Holy Grailing

‘But then how could they pass on the secret?’ Sophie asked.
   ‘That’s where the keystone comes in,’ Langdon explained. ‘When one of the top four members dies, the remining three would choose from the lower echelons the candidate to ascend as sénéchal. Rather than telling where the Grail was hidden, they gave him a test through which he could prove he was worthy.’ […]
   ‘So the keystone is a preuve de mérite,’ Sophie said. ‘If a rising Priory sénéchal can open it, he proves himself worthy of the information it holds.’
   Langdon nodded. ‘I forget you’d had experience with this sort of thing.’
   ‘Not only with my grandfather. In cryptology, that’s called a “self-authorizing language”. That is, if you’re smart enough to read it, you’re permitted to know what is being said.’

The Da Vinci Code (Brown, 2004, p. 279)

Seventeen children. Desks. Chairs. A supervisor. Me. Becoming- teacher glances at handwritten lesson plans on pages that refuse flattening. A soft cacophony of muted voices from all directions. Chairs making scratching sounds off beat. Backpacks hung on the backs of chairs. Seventeen pairs of eyes flickering. Markers in reach. A hand goes up. Someone wants help. Another child wants to say something. Giving one child the floor – someone else answers. A classroom assistant enters. Remember to go through today’s menu. Go through lesson objectives. The supervisor is looking –or not looking. What is next? Where to put one’s hands? Looking at the time. What are the children laughing at? 

The act of teaching, so effortlessly enacted by teachers, makes you forget the labor that goes into creating that illusion. For teaching is laborsome and the encounters during a single lesson countless. Just like standing in front of a class is a fragile space to occupy, more so when you yourself are a learner of the trade. During practicum, teaching therefore risks turning into a Brownian ‘keystone’, a teacher becoming ‘preuve de mérite’[1]. But teaching need not be a ‘secret’ where one must ‘prove oneself worthy of information’. Nor does teaching have to be an event where a becoming-teacher is assumed an already master ‘cryptologist’ whose use of a ‘self-authorizing language is expected to show they are smart enough to understand’; instead, teaching during practicum could be about creating openings that nurture learning.  

And from the look of it, there seems to be an arrangement in play that enables a form of ‘holy grailing’; an assemblage  where a becoming-teacher gets company to go treasure hunting in shared experiences and recycle recent pasts. In so doing, lost grails can be brought back into unfolding presents through the process here coined as holy grailing.

This mosaic maps all registered encounters during fifty minutes of a becoming-teacher’s first-time teaching solo, as part of a practicum lesson. By examining the first of two subsequent math lessons where a becoming-teacher is given the opportunity to teach the same lesson in two different classes, the map pinpoints encounters that post situ are turned into decisive moments for teacher- becoming. For it seems that during the act of teaching, navigating the myriads of encounters becomes a labor in itself that buries treasures underneath layers of intensity. But first, a look at the moment where becoming-teacher first introduces the preprepared math problem to the class.   

First Time Teaching Solo

The first solo teaching takes place during a practicum lesson in the subject math. The activity involves ‘problem solving’. The planned problem is shown and approved by the supervisor before class starts, whereafter becoming-teacher writes the targeted lesson objectives on the whiteboard:

Objectives:
Understand how addition and subtraction belong together.
Be able to use subtraction and addition when doing equations and problem solving ^[2].
(K, p. 2)  

To illustrate the relation between subtraction and addition, becoming- teacher writes a math problem next to the objectives. When the problem is paraphrased verbally, a child with years of training in school math immediately identifies the anomaly of the proposed problem:  

The ensuing problem is written on the whiteboard:

“The fair has had 3289 child visitors and 5706 adult visitors this year. Last year, there were 6045 child visitors and 2889 adult visitors. Which year rendered most visitors?”

Becoming-teacher asks the class what one needs to keep in mind when dealing with a math problem, and a child answers. Becoming- teacher paraphrases the question on the whiteboard: Which year had most visitors?

What do you mean?, a child asks before offering a revised version of becoming-teacher’s question: Do you mean, ‘what is the difference’? Becoming-teacher replies that it would be possible to calculate the difference but returns to the question about quantity. (K, p. 2)

Becoming- teacher’s question about ‘more or less’ is a problem ocularly available to the children, which can be solved without using subtraction. The child’s question about ‘difference’, on the other hand, necessitates both methods and illustrates the relation between addition and subtraction addressed in the lesson objective. But becoming- teacher does not identify what the child’s observation points at.

The situation becomes a Meno’s paradox; in other words, becoming-teacher does not know the knowledge not yet known as knowledge. Or is it perhaps a question of not noticing due to the affective intensity of the situation. Considering that there is a second round of teaching waiting around the corner, also targeting the relation between addition and subtraction, suggests that it is in everyone’s interest that becoming- teacher’s capacity to become affected by math is somehow augmented before the ensuing math lesson.   

Yet, one of the challenges with reality is that it never offers itself in intelligible chunks. Nor does teaching come with a sifting mechanism that alerts us to defining moments. Instead, teaching is a relational cryptology that demands what is here proposed as read-act-ing. That is, a mode of teaching which involves a continuous, active, and instant reading of encounters, while also including a capacity for acting on and with them.

Read-act-ing is exhausting since reality is neither tidy nor sequential. Furthermore, teaching is an activity that takes place in a thicket of relational nerves, entangling the becoming-teacher. The becoming-teacher is therefore never located outside events looking in. but acts from within messy bundles of affect where bodies brew in a chemical concoction of adrenalin, endorphins, and cortisol. An investigation of the math class is necessary to examine the conditions that make a child’s question go unnoticed, in other words what makes a ‘holy grail’ of teaching go unnoticed. The mapping is shown as a Lesson Cartography whichpresents all encounters during this first lesson.Why a cartography? Because a cartography offers a map that is “an experimentation in contact with the real” (Deleuze & Guattari, [1980]1987, p. 12). But first a look at the conceptual elements that build the cartography model, together with a presentation of the Deleuzian concepts we need to think about time in new ways.  

Conceptual Intuitions

Inquiring within what is referred to as ‘a one-world ontology of immanence’, means that one does not go outside events looking for explanations; instead, one stays examining what happens in the unfolding present. The questions explored through the Lesson Cartography are ‘what bodies are actualized through encounters, and who/what is engaged doing what’.

The math lesson is conceptualized as an assemblage, which means that there have been and are, unfolding processes of inclusion and exclusion. That is to say that some non/human bodies in shared space-times are actualized as resources, whilst others are dismissed. A classroom can therefore contain bodies not enacted as resources; thus, what there is is not the same as what becomes actualized as being there. And what is actualized during a math class is what is at stake here.

In the two stripped versions of the cartography below, we begin exploring necessary concepts (duration, encounter, and cartography), thereby aiding an understanding of how they will be employed in the third, fully-fledged cartography. One step at the time we examine the cartography from different angles and through different concepts to make sense of the third visual where we examine what is going on during math class.

Duration

The conventional representation of time is as a straight line that indicates progress, and where the past is left behind. The duration of the actualized math lesson, however, is here shown as a circular enveloping of time where the present encapsulates the past:

[T]he present is not; rather, it is pure becoming, always outside itself. It is not, but it acts. Its proper element is not being but the active or the useful. The past, on the other hand, has ceased to act or to be useful. But it has not ceased to be. […] [I]t IS, in the full sense of the word. ([italics in original] Deleuze, [1966]1988, p. 55) 

The outer yellow line in the below disc (Illustration 1) shows becoming-teacher enacting the present. During the math lesson, becoming-teacher affects and becomes affected by other bodies doing, saying, and moving. As the later and detailed Lesson Cartography will show (Illustration 3), these doings, utterances, and movements stay with the lesson in the form of non-/material traces – a past that IS in the present where bodies ACT.

Illustration 1: Becoming-teacher and unfolding present

A present shown as enveloping the past actualizes key ontological underpinnings by making visible how transient bodies such as ‘utterances’ and ‘actions’ become potential resources to utilize in later presents. Note also that when the circle becomes flipped over, we end up with a line where the present is double-arrowed rather than one-directional.

Duration shown as a circle also visualizes how math lesson as an assemblage entails a territorialization of a shared space-time; available resources in a space – when territorialized (enacted as part of math class) – turn into material conditions of creativity. If there is no projector, which is the case here, one ought not to speak of its absence as a lack. Rather, there being no projector is just one of the many particularities of this assemblage.    

Deleuze’s Bergson explains that “[t]he present is only the most contracted degree of the past, matter the most relaxed (détendu) degree of the present (mens momentanea)”, ([italics in original][1966]1988, p. 75[3]). Another way to say this is that materiality is the past encountered in the present. The past becomes unescapable. Tables, supervisors, and books, last. And that which lasts we interact with in the present. The present is also where new bodies are produced; like what becoming-teacher ‘writes on a whiteboard’, or children’s ‘questions’, and becoming-teacher’s ‘instructions’, all examples of expressions that become ‘bodies’ with affective capacities. 

Encounters

When a body "encounters" another body, or an idea another idea, it happens that the two relations sometimes combine to form a more powerful whole, and sometimes one decomposes the other, destroying the cohesion of its parts. (Deleuze, [1981]1988, p. 19)

Each encounter with another body, may it be questions, children, or books, has the capacity to give rise to an augmentation or diminishing of affective capacities. The illustration below presents the same disc as in the above illustration (Illustration 1), only this time it is flipped over so that we can look at it as a cross-cut. The cross-cut shows how affective encounters either increase or diminish becoming- teacher’s capacities in the unfolding of the present:

Illustration 2: Diminishing and augmentation of affect in encounters.

Were intensities not virtual and as such non-observable, they might look something like the fluctuations in the above illustration. We must think of encounters as creating such differences in ‘intensity’[4]. What is monitorable are the effects of affect, and this is what the ensuing cartography offers.

Some human bodies, comments, sounds, or materials, have greater affective capacities than others and would, in our fictitious cross section, therefore generate steeper peaks or lows. But affect is not only virtual, as it can also entail what Deleuze and Guattari conceptualize as a kind of microperception ([1980]1987), or what Massumi speaks of as ‘shock’: this is “not smaller perception, it’s a perception of a qualitatively different kind. It's something that is felt without registering consciously. It registers only in its effects” (Massumi, 2015, p. 53). That is to say, we must not think of all affects as conscious events, instead

the model of the body, according to Spinoza, […] [is] a devaluation of consciousness in relation to thought: a discovery of the unconscious, of an unconscious of thought just as profound as the unknown of the body. ([italics in original] Deleuze, [1981]1988, pp. 18-9)

The body therefore has capacities beyond what we can ever know about a body, including ‘an unconscious of thought’ that exceeds conscious thought. We must also remember that the Deleuzospinozian “body can be anything”, and that it entails “relations of motion and rest, of speeds and slownesses”, together with its singular capacity to affect and become affected (Deleuze, [1981]1988, p. 123).

Cartography

The challenge is to rethink the present, not as encounters between pre-defined entities but as a navigation in a non-chunked chaos where we act in pre-conscious affective states. Lines illustrate potentialities, because “in the instant of the affective hit, there is no content yet. All there is is the affective quality, coinciding with the feeling of the interruption, with […] felt transition” Massumi states (2015, p. 54).

Mapping encounters in a lesson cartography thereforeinvolves paying attention to the ‘speeds and slownesses’ of a body together with its ‘affective capacities’. These two aspects, one kinetic the other dynamic, constitute the longitude and latitude of a body,    

the sum total of the material elements belonging to it under given relations of movement and rest, speed and slowness (longitude); the sum total of the intensive affects it is capable of at a given power or degree of potential (latitude). […] Latitude and longitude are the two elements of a cartography. (Deleuze & Guattari, [1980]1987, pp. 260-1)

To repeat, creating a cartography of the math class therefore offers a map that is “an experimentation in contact with the real” (Deleuze & Guattari, [1980]1987, p. 12) where we can examine how math class works.  

In the light of what Massumi (2015) speaks of as the content-lessness of the ‘affective hit’, it becomes easier to understand how a child’s question about ‘difference’ in the moment it is uttered could be seen as content-less. It is not an ‘insightful question’ but has the potential to become an ‘insightful question’. As such, it might augment becoming-teacher’s capacity to teach math. Encounters during teaching are thus an experience that entails what Manning speaks of as a ‘not-quite-yet’[5], a potentiality never fully exhausted:

Pure experience is on the cusp of the virtual and the actual: in the experiential register of the not-quite-yet. […] [P]ure experience is the in-folding of potential that keeps actual experience open to its more-than. The virtual is never the opposite of the actual—it is how the actual resonates beyond the limits of its actualization. (Manning, 2015, p. 55)

‘Not-quite-yet’-ness therefore points at the always present ‘more-than’ of the math event. The ensuing cartography is therefore a semi-stabilization, a retrospective creation that presents experiences that involve facing the sensed but never entirely known. And the never entirely known, is what monitored bodies courageously maneuver. Now to the Lesson Cartography.

A Lesson Cartography

The Lesson Cartography comprises all registered encounters during a fifty-minute math class, in which a becoming-teacher teaches solo for the first time. The solid lines that connect to becoming-teacher’s outer yellow line are registered encounters where becoming-teacher becomes affected and is seen read-act-ing another body. Dashed lines indicate affects that are registered moving through the classroom without monitorable effect on the becoming-teacher[6] (BT). Below the illustration, a list of symbols indicates what bodies are actualized through encounters (symbols), and who/what (color) is doing what (symbols).

Illustration 3: A Lesson Cartography

Holy Grailing Shared Pasts

In the tangle of encounters interrupting and making cuts in becoming- teacher’s present, there is one line in the above Lesson Cartography (Illustration 3) that is particularly intriguing:   

Illustration 4: Holy Grailing as a Line of Flight

The process examined in the above close up (Illustration 4) of the Lesson Cartography, is the encounter where the supervisor approaches the becoming-teacher after the just finished introduction. Let us see what the supervisor says to becoming-teacher in this encounter to get a better idea of what happens when the red line in the Lesson Cartography forks and connects becoming-teacher to supervisor and a child’s question:  

The supervisor approaches becoming-teacher and talks about what questions to ask and in so doing gestures towards the child who asked the question ‘What is the difference?’. The supervisor then adds that one could also have asked the class ‘What calculation method [should they use]?’. Becoming-teacher nods smilingly toward the supervisor, and immediately walks away to make notes in a notebook. (K, p. 3)

The zoomed encounter shows how a supervisor in an unfolding present points back at a child’s question and explains why it was an important question. In so doing, the supervisor recycles becoming-teacher and supervisor’s shared past (the lesson introduction), and engages in what is here proposed as ‘holy grailing’ (the red supervisor-line travels from the [information-symbol] and creates a second connection next to the existing green child-line [questionmark-symbol]). The ‘holy grail’ retracted is knowing children’s questions as a source for further knowledge-ing[7]. It is also the process itself that is of interest – of being shown how to activate the past as a resource for knowing. In short, the supervisor supervises a becoming-teacher by retracting a holy grail from a shared recent past and recycling it in the present. The question now is, what conditions enable the unfolding of such ‘holy grailing’? What can we learn from exploring fifty minutes of math through a Lesson Cartography?     

Matter becomes Math Material

“How and under what conditions does matter become material”, Buchanan asks (2021, p. 131), and an answer offered through the Lesson Cartography (Illustration 3) is that matter becomes lesson material through proximity. Mappings(Illustration 3) show how nerves connect from all directions, cutting and sowing encounters to the yellow becoming-teacher membrane, “[f]or the underlying activity is a push that pulls” (Manning & Massumi, 2014, p. 24). The cartography names becoming bodies and plot them by following the processes where a wood-led-stick becomes ‘pencil’-material, and a voice-sound becomes ‘question’-material. What is available in the classroom therefore has the potential to become part of the arrangement when bodies use them as part of their math class. A math key hidden in a bag, for instance, becomes math material and yet another body to ally with that can augment a becoming-teacher’s capacities to do a math-teacher (more about the affective powers of a math key in Deleuzian Ontology in Education). 

Time Hiccups

Lines bifurcate, nestle, push-pull entire webs of relations. The linearity of actualizing the preprepared lesson plan becomes disheveled as minor events such as keys around a becoming- teacher’s neck, clinking on a table, intervening in a becoming-teacher’s movements in space (takes a hand, grabs the keys to stop the sound). Affective encounters work against structure, by enfolding, unfolding, and refolding bodies. Chronology begins hiccupping and the linearity of time coils as bodies’ shared past becomes a resource for learning.

Whilst timelines push in one direction, implying progress and leaving what was behind, we may note that a whiteboard hangs there not merely after the encounter, but before. The whiteboard lingers. Just like doorways, laptops, pupils, and curricula neither appear nor disappear. Stating the obvious is a way of pointing out two things: that encounters during fifty minutes of teaching rely on availability (actual side of reality), and that there is a simultaneity where what was also is and has the capacity to become (virtual side of reality). The past coexists with the present.

There are thereby things and people encountered during todays’ math lesson that existed long before becoming-teacher came into teaching and that outlasts today’s teaching – may come to outlast becoming- teacher, even. But there is also non-material bodies produced in the course of the lesson that can have lasting effects, like a child’s question about ‘difference’. But in order to bring back a transient statement made a few minutes ago to the present requires that someone actualizes this part of the past, like when a supervisor goes holy grailing in a shared recent past.  

Read-act-ing

Performing the human body is a labor that requires organizing gaze, gesture, voice, pose, emotion, thought, breathing, with material extensions in the public eye of an entire class; all whilst trying to plug into the seventeen learner machines engaged in similar processes. Teaching thus requires arranging the affectively charged tangle in a striated institutional space. Put differently, teaching turns into a relational cryptology that requires read-act-ing rather than re-acting in encounters.

But each encounter is also a ‘bodily microperception’, an “affective re-beginning of the world” (Massumi, 2015, p. 54). Each encounter becomes a labor that sets off a re-beginning:

The change in focus, or a rustle at the periphery of vision that draws the gaze towards it. In every shift of attention, there is an interruption, a momentary cut in the mode of onward deployment of life. The cut can pass unnoticed, striking imperceptibly, with only its effects entering conscious awareness as they unroll. (Massumi, 2015, p. 53)

As encounters overlap, pile, and mix, it is up to becoming- teacher to identify threads of importance in a split second of ‘not-quite-yet’-ness (Manning, 2015). And becoming-teacher will be the metric that actualizes some bodies as competent while others, of similar potential, go under the radar because of limited affective capacities in that particular moment.    

The Politics of Supervision

There is a ‘politics of affect’, Massumi explains:

Politics, approached affectively, is an art of emitting the interruptive signs, triggering the cues, that attune bodies while activating their capacities differently. Affective politics is inductive. Bodies can be inducted into, or attuned to, certain regions of tendency, futurity and potential, they can be induced into inhabiting the same effective environment, even if there is no assurance they will act alike in that environment. (Massumi, 2015, pp. 56-7)

Massumi discusses ‘affective politics’ in the context of an alarm going off. Bodies in that shared ‘affective environment’ of the alarm-event “respond differently together” to the alarm-as-threat; this ‘to respond differently together’ and its sum total variation of difference in their responses, is the ‘political’ dimension of the situation (2015, p. 57). Thus, it is a joint read-act-in the alarm-as-threat, that becomes political insofar as it sets off affective responses that vary according to certain regions of tendency common to their assemblage.  

In the case of holy grailing, similarly, a supervisor triggers children’s questions to be read-act-ed in particular ways. Supervision is an affective politics. Becoming-teacher is learning to become attuned to children’s questions as affective holy grails. Said differently, the supervisor inducts becoming-teacher in the art of staying attuned to children’s question as ‘regions of tendency, futurity, and potential’, as Massumi (2015) phrased it. Perhaps this kind of affective politics might be a desirable alternative to the Brownian ‘preuve de mérite’? So as the supervisor’s red-line re-activates the child’s green-line (see Illustration 4), the circularity of time is broken by drawing a line of flight “to open onto a future” (Deleuze & Guattari, [1980]1987, p. 311).      

Epilogue

The second math lesson is about to begin. Becoming-teacher has written the lesson objectives and the math problem on a new whiteboard in a different classroom. Fourteen children are waiting, the supervisor observes. Becoming- teacher starts the introduction, asks:

‘What calculation method should we use?’ […] Continues asking, ‘What is the difference between the number of visitors between this year and last year?’ (K, p. 3)

 

References

Brown, D. (2004). The Da Vinci Code. Corgi.

Buchanan, I. (2021). Assemblage theory and method: an introduction and guide. Bloomsbury Academic.

Deleuze, G. ([1966]1988). Bergsonism. Zone.

Deleuze, G. ([1981]1988). Spinoza, practical philosophy. City Lights Books.

Deleuze, G. (1989). Cinema: The time-image. University of Minnesota Press.

Deleuze, G. & Guattari, F. ([1980]1987). A thousand plateaus: Capitalism and schizophrenia. University of Minnesota Press.

Manning, E. (2015). Against method. In P. Vaninni (Ed.), Nonrepresentational methodologies: Re-envisioning research (pp. 52-71). Routledge.

Manning, E. & Massumi, B. (2014). Thought in the act: passages in the ecology of experience. University of Minnesota Press.