Lead with your heart.

In practicing yoga, the cue to “lead with your heart” often is interpreted to mean shoulders back and down, abdomen in to support a strong core, arms perhaps stretched out like wings or clasped behind your back and down, with heart-center the leading force of your physical movement. (Think of doing a forward fold swan diving with your heart leading the way, or a humble warrior bowing down in reverence and respect, heart forward.)

As a physical exercise it might feel vulnerable to lead with your heart, especially when energy levels aren’t grounded. On the other hand, if your heart energy is strong, it might be empowering and feel quite full and alive to lead with your heart.

I intend to lead with my heart both on and off my yoga mat.

As an educator leading with my heart brings a smile to my face. It means putting ego aside. It means embracing the unknown for whatever it is, not good or bad. It means working toward positive change, to bring greater joy from suffering. It means acknowledging the complexity of being human, of suffering, and of the possibility of transforming suffering into something beautiful.

Heart-centered in yoga and heart centered in mindfulness and heart centered in mathematics, need not be disparate ideas and practices. I find great beauty in working at the intersection of disciplines and practices.

For me, the way I see the world, yoga and mindfulness are everywhere. Art and mathematics are also everywhere. There is a subtly here that I wish to explain. It is my own lens that helps me “see” these practices in all that I do. And it is my intentionality to cultivate meaning through the practices of yoga and meditation, and through the practice of expressive mathematics, that help me to cultivate and strengthen my lenses.

 

Habit forming.

Habit forming.

March 2, 2018

 

I’m working on a new habit of opening my computer to continue my writing.
I’m working on a new habit of being OK
even when I’m in what I sense to be an uncomfortable situation.

With bells ringing, trucks beeping, people talking,
fans whirring, engines, motors, beings,
all conceivably in motion all at once all around me.

It is notable, however, that understanding of my experience is self-centered.
It is not too surprising, and I am not alone in this way of understanding my experience.

Of course I understand my experience from my own lens,
from my own person, from my own self.
It is in this sense that I am centered on self.
For being centered on self, I come to understand myself, my voice, my story.

However, one way to de-center from this lens is to notice what is, and to not take it in as my own.
The noises from the parking lot are not a part of me.
I can sense them.
I perceive of them.
I am aware of them.
But they are not me.

The story that I create about these sensations,
perceptions, and my awareness of them,
is something that I create myself.
Yet the story is not me.
It is a story.

With training, I can choose to separate myself from the experience of is-ness, of being right now, right here, breathing, typing, and my experience of sensations that are uncomfortable.

I do not believe that I am alone in being uncomfortable in noisy situations. I believe this discomfort has been created as a form of habitual patterning that has evolved from my experiences.

Being aware of this habitual patterning (loud noise, discomfort, distraction, frustration, discontent, ungrounded, anxiety, urge to flee from the situation… loud noise, discomfort, distraction, frustration, discontent, ungrounded, anxiety, urge to flee from the situation…) is a starting point.

It is from this awareness that I can work toward creating more productive patterns that spring from my intention to be at peace. To be at peace with myself in the world. With my decisions. With my being. With my work. With who I am.

I’m working on being ok in the stillness of my own typing.

Resting in the consciousness of my mind that I am sitting at my computer, I am typing.

To have clear train of thought I sometimes create an expectation that I need to be in silence, in isolation, or otherwise be uninterrupted.

The fact of the matter is that I do not live in a world of uninterrupted spaces, places, and experiences.

My experience of the world is largely interrupted all of the time.

The question then becomes – how do I form new habits that take me into the peaceful state of writing – of being – of meditation on thought – of getting the ideas down on the page – rather than existing outside of myself in a noisy and busy world?

This is the practice.

Habit forming
Heart-centered practices. Mindfulness. Boy resting on tree. Growth of flowers in supportive environment. By Nicole L. Fonger @nmlfonger

Being while doing.

I wear multiple “hats” if you will. Mom, wife, researcher, collaborator, teacher, mentor, sister, daughter, granddaughter, aunt, to name a few. In each of these roles, I am asked to communicate, to lead, to converse, and to do. Often all I want is to just be.

In drawing inward I find a great sense of calm. I prefer to sit quietly in a meditative state, to be independently writing at my desk, or drawing and sketching to re-create and generate new ideas.

Where is the balance? I find social activities to be exhausting. I get distracted easily when several others are asking of my time, my presence, and my energy. And often, in interaction with others, I give a lot of myself. I don’t see a real reason to “be” somewhere, called to “do” something if I’m not really going to “be” there.  Yet in giving myself fully to a social situation, I easily get depleted of energy. Over time, this repeated depletion leaves me vulnerable and susceptible to illness.

Again, where is the balance? I forced a yoga class to happen today, with crying toddler in tow, I barely made it there in time, squeezing my mat in the corner of the studio space. Yet in being in that space, I remembered the importance of taking time to fill up. In yoga class I am in a social space, I am fully present, yet I’m not asked to talk and teach and lead.

I’m asked to breathe and to link breath with movement. I’m guided on an inward journey to come in tune with the true version of myself. To transform stuck energy into something beautiful.

Is it possible to take this stance of introspection in social spheres? To perhaps give a little less of my full presence to others, and instead prioritize full presence to myself. Perhaps I push too hard. When my body aches, I often ignore it and keep working. When my hunger pains I often ignore it and keep working. Even now I can feel the pain of my belly, the tension in my jaw, the ache of my spine, the thirst in my throat.

—“Hey mom. We didn’t have dinner”
(I laugh. We had dinner before tee-ball practice tonight).

“Didn’t you say we could have smoothies and pancakes?”
(Yes! I did. Let’s do bath, and then have smoothies and pancakes.)

And here I go. The next test. To move through an introspective moving meditation of bath time, dinner, stories, bedtime. While attending to my own needs, being present with my children and spouse, and not pushing too hard. Doing while being.

“Do you have to finish all your work?”
(I’m just writing)
“Can’t you just not write, can’t you just help your boys?”
(Breaking away, from this quiet introspective space, a calm I create while creating. Now my work is to re-create a sense of calm in interaction and leadership with others. A state of being while doing.)
“Are you writing about me, mom?”
(Yes. I love you. Let’s go.)

Time and space.

Taking time.

Creating space.

To be.

To wonder.

In this space.

I am.

With nothing more.

Nothing less.

Noticing the incessant voice.

That calls otherwise.

Noticing and being OK with what is.

This is the practice.

Waking to a call from somewhere that feels outside of myself.

Yet deep inside I am called from within.

I am called home.

To do my work.

To work for those who cannot.

To give voice to those who are silenced.

To create and express that which cannot be heard.

To free myself, and others, from being trapped.

On dark days.

Gray skies linger.

I celebrate and salute the sun.

Especially when her rays are not able to kiss my skin.

Yet here I am.

Reminded again.

No mud, no lotus.

 

Knowing when to rest.

March 3, 2018.

I’m not good at knowing when to rest.

Usually I work through my day, pushing from one thing to the next, with little time spared in between.

When my stomach hurts, I know I have gone to far.

The ideas and work flows from my finger tips yet but body urges me to rest.

April 25, 2018.

Yet here I am again. Body aching. Longing for movement.

Yet I write.

My writing keeps me quite literally chained to my desk.

And not in a bad way.

I surround myself with sights, sounds, laughter, images, papers, pens…

Ways to express and reflect on expression.

And write.

Now, it is time to move.

Drink water.

Breathe deep into my body.

And relax.

For relaxing is part of writing.

Current Projects.

Across all of my research I seek to better understand students’ meaningful learning of mathematics and the nature of supports for that learning.

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Characterizing and Supporting Meaningful Learning of Mathematics @nmlfonger

Lately I’ve been playing with new framings of ideas, pushing the boundaries of my comfort zone.

Below is a list of my current projects (and the stage they are in, last updated May 2018). Sometimes I struggle with having so many projects. One thing I find to help alleviate the struggle is to continue to curate, refine, and clarify both the SCOPE of my projects and the FOCUS of the work. This way I can not only move the work forward, but I can also more easily share the work with others.


 

Reality Math Circle

Focus: How do students experience meaningful learning of mathematics? How do the components of reality pedagogy (vis-a-vis @chrisemdin #HipHopEd) play out in an after school enrichment opportunity? See video on reality pedagogy here.

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Phase: sprouting seed, design, management of initial phases, building relationships – showing up, asking questions, being open and curious

 


Learning Trajectories in Algebra

Focus:A learning trajectory integrates conceptual learning goals, mathematical instructional activity, and students’ conceptions vis-a-vis their discursive activity. How does students’ conceptual understanding grow in relation to instructional supports? What is unique about a learning trajectory approach in modeling learning and supports for learning?  See video on learning trajectories here.

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Phase: writing, visualization, refining journal target; this work extends work on learning progressions in early algebra

 


Heart-Centered Pedagogy

Focus: What does it mean to teach mathematics with kindness in mind? How are cognition, emotion, social relation, and sensation experienced in math learning? How do these dimensions of experience amplify meaningful math learning — especially at the intersection of mathematics and mindfulness?

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Phase: seed idea, writing and sketching and reading to develop idea, asking others for feedback through peer-review drafts and discussion.

Research and Practice

Focus: How are community, collaboration, and communication central to linking research and practice in mathematics education? What are productive images and metaphors for linking research and practice (that help us move beyond a deficiency or ‘gap’ focused storyline). Here is an example of a video I created on linking research to practice.

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Phase: developed idea, need to revise research manuscript for target journal, curate visuals of current work to incorporate, draw insight from #EDU700 course to inform writing and visualization.

 


Representational Fluency and Meaning Making

Focus: Representational fluency involves creating, interpreting, and connecting  multiple representations to draw meaning about mathematical ideas. Here is a video of this work.

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Phase: developed idea, manuscript under review, another in draft form, graduate student working on related project

 


Another thing I struggle with is when it is OK to share the work. Sometimes the formalism of journal publications makes it seems as though that is the best time to share the work – once formally accepted by the community. This masks so much of the nature of research – the forming of the ideas. It is truly a creative process.

As such, you will notice in these projects that some are seeds, while some are sprouting. Like these flowers, that represent a learning trajectory for children’s mathematics. With the right supports and conditions, they, too, will grow and flourish.

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Does this work interest you? Reach out. I’d love to hear from you.

@nmlfonger Nicole L. Fonger. (aka the notorious Dr. Nicky)

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Current research projects. April 2018. @nmlfonger Nicole L. Fonger

Dr. Nicky. The Scientist.

For a while now, perhaps ever sense I was introduced to a “lab” model of scientific and education research, I’ve wondered, what is a lab? How do I build my own “lab”?

In working on this, I came to the following conclusions:

I am the leader of my own lab. My lab is focused on understanding and supporting students’ meaningful learning of mathematics.

The people whom I share my work with are a part of my lab. My grad student, for example, is in my lab. The students, teachers, and other researcher collaborators I work with are a part of my lab. A lot of our time and effort and intellectual energy is represented in the various projects we’ve worked on together.

My lab is grounded in my practices of writing, reading, teaching, and systematically studying learning to better understand the human experience of meaningful learning of mathematics.

Lately I’ve been adopting a multi-dimensional lens on being. This involves awareness and study of: cognitive (thinking, e.g., mathematical equivalence, covariation and correspondence), emotional (feeling, e.g., anxiety), social (participating, e.g., representing, creating), and bodily (sensing, e.g., perception) dimensions of experience.

Largely I have come to this multi-faceted lens as a way to understand my own experiences, on and off my yoga mat.

I drew this sketch to represent some of the ongoing work in my lab. Much of the work is collaborative. All if it is focused on students’ meaningful learning of mathematics.

Again and again I find that by expressing ideas in writing, in pictures, or other visual imagery that I learn. Sketching to learn, learning to sketch.

 

 

DrNicky_TheScientist

Vulnerable, and listening.

Lately I’ve found myself in vulnerable spaces.
Of my own design.

Opening myself up to uncertainties.
Of uncharted territory.

Asking new kinds of questions.
Seeking connections in new and deeper ways.
Looking to really feel something.

And when I look into someones eyes, to really see them.
With a quest of better understanding how they see.
And how seeing through their reality, I might also better come to understand myself, and the intersectionality of our experiences.

This is a vulnerable space.
And a tiring space.
For truly listening, means embracing genuine kindness.
Embracing  openness toward another being.
Seeing them for what they are: a human being.
All of us, on a quest for meaning.

In this vulnerable space, I also find myself more woke–to the ways in which our systems of education are oppressive.
No longer sleeping, silently, unaware.
I wonder about the ways in which my participation in dominant forms of discourse may be perpetuating the oppressive nature of schooling.

I don’t understand it.

But it think seeing it,
and asking questions,
and showing up,
and truly listening,
however vulnerable…
is a good place to start.

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Vulnerable, listening.

 

Research and practice: representational fluency

One way to link research and practice is to interpret theory with the aim of improving practice.

In one study I conducted I developed a framework or lens for seeing how students create, interpret, and connect one or more representations for doing and communicating about mathematics as they solved problems.

 

A first implication of this work is to get students to ENGAGE with one or more representations by ASKING…

—what do you see?—explain it

–Show me, so we can both see—create it on your paper or technology

–Tell me, how are these related?—elaborate the connection

 

A second implication of this research is to value emerging representational fluency. As students are learning new ideas, students might create incomplete representations, or might interpret their meaning in a way that doesn’t match the disciplinary conventions and norms.

–From a growth-mindset perspective, emerging fluencies are opportunities to grow and develop sense-making

–I am reminded of a quote from Brené Brown – that as long as we are creating, we are cultivating meaning—

 

Finally, to grow meaningful representational fluency, it helps to ground instructional design on supporting core mathematical concepts. For example, the data for this research was focused on mathematical equivalence of expressions and equations to support equation solving with multiple representations. Functions are a rich area to support meaningful understanding of correspondence and rate of change in linked quantities.

 

I invite you to engage with this work, and to reach out. I’d love to know… what are you noticing? What are you wondering? You can reach me, Nicole L. Fonger, at NMLFONGER on twitter and Instagram.

Making sense of experience.

I recently had the pleasure of visiting a mathematics classroom in an urban public high school. I created these sketchnotes to make sense of my experience.

The context of the visit came from a shared interest — mindfulness in mathematics. The teacher, whom I will call Mrs. MT (math teacher), invited me to visit, to learn, and to observe how she is incorporating mindfulness with her 9th grade algebra students.

As a mathematics educator and faculty member, most of my time is spent in my office (at home or on campus). Visiting schools and classrooms (such as my kindergartener’s math circle time), and this visit, help keep me grounded and invested in the important work of supporting and characterizing students’ meaningful learning of mathematics.

Mindset_March2018

A Math Task. Mrs. MT introduced a task for students to work on.

There are 310 tickets to be sold for a school event. The number of student tickets sold is 25 more than twice the number of adult tickets sold. How many student tickets, and how many adult tickets were sold?

I noticed… a lot of cell-phone use by students, and with that, a fair amount of passive or cursory engagement. Mrs. MT was asking questions like “Whose head is spinning?” “Where is the question?” “Is it scary?” Noticing at one point when solving the task that “This is messy.”

I found myself wondering… Who is doing the thinking in this solving this task? What is new here for students? Is it review? What is the buy in from the students’ perspective to engage meaningfully with this task? Are they making sense of this scenario? Of the mathematics?

Learning Something New. Then we shifted to a segment Mrs. MT called “Learning Something New.” We watched a YouTube Video: Time-lapse of Baby Learning to Walk. After watching this short video, Mrs. MT asked:

“What did you notice?”
“How could this be applied to anything new I have to do?”

Almost all students were engaged. Mrs. MT elicited responses from over 6-8 students who said things like:

“She had a hard time”
“She kept going everyday”
“She was happy”
“She got back up”
“She kept trying.”

I think the intent was to share the notion of struggle in life and in mathematics. As Mrs. MT shared later in our conversation,

Math is a great reflection of life — the struggle is so much more important

– Mrs. MT, March 2018

Mindfulness. The next part of class was focused on mindfulness. Mrs. MT has routines to engage students in mindfulness practices during class. She followed a student suggestion to do the “chime” because, in the student’s words:

“the chime is the best one.”
“with the lights off it’s more calmer”

At the student’s request, Mrs. MT turned out the lights and instructed:

“Close your eyes.”
“When you stop hearing the bell,”
“Raise your hand.”

All students’ technology (cell phones) were put away. Everyone was silently, calmly sitting with their eyes closed. They raised their hands once the sound had dissipated. And they did this two times.

It was quite peaceful. Mrs. MT shared later that perhaps this is one of the rare moments in these adolescents’ daily routine where they are conscious without their technology (phones).

Reflection. In making sense of this experience, I see it as linked to a broader discussion and issue of

how to support students along social, emotional, and cognitive dimensions of well-being.

Doing math is more than solving tasks.
Doing math involves learning new things.
It involves struggle- just like life.

Our job as mathematics educators is also to educate the whole student.
In this case, the intersection of mathematics and mindfulness looked like creating a safe space for struggle, for learning new things, and for finding a sense of calm in the classroom.

For me, school has always been a sanctuary of sorts.
A safe place to grow and to nurture creativity and logical reasoning.
I didn’t feel safe at school because I walked through a metal detector, and had forced entry at only one door of the building. (The current norm in so many school buildings.)
I felt safe at school because I participated in a supportive community who saw me, and believed in my potential to grow as a human being.

From a humanistic perspective on mathematics education, and on learning, students are people, not data points.
Young people need supportive environments and leaders to help them grow and flourish along cognitive, emotional, and social dimensions of learning.
Perhaps an exploration at the intersection of mathematics and mindfulness will help us learn more about the kinds of supports learners need along the multi-dimensional facets of learning.

 

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