This is a result of the disidentification process. They are not accustomed to speaking in their own authentic voices in math class. They have become conditioned to attending math class under what Brousseau called “the didactic contract.” Under the didactic contract — the implied contract to which they have become conditioned — they are required to check their authentic self at the door, with all its attendant messiness, blurting-out, hesitant and half-formed ideas. Instead, the didactic contract demands that they conform to very narrow ideas of what a “good math student” is supposed to do: Sit down. Shut up. Pay attention. Get the right answer. Don’t ask why.
There’s no point in our denying that this is what most math students have become acculturated to. They didn’t make up these requirements themselves. Somewhere along the way, everybody encounters a math learning environment in which these are the expectations.
This situation is what the great Swiss psychoanalyst Alice Miller spoke of in her book, The Drama of the Gifted Child. In an adult-centered, authoritarian society (which most societies are), the social constructs are organized to side always with the adult/parent/teacher instead of with the child. And in fact, as Miller’s work showed, not just *instead of* the child, but at the child’s expense.
This is the general situation for discouraged learners in math classes. Many students perceive early on that their authentic selves are not welcome here. They quickly learn to wear a mask in math class and to pretend to be smart, compliant, and “mathematical” — in other words, to adopt a false persona in math class.
The problem for us as math teachers is that it is not easy to crack through this false self. Disidentification is not an easy or a straightforward process. The psyche adopts these masks as defense mechanisms — and for very good, if outdated, psychological and emotional reasons: fear of abandonment, fear of humiliation, fear of shaming, fear of annihilation.
These may be outdated, outmoded fears by the time a student reaches middle school or high school, but that does not make them any less real or active in the present moment. For a traumatized math learner, they are the most real thing in their world during 5th period.
In their own different ways, the psychologists Eugene Gendlin, A.H. Almaas, and Francine Shapiro have all posited that trauma in the past forms a kind of “stuck place” in the human mind/brain/psyche. Whenever we encounter a stimulus that “triggers” that stuck place, we “flash back” to the moment of trauma and our defense mechanisms lock into place.
This is what makes disidentification so difficult to achieve in practice. A defended psyche is not a receptive psyche. And a student may *hear* that s/he needs to adopt a growth mindset in math class, but s/he hears this message from his or her bunker, thirty feet under ground and behind several feet of concrete protective functions.
Raise periscope. Spot the threat. Lower periscope and retreat.
Evolutionary psychologists consider this fight-flight-freeze response and its replay during anxiety dreams as a most ancient form of threat rehearsal. Knowing what they know from their previous experience, the protective functions of the psyche leap into action and do their best to make sure we remain vigilant and safe from incoming threats. They perceive this to be a matter of survival, which is why they go to such great lengths to make sure we perceive it that way too whenever we step over the threshhold into math class.
So the first order of business in the process of disidentification is to establish trust and to form a safe — and sane — alliance with all learners. If math class is to become a growth mindset place for all students, then it must first be established as a safe place in which to remove our masks and to return to being our deeper, authentic, creative selves.
To make any place safe for the authentic self to come out, it helps to have a structure in place. That way, the structure can provide the psychological and emotional safety (and freedom) in which we can drop down into our authentic selves.
In all forms of mindfulness meditation, this structure consists of three things: a posture, an anchor, and a timed period.
In Zen, we sit on a black cushion in the lotus or half-lotus position (or forward on a chair with both feet flat on the floor). We place our hands on our knees or in the cosmic mudra and we face a white wall. We lower our gaze to a 45-degree angle with the floor, and we anchor our attention on our breath.
Whenever our attention wanders — and monkey mind guarantees that it will inevitably wander — we gently redirect it back to our breathing.
The Vietnamese Zen teacher Thich Nhat Hanh teaches the use of a gatha, or mindfulness verse, as an attentional aid during meditation. With each in-breath or out-breath, one thinks a line of a simple verse:
Breathing in, I calm my mind.
Breathing out, I smile.
Dwelling in the present moment,
I know that this is a wonderful moment.
Which reduces to:
In,
Out.
Present moment,
Wonderful moment.
I’ll say this about Thich Nhat Hanh: you have to be a pretty evolved being to be able to teach this kind of clarity and sanity to the very countries that launched your own into chaos.
We do all of this for the whole timed period, whether it is ten minutes or 45 or an hour. Gradually, with patience and lovingkindness, we learn how to do this for longer and longer periods, until the timed period we are working with is every day for the rest of our lives.
We do this because this is our structure.
To the uninitiated, a structure might seem to be a rigid thing, but that is a misunderstanding, and I will tell you the secret: it is actually the essence of freedom.
It gives our defense mechanisms and our wounded child ego-self-psyche something important to do while we drop down into the vulnerable place where our authentic self is kept safe — beneath all those layers of protective functions, social masks, people-pleasing, snark, and our “on-stage” personas.
The structure makes it safe for a human being to reconnect with that deeper, authentic self.
So it is natural to experience a kind of euphoria afterwards. Our culture generally doesn’t encourage us to connect with our authentic selves, so when we do, many people experience it as a kind of homecoming. Intuitively, we know that it is the source of all our greatest ideas and energy and creative fire. Finally, it is a relief to drop the masks we wear and to just be fully and authentically ourselves.
The Enlightenment poet Friedrich Schiller described this experience of flow as arising from the competing impulses toward being present and toward thinking, which operate in a kind of luminous reciprocity, with their harmonious interaction producing a third impulse which he terms the Spieltrieb (or 'play impulse'):
Irresistibly seized and attracted by the one quality, and held at a distance by the other, we find ourselves at the same time in a condition of utter rest and extreme movement, and the result is that wonderful emotion for which reason has no conception and language no name.— Friedrich Schiller, Twelfth Letter on the Aesthetic Education of Man
When the mind is both fully at play and fully at rest in this way, it is at home.
And when this experience happens in math class, students are growing and truly experiencing mathematics.
This is the sanest, healthiest, richest, most creative human state I know — and I want all of my students to experience it in my math class. Only then can they connect with the growth mindset and the mathematics that are their birthright.
But the key to unlocking that moment is through structure. And for me, in my math classes, that structure is Talking Points.
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