What do you notice?
What do you wonder?
*What do YOU think? (I will add my thoughts later…)
*What do YOU think? (I will add my thoughts later…)
Our experiences create our beliefs, from which spring our values, upon which we hang our decisions and actions and words.
I wasn’t going to read it but I did. I wasn’t going to write a response, but I am. I wasn’t going to make it another opinion piece, but it is, with additional resources below.
My life experiences as student of both music and math and as an educator have shaped my opinions about learning and inform my pedagogical philosophies. I know first hand one can appear to be “successful” at math or piano by simply being compliant and willing to please, which can easily be mistaken for dedication. When told exactly what to do, I could. A’s in math, scholarships in music. I also know first hand the thrill of realizing there was so much more, that instead of passively following directions, I could actively listen and notice and explore and question and make sense of and mess up and try something else and reflect and maybe most important of all, feel competent and joyful.
Whenever anyone over-simplifies anything as intensely complex as teaching, learning, math, or music in order to justify a particular personal stance, its a whopping red flag for me. I cringe at math-music (or math-sports, etc.) metaphors that appear to convince but under scrutiny, fall apart. I am skeptical whenever words like “drill”, “understand”, “practice”, “learn” and (good grief) “ingrained” are used liberally without any clear, consistent definitions by the writer, especially when said writer makes claims about what’s wrong with teachers (or kids) these days and here’s exactly how to fix it. I am perplexed by beliefs that Only This is Right and Poo-poo to That (Its Not How I Had to Do It). I know how easily the general public latches onto back-to-basics type opinions and then banters them about as utter truths, forgetting about bias, prejudice, and self-interest and heaping more myths and misconceptions onto the pile about teachers and teaching, learners and learning. I cringe whenever motivations for transforming education are driven by competitiveness and better test scores. And I feel quite, quite sad that someone who confesses to hating math as a child believes its OK for learning to lack pleasure— to the point of being painful— and that we should make our daughters (OK, sons, too) experience the pain we did, and expect them to be grateful for it.
While some people have a NY Times op-ed piece or masses of twitter followers, I just have my nearly invisible little blog. This does not mean my reflections (which give me clarity) and opinions are any less important. I’m just less influential.
I leave you with links to Mark Chubb’s response to the same op-ed piece that’s particularly thoughtful and constructive (and influential), and to Dan Meyer’s follow-up question that re-focuses an out-of-control discussion. In my opinion, of course. As always, any additional resources you find valuable and/or insights you include in the comments are greatly appreciated.
Mark Chubb: The Role of Practice in Mathematics Class
I have read and re-read and started processing Chapters 3 and 4 (Language and Time, respectively) in Creating Cultures of Thinking by R. Ritchhart. Mind blowing. (Download it on iBooks to read and discuss with me!) I am beginning to see some recurring themes: beliefs, values, choices, and messages. Passive vs Active student roles (my personal soap box). Its about CHANGING THE PARADIGM so that students and teachers experience different learning stories. (If interested, my visual notes are below.)
Serendipitously, Dan Meyer recently blogged about teacher’s beliefs and how our own experiences as students shape our pedagogical choices. He asks,
“What experiences can disrupt the harmful messages teachers have internalized about math instruction?
I appreciate this question for two reasons.* a) the numerous responses were varied and offered sensible ideas I recognize as useful and timely as I find myself gradually drifting toward a mentoring role and b) the question moves us beyond information/opinions about beliefs and pedagogy toward at least a partial yet practical solution to a very real problem: lack of significant and sustainable change. If a person in education (any position, right? This is not just a math thing!) has not yet had a disruptive experience that “breaks the circle”, reading or being told about a different paradigm is not too likely to yield a shift in values. If the horse isn’t thirsty, it’s just not going to drink. Or it may believe a constant state of thirst is the norm and blindly accepts it. Or the horse feels threatened by a top-down decision that it must drink this water, now. Or it might be really OK with a drink if it just could make sense of what the hell that meant and looked like and had genuine and ongoing support in making it a reality.
Change is imperative, and paradigm-altering experiences are definitely one way to get there. Creating Cultures resonates with me because my beliefs already align with the author’s because, fortunately, I DID have a disruption in my learning experiences that impacted my beliefs. Cycle broken, singing now possible. Also, I tend to be rather reflective and highly interested educational cultures. But that’s just me, and obviously everyone is different. What if this (or another) book was assigned and the plethora information within it overwhelms me so I just keep doing what I always have done? The wonderful suggestions solicited by Dan (video recording with reflective analysis, joining a math teachers circle, imagine something different and plunging in, becoming a learner to gain perspective, shifting from talking to listening, etc.) all seem to share a common trait: these teachers are the horses that already recognized they were thirsty and went looking for water on their own. It seems first-hand experiences are the most powerful, but I wonder about colleagues who are not at the point of seeking water (yet). Not that they are intentionally staying away, they really do care (because they’re people, not horses); honestly examining individual or group experiences, actions, messages, and practices is an emotionally challenging endeavor and knowing so may be enough to want to avoid it.
What I wonder is, what are possible, effective ways to invite
horses educators over for a drink, so to speak, so that many more disruptive experiences can take place?
I invite you to share your suggestions in the comment section. This is a genuine question I have, so I am looking forward to your insights!
PS. I find it interesting that for some commenters to Dan’s post, drill-based math instruction became the question to discuss. Hot Topic #358. Interesting reading, to be sure. Like all other highly-debated beliefs in education, there seems to be too much polarized “This OR That” going on, and not enough This AND That, carefully and thoughtfully balanced to promote learning. We’re not just emoji yellow OR Tardis blue— it is much more likely that most (if not all) of us are some lovely shade of green. Which means instead of an all-or-nothing tug of war more productive discussions (and PD**) could focus on examining beliefs, with honesty and without threat of judgement. Our beliefs shape our actions, our actions send clear messages, both subtle and obvious. What messages are being sent? Are they supportive of or detrimental to learning experiences students have today?
*Also note how Dan’s question was open-ended and accessible to everyone, and how he refrained from sharing his thoughts until he had respectfully listened to other voices. I see what you did there, Dan. Smooth move.
**If you’re part of a group that examines culture in your classrooms, department, or school you could call yourselves….Culture Club! (If you don’t get that lame joke, you’re too young. Look it up.)
This is just a test post while I figure out how to send out a tweet automatically as I post. IF you got here from seeing the tweet, please let me know! Much thanks.
First, a little context:
My granddaughter is über-prepared and excited to enter Kindergarten in a few weeks. Her 5th (unicorn-themed) birthday falls 22 days after the state cut-off date, so last May she had to demonstrate end-of-year proficiency in order to enter Kindergarten 22 days early. Yes, END of year. She is (without any bias whatsoever, right?) a happy, curious, enthusiastic learner. Like many kids, she’s a sponge, soaking up everything in her path, freakishly observant, perseveres like nobody’s business, memory like a steel trap. Sings at the top of her lungs, too. Just the other day, she was reminding me her bedtime was 8 o’clock and asked me what my bedtime was. I told her usually around 10, and she comes right back with, “That’s two minutes after my bedtime.” Not the right time unit, but definitely knew the difference was two. Damn, girl.
She also confided this little gem: “I hope we don’t have to do math in Kindergarten.”
Somewhere in her short life-time of learning, she has developed an idea of what “math” is, and she already dreads it. This is the girl who counts to 100 just for the hell of it, points out patterns she sees, and makes numerical comparisons. Her parents did not drill her with flash cards or give her a barrage of worksheets to complete; they merely helped her learn the language and meaning of numbers by counting with her—steps up to the top, apples on the page, carrots on her plate. Some other ideas, like patterns, developed in pre-school. Yet she does not want to do math in Kindergarten. Incredible. I was so floored I did not have the sense to ask her more about her concerns, a missed opportunity I hope to rectify soon.
Speaking of incredible, The Incredibles 2 was a summer movie that did not disappoint. There’s a connection here, trust me. (Small spoiler ahead. Skip a bit if you need to.)
In the movie, Mr. Incredible is trying to help his son, Dash, with his homework. Which homework? MATH, of course, and everybody is Super Frustrated. Dad wonders if new math has been invented since he was in school, and Dash informs him that he is not doing it the way the book says to do it.
Is this funny? Sort of, maybe, I don’t know. It IS definitely something that many (most?) people relate to, a shared, all-too-familiar reality, an inside joke. Oh, goodie; math, the dreaded subject that has the power to unite us through misery, generation after generation. Hahaha?
On the way home, my husband just knew I was going to
bitch about address that scene. If “doing math” is perceived as a frustrating, required chore in our culture, even to an almost five year old, doesn’t that say something is definitely NOT RIGHT and CHANGE is urgent? How can our culture jokingly, begrudgingly accept this as normal, even perpetuate it? If so many learners, from toddlers to great grandparents, from educators to policy makers, believe with conviction that “real” math is the drills/rules/tests/memorizing you do in and at school, (and you are either good/fast/smart/superior or bad/slow/stupid/inferior), while simultaneously denying “real-ness” to any mathematical reasoning beautifully and successfully applied outside —or even inside—school, doesn’t that scream volumes that something is MOST SERIOUSLY DEFECTIVE and EFFECTIVE TRANSFORMATION is effing imperative?
There’s plenty of resources and information available explaining to how we, as a society, evolved into this detrimental not-really-learning culture. You can’t blame kids or their parents; look at the learning experiences they have had! Unfortunately, there is a vicious, self-perpetuating cycle going on with school and home experiences that is stubbornly impervious to healthier, alternative messages. Status quo is a powerful, yet strangely invisible super villain, my friends. MTBoS participants, Desmos, and Illustrative Math , are just a few of many top-notch super heroes fighting the good fight (FOR FREE!), but lets face it, many more are needed in order for new visions to gain a foothold and gather enough momentum to become the established, embraced norm in our schools, homes, and communities.
In an effort to arm myself with information and a vision and thoughtful strategies to BE THE CHANGE, a teaching friend and I have started reading Creating Cultures of Thinking. It inspires and resonates with me. FWIW, below are my take-away notes on the first two chapters. I happen to have time right now to process at this level, which feels luxurious and worthwhile and helpful.
I know you are busy because you’re educators, yet I invite and urge you read this book and examine your beliefs. This is a call to action, folks, worthy of your precious time. Please share your thoughts, insights, learning stories, and/or questions with me as you go, and if you are in a classroom (any content, any grade) describe the shifts you are consciously making and their impact on classroom and school culture. Involve others as much as you can, including me! If you live within driving distance (say an hour or so from Wilsonville, OR), I would be delighted to get a cuppa or glassa with you and dig into hidden messages and visible thinking.
Grab your cape and let’s go.
There may be some food for thought here. Not a lot, just a morsel.
My daughter owns her own dessert catering business. As it is a one-woman show and its tough to turn a profit, I help her two days a week in her kitchen. Of course, I can easily follow a recipe she has kindly transferred from her head to paper (I never memorize them), but sometimes she asks me to mix something that is less specific, measurement-wise. Like buttercream.
Buttercream fillings for her French almond macarons* are my weekly task; she never provided proportions, just ingredients, and you just make “enough” and make it “stiff enough”. A bit too vague and nerve-wracking for me at first, I feel I get it right now—most of the time.
Today, the conversation went something like this:
“Remember that cream cheese pastry filling I had you make a couple of weeks ago?”
“Uh, no…maybe. It has cream cheese and….?” I’m fishing for a recipe here.
“Powdered sugar, egg yolk, vanilla.”
“OK….How much cream cheese?” (Still fishing.)
“I don’t know, start with 8 oz. Make it stiff, like buttercream.”
Again with the vagueness, but I can do this, right? Its not complicated.
Well, as I mix, the consistency is not at all like buttercream, so I keep adding more sugar, beating the hell out of it. Finally, I pull her away from her baking; its getting stiffer, but kinda gooey and weird…is that the way it is supposed to be?
She takes one look at it and asks, with some angst, “HOW much sugar did you put in?!?”
“Well, several scoops; it took that much to make it stiff.” I do not like the direction this conversation is headed.
“What? That’s waaaay too much sugar. I said ‘NOT stiff like buttercream’. Do you remember what it looked like last time?”
Shit. “No! I really don’t! And…..well….I heard….‘stiff, like buttercream.’”
We look at each other wildly, almost laughing/freaking out, me feeling stupid and her feeling IDK what, then she quickly moves to finding a solution to the ample mess I made. (I hate hate hate making these kinds of mistakes, and to her credit, she is always gracious.) Now that the pastry filling has an emotional attachment, you can bet I WILL remember making it!
So what is the take-away here? I’m not really sure (you tell me), but I feel something happened that speaks to the complexities of teaching and learning, or sheds light on risk and trust, or addresses memory and communication. Or. Little moments like these take place all the time in our lives, at least they do in mine, that at the very least remind us what its like to be in the vulnerable position of learner. Ah, empathy as a guide. Now there’s a take-away!
* Yes, only one ‘o’. Macaroons with two o’s are something else entirely. The first is a hoity-toity, finicky-to-make meringue and almond meal cookie. Filled with delicious, flavored buttercream, of course. The second is a mostly coconut drop cookie, like a haystack. Both, however, are naturally GF, so there’s that.
For more time this afternoon than I’d care to admit, I’ve been attempting to organize my ongoing and somewhat rambling thoughts around teaching, learning, and mentoring. Much of my reflecting goes on in my head and never gets formalized somehow via blogging or journaling; worse yet, I don’t have much opportunity to actually talk with other educators about these kinds of questions that, IMO, really, really matter.
This graphic is a product of my organizational efforts, and it became my first ever #MTBoS tweet. Amazingly, I immediately received a comment and a ♥️ . Well, that was cool, but I have more to say 😉
It is my belief that these urgent questions (and their natural sub-questions, including WHY?) should be seriously, honestly, and throughly addressed, ideally as a school, or at least as individual classroom teachers. How we respond speaks volumes about our pedagogical beliefs, the culture of our schools or classrooms and, for better or worse, most definitely impacts students and their learning.
I invite you to consider any or all of these questions, and to share your thoughts in the comments. Or on twitter, if you can find my tweet! (Sorry, I don’t know how to direct you there…) Over time, I will do the same. ♥️
Integrating Technology and Mathematics
Exploring the World of Technology in Education
Can you teach an intuition?
We can do this better
Thoughts about Teaching
Better through reflection
The Writings Of Alfie Kohn
Inspiration and resources for mathematics teachers
Musings on math and teaching
I research mathematics teaching and learning in secondary schools
Math Change Agents
Lighting the world with math, one student at a time.
Not everything that can be counted counts, and not everything that counts can be counted. -Einstein
In Math, the Journey IS the Destination.
Not everything that can be counted counts, and not everything that counts can be counted. -Einstein
Reflections on teaching and parenting young mathematicians