's behalf.) We talked through a close reading lesson designed around JFK's famous civil rights address, giving our own critiques of the lesson and then reading the critiques by Common Core co-author David Liben and extracting from these some huge lessons regarding Close Reading. These takeaways were fairly life changing:

1. Yes, close reading is about the text. Specifically, a deep understanding of the central idea(s) of a text should guide what kids do. I'm proud to say I knew this one; I'm more proud to say that my understanding of close reading before today stopped pretty much here. So I learned something from this experience :)
2. Close reading is also the activity where we get the most traction with metacognition. Generally, I'm not a huge fan of metacognition as a reading strategy, and I think it leads to a lot of wasted time...but in this context, it makes a lot of sense. To me, it sounds a bit like this: "So notice where you stopped there. Why did you do that?...Which of these sentences seems to jump out? Why did it catch your mind's attention? Make a mental note; that's what you can do as a writer to catch your audience's attention...and as a reader, think of where the author is trying to grab your attention and what they're trying to tell you at that moment."
3. Close reading is one of the best ways to teach and reinforce specific vocabulary.

Points 2 and 3 were new to me, and point 3 had me reflecting on everything I had ever learned, leading to the stream of consciousness you may have wisely abandoned by now. Because when you read a small sample of text over and over again, and focus intensely on its meaning, you are exposed to the same words in the same context to the point where you essentially memorize certain lines of text and their literal meanings. From JFK's speech you may remember "a moral issue" and "a partisan issue" and the amount of time each of these stayed in your working memory while grappling with larger issues...from there, you'll likely associate (at least for some time) the words "moral" and "partisan" with these specific lines.

When I was first learning Spanish (now over half my life ago), I learned through a lot of close reading in the form of listening to the same songs over and over. Juan Luis Guerra taught me the subjunctive and "la fuente" (as opposed to the incorrect "el fuente".) Joan Baez and Mercedes Sosa taught me how to express gratitude while reinforcing what little I knew about the present perfect tense. I was reminded in our Close Reading conversation that repeated exposure to many of these song lyrics led to a level of memorization that allowed me to call specific experiences to mind in order to remember - even at the word level.

In math, this brought me to the idea of a problem-based approach to learning. Sha Reagans, incredible math teacher and current principal of Newark Collegiate Academy (High School), used to teach an 'anchor problem' for every concept, so that students could refer to this problem when thinking through the concept later. From my own schooling, I still remember the "interior angle of a five-pointed star" problem when it seems a situation could become more clear by circumscribing (drawing a circle around) a figure. I remember "Twelve Days of Christmas" and "Snail Climbing a Wall" when thinking about the limitations of discrete functions. This may be another case of me looking for confirming evidence, but this line of thinking leads me to believe ever more firmly in a problem-based approach to math teaching and learning.

Throughout our lives, though we are subconsciously choosing anchors to represent various experiences, these anchors don't always telegraph themselves. That bamboo curtain didn't jump out and say, "Take note: I'm more important than the dusty backyard," but I always think of it first regardless. In school, however, the anchors I remember first when thinking of Spanish or math or chemistry are usually the carefully chosen and designed experiences chosen by my teachers. Furthermore, we didn't simply experience these once and move onto the next thing - we spent time with each to ensure that the memory would stick.

For teachers, I see one clear implication of this idea:

Know what you want the anchors to be, and design students' learning experiences around these anchors. Prioritize the most important content and ideas, and ensure that students have repeated exposure to this content and these ideas. Get the most out of small experiences, rather than simply trying for more experiences.

I'm curious what parts of this do not resonate with folks. Does anybody experience anchors in their own lives differently? How do we reconcile the idea of learning primarily through a small number of well-chosen experiences with the (conflicting?) idea of exposure to a broad base of content, breadth of vocabulary exposure? I'd appreciate any thoughts you have in the comments.