All the Lovely People...

This morning, my husband asked Alexa to play the Beatles over breakfast.The songs began to shuffle. Unconsciously, as much as I love the Beatles, I  tuned it out. About three or four down the playlist, I hear the familiar strings begin to mourn Eleanor Rigby, followed by my daugther's voice: "All the lovely people," she says, "like boys."

"Boys are lovely people."

I didn't correct her - lyrically or conceptually. What's the harm in letting her persist in this small misinterpretation? It might very well be an improvement on what Lennon and McCartney originally intended.

And many boys are, in fact, lovely people.  (I resolutely refuse to acknowledge in any way that her comment, at five years old, might suggest she is becoming boy crazy).

But it did get me thinking. About listening.

Listening is an important part of our parenting philosophy. There's a whole book about it. And while we don't subscribe to all of the techniques proscribed therein, it does help give us a framework for one crucial strategy to maintain connection with our offspring.

Indeed our entire marriage succeeds only because we strive for good, solid communication - only achievable through listening. Not the passive kind that often suffices when jamming some tunes, but the active kind (of which you've surely heard) that involves soliciting feedback to make sure that you've heard (or been heard) accurately and that you understand.

And, yes, listening is an important part of our girl's musical education (through the Suzuki method), where we know if we've played it beautifully or not by the quality of the sound.


Someday, our daughter will find out that Eleanor Rigby (and all the rest of us), while perfectly lovely, are also a lonely lot. Who will give her this feedback remains to be seen... perhaps she will read the lyrics somewhere, or a friend or relative will offer correction, or she will hear a cover in a slightly different way than she heard the original and it will send her on a quest to find out the real words.

A harmless error in listening requires no feedback.

And yet, how many times, in my classes, have I offered some guidance or insight that was misheard and I never even knew it? It begs the question of whether I am giving my students enough opportunity to practice active listening. And other questions besides: do I solicit their feedback, sufficiently and effectively? Do I know not only how well they understand, but how well they have understood through me.

Lately, I have adopted some of the metacognitive strategies from the Reading Apprenticeship framework, that emphasizes reading for understanding. As part of this, I have stressed graphicacy skills and encouraged students to develop habits that build their learning independence. But reading is just one of many ways of learning.  Perhaps I have been putting too much emphasis here while neglecting the other important modes: aural, visual, kinesthetic, social, etc...

Likewise, learning is not a solitary enterprise. One of the advantages of RA is the way it acknowledges and leverages the social aspects of learning.

So as I sit down to re-tool my classes, as I do during every intersession (but especially so in summer), my daughter reminds me of the fundamental thing that makes relationships work: listening.

Teaching and learning is the meta-relationship.

I'm going to have to open up my ears, to model active listening and thoughtfully consider how to get meaningful feedback from my students more regularly. They are all truly lovely people. And I know right where they belong: right here, right now, in relationship to where they sit in a sea of new knowledge.

Love is the Learning Space

In the same way that science is self-correcting, so too is nature. That's really what I mean when I wax theological and claim that we are all gods of a vast and incomprehensible uber-god, all working in tandem for the greater good. What that greater good is has yet to be defined, but I think it has something to do with balance, equilibrium. Of course in the end, entropy wins. What a bleak future that will be. It leads one to question whether the universe has a moral code... a question to ponder another time perhaps.

As living beings on a living world, we've got two  main jobs to fulfill: (1) to eat, thus transferring energy onward and (2) to reproduce, thus propagating genes to carry life forward through time. Anything beyond that and we enter moral territory. And I'm not sure that morals, at least in the limited way that humans tend to think of them are a concern of God-nature. You might make the claim that religions offer the basis of a good moral compass, but there is plenty of evidence to the contrary.

So we're left with a big question - what does it mean to live a moral life?

The Hippocratic Oath comes close, but is pretty unrealistic. I think the best that we can strive for is to minimize harm. At some point, however, that becomes a subjective target - one that moves with the addition of more variables.

Recently, I was speaking with a friend, relating a story about my spawn and I remarked that my daughter is a better person than I am. There was an undercurrent of sadness in this statement, but it did not arise from inner self pity (as my friend believed), so much as reflection on control - the things within it and the things beyond.

Of course all children are better than adults - that is just as it should be - what with their curiosity, honesty and receptivity. As a mother, it is my job to nurture those qualities, to fail to quash her innate goodness. And sometimes I do. And sometimes I don't. (Thankfully, children are also resilient). She requires that I be(come) a better person. This is a good thing. But I don't always rise to the challenge. Sometimes I let the world break my spirit, to get me down, to quash my innate goodness. And when this happens, it's a chance to model for her how to climb back up out of the deep, dark hole. (Why do we fall Master Bruce?)

But all this is a bit naive because it neglects the fact that all people - especially children - are exceptionally self-centered and indeed selfish. I question every single day whether I have been selfless enough, while still standing up for and fulfilling my own needs. Because there has to be a balance - to find what serves us in our service to the world. To give and to take.

Am I a good mother? The proof is in the pudding. And most days, the answer is yes.

She learns. She grows. And she teaches me. All children do.

Last weekend we celebrated the fourth birthday of a dear friend at a local park that had the usual playground equipment: swings, slides, rock climbing wall. I was helping support my daughter against the downward pull of gravity - another force of nature that always wins - when out of the blue, we hear someone greet us: "hi." I looked around, but didn't see anyone. Then I looked up. There was a young boy smiling down at us, the blue sky a perfect frame for his cherubic face. He turned out to be nine - four years older than our girl - and not affiliated with the party. We returned the greeting and all resumed the climb.

A bit later, we were having more fun with gravity, this time on the swing. Like all good parents, I gave her a push to get her going, but then stepped back to let her have the full kinesthetic experience of pendular periodicity. And who should come along, but the little cherub.

He literally jumped into the saddle of the neighboring swing and began to pump his legs, fully aware that our daughter was watching him, wanting to go high like he was. He offered advice unobtrusively, mostly enjoying his own motion, but occasionally suggesting things to try.

I sat watching from a distance and noticed that at, some point, he closed his eyes. For a long time. Was he going to sleep? No... he began to move his hands as if conducting a orchestra. When he finally opened his eyes, you could see the wonder written across his face. After marveling for a few moments, he said to our girl "try closing your eyes for a long time. I'll tell you when to open them."

Hesitantly she did, though she opened them before he told her too. When he finally opened his eyes, he described how the colors all looked brighter, the greens more green and the blues more blues. And I was amazed at the deep wisdom that was surely growing inside them in that moment. Indeed, I was reminded of my own experiences falling in love.

Now, I don't mean to suggest that this was a playground romance. Hardly. And yet, you cannot deny that the world shines a little brighter when you are in love. It removes you from the mundane and invites you to see things in a new way. This is why I am grateful to be a parent. To be a teacher. To be alive. Everyday is an invitation to fall more deeply in love, if you can only remember to cultivate that childlike receptivity.

Surely, you have heard the story where a teacher asks a group of students to imagine they are holding a glass of water at arm's length. At first, all agree, it's easy. But after a minute or so, your muscles being to ache and burn. If you keep holding it up, pretty soon other parts of your body begin to tense in order to compensate. The analogy is of course that anything you carry for too long - even if it's not that heavy - is going to distort you with pain, agony, eventually numbness bordering on indifference. Perhaps you even forget that you're carrying it in the first place. But when you are finally free to put it down - Ah! Sweet release.

That's what this boy on the swing was doing. We don't usually think of sight as a burden, but spend four, six, eight hours in front of a computer screen, straining your eyes and you'll want to close them for a while.  Sensory deprivation temporarily relieves us of a burden. When we reawaken to those senses, they are stronger and better resolved.

It's also why I prefer to run on hilly terrain. If you run on the flat for any appreciable distance, your whole body fatigues. Changes in topography demand that you shift your burden. Different muscles have to work. Different synapses have to fire. Different parts of your body get to stretch and bend in different ways. You have to adjust.

And so I suppose that all living things have a third job that they must do. They must change.

As we age, we are slower to embrace change. The wet cement of our minds begins to harden as we become more set in our ways. Children - especially our own - are the perfect mirror to show us how we fit in the world, and how we must change if we want to continue to fit. Truth is, we're all mirrors to one another, if only we choose to open our eyes.

Affirmation of Life

intend love and send it.
don't fear love, but free it
forgive love and live it.
you are love so be it.

On Roles and Models

As a scientist and educator, I am very sensitive to the mantle of authority that is foisted upon our shoulders in the role of the teacher. Appeals to authority are a big no-no in scientific thought and discourse. While I may be the subject matter expert, like my students, I too am on a learning journey. I work hard to portray myself in such a way that students recognize we are equals - that their questions are valid and, indeed, more important than any question that I might ask to spark a discussion or solicit a response.

I strive to break down any perceived barriers in the teacher-student relationship because I want to empower my students with the recognition that they are their own best teacher, so that they may become effective life-long learners. Who better to identify the most effective learning strategies than the student herself?

More than anything else, I see my job as helping my students feel comfortable in confusion. As Brian Greene says: "Science is the process that takes us from confusion to understanding." Indeed, it is only by recognizing our own ignorance that we are able to relieve ourselves of that burden.  Like Houdini wrapped in chains, my students are their own liberators from the locked box of the unknown. How to undo those metaphorical chains? By asking the right kinds of questions. This takes curiosity, initiative and confidence, but it starts in a very uncomfortable place - the place of feeling confused.

On the very first day of class, as part of an "icebreaker" activity, I ask my students to write down what feelings come up when they find themselves in a place of confusion. What do they do when they are confused? After a couple of minutes, I invite them to pair and share what they've written with a partner. Then we open it up for a whole class brainstorm. Time and again students identify all the negative emotions associated with confusion: shame, embarrassment, annoyance, anger, frustration, apathy, hopelessness, isolation.  When students realize that others feel alone in their confusion, it begins to foster a little trust that maybe being confused is okay. Indeed, it is a necessary part of the learning process. Something I emphasize this throughout the semester. Doing the work means finding the right questions to ask and seeking answers to get out of the muddle.

Don't get me wrong, many students also identify positives that flow from confusion, like curiosity, motivation and opportunity. This is one of the reasons why it is SO important to leverage the social dimension of learning. These glass-half-full students can model the strategies that they use to find their way out of confusion, but this only works if all take on the shared responsibility to create a safe space for learning to unfold. Physical safety is all but assured. Emotional safety on the other hand, is a little more nebulous. It can feel very vulnerable to admit that you don't know or understand something. Students are often unwilling to put themselves into such a vulnerable position, thus prolonging their sojourn in the land of confusion. The struggle is two-fold. First, they have to be willing to admit when they don't understand. Second, they have to able to articulate the source of their confusion. This second part can be very tricky, especially when delicate egos are doubly on the line - first feeling dumb for not knowing and then dumber for not being able to express how or why they don't know. So how to cultivate emotional safety, so that all students feel safe to express themselves?

Naturally, I find myself wanting to model this confusion for my students and show them how I get out of it. To show that vulnerability is part of the process, and that it is indeed a strength, not a weakness (thank you Brenee Brown for so eloquently expounding on this). And while I have found comfort in confusion and the problem-solving process, I am not always comfortable being a role model.

When one takes the role of the teacher it comes not only with the presumed mantle of authority, but also with an assumed role to model. I fully recognize that some students (not all) view me as a role model, but it baffles me and is something I take on with reluctance. Who me? A role model? You've got to be kidding! With all my foibles and flaws? With all the mistakes that I've made. But there it is. The wisdom we gain from living is exactly what gives them cause to look up to us, to learn from our missteps that they may forge a more efficient path forward.  I've learned to share that role of model with my students, thus reinforcing the idea that we are equals in our learning journey though coming at it from opposite sides of the mirror - they learning Earth Science and me learning how best to reach this particular group of students, all of them bringing their own diverse backgrounds and biases. From this I must help them find a firm foundation upon which to build a sound structure. And every semester it is a new learning journey. And we shall let our confusion and uncertainty play the role of guide and see where the journey leads us. Onward.

The digitization of education - A Memoir

This week the Reflective Writing club invites us to consider the impact of digital technologies. For me, the best entry point to explore this topic is to consider how my experience has evolved over time. Only then will I have enough perspective to reflect on my relationship with such technologies and how they influence my learning and how I interact with students. 

As a xennial - that strange micro-generation that is not quite Gen-X, but not fully Millenniel either - I have been profoundly shaped by the advent of digital technologies over my lifetime. Unlike my students, I can remember life before the internet. However, unlike many of my colleagues and mentors, I entered the New Age of computing while my brain was not fully formed. 

At the tender age of six, I was given access to our home computer. I learned how to navigate DOS and load content from floppy disc to play fun learning games. It wasn't until much later in life that I would grapple with how I wanted to shape my relationship with computers and the larger interwebs - indeed, it is something that I am still grappling with (and perhaps will continue to do so until the end of my life).

I attended high school as the internet was entering its toddlerhood.  It was the mid-1990s and BBS were all the rage. I had dreams of becoming a hacker and enthusiastically immersed myself in the digital world whenever I had the chance... until a dear friend of mine, who was quite a bit farther down the path of being a hacker, got busted by the FBI. After that, I lost some of my enthusiasm for the nuts-and-bolts of internet protocol. 

But still I recognized the value of this new way of connecting with people, even as I failed to grasp the concept of having an on-line identity.  If I gave it any thought at all, it was to affirm that I wanted anonymity to the fullest extent possible. It is in the teen years that we forge our identities as individuals. My on-line activities would surely become a part of that process, but I was not fully cognizant of that fact until much later. Indeed I was barely aware that I was, at the same time, developing a digital identity in the on-line world.*

When AOL became a nationwide sensation, I was just making the transition from high school into college. I spent a lot of time in chat rooms and eventually started a LiveJournal account to document my college experience and my travels abroad - in all its

tumulteneity Yes, this is a portmanteau word of my own creation that combines tumult with sponteneity

.  I participated in some file sharing, but none of my college classes ever required any kind of on-line interaction - at least as an undergrad in the Liberal Arts. The greatest use my computer saw in those days was as a word processor to type essays. Sometimes I also used spreadsheets to record data for my job in the Environmental Engineering Lab.  Sure I surfed the web for fun and occasionally did a scant bit of internet research for school projects, but the vast majority of the information I needed was in my textbook, lecture notes and course packets. And of course the library. God how I loved to get lost in the stacks! What wonders I would find! (Now-a-days it is the Wiki wormhole that makes me lose track of time and space. Call me old-fashioned, but without the musty smell of old paper it just doesn't have quite the same appeal).

After I earned my B.A. in Latin American Studies, I entered the world of work as a preschool teacher. It would be about three years before I would return to higher learning and go on to complete my M.S. in Geology. In that time, the internet grew up. And how! We relied on the internet A LOT more for research. And although we did not use them in any of my classes at first, LMS were coming on the scene of higher ed. It was in my PhD program that I first encountered Blackboard. Course content was beginning to be aggregated on-line. Assignments were posted (and often completed) on-line. Web-site design became an important skill for me to develop. As a grad student, laser-focused on her research, I did not give much thought to how the increased use of digital tools was changing landscape of higher ed.

After grad school, I once again entered the world of work - this time as a consultant. It was enjoyable work, but I felt a familiar lack - I was not fulfilling my life's work. From the age of eight, I always knew that I wanted to be a  teacher. By ten, I knew that it was science I wanted to teach, so when an opportunity arose to take on a part-time teaching assignment at a local community college, I jumped on it with gusto.  Finally, I was on the path, working the job of my dreams, helping to inspire and enlighten young minds.

My mentor was not an advocate of on-line learning. He was the complete opposite in fact. Instructors had previously developed on-line classes in the discipline, but he dismantled them and brought the classes back to the standard face-to-face format. Still, I could see the value of offering on-line classes to students, so when the college offered an on-line training to learn how to teach on-line, I once again jumped at the chance. This first training was in the Moodle platform, but the very next year we switched to Canvas, so I repeated the training again in the new LMS.

As part of the class, I began to design a hypothetical class focusing on California's water resources. It was exhilarating. I was hooked. At first, I only used these LMS as a way to share resources with students: readings, lecture notes, URL's, and stuff like that. In addition to Moodle and Canvas, I also got to work somewhat with Etudes at another institution. Slowly, tentatively I began to experiment with designing low-stakes quizzes on-line and surveys to integrate with my classes. And I continued to learn about all variety of digital tools - some seemed too cumbersome to be worth implementing, but others sit on my ideas shelf, waiting for their chance to shine.

Just this past semester, my students initiated a collaborative project to build a study guide for the class in Google Docs. It was such a brilliant idea that I've adopted it as a group assignment. My students are naturals at digital collaboration. When assigned a group presentation project, they immediately began working with Google slides, all simultaneously editing and refining their work, chatting face-to-face in the computer lab, while fully aware of the on-line chat capabilities.

I offer my classes now in a light-hybridized format, but am looking forward to teaching my first fully on-line class this Spring. I fully recognize how rich the digital world has become and how much I still have to learn. I am also aware that the digitization of education continues to innovate - for better or for worse: 

• better because sometimes the innovations really do fulfill an essential need and facilitate learning in a meaningful way, 
• but worse because it adds yet another digital tool that must be learned in order to extract some marginal benefit therefrom, thereby detracting from the deeper learning higher up on Bloom's Taxonomy.

It seems like on-line education is itself still in its childhood, with still much neural pruning to take place. Each of us has a role to play in wielding our metaphorical pruning shears - and what one educator values in their garden, another will eschew. Still, it is helpful to be connected with other educators - both those who value on-line education and those who don't. For that reason,  I am grateful to be a part of the Reflective Writing Club #CCCWrite.


*Forming a digital identity is something our students have had to grapple with from the very beginning of their lives and I wonder how society's relationship with digital tools might help (or hinder) them in developing a meaningful relationship with themselves and others. This is a HUGE question that I will likely elaborate on in future posts (what with the latest research finding links between social media use and depression).

To confer...

Confer - (verb) from the Latin con = to bring and ferre = together

This week the Reflective Writing Club (#CCCWrite) prompts our community to consider the role of conferences in our professional learning - their value in the moment and in the years to come.

In my life, I have been very fortunate to attend quite a few conferences. My first experiences were to present research findings as a graduate student. I still remember how incredibly nervous I felt at my very first poster presentation. It was a local symposium hosted by my home institution. As my confidence grew, I found myself venturing into larger forums - even presenting at the annual conference of the American Geophysical Union (AGU) and Environmental Science & Technology (EST).

Looking back I can recognize how the skills I developed there inform my teaching practices today. Lots of those presentations were given in stuffy, dimly lit conference rooms that were very conducive to napping (especially after lunch). I noticed how easily the audience became disengaged. I also noticed what styles of presentation kept people interested. Gradually I adopted a more conversational and engaging style (and even won a few awards along the way, which helped me realize that there is value in at least some of what I have to say).

Being a good science communicator is critically important because a functioning democracy depends on a well-informed electorate. (Thank you Thomas Jefferson for this wisdom). A lot of the issues that face our country - and indeed our world - require a basic knowledge of fundamental concepts and understanding of how science works, that is what it can do and what it cannot.

Flash forward a decade. I now find myself attending professional conferences whose focus is less on scientific research and more on pedagogical approaches. In fact I was lucky enough to attend one just this past week to learn more about how to better implement metacognition and active learning through the Reading Apprenticeship framework. Thankfully, I am part of a great community of educators with varying years of experience in this approach, so we help each other out along the way sharing what works (and what doesn't). This community serendipitously spans several institutions, in part because of the connections made at conferences.

Every year the National Association of Geoscience Teachers (NAGT) hosts a conference. As much as I have enjoyed all of the conferences I've attended over the years, this one is probably my favorite. It has lots of rugged Earth Scientists in attendance (like me) with lots of cool ideas about how to bring more hands-on learning to the classroom (not just in lab). Plus it has FIELD TRIPS!!! I've got to get back there soon. I didn't have a chance to go this past year, but the year before that I got to meet Dr. Tanya Atwater - one of my personal heroines - and get my hands on some really cool models (some of which I got to build myself). So now we have in my department a model of seafloor spreading that shows how fracture zones form along transform faults. (Here's where you can go to learn how to build one yourself). In fact, she has all kinds of other incredible resources available on her website.

The common theme here is where we started - it is the coming together of other seekers on the path to becoming great educators that is of greatest value (both to me personally and to our students who benefit).

Without question, the most valuable thing I take from these conferences is the connections I make with other educators. Over the years I have built up my own Professional Learning Network of adopted mentors. These are the people I emulate, often joking that "when I grow up I want to be just like ____________" - except I'm not really joking. I cherish these relationships because of the shared learning they inspire. And I do my best to pay it forward and share these inspiring ideas with others.

That we inspire one another to greatness truly is revolutionary!

The Power and Peril of Positive Reinforcement

At the end of the now classic Wes Anderson film Rushmore, a movie about an idiosyncratic young man coming of age in a private school setting, there is a beautiful acoustic number that reminds me of the prompt for this week's post:

"I wish that I knew what I know now" Rod Stewart croons in the 1973 folk-rock ballad by The Faces.


Music permeates my life and the lessons I've learned along the way. So when I was invited to reflect on this theme as part of the #CCCWrite Reflective Writing Club, this song started playing on my internal soundtrack and has been on repeat ever since. (Now I share it with you, dear reader).

There are SO MANY THINGS that I wish I'd learned earlier in life and still I recognize that, as much as I've learned, there's still SO MUCH TO LEARN. Just as my former boss and mentor Dr. Joe Birman used to say: If you ever stop learning, it's time to die (which is close kin lyrically to another great song by Blind Melon).

Sadly, I know he passed on to the next life with an inexhaustible hunger for new knowledge. On his behalf, I gladly carry the torch onward, to continue the learning journey with the hope of inspiring others along the way. And a big part of my quest is to find effective ways to help others learn. Whether motivational, inspirational or merely practical, anything I can use to this end is pure gold.

Of the many hats I wear, one of the most cherished is that of mother to my almost-5-year-old daughter. We are learning to play the piano together following the Suzuki method. The main goal of the Suzuki method is to raise excellent young men and women who happen to be very good piano players. Mr. Suzuki emphasizes that the best way to do this is through good role-modeling and positively reinforcing desirable behavior. We are very fortunate to have an excellent teacher who does an excellent job modeling, not only proper piano technique, but effective strategies for positive reinforcement. She always looks for the good and brings our attention to it (sometimes with praise, sometimes without).

And it is such a powerful reminder. Look for the good.

You see, like so many people I tend to be overly self-critical. But it is possible to have high expectations without being so hard on myself. I also have high expectations of my daughter and of my students - though I am not nearly so hard on them, but I have not had a clear strategy for how to best help them meet (or exceed) those expectations - until now.

Just like Fatboy Slim says in "That Old Pair of Jeans "now I found the good and I emphasize it"

And it helps in SO many ways. 

First, the personal. I can more easily recognize my successes and forgive myself on those occasions when I can't quite keep all the balls in the air.  It builds my self-confidence and motivates me to keep going, whatever obstacles may obscure my path. It makes me a more loving and effective mother.

Then there are the professional boons, those that benefit my students (and also helps fulfill my personal quest of being the best teacher I can be). It builds their confidence. It helps them develop a sense of what are important skills in the discipline. When I acknowledge their effort with analytical thinking, they experience the satisfaction of success and are motivated to become more effective learners. And yet still... I have questions

* How much praise is too much? The last thing I want is for my words of encouragement to ring hollow, but if I shower too much praise that is exactly what happens. The law of supply and demand dictates that a large supply of goods fetches a cheap price. So I have to be careful how I apportion it. 

* Am I effectively distributing praise equitably and in meaningful ways to encourage the kind of learning that is valued in science? This one is a doozy.  First of all, as someone who has struggled with insecurities most of my life, I know all too well the sting of jealousy when someone else gets all the praise and I am left in the shadows. Whenever I offer positive reinforcement to a student or group of students, I wonder: who feels left out? And more importantly, how can I bring them back in so that they don't (continue to) feel marginalized? I want all of my students to recognize their value - and the amazing thing is that we all bring value with both our strengths AND our weaknesses. 

For example, someone who is not very outspoken is likely to be a very good listener. This receptive quality is definitely something that should be encouraged as it is truly a gift to be heard.  Good listening also has its own intrinsic rewards - it is often a very effective way to acquire new knowledge. Plus it models excellent behavior for others in the class. And yet, am I praising this quality enough or am I still criticizing those who hold outside conversations in class at inappropriate times?

Another example, of a weakness that can also be a strength, is a student who may be under-prepared - maybe his math skills are not as strong as they should be or maybe her English skills still need to develop more. This may at first seem like liabilities in the classroom, but they don't have to be. I frequently have my students do pair-and-share activities that include analytical tasks (yes,even those that involve math). Of course such small group work necessitates decent skills with oral communication, so how does the ESL student bring strength? Likely in myriad ways that have nothing to do with her English-language abilities, but even her struggle to communicate is a boon as it requires that other students become better listeners. Together they will struggle to translate complex ideas into simple terms and in so doing develop a deeper understanding of a particular concept or skill. 

What about the student with weak quantitative reasoning skills? Such students can be difficult to motivate because being "bad" at math has its own special stigma. Really, no one is "bad" at math, rather some have had more practice with it than others. Math is the language of numbers, so you might think that there's just one way to "speak" or "translate" it, but nope. 

People learn to "speak" math in many different ways, that is, they have different problem-solving strategies. Often these people who think they are "bad" at math just look at numbers a little differently than it has been formally taught in many classrooms and so these students lack confidence in their skills. If through praise or empathy, we can invite these students to engage with the problems, they may demonstrate a novel way to approach it that leads to an effective solution that helps the group to think about it from a whole new perspective. I have seen this happen on many occasions. 

At other times, the challenge with such students is to encourage grit or persistence. They are often all too ready to give up, wielding the convenient, but completely invalid excuse that they are "bad" at math. It's easy to encourage persistence in those that demonstrate it, but here's the challenge - how do we make sure others know we are praising effort and stick-to-it-iveness, not ability? You see, from the outside - if you're the student who thinks he's "bad" at math - when I praise the student who found a way to solve the problem and arrive at the correct solution, it looks like I'm praising their ability. Even, if I'm very careful with what I say, it can come off that way. 

So ingrained is the story we tell that we're "bad" at math, that we fail to recognize it as a skill we can grow and develop. And so, when it comes to positively reinforcing the development of quantitative skill, I often get stuck in the worry that I have not "saved" enough students from this defeatist thought pattern. Don't get me wrong, I do reach some of them and help them find the path toward a growth mindset regarding math, but I know that idea is so prevalent in our society. I feel like it is my personal mission in life to uproot that weed wherever I find it, so I keep looking for the most effective strategies to weed and re-seed.... anybody know of the best "herbicide" to kill of the "I'm-bad-at-math weed"?

And so we come to the most difficult doozy of the question posed - is my praise encouraging the kind of thinking and learning that is valued in science? Each semester I teach my students about the scientific method and the characteristics of science, one of which is that science makes no value judgements. You see where I'm going with this one? That's right science does not set out to say whether something is good or bad. It's not the right system of knowledge to make such assessments. And yet... every time I offer praise or encouragement, I am making a judgement. Does that mean I am failing to model the thinking patterns of a good scientist (or am I just trying to be a good mentor)?

As the little green man says "Do or do not. There is no try."

Which leads me to my last question: Is there a meaningful difference between offering praise or encouragement and giving positive reinforcement? With my daughter, positive reinforcement sometimes comes in the form of stickers or fruity o's. Not all parents believe in such rewards systems, but we use them to good effect (and I would kindly ask you to please withhold your judgement if you disapprove - we parents are all doing the best we can with what we have). Can I bring such trifling rewards to my class? Perhaps some kind of candy? It is different than praise (though it still requires a value judgement, it is less obviously demonstrated and perhaps encourages some sort of Pavlovian response). And it's funny, but as I am reflecting on this, I cringe a little bit when I think about bringing this kind of positive reinforcement into my classroom. (Why? Why on Earth would I be comfortable using this strategy with my daughter but not my students?) In my mind, praise is a lot like encouragement, but they are not necessarily the same thing. Praise typically takes the form of "Good job!" or "I like the way that you did ...." or (making it less personal) "That was a very effective approach to solving the problem..." or "I  saw you working together really well..." etc... Such praise can be encouraging, but pure encouragement is more like what you shout from the sidelines of a sports match: "You can do it!" "Keep going!" "You've got this!" 

Perhaps all of these are important ways to look for and acknowledge the good, so we can grow the kind of garden that produces quality fruit. All I know is that, while I wish I had learned this skill sooner, I'm grateful to have it in my toolkit today. And, like all good discoveries, it leads to more questions than answers. Journey on learners, we shall find what we seek.