Beyond equality and inequality in education : Bakhtinian dialogic ethics approach of human uniqueness to educational justice

In our essay, we challenge the hegemonic Kantian discourse of defining justice as equality (in a broader sense) and injustice as inequality in education (and elsewhere). We argue that this discourse is based on the underlining assumption of replaceability and measurement of people and of educational practice itself. In contrast, we argue that people and their education are unique. Thus, it is necessary to develop an alternative notion of justice based on uniqueness and immeasurability of people and their education. We found that Bakhtin’s dialogic ethics framework is helpful for developing such an alternative approach. According to the Bakhtinian dialogic ethics, people are engaged in self-contradictory deeds, charged with ethical tensions. These ethically problematic deeds must be challenged by others and the self in critical dialogue and must demand responses by the authors of the deeds striving to achieve justice. Taking responsibility is not merely a discursive process of answering – it is not “answerability” – but rather another ethic deed of defining ethically good or bad, defining quality and values, accepting blame, standing grounds, committing to fixing negative consequences, emotional sympathy, and so on. The process of challenging people’s deeds in critical dialogue and their taking (or not taking) responsibility defines (in)justice of people’s deeds. We examine two cases of educational injustice based on the Bakhtinian dialogic ethics framework of uniquness. We try to show that education and its justice are essentially authorial and, thus, unique processes. Even when justice involves measurable things like money, it is still about unique people with unique educational goals, interests, and needs in unique circumstances that these measurable resources afford. We consider a case of allocation of measurable resources as a compromise between the Kantian formulistic and the Bakhtinian dialogic ethics approaches. We conclude our essay with developing a vision for a just educational practice based on students’ academic freedoms for authorial education. Eugene Matusov is a Professor of Education at the University of Delaware. He studied developmental psychology with Soviet researchers working in the Vygotskian paradigm and worked as a schoolteacher before immigrating to the United States. He uses sociocultural and Bakhtinian dialogic approaches to education. His recent books are: Matusov, E. (2017). Nikolai N. Konstantinov’s authorial math pedagogy for people with wings, Matusov, E. & Brobst, J. (2013). Radical experiment in dialogic pedagogy in higher education and its Centauric failure: Chronotopic analysis, and Matusov, E. (2009). Journey into dialogic pedagogy. Ana Marjanovic-Shane is an Independent scholar in Philadelphia, USA. She studies meaning making in human development, dialogic educational relationships and events, democracy in education, dialogic ISSN: 2325-3290 (online) Beyond equality and inequality in education Eugene Matusov, Ana Marjanovic-Shane Dialogic Pedagogy: An International Online Journal | http://dpj.pitt.edu DOI: 10.5195/dpj.2018.236 | Vol. 6 (2018) E2 teacher orientation, the role of imagination, drama, play and critical dialogue in education. In her studies, she is developing a dialogic sociocultural paradigm, inspired by a Bakhtinian dialogic orientation. Her articles were published by "Mind, Culture, Activity Journal", "Learning, Culture and Social Interaction", and as book chapters in books on play, education, and democracy. Her most recent publication is: Marjanovic-Shane et al, (2017). Idea-dying in critical ontological democratic dialogue in classrooms. Learning, Culture and Social Interaction.


Introduction
The purpose of this editorial essay is to discuss the notion of educational justice, criticize the mainstream Kantian discourse on educational justice as a discourse on equality or inequality of educational outcomes, and propose a new definition of educational justice based on the Bakhtinian dialogic ethics framework of human uniqueness (Bakhtin, 1999;Matusov, 2009, ch. 5;Morson & Emerson, 1990).At the beginning of this essay, we define the notion of educational justice heuristically as a feeling of (in)justice about one's education, experienced by the participants or observers of this education.This definition is intentionally vague to engage proponents of the mainstream definition of educational justice as (in)equality of measured educational outcomes and/or educational funding (e.g., grades, test scores, diplomas, certificates, employment, student expenditure).Later in the essay, we clarify and fully develop our definition of educational justice.We criticize the mainstream definition of educational justice based on the discourse of equality and inequality and discuss why it has been so prevalent in the past and currently, but not necessarily in the future.

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In the paper, we discuss the conceptual problem of the equality/inequality approach to educational justice.We argue that this approach emerges from viewing students (and teachers) as people with replaceable, transparent, and measurable consciousnesses.We offer an alternative vista of students (and teachers) as unique, opaque, and unfinalizable consciousnesses (Matusov, 2015a).We develop the latter concept using an educational case of teaching first graders 2+2=4.Based on the new vista of human uniqueness, we introduce a new paradigm of the ethical dialogic justice rooted in Bakhtin's framework.Using this new paradigm of justice, we analyze two problematic cases of educational injustice.We consider complex dilemma of just distribution of resources for education from this new paradigmatic vista.Finally, in conclusion, we discuss the notion of a just educational practice from the Bakhtinian dialogic ethics framework of human uniqueness.

Problems with educational equality justice: "All children are above average"
The mainstream definition of educational justice through (in)equality is based on the discourse of equal (or unequal) quality of educational outcomes and conditions (e.g., "Educational justice is nothing less than passing the [same] knowledge [to each and every student] that makes for a level [even] playing field in the [future] competition for life's resources and rewards" 1 ).It involves two major phases of the equal distribution of goodness: 1) establishment of the rigorous criteria of educational quality in advance, i.e., defining educational goodness (e.g., particular knowledge that is necessary for the future successful "competition for life's resources and rewards"), and 2) assuring achievement of the same educational outcomes for all students (i.e., making for a level [even] playing field in the [future] competition for life's resources and rewards).
From the proponents of this mainstream view, the rigorous quality of educational outcomes and conditions has to be defined first by the society through political, academic, bureaucratic, philanthropic, publishers of testing and curricular materials, and practitioner means.Politicians make laws defining the rigorous quality of education, based on wishes and demands of political stakeholders (e.g., employers, parents, academicians, teachers, educational agencies, professional unions and organizations, bureaucrats, taxpayers, religious organizations, philanthropists, corporate lobbyists), political struggles, means to promote it, and means to enforce it.The two recent educational reforms in the United States: 1) No Child Left Behind (NCLB) under President George W. Bush (2002) and 2) Race To The Top (RTTT), involving the Common Core State Standards (CCSS), under President Barak Obama (2009) are the most dramatic examples of political means to define the quality of educational outcomes.
Academicians are involved in academic scholarship discourse defining the rigorous educational quality through research, evidence, reasoning, paradigmatic wars and so on.For example, academicians have launched a series of concepts defining the quality of educational outcomes, such as: "best practices," "research-based practices," "evidence-based practices" and so on often borrowing these notions from the mainstream medical research (D. H. Hargreaves, 1996Hargreaves, , 1997)).
Educational officers, staff, and functionaries work to interpret, organize, and implement political mandates enforced on them.For example, governmental departments/ministries of education and even some local educational institutions are often involved in defining a list of core knowledge, skills, and competencies that teachers and students must master to be institutionally credentialed (e.g., a Grade 1 math competency is defined as: "Represent and solve problems involving addition and subtraction" 2 ).
The second phase of the mainstream approach to educational justice is ensuring equality of educational outcomes.Some educationalists argue that it is better to express this point with the notion of "equity" rather than "equality.""Equality," in this narrow sense, is defined as treating everybody equally.Meanwhile, "equity" is referred to as "giving everyone what they need to be successful 6 " to achieve the same outcomes.Some proponents of equity like to illustrate this notion with the following famous cartoon depicting the contrast between equality of treating the same and equity of achieving the same outcomes: For our discussion, we do not need to distinguish between the notions of "equity" and "equality" because the mainstream equality-based approach to educational justice focuses on the equality/sameness of the treatments, opportunities, or educational outcomes as its goal defining educational justice.
In practice, the equality of educational outcomes is manifested in and operationalized by a widespread discourse on "educational achievement gaps" -e.g., inequality of standardized test score results for different social groups (e.g., male vs. female students, African-Americans vs. White students) (for example, see Haycock, 2001).Other educational achievement gaps may involve unequal statistics regarding the distributions of school dropout, diploma, subsequent employment, college enrolment, educational degrees, grade retention/repetition, and so on among these social groups.As advocates of the notion of equity argue, achieving the same educational outcomes by different students may require different treatments, different guidance, different resources, different conditions, and different schedules of arrival at these same preset educational outcomes.Probably, this idea has been mostly realized in the area of special education, where American teachers are supposed to develop the Individual Educational Plan (IEP) for each student with a diagnosed disability and revise it on a regular basis (e.g., McLaughlin, 2010).
Elsewhere, one of us (Matusov, 2011b) has criticized this mainstream educational justice approach based on the (in)equality discourse.He developed four major critiques.First, the notion of "rigorous high quality of education" contradicts the notion of "educational equality/equity" and, thus, makes it unachievable.Second, just education cannot be based on equal educational achievement in principle.Third, presetting curricular endpoints cannot define the quality of education.Fourth, the student is the highest authority for defining the quality of his/her education.Based on the quote from David Graeber, with which we started our essay, we are adding the fifth critique here.We argue that education of each student is unique and cannot be measured.
In his article, Matusov argues that rigorous high quality of education contradicts equality/equity of educational outcomes because the notion of rigorous educational high quality is based on inequality,

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The high-level educational standards are set up through normalization of the targeted population of the students: If too many of the total targeted students (e.g., all third graders in the United States) pass the standard, the standard might be considered too easy and too low [i.e., not rigorous] and [thus] has to be moved up by making it more challenging, thus failing more students.... [Similarly], when too many of the total targeted students fail the standard, the standard might be considered too high and insensitive (what some might term developmentally inappropriate) and it would be adjusted to let more students to succeed in the future … (Matusov, 2011b, p. 1).
Thus, quality is defined by the proportion of accepted inequality: how many students have to fail or succeed for it to be rigorous high-quality education."There is a catch-22 as the concerns for equality and quality in the high-stake assessments annihilate each other (Taubman, 2009)" (p. 1).This contradiction of equally distributed high educational quality, which in itself is defined by inequality, in the modern approach to educational justice was sarcastically criticized by the former NPR host of the show "A Prairie Home Companion" Garrison Keillor who always finished it with "the news from Lake Wobegon, where all… the children are above average." Matusov's argument continues that even when all social groups equally succeed and fail on some "rigorous" tests, it cannot constitute just education (even from the mainstream point of view).Let us provide an extensive quote of this argument.It starts with the following example of previously "resolved" educational inequality, …we know that there are no vestiges of educational problems with previously oppressed immigrant minorities in the United States (such as descendants of Irish, Polish, and Italian immigrants), since their high-stakes test results are not much different from those of other White students (Ogbu, 2003).So, [following this example] all social groups [must] have nearly the same rate of success (and failure) with the high-stakes achievement tests for a system to be "fair" and "working well."Such an educational system could be said to realize the spirit of equal opportunities, prevent social stagnation, and promote social mobility in each social group.
I argue that this is a rather honest, although unachievable, … [mainstream] account of educational equality.I call this … account honest because it is driven by sincere concerns about social stagnation and fragmentation within the society (Labaree, 1997).I call it unachievable because it has many internal and external problems and contradictions.… [The main contradiction involves the following reasoning: imagine] if the social groups with equal proportional presence are reshuffled, [then] the achievement gap emerges again.Indeed, if social groups A, B, and C (e.g., middle-class Whites, Blacks, and Latinos) have the same rates of success on a high-stakes test, all at 80%, then it is possible to develop new social groups X and Y by placing all students from the A, B, and C groups who passed the test into group X (i.e., the group of absolute success with 100% success) and those who failed in the group Y (i.e., the group of absolute failure with 0% success).Critics might protest this reshuffling, arguing that these new groups are not like known social groups (those based on ethnicity, race, socioeconomic status, gender, and so on) that have their own cultural values and practices but are instead purely mechanical aggregates that do not represent any social reality and culture.However, students who experience institutional success and students who experience institutional failure on a systematic basis tend to flock together into stable social groups and cultures (Eckert, 1989;Ogbu, 2003).It seems that group equality can be achieved only through [individual-defined justice] with the total absence of educational failure.Thus, the "no child left behind" slogan (not G. W. Bush's policy!) requires the total absence of E7 educational failure rather than closes the achievement gaps among existing diverse social groups (Matusov, 2011b, pp. 2-3).
His second critique is that setting the same educational outcomes for all students is educationally unjust."Students have diverse educational needs, interests, learning paths, and learning paces.There is no one existing psychological or pedagogical theory that predicts that children with the same chronological age and exposed to one good instruction can all learn the same preset curriculum at the same time" (p.3).
Even more, in the third critical point, in just education curricular endpoints emerge in practice rather than can be preset.Matusov argues that preset curricular goals distract the student from the practice and its learning itself: … when a young child speaks unclearly for parents or peers outside of conventional schools, efforts are usually made to help the child get through and to understand the message.In this case, the conventional form of the child's message emerges as a mere by-product of the parent's or peer's pragmatic understanding efforts (even when they use direct correction) (Rogoff, 2003).
[Here, the success of communication is negotiable and defined by the participants themselves.]In contrast, in conventional schools the teacher's focus is on making the child arrive at the conventional correctness of the form of the message rather than on [the meaning of] the message itself.Thus, in conventional education, conventional correctness of the form is a self-contained goal (Matusov, 2011b, p. 5).
When the goal of the student's activity becomes achieving preset curricular endpoints, the practice loses its meaning for the student.To continue this example of young children learning to speak, when the focus of communication becomes making the student's speech conventionally correct, the student loses his/her focus on the meaning of the communication and on voice.In practice, speech conventionality primarily serves communication comprehension.However, in conventional school, the relationship becomes distorted: communication comprehension is sacrificed for the sake of the accuracy of conventionality.Thus, in one second grade conventional classroom, a child wrote, "Im diprsd," and the teacher started immediately correcting the child's inventive spelling instead of addressing the disturbing meaning of the message7 .In contrast, in an innovative classroom running as a community of learners, a third-grade teacher overheard her two students being puzzled over their computer's reports about their spelling results.Both of the students made only one spelling error but their computers reported 95% versus 94% of accuracy.They thought that the computer might have made a mistake.The teacher used this opportunity to engage the whole class in a discussion of proportions and percentages, which became an emergent math curriculum in a spelling and typing lesson (Drier, 2000).
Fourth, Matusov argues that the student is the highest authority for his/her education (Klag, 1994) defining its quality, "In democratic education, what is educationally good for the students has to be rooted in the students -in their interests, strengths, and needs -and embedded in the socially desired practices (Dewey, 1956)" (Matusov, 2011b, p. 5).Educational quality cannot be based on "the state bureaucrats' defining the curriculum standards, as it is in mainstream schools, or in the teachers' consideration of 'big ideas,' as it is done in many innovative schools (Smith, 2010)" (Matusov, 2011b, p. 5).The idea of the students' defining the quality of their own education is rather controversial because

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students are often viewed as ignorant by definition -not always knowing or even being able to know the goals of their education.In his article, Matusov addressed this important concern by pointing out that students' education has always involved critical examination of this education in itself, A counterargument that students are not ready to define the goals of their own education because they are not equipped with the right skills and knowledge is similar to arguments against democracy as a whole: that common citizens cannot govern themselves because of their ignorance and incompetence, and only a well-informed and skillful elite is competent for governance (Plato & Waterfield, 1993).A response to this counterargument is that the democratic process of governance is also an educational process-in order for it to be viable, it demands from people decision making and guidance (Dewey, 1966;Greenberg, 1992) (Matusov, 2011b, p. 6).
This educational process of the student defining the quality and goal of his/her own education can be assisted by the teacher.
Finally, we have arrived to our own point, the fifth critical point, informed by the work by David Graeber (2013Graeber ( , 2014)).We argue that education is authorial and unique for each and every student and moment and, thus, it cannot be measured.We will develop this argument in the next section.

Why both education and students are unique
Together with Osberg and Biesta (2008) and Lobok (2017), we argue that genuine education, which is based on meaning making, is unique.This uniqueness of education is based on the uniqueness of its participants -the students and the teachers acting, living, and making sense in unique circumstances and relationships.Proponents of the mainstream education may also argue that they appreciate the meaning-making process (along with drills of skills and tacit socialization based on pattern recognition and production).However, their appreciation of the meaning-making process does not necessarily imply its uniqueness.A conventional understanding of meaning is based on the idea that meaning is rooted in statements.The very reason for why standardized exams and tests are possible is that they can legitimately check if diverse people have the same stable meaning by producing the same (correct) statements or not (Osberg & Biesta, 2008).
In contrast, Bakhtin disagreed that any statement or utterance has its internal self-contained meaning, "An utterance is never just a reflection or an expression of something already existing and outside it that is given and final.It always creates something that never existed before, something absolutely new and unrepeatable, and, moreover, it always has some relation to value (the true, the good, the beautiful, and so forth)" (Bakhtin, 1986, pp. 119-120).He argued that meaning is a relationship between a question genuinely searching for an answer and a serious reply to it.
By meanings I understand answers to questions.That which answers no question is meaningless to us8 .… The responsive nature of contextual meaning.Meaning always responds to particular questions.Anything that does not respond to something seems meaningless to us; it is removed from dialogue.Contextual meaning and formal [dictionary] definition.Formal [dictionary] definition is removed from dialogue, but it is deliberately and conventionally abstracted from it.It contains potential meaning (Bakhtin, 1986, p. 145, italics is original).

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According to Bakhtin, the relationship between the authentic question and serious answer cannot be reduced to a mere logical relationship that can exist in one consciousness, but it is a social, dialogic, relationship between different consciousnesses, Question and answer are not logical relations (categories); they cannot be placed in one consciousness (unified and closed in itself); any response gives rise to a new question.Question and answer presuppose mutual outsideness.If an answer does not give rise to a new question from itself, it falls out of the dialogue and enters systemic cognition, which is essentially impersonal (Bakhtin, 1986, p. 168, italics is original).
Thus, meaning has always a social, emergent, contextual, and unique nature.It always is ephemeral, non-tangible, and exists here-and-there (Osberg & Biesta, 2008).It is always open and unfinalizable.It cannot be repeated.It is always creatively co-authored, Meaning is always unique and unrepeatable… Meaning always has authorship rooted in a) its unique addressivity and responsivity and b) dynamic networks of relations with other meanings.For example, such a simple mathematical fact as 2x2=4 addresses and responds to many explicit and implicit questions that the person might have in mind, like "what does it mean?","why bother to think about it?","why now?", "why doesn't 2x2=5 or 3 or any other number but 4?", "under what circumstances does 2x2 equal 4?", ["what does equal mean?"], "what does 'multiplication' mean?", "why do people use multiplication?","can I avoid it?","why did the author of the article bring this particular example?", "what is it going to do with me?", "who cares about 2x2=4?", "why don't we go to see movies rather than focus on this 2x2?" and so on.The number of such questions is unlimited, situational, and dynamic.Similarly, the math fact of 2x2=4 is always in relationships with many other activities and practices (math and non-math based).For instance, it connotes with a popular phrase, "it is as clear as two by two" which does not necessarily have mathematical meaning.Mathematically, 2x2=4 can be reworked as power 2 2 =4 or as addition 2+2=4, which is probably unique for the relationship between twos (is it?).Geometrically, it can be represented as a search for the area of a 2 by 2 square.I have a good memory of learning multiplication in my elementary school.It reminds me [of] my classmate friend in the second grade whom I taught successfully the concept of multiplication.The math fact 2x2=4 both triggers and is supported [by] these chains of my personal memories.…although [the] meaning [of 2x2=4] seems "self-contained," in actuality, [it] is unique, limitless, contextual, dynamic, and very personal (Matusov, 2009, p. 119).
Dialogically meaningful education is always eventful.It involves dramatic unique events, in which a genuine encounter of different consciousnesses occurs (Lobok, 2014).The following example from our (the first author's) pedagogical practice illustrates this dialogic unique eventfulness in such an encounter.
Math drama: Is 2+2 always 4?9 I (the first author) was always interested in learning disabilities.When two of my undergraduate university education students, future teachers, invited me to visit their teaching practicum classroom to observe a first-grade boy with "math disability," I immediately accepted their invitation.Math disability!What was it about?My students told me that the boy had "a math logic disability" as he could not

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understand the simplest arithmetic calculation operations like addition and subtraction even with single digits, despite repetitious exhaustive instruction.I was intrigued.
I arrived at the school around 10:30am and after some brief security procedures of signing up as a visitor from the university, I was directed to the first grade classroom.My students were already there waiting for me and the teacher nodded at me in acknowledgement.The classroom was full of sunlight.It was a rather spacious room for 19 students, who were sitting in clusters of four at individual desks facing each other.The children did not pay much attention to me, perhaps being accustomed to visits by adult strangers.They were busy working on math worksheets that the teacher gave to them.The teacher was sitting next to one of the cluster groups, discussing something with one of the children there.My undergraduate students pointed at a boy sitting at one of the desks in a cluster.I moved to stay in close proximity to his cluster to observe and hear the children's work and conversations.
The children of his cluster -two boys and two girls -worked silently and independently on their math problems on their worksheets at their own pace.The boy selected the next problem "1+4=", turned to the girl, sitting next to him and working on her problems, and silently showed her the problem with his two fingers.The girl briefly glanced at the written problem and replied, "Five."The boy nodded in appreciation, turned back to his desk, and carefully drew the correct number on his worksheet.He picked up the next problem in a column, "3+2=" with his fingers and turned again to the girl.She glanced again and said, "The same."The boy nodded in appreciation, turned back to this desk, and drew the number five.The next problem was "2+2=".I waited until the girl replied "four" and asked her, "How do you know that?How do you know for sure that two plus two equals four?"The other two kids looked at me with an interest and so did the boy.The girl smiled self-assured and with anticipation of a triumph, as apparently, she heard this question before and was ready to shine with the correct answer expected by adults.She drew two lines on her own worksheet below the math problems she had to solve and then other two lines, slowly counted them, and declared almost with triumph, "Four!Two and two is four."I glanced at the boy -he looked perplexed.His perplexed look guided me to push forward.I replied to the girl, "Yes, two lines plus two lines is four lines.But, I didn't ask you about the lines.I asked you about two plus two."The boy turned to the girl as if it was him who was asking this question and not me.My question did not perplex the girl in any way.She picked two pencils from her pencil case and then two more and counted the pencils, "Four."She smiled at me.But, the boy was not moved by her pencil reply.Again, I pursued my investigation, "Yes, four pencils.Two pencils plus two pencils is four pencils.I can see it.But I asked you about numbers, not pencils."She stopped smiling and replied without any doubts, "It doesn't matter.Two plus two is always four.It does not matter what to count."The other two kids in the cluster were attentively listening to our conversation.The boy turned to me.It seemed to me that he was not satisfied with the girl's answer but did not know how to challenge her.I asked the girl, "How do you know that it doesn't matter what to count?What about Russian pencils?You know, I'm from another country that is called Russia.What about two Russian pencils and two Russian pencils?"The girl smiled again at me and replied, "Four!"She moved her fingers in the air as if counting the invisible Russian pencils.I continued, "But how do you know that?You haven't seen Russian pencils!"She giggled as if we played a funny game, "It doesn't matter!It's four.Four Russian pencils."I asked, "What about Martian pencils?"The group exploded.The other girl started clapping, laughing, and exclaiming, "It doesn't matter!It doesn't matter!It's four!It's four!It's four!"The first girl also joined her with joy.The two boys started talking about a battle between Superheroes and Martian Aliens.I waited for a while and asked the girls, "How do you know that it's four?I bet you both have never seen

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Martian pencils!What if Martian pencils are round like balls?!" The girls were giggling with joy, "It doesn't matter!It doesn't matter!"The first girl counted imaginary round ball-like Martian pencils in the air with her hands, "Two and two: one, two, three, FOUR!"The noise in our group attracted attention of the rest of the class but when I looked at the teacher, she smiled in apparent appreciation that the kids in my group enjoyed a discussion of math.Two of my university students who stayed behind me and observed attentively our conversation were smiling as well.I lowered my voice and asked the girl, "But what if Martian pencils are liquid?"The girls became almost hysterical with laugh, "Liquid pencils!It doesn't matter!"The first girl counted imaginary four pools of liquid Martian pencils, while the boys were in the mid of their imaginary battle between the Superheroes and Martian Aliens gesticulating with their hands.
I lowered my voice even more, almost to whisper, and asked all kids, "Ok, kids.What is two hundred plus two hundred?"The boys stopped immediately their imaginary battle.The first boy, who, according to my university students had math logic disability, asked me to repeat the question.I did.The first girl replied with perplexity, "We didn't study such big numbers yet."I asked, "But you didn't study Russian and Martian pencils but you were eager to provide answers.What stops you now?"She looked at me with surprise.There was some silence as the kids were apparently thinking and then the first girl broke the silence by saying without enthusiasm, "Ah, I remember now.It's three hundred.My mom told me."I did not reply but kept waiting for the other kids to comment.
Suddenly the boy, who was initially suspected to have "a math disability," said calmly, "It's four hundred."I asked him, "How do you know that?"Like the girl before, he drew two and two lines on his worksheet and counted them, "One hundred, two hundred, three hundred -four hundred."When he counted the last line he circled all four lines with his pen in the air.The girl objected, "No!You can't draw one hundred with one line!One hundred has many-many lines!It's difficult to draw them and count them.We didn't study such big numbers!"The boy calmly replied, "It doesn't matter."The girl grabbed his worksheet, on which the boy drew his lines representing hundreds and started rapidly, almost violently, drawing many-many lines without counting under each of his lines.She yelled with frustration when she finished, "These are hundreds.It's difficult to count them!See, how many of them there are!"The boy replied calmly, "It doesn't matter!"He circled her chaotic lines with circles and counted them, "One hundred, two hundred, three hundred, four hundred.It's four hundred.""No!" -yelled the girl, -"You can't do it!You must count all these…" She was pointing at her chaotically drawn lines within the boy's four circles.The other boy joined the discussion, "No, you mustn't!"The other girl kept silence, but she was perplexed… At this moment, the teacher started clapping loudly gaining all kids' attention.The lesson was over, and the kids were supposed to form a line to go for a lunch.In the line, the discussion about adding two hundreds and two hundreds spread rapidly.The kids' opinions split.I could hear, "It doesn't matter!" "No, it does!""Too big numbers," "Martian pencils," "Superheroes…" When my two university students and I left the classroom, one student exclaimed, "The boy is just a genius!I thought he had a math disability, but he was just a deep thinker.I thought that the girl was a very advanced learner but she was just a shallow learner!We can't teach math through worksheet drills.We need to have deep math discussions with our students!"The other student asked me, "What the hell just happened?! Can somebody explain it to me, please?"I apologized to both of them as I had to run back to my office for a meeting, but I asked them to bring this event for our class discussion the next day and they both promised to do that.

Beyond equality and inequality in education
Eugene

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I went back to my office being rather satisfied with my improvisational teaching and my students' reflections.I liked that I grabbed the kids' attention by creating an interesting and deep math discussion.I liked the fact that I apparently managed to recognize the boy's struggle with the mathematical idea of the universality of numbers: it does not matter what one counts: lines, pencils, Russian pencils, Martian pencils, or hundreds.I liked that the kids left the classroom while discussing math.I liked the flip in of my students' assessment of the kids' learning: the advanced kid turned to be a shallow learner and the kid with math disabilities turned to be "a math genius.""Many great scientists were "slow learners" in school, like, for example, Albert Einstein 10 .Their slowness was a sign of their deliberateness, their thoughtfulness of not to follow, not to conform to the procedural teaching imposed on them by their conventional teachers," -I thought.I also liked that my students saw a link between teaching procedures of calculation -common in many schools -and students' shallow learning.Finally, I liked pedagogical perplexity of my second student.
Yet, the more time passed since the event during the day, the more a sense of some kind of dissatisfaction with my teaching was growing in me.I sensed that something was wrong but it took me a few hours before I could realize what the problem was.The girl's voice that you cannot easily add big numbers penetrated me (cf. the notion of "penetrating discourse" in Bakhtin, 1999).I was always interested in math and these types of issues have always grabbed my attention firing in action a swarm of many math thoughts in me.For example, two infinities plus two infinities is one infinity and not four infinities: 2+2=1!Well, infinity is not a number.But is it?Can you circle infinity like the first grade boy circled a hundred?
Two triangles plus two triangles can be five triangles, 2+2=5 for the following triangles (the original small and one big): 5. Finally, two friends plus two friends equals uncertainty as there can be four friends, three friends, two friends, or even zero friends as a result.
I wish I could share these new ideas and puzzling examples with the first-grade children!With all these examples, I started thinking that maybe the girl was not such a shallow learner and the boy was not such a mathematical genius after all.This was another flip for me on the same day.It is not true that the result of addition does not depend on what objects are being added.Two and two big numbers do not always add to four.What might be great was not necessarily the individual mind of a child but all their minds in the deep and critical mathematical discussions in which they were authentically involved.Thus, I decided to focus my upcoming discussion of the event with my university students not so much on mathematical geniuses and shallow learners but on organizing deep pedagogical discussions of children around deep mathematical issues as the most desirable way of teaching.I decided to share my five examples above with my university education students, future teachers, so they could appreciate the depth of math and how it could have been possible to continue the deep discussion that I started with the four kids in the first-grade classroom.After the excitement of my two students, I expected that the rest of my students would become excited to hear about how little children could be involved in deep discussions about math.However, my class did not go exactly as I had expected.After my two students presented the event described above, some of the students became perplexed and some excited.Although I noticed the difference, I did not explore it at the time.Rather, I raised the question for the class about who of the two children were more mathematically advanced learners: a) the boy who was constantly asking the girl for the answer to his arithmetic problems or b) the girl who asked her mom about the result of adding 200+200?Initially the discussion went in an interesting but predictable direction for me.Most of my students agreed that the boy became more sophisticated than the girl, when he was able to understand that a hundred can be united as one and that it does not matter what you count: Martian pencils or hundreds.I problematized this pedagogical issue even further by asking my students, future teachers, "Is it better to reject a mathematical rule that you don't understand but the teacher imposes on you like apparently the boy before I had engaged him in my lesson did OR to conform to the adults' math rule without deep understanding of it, as the girl seemed to do?"The class erupted in discussions: many students were speaking at once creating small discussion groups or trying to address the whole class in vein as it was too noisy and chaotic.When the initial chaos subsided, I asked my students of what kind of

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students they would prefer in their future classrooms: ones who would follow math rules and procedures regardless of how well they understood them (like the girl) or ones who would refuse to follow math rules and procedures until they deeply understood them (like the boy).I suggested voting on this choice but one student raised her hand and said that it was a false choice.She insisted that good teachers should not throw kids in this situation at all by teaching them deep conceptual math and not procedures.To my surprise, some other students disagreed saying that if we did not teach our students math procedures and rules, they would fail their math standardized tests based on testing students' procedural math knowledge.Some students suggested a compromise of teaching both: procedural math knowledge and deep conceptual knowledge.A student asked why standardized tests could not focus on testing deep conceptual knowledge.And at this moment, I decided to make another flip and introduce my students to my paradoxical examples when two plus two is not necessarily four.
I told my students that I suspect that a genuine standardized test on deep conceptual understanding might be impossible, ever.My students became quiet listening carefully to my words.I said that deep conceptual understanding unfolds only in a dialogue.It never stops.It is bottomless (Bakhtin, 1986).It belongs to all its participants.I saw that my words made my students interested, mystified and yet not quite understanding what I meant.I said, "Let's consider the boy and the girl one more time.We all agree that at the end the boy was more mathematically sophisticated than the girl because he could see the universality of numbers.He could add hundreds while the girl couldn't.He could probably add thousands and millions while the girl couldn't.The boy understood that it doesn't matter what you add: imaginary Martian pencils or hundreds -the result is the same: 2+2 is always four regardless of what you add.In contrast, the girl doubted that one could add big numbers so easily, arranging them in units.She agreed that one could easily count imaginary Martian pencils but not necessarily big numbers.We sided with the boy.But are we really correct in doing that?"And then I shared my addition examples of infinity, drops, hungry cats and fat mice, triangles, and friends.My students were in shock.My paradoxical examples and the additional flip were shocking for them.However, they were shocked about many different things: some of what they were shocked by was contradictory to what other students were shocked by.Here is a list of their shocks and objections that I remember: 1. Infinity is not a number because you cannot count it.Numbers are countable but infinities are not.My counter-argument was that we can add uncountable quantities (e.g., water) that we represent with regular numbers (e.g., with pounds of mass or liters of volume).So why can't we add infinities and represent them with numbers?
2. Some of my students charged me with tricking them.They said that two plus two is always four but I tricked them.They claimed that I was tacitly adding "apples and oranges" and not the same objects.Only the same objects can be countable.But I added different things: small drops of water but counted a big drop of water; cats and mice but counted "animals"; small triangles but counted both big and small triangles; and hydrogen and oxygen but counted molecules (they could not find my "trick" about friends but kept exploring it).My counterargument that we always count different things by abstracting some "same" ideal was not convincing for them, as they could not come to terms with the idea that two plus two may indeed not be four for some objects.
Many years after the class was over and these students became teachers themselves, one of them sent me an email with the subject, "2+2 is always 4! J", when he wanted to remind me of our class or asked a question.There was something deeply personal in their rejection of my paradoxical examples, as if a rug was violently taken from under their feet.

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horizon that they opened for them and about new dialogic pedagogy that can open this new horizon.Thus, I remember that one of these students was able to make 2+2=9 by adding two and two equal small rectangles to create one big rectangle carrying 8 diverse smaller rectangles inside.Another student tried to make 2+2=-1 (a negative number) or 2+2=0.5 (a fraction) but she was not able to do that (at least at that time).Some of them asked what might be a next "flip" and how to achieve it.My response to that was that future mathematical "flips" (i.e., unexpected new mathematical vistas) probably required our moving deeper and deeper into math practice and critical math discourse with people who are interested in it.We discussed the difference between learning about math and doing math and tentatively came to a conclusion that there might not be a clear boundary between these two activities.
4. Yet, some other of my students became pedagogically upset with my paradoxical examples with "2+2 is not always 4." They said that before the examples they had been leaning toward dialogic pedagogy11 that I demonstrated in the first grade classroom.However, after my examples and discussion, they firmly decided to teach mostly procedures and rules.It was because teaching for deep understanding would be very confusing for little children and for the teachers themselves.Also, the children's parents might get upset that their children became too philosophical while not demonstrating mastery of simple math.Also, those children might not do well on standardized tests, which might reflect poorly on the teachers and the school.Finally, employers might be upset that their employees -the past students of deep math understanding -refuse to follow rules because they could not fully understand them.This criticism of my dialogic pedagogy provoked very interesting and important discussions about the purpose of math and general education.
5. Lastly, one student shared her realization that she probably struggled with algebra because algebra mostly studied non-linear relations among objects.But because she learned that 2+2 is always four, it was very difficult for her to understand non-linear math relations, for which 2+2 is not 4 (see the discussion of this math and pedagogical phenomenon by Russian mathematician and educator Konstantinov in Matusov, 2017).Her comment provoked the class to discuss the features of the objects, for which 2+2 is always four.We came to a conclusion that these objects should be indifferent to and not interact with each other.Some students became excited to find exceptions from this rule but some wanted to know what "indifferent" or "not interact" meant.
Like the first-grade class on Russian and Martian pencils, this undergraduate class for future teachers was very memorable and eventful.During the semester, the students and I returned to the themes of this discussion again and again.As I mentioned before this discussion colored our class as such for many of the students.

Human uniqueness vs. human replaceability in education
So, when a student replies "4" to the school test question "2+2=?," what does it mean?In mainstream education, it means the student is correct; especially when, in addition, she or he can justify his/her answer correctly.In mainstream education, students are replaceable, people are replaceable.There is little difference among students who correctly reply to the school test question "2+2=?"They constitute a group of those who know what two plus two is, according to the school authority.Although students in this group may vary by what kind of correct explanations they can provide, these differences are educationally inconsequential.These students can all reliably arrive at the correct answer on a systematic and correct basis.In gist, these students can act as a human-machine, a smart machine (e.g., a calculator).In contrast, the other group of students, who provide either a wrong answer, or no answer at all, or cannot justify the right answer correctly, are students who cannot work as a reliable and correct

Beyond equality and inequality in education
Eugene E16 human smart machine.One can measure via a standardized test which student belongs to which group or remain somehow in a grey area in-between.
In mainstream education, students and education itself are measureable.The goal of such mainstream education is to make all students into human smart machines that can reliably produce the correct answer or the correct solution to a presented question or problem on a systematic basis.This education is essentially algorithmic: if X (question/problem) then Y (correct answer/solution).The justice problem for mainstream education is to make ALL students arrive at the preset curricular endpoints: no student left behind in making all of them reliable multi-functional smart machines.This justice problem is a problem of equality in a broader sense, including equity.Alexander Lobok provides similar critique of the mainstream psychology, The problem with this conventional approach to psychology, however, is that the human being is the only 'object' in the Universe that is defined by a subjective cognizing world of her or his own, building above the subjective lived experiences and feelings and redefining them -a world, unique for each person, which cannot possibly be viewed from outside, except for some of its outward objective artifact manifestations of this subjective cognizing world.If so, a question emerges: can a particular human being, his/her particular and unique subjective cognizing world be a subject of science -a subject of scientific observation and interpretation?Can a particular child with his/her unique subjective world, subjective Cosmos, not overlapping with subjective cognizing worlds of all other people in principle, be a subject of science?(Lobok, 2017, p. SIa:2).
In contrast, from the point of view of the ontological dialogic pedagogy illustrated above, providing "the correct" answer to an authority's question may be evidence of an authoritarian regime where a student has learned how to please the authority well, which may have little to do with genuine math and genuine education.Participation in genuine math practice and genuine math education means a student's engagement in critical unfinalizable mathematical discourse, where meaning is a relationship between genuine questions and serious answers and among other meanings, Contextual meaning is potentially infinite, but it can only be actualized when accompanied by another (other's) meaning, if only by a question in the inner speech of the one who understands.Each time it must be accompanied by another contextual meaning in order to reveal new aspects of its own infinite nature (just as the word reveals its meanings only in context).Actual contextual meaning inheres not in one (single) meaning, but only in two meanings that meet and accompany one another.There can be no "contextual meaning in and of itself"-it exists only for another contextual meaning, that is, it exists only in conjunction with it.There cannot be a unified (single) contextual meaning.Therefore, there can be neither a first nor a last meaning; it always exists among other meanings as a link in the chain of meaning, which in its totality is the only thing that can be real.In historical life, this chain continues infinitely, and therefore each individual link in it is renewed again and again, as though it were being reborn (Bakhtin, 1986, pp. 145-146).
In ontological dialogic pedagogy, people are interested in each other and their ideas, expecting to be surprised by their uniqueness and difference from each other.Nothing is replaceable and, thus, nothing is measurable: neither meaning, nor people, nor education.E17 machines because they are unreliable and non-systematic.People in dialogue are constantly ready to transcend any given meaning.People in dialogue are not replaceable and, thus, are unmeasurable.People in dialogue are unique in their education, their emergent curriculum is unique, eventful, and unpredictable (Lobok, 2014(Lobok, , 2017;;Osberg & Biesta, 2008).To engage in human subjectivity, it is necessary to focus on the uniqueness and unfinalizability in human beings (Nancy, 1991;Nikulin, 2010).
The goal of ontological dialogic pedagogy is for people to freely (leisurely) engage in an endeavor of examination of the self, life, society, world, including their own education in a (critical) dialogue (Matusov & Marjanovic-Shane, 2018, submitted-a).It is about people's self-actualization, self-transcendence, and self-realization.It is about a person's development of creative and critical voice in dialogue.The existential justice problem for this approach is for each and every person to be able to engage in selfactualizing examination and (critical) dialogue.This existential justice problem is a problem of dialogic self-actualization based on people's genuine interest in each other and mutual respect.Like any existential justice problem, it is self-contradictory.However, the self-contradictions of existential justice are addressed very differently by the equality-inequality approaches and by the Bakhtinian ethical dialogic approach to justice.

Beyond equality justice: Relational and dialogic types of justice in education
Before turning to discuss the inherent self-contradictory nature of the notion of justice, let us consider a similar inherent self-contradiction in the notion of freedom through a dialogic approach to this inherent self-contradiction 12 .Both justice and freedom are relational concepts and a discussion of freedom will guide us in our discussion of justice.Anthropologist David Graeber tracked the etymology of the Germanic word "freedom" to the word "friendship."In our interpretation of his views, freedom is about establishment, maintenance, and breaking of the web of personal relationships based on personal desire and choice.In slavery, a person is stripped from the possibility and legitimacy of establishing, maintaining, or breaking the person's relational web (Graeber, 2014), "Slavery was, in fact, a social system designed to destroy social capital among slaves and between slaves and freemen" (Putnam, 2000, p. 318).Although Graeber did not discuss it, this relational notion of freedom is inherently selfcontradictory.It is because when a person has a choice and legitimacy to establish, maintain, and break his/her relationships with others, it may infringe upon the relational freedom of other people who may make a different choice and have a different desire than that person (Perel, 2017).Thus, this infringement may be felt as unjust.Although under some circumstances these differences among involved people in defining freedoms can be negotiated and compromised to the satisfaction of all the sides, these negotiations and compromises can be limited and even unsuccessful in some cases.This is where the Bakhtinian dialogic ethics framework of human uniqueness can be helpful.
A conventional approach to resolving the inherent self-contradiction of the relational notion of freedom, leading to injustice, is often Kantian.It is based on the development of duty, obligation, rules, principles, imperatives, and laws -universal or conditional but always abstract and finalized, above the unique people with their unique needs, interests, and desires and above their unique contexts (c.f., Bush's educational policy "No Child Left Behind" or Obama's policy of "The Common Core State Standards").A good example is the Kantian imperative, based on the Christian morality, to treat others as 12 Sergeiy Sandler raised an interesting issue of how these "good" self-contradictions, we are going to discuss here and further, are different from "bad" contradiction between quality and equality, inherent in Kantian equality-based approach to justice, we discussed above.Hegel defined "good" internal mutually-constitutive self-contradictions as productive for the development of the phenomenon, while "bad" external contradictions destructive to integrity of the phenomenon (Hegel, Geraets, Suchting, & Harris, 1991).We agree with Hegel on this matter.Thus, quality and equality, discussed above, do not mutually constitute each other: there can be equal misery or unequal quality -these concepts can exist independently of each other.When people define educational quality through inequality of test successes and failures as it is in the case of developing a "rigorous" standardized test in education, they cannot commit to educational equality at the same time.The integrity of the people's commitments collapses.

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one wants to be treated by others.The Kantian approach to solving moral contradictions and dilemmas is non-subjective, universal, and decontextualized.It is based on an impersonal agreement of objectivity among reasonable and moral people (Rawls, 1971).Bakhtin criticized this approach making people ethical slaves of the rules, principles, and laws and, thus, making them irresponsible hiding behind objective universal principles.The history of the 20 th century totalitarianisms has challenged the conventional ethical modernist approaches 13 .
Mikhail Bakhtin, a Russian philosopher of dialogism, dialogic ethics, eventfulness, and human uniqueness, argued that people constantly author their deeds, charged with ethics, along with authoring ethic judgments about these deeds and new ethic values, emerging from these judgments.In turn, these ethically charged deeds, judgments, and values define the authors of these deeds -what kind of persons they are -to others and, consequently, also to themselves (Arendt, 1958;Bakhtin, 1993).According to Bakhtin, ethics is socialized through a special critical dialogue of responsibility, involving words and deeds.The ethical meaning of the authors' deeds can be problematic as we already discussed in the case of freedom.Others have rights to challenge the ethics of these deeds and reveal inherent relational contradictions, if not injustices, deeply rooted in them.Sometimes even the author him/herself can challenge the ethics of his/her own deeds based on a sense of unease with his/her authored deedwhich is often referred to as a person's "conscience."Further, the author of an ethically charged deed has an ethical obligation to respond to these charges produced by others and him/herself with his/her words and/or deeds.This ethical obligation of response is called "responsibility" to stand behind the authorship of the deed, to accept diverse positive and negative judgments and obligations, and to take care of consequences of the deed to diverse involved suffering parties (Bakhtin, 1993).Responsibility for a deed is not isolated but rather it is enmeshed in a web of the person's responsibilities for other deeds and relationships.Again, how a person deals with this hanging responsibility, demanded by others and the self, defines the ethics of the person (i.e., what the person considers (un)ethical and why and how well/badly he or she follows his/her own ethics).Thus, Bakhtin's approach to self-contradictions of ethics is dialogic, through the notion of unfinalized personal responsibility, which is always unique, authorial, and contextual.Now let us go back to the notion of justice in general and in education in particular.We want to demonstrate the notion of justice is also self-contradictory, thus, requiring to be addressed as a problem to others and the person him/herself through a dialogic act of responsibility.Again, we prefer the Bakhtinian dialogic framework to the mainstream Kantian one.Justice starts with a discursive appeal to a community about a relationship, which is deep down felt as wrong by one involved party, demanding to fix this relational wrong; while this relationship feels right by, at least, another involved party.Justice is all about relational conflict of opposite claims.The self-contradiction of the notion of justice is inherent in it: what is good for one is bad for another.When a situation feels good to all, it does not generate a justice problem -paraphrasing the famous quote by Eleanor Roosevelt, it is possible to say, "Harmony -i.e., the absence of perceived injustice -cannot be for one side alone, but must be for both."When it feels wrong to all (e.g., a natural disaster), again it is not a justice problem.As Bakhtin argued, there cannot be any theory of right and wrong -it is an authorial judgment, for which people must take responsibility.Bakhtin contrasted his ethical dialogism with Kantian "theoriticism" (Bakhtin, 1993), which he would later call "excessive monologism" (Bakhtin, 1999).

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The Kantian approach to addressing the self-contradiction of justice is to develop universal or semi-universal (conditional) rules and laws.This Kantian approach may have diverse realizations in education.For example, all schools must receive the same funding expenditure per student (i.e., equality in the narrow sense), which is a response to a justice problem of unequal school funding.Or, it can be amended based on the students' particular needs through categorization of the students' special needs with a price tag attached to each of these categories (i.e., equity), which is a response to a justice problem of school funding in special education.Or, the Kantian approach may lead to a demand to have the same educational outcomes (e.g., No Child Left Behind, Common Core State Standards) -an approach we discussed above, which addresses a justice problem of achievement gaps in reaching the same preset curricular endpoints.Or, the Kantian approach can demand a minimum of educational equality in achieving the basic educational standards, after which students can be let to be creative and diverse, as some progressive educators argue (e.g., Ravitch, 2013).We reject all these Kantian equalizing approaches because they eradicate the uniqueness in people, their education, and their circumstances, making them mutually replaceable, measurable, predictable, controllable, and machinelike (even at a minimum basis level).
A Bakhtinian approach to the justice self-contradiction is based on the uniqueness (i.e., ultimate diversity) of people, education, circumstances; authorial agency (Matusov, von Duyke, & Kayumova, 2016); responsibility; and dialogicity.In education, we argue that the core problem of educational justice lays in the notion of student authorship, on which genuine education is based (Matusov, 2011a).Authorship involves a person's transcendence of the given -e.g., culture, knowledge, skills, traditions, established relationships, -recognized and evaluated by relevant others and/or the self.This evaluative recognition is in itself an authorial and creative process (Matusov, 2011a).Both authorship and its evaluative recognition, required by authorship, are unpredictable and unique processes.Recognition is not guaranteed.This raises a justice problem.A student's bid for authorship may not be met by relevant others' positive recognition.This is especially important when the lack of positive recognition comes from the student's trusted teacher.There can be many reasons for why, let's say, the teacher does not recognize positively (or at all) the student's authorship.It can be because of the teacher's lack of understanding or imagination, insensitivity to the student's pedagogical needs, ideological rejection of the student's values and beliefs, envy, ignorance, and so on.Alternatively, the student's authorship can be really bad or not even worthy of recognition: it can be wrong, of poor quality, plagiarized, clichérized, evil (e.g., aiming to be mean, to hurt other people), careless, not intellectually honest, and so on.Negative (or entirely absent) recognition of the student's authorship by the teacher may feel unjust to the student while positive recognition of the student's authorship, expected/demanded by the student, may feel unjust to the teacher.Bakhtin's ethical dialogic denies any attempt to develop rules, patterns, or procedures -what he criticized as "theoriticisms" (Bakhtin, 1993) -to resolve this justice problem in a satisfactory way or even that satisfactory ways may exist (or pre-exist) at all.Bakhtin calls for the participants to take responsibility for their unique (pedagogical and educational) actions/deeds and to demand this responsibility from others, by challenging others and responding to challenges by others, by their open mindedness in accepting wrongs of their doing, by their desire to ameliorate these wrongs, by standing one's grounds when feeling right to do so, by accepting the guilt, by mitigating negative consequences, and so on.The dialogic ethic process of responsibility (or lack thereof) defines the educator and the student.As Bakhtin claimed, "there is no alibi in being" (Bakhtin, 1993) -which in our view, means that there is no justification for one's wrongs in one's circumstances but excuses and guilt mitigating circumstances are fine.
Inspired by the Bakhtinian dialogic ethical framework, we argue that justice is not defined by individual complains about injustice, not by resolutions that satisfy all or many, not by some universal or

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conditional principles.Rather, in our view, justice is defined by the totality of critical dialogue of unique words and unique deeds in unique circumstances asking for responsibility, challenging words and deeds of others, and replying to these challenges.Justice does not belong individuals but by the Big Dialogue unfolding in the human history (Bibler, 1991(Bibler, , 2009)).
Below we present two educational cases involving educational injustice and provide our Bakhtinian analysis of them.These particular cases were chosen because in each of them, the teachers focus on teaching their students the concept of justice while trying to eliminate injustice caused by the students themselves (from the teachers' point of view), although in different contexts.In our analysis, the main tension, which caused educational injustice in both cases, was between the instructors' teaching about justice and their attempts to impose what they considered was just.In the first case (the case of Ana shaming a behaviorist teacher), the professor, Ana (the second author), tried to make her student, Sarah (a pseudonym), an in-service teacher of autistic young children, realize that Sarah was harming her students by using the behaviorist approach of Applied Behavioral Analysis to shape her students' behavior in a desired way.In the second case (the case of Vivien Paley excluding exclusion: "You can't say you can't play"), the preschool teacher Vivien Paley tried to make her students stop systematically excluding some children (mostly of minority and working-class descent) from playing together by imposing a new rule of excluding the exclusion on them.According to our analysis, in the first case, the teacher took responsibility for the educational injustice she caused in her classroom, while in the second case, the teacher was apparently so invested in her truth of imposing social justice that she refused to take responsibility for the educational injustice she caused and was aware of.

The case of Ana shaming a behaviorist teacher
In our current interpretation, the injustice that happened in a class I (the second author) taught, involved my attempt to "teach the ugly truth" about behaviorism -i.e., molding my graduate education students' mind in a way I desired to prevent them from harming their own young pupils.All but one of my graduate students were current early childhood education teachers.Later I realized I did not provide them an opportunity to test their own ideas, opinions, positions and desires but rather tried to impose my truth on them.The situation was complicated by the fact that it turned out that what I set to teach as the uncontestable end-point and final truth was rather critical of the educational practice, to which some of my students were profoundly committed.Thus, at least one of my students, Sarah, was personally invested in behaviorism in her everyday work with very young autistic children.Sarah regarded herself a kind and skillful and caring teacher who loved her young pupils.
Looking back, I realize that during the event, I did not really listen to Sarah's teaching experiences about her work with young autistic children nor to her own dilemmas, problems, and doubts when making her own pedagogical decisions.I did not create a place where such real-life experiences can be safely examined and perhaps transcended, and where I could also learn something from an experienced practitioner.Instead, I brought up ethical issues condemning behaviorism, in which wrongness I did not have any doubts.Ironically, by desiring to prevent Sarah (and some of her agreeing peers) from harming their students by behaviorism, I similarly harmed them by making them objects of my pedagogical actions.Like Sarah using behaviorism for molding autistic young children, I was using Socratic dialogue pedagogy to mold my students' minds about behaviorism in education.
This event was an important transformational point for all participants in this class including me, the professor, a dramatic transformational event in a dialogic pedagogy run class -in two acts (Marjanovic-Shane, 2016).It involved Sarah's intense feeling of being stunned or numbed by a penetrating Socratic "torpedo's touch" (Matusov, 2009;Plato & Bluck, 1961)

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existential, ethic being (Matusov & Brobst, 2013).Sarah reacted with a very powerful cry against the injustice of being implicitly accused by me and other students of unethical behaviorist treatment of children with autism she was teaching.
I was faced with my pedagogical desire to disrupt and undermine effectively some of my students' commitment to behaviorist techniques of punishments and rewards as their main approach of working with younger children with autism (for more description and analysis of the case see, Marjanovic-Shane, 2016).I deeply felt that the use of behaviorism in education was very harmful for children in general and for little children with autism in specific.Thus, to engage my students in critique of behaviorism, I showed my students a video on "Operant conditioning14 " about B. F. Skinner's behaviorist approach and made a parallel between Skinner training pigeons by starving them, and Sarah using this kind of behaviorism with her young autistic students when using punishments and rewards.I moralized the parallel between treating pigeons and autistic children, " With these words, she left the class.Later that evening she posted a message on the class' online discussion forum her protest of the injustice of my and other students' accusations that she may be an unethical teacher, Sarah: I was rather embarrassed when I left class … and was surprised that I had engaged in such a, shall we call it, spirited discussion with the Professor… I believe that I reacted in such a single-minded fashion because it went straight to my heart rather than my head.With views so opposite to mine so readily expressed I felt that the care I feel and show for my students was seen by another as a disservice to the child.As a teacher, it makes my heart ache when it is thought that I am not trying to do all I can for students… I know that these strategies, if implemented with caring and respect, can help many students discover more about their world and themselves and to embrace school life in a more positive way for themselves.[…] It is my opinion that children are motivated in much the same way as I am, and that sometimes when they need that extra boost to change their way of thinking or their behaviors … I should be able to assist them in this process.[…] One of the most important roles of schools is to reach out to children and help them grow with the partnership of the child and the parents to do so.I hope that I did not offend anyone with my spirited outburst, or impolite argument with the Professor at the close of class.I am sorry and hope that I will be able to control my own behaviors E22 in the future so that I retain my respectful demeanor even when confronted with ideas or statements that are different than mine.Hopefully this class will continue to allow me to learn to respectfully dissent, stand up for what I believe in with clear statements, and to keep an OPEN mind about new techniques and ideas.Thanks for listening (Marjanovic-Shane, 2016, p. A62).
This new development made me not only puzzled, distressed, and dissatisfied, but it also threw me into self-examination and deep reckoning of what I was doing as a professor who wanted to become "a dialogic humanist teacher."Something was going wrong, I could clearly see, but I didn't know what.This was far from what I wanted to achieve as a teacher, … to create "a safe learning environment," in which it was safe for the students to bring any ideas and positions into the class for class discussion and testing.[I] was also concerned with [my] lack of dialogic guidance for the students: that [I] was not able to deepen the discussion on behaviorism and humanism...] [I] also saw the stinging and numbing "Torpedo's touch" effect (Matusov, 2009;Plato & Bluck, 1961) [was] on Sarah and worried that Sarah would close up, that I had lost Sarah's trust, and with that, potentially the trust of the rest of the students.For [me], Sarah's […] outburst at the end of the class meeting and her web posting became a signal.It was a powerful signal that [I] needed to make a change in [my] pedagogy, in order to restore the trust, the respect, and most of all, the ease everyone in the class had with each other -so that they could continue to freely test their ideas, opinions, positions and desires with each other (Marjanovic-Shane, 2016, p. A62).
I needed to do something to restore justice in our class -justice as a response to my student's outcry of pain and being wronged.At that point, I consulted Eugene (the first author), as my colleague and dialogic mentor, who was more experienced in dialogic teaching.Eugene focused my attention on my own unexamined pedagogical desire to "educate" the "behaviorist" Sarah, and two of her supporters, in order to "convert" them from "behaviorists" to "dialogic humanists" like me and two other students.Eugene pointed out that I was not seriously interested in Sarah's concerns, and above all that I was not interested in testing my own dear ideas about behaviorism!Instead, it looked like I was only interested in "molding the students in the preset ways dear to me." Eugene suggested searching for situations where the application of behaviorism might be legitimate from my perspective (e.g., when a person wants to quit smoking).Thus, Eugene helped me problematize behaviorism for myself making me interested in what other people, my students and especially Sarah, might think about the limits of behaviorism's legitimacy and the reasons behind these limits.
The talk with Eugene was another Socratic "torpedo touch" experience for me -as it revealed what I was doing in my teaching to be so far apart from what I was aspiring to do: while I desired to create "sincere dialogues" with students, I was undeniably monologic, listening to the only truth I knew -my own one, and unjustly imposing it on them.This was a turning point for me.I had to "transcend" my own teaching persona, and find a way to let the students' ideas guide me, as much as I wanted to guide them.
Eugene suggested that we reopen the discussion of the behaviorist approach in education -with a twist, using the metaphor of the "Magic Wand," to create a new exploration focused on the teacher's The] next class meeting was completely overtaken by … critical dialogue about the "Magic Wand"… When would we use "the magic wand" on ourselves?When would we use it as teachers -on our students?Is it educational to make our students unconditionally conform to the teacher's desire, however good or bad this desire might be?When would it be better and more efficient to learn using a "magic wand" to make the students well behaved?Should students become involved in testing ideas about what is good and what is bad, what is right and what is wrong?Is it educationally worthwhile to let our students make their own decisions about their own behavior -moral decisions about what is right and what is wrong -and then reflect on them?... What would make a difference in our own development and for our own subjectivities?What does it mean to be "educated?"Do we want to raise citizens who unconditionally follow the authority, however good the authority may be? (Marjanovic-Shane, 2016, p. A63).This time, I was attentively listening to my students' stories and critical analyses.Our critical dialogue about the "Magic Wand" led to many interesting and fruitful revelations about each one of us as teachers and as people.Some of the "behaviorist students" including Sarah, "raised important issues about their institutional settings.They […] said that they were concerned with the institutional pressure to use behaviorist classroom management aiming at active[ly] suppressing the students' 'bad' behavior [loudly running through school corridors, paying no attention to the class, etc.]" (A63).Another student, Nora, did not believe that the given school institutional environment could ever be changed, and made a cynical remark that "her professional responsibility [is] simply to follow institutional orders, although she did not mind most of these institutional orders.From Nora's professional position, the 'Magic Wand' inquiry seemed to sound interesting but a bit [of a] frivolous and [an] inconsequential exercise" (Marjanovic-Shane, 2016, p. A63).And yet, she did worry that "having too much structure in the class, could take away a child's ability and right to be a kid." 15 I learned that Sarah did not like "negative reinforcements," i.e., punishments, but preferred "positive reinforcements," i.e., rewards, which my other two "humanist students," Mona and Kathy, criticized as "bribery by rewards."Sarah's credo as a "good teacher" was to do only what is good for her students.
It seemed that the "Magic Wand" inquiry, actually made Sarah test her own pedagogical desires.Sarah (and other students) started developing a list of circumstances for which she would use the "Magic Wand," and for which she would not, along with reasons for that.Thus, she said that she would use a "Magic Wand" to "fix medical conditions like cancer" but not for an "autistic child to learn that she/he should not hit their sister on the head.… that kind of learning should be a process, because the children

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are growing."Sarah would definitely use a "Magic Wand" to eliminate acute and severe self-hurting behaviors by autistic children, like their banging their heads on the wall.She would also use a "Magic Wand" to give just a little help to a child to make eye-contact with a teacher or a member of the family.And then, this eye-contact would boost the child's spontaneous communication, "which would be so important for the child and the whole family to grow together."However, Sarah, would not replace this "process of family growing together" with a wave of the "Magic Wand's" fixing.
Mona, a "humanist student," compared the process of a "family growing together" with her own family learning to live with and love her uncle who has Down syndrome.Mona cherished her family's love for her uncle and she would never use a "Magic Wand" to change anything about her family.However, Mona agreed with Sarah that she would also use the "Magic Wand" for children's acute and severe selfhurting behaviors.
Like Mona, Kathy, another "humanist student," said that she would never use the "Magic Wand" to change the behaviors of others, including her own children and students.She would always be afraid to "break" the others' personal integrity and autonomy, and hurt their real, deep needs.Nevertheless, she would use a "Magic Wand" on herself, to make herself gain insight and understanding of each child's strengths and needs, so that she as a teacher could provide the best guidance to children.The children, in her opinion, should still need to learn by themselves, through a process.Kathy thought that if a "Magic Wand" would make you have "a photographic memory, [and] incredible knowledge base, but not [deeply] understand it… that means you didn't really learn it."Ironically, as a teacher she did not wish to learn through a process together with her students how to be sensitive to their needs but instead wanted to become a sensitive teacher instantaneously.Unfortunately, I did not notice this contradiction in Kathy's reasoning at the time and, thus, missed this teaching-learning opportunity.What was important, however, was that nearly all of my students found the "Magic Wand" (and, thus, behaviorism behind it) legitimately useful in some circumstances and not in others.
As the class discussion exploring the boundary of legitimately using a "Magic Wand" progressed, Sarah became baffled: in her opinion, behaviorist ABA training can help children to gain self-control and focus their attention, and that is precisely what "children 'on the autism spectrum' [were] 'lacking.'… How could such a beneficial technique be un-ethical?At what point would it become un-ethical?"(Marjanovic-Shane, 2016, p. A63).It seemed that, for Sarah, the "Magic Wand" discussion was becoming "professionally and personally important, exciting, and revealing" (p.A63).Sarah started wondering if this discussion would change her professionally, making her doubt in the ultimate power of behaviorist ABA techniques, "You know… its… I'm not so sure anymore... if I'd wave the "Magic Wand" for all the things… all the time...The kids need a process [of learning] … I think that that's true communication 16 …, and that it's so important for them… You know -to grow…".The situation was complicated for Sarah by the fact that she was obliged to use the ABA techniques in her school all the time.This could potentially "put her on a collision course with her conventional institution" (p.A63).
For all of us, the participants in the class, the "Magic Wand" discussion became an examination of limits: the limits of behaviorism and the limits of humanism in education.When is each one of them legitimate?We, the class participants, tentatively agreed that behaviorism (the "Magic Wand") would not be unethical when used to stop self-hurting and other violent behaviors (like hitting and hurting others).But there was no agreement among all of us about behaviorism when practiced because of E25 were fuzzy about what does it mean to "have too much structure, that could take away from children's ability to be a kid." "The [class] event seemed to have a lasting effect on [all] the participants.Afterwards, during the class and many months and years after the class was over, 'behaviorist' Adele contacted [me] on several occasions.She said that she often felt as if Little Professor Ana was sitting on her shoulder, asking whether Adele liked her own pedagogical desires behind her pedagogical decisions and actions or not" (Marjanovic-Shane, 2016, p. A64).Other students, often recommended my classes to new students… It seemed that justice was restored.Or, possibly not.I never again, after the course was over, heard from Sarah.
Painful torpedo touch can often create powerful memorable events in people's lives.Based on the Bakhtinian notions of "internally persuasive discourse" (Bakhtin, 1991;Matusov, 2009;Matusov & von Duyke, 2010) and "penetrative discourse" (Bakhtin, 1999;Matusov, 2009;Matusov & Brobst, 2013), torpedo touch may forcefully start vicious internal dialogues in students.Critically analyzing the use of the torpedo touch approach in dialogic pedagogy, Matusov and Brobst (2013) do not reject torpedo touch as such, which may be both unavoidable and even desirable by some students.However, they question a non-consensual torpedo touch and, of course, the pedagogical utilization of humiliation.They argue that torpedo touch has to be welcomed by the students and not imposed on them -it should be consensual, like in the case of Plato's Meno dialogue (Plato & Bluck, 1961) or, in this case, as with Eugene's guidance of Ana.Although pedagogy based on Socratic torpedo touch may lead to important critical reflections and deep learning, it raises serious questions about educational justice.When imposed by the teacher, a torpedo touch experience may undermine the student's right to control, initiate and invite such experiences.
Looking back, I (Ana) can see that as a teacher, I did not question my educational decision to "shake" Sarah and two other students out of their behaviorist beliefs by accusing her of potentially being "professionally unethical" with her students.At the time, this decision was in accordance with my "dialogic humanist" beliefs about good (and just) education.From this "dialogic humanist" point of view, treating autistic children as animals to be controlled and trained by punishment and reward is deeply inhumane, disrespectful, and abusive.It denies children the possibility and the right to make their own meanings about the world, make their own judgment about what is good and what is bad, to have a right to be frustrated and not cooperate with others, or at least to express their frustrations, etc.
However, now I realize that I fell into my own trap: I was educationally unjust to Sarah!First, in contrast to my wish to be "dialogic," my own desire to "tell the truth" about the problems of behaviorism, overtook my pedagogical decisions, and I stopped being interested in seriously considering Sarah's points of view and her complex and difficult work with young autistic children.Second, I was not ready to be truly a dialogic partner in jointly thinking through a tough and complex issue, letting myself deconstruct my own dear beliefs.Third, I did not take into account my institutional authoritarianism in the relationship between Sarah (and the other students) and me, the authoritarianism that made my truth about behaviorism almost uncontestable for her, crushed her, and made her "heart ache when it is thought that I [i.e., Sarah] am not trying to do all I can for students…" (Marjanovic-Shane, 2016, p. A62).She lost her power to defend her truth "that children are motivated in much the same way as I am, and that sometimes when they need that extra boost to change their way of thinking or their behaviors … I should be able to assist them in this process" (Marjanovic-Shane, 2016, p. A62).Ironically, I was fighting Sarah's authoritarianism directed at her young autistic pupils with my authoritarianism directed at her. Fourth, the torpedo touch I tried to create for Sarah, was not consensual -she was not in any way doubting her
I did, however, hear her pain which was for me that "extra boost" to change something in my teaching and take responsibility for the educational injustice I caused.However, although I can say that I tried hard to restore the educational justice, it may have come too late for Sarah.
We argue that although plunging students into powerful emotional examinations of their own beliefs, positions, desires and acts in critical dialogue, may potentially lead to the students' transcendence of themselves, such educational acts do not necessarily serve educational justice.Without students' explicit welcoming and/or initiating of dramatic and potentially existentially undermining confrontations of their own living being, such educational acts are not only existentially dangerous for the students' wellbeing, but are experienced by the student as unjust violations of their educational integrity.If we compare the "torpedo touch" experienced by Sarah and by me (as a student of dialogic pedagogy), we could say that Sarah experienced "torpedo touch" as unjust violation of her existence as an ethical human being and a skillful professional.This educational injustice may have potentially never been overcome, not even by the innovative "Magic Wand" pedagogical approach.On the other hand, in my learning to become a dialogic teacher, I needed and I invited my own "torpedo touch" experience from Eugene.I already felt that "something" was wrong in my teaching, and I needed to confront my own fears and desires.There was no injustice in Eugene's "torpedo touch."

The case of Vivian Paley excluding exclusion: "You can't say you can't play"
Vivian Paley, a preschool teacher, was faced with the following pedagogical problem in her classroom.Her 4-year old children systematically excluded some minority working class peers from their play and thus from their networks of friendships, making them outcasts in the classroom.She sent two major pedagogical goals for herself: 1) integrating the outcast students in the networks of friendships and 2) teaching her students about the problem of systematic exclusion and searching for a solution with them.As a conscientious teacher deeply committed to issues of social justice in education (and beyond) Vivian Paley eventually prioritized her first goal of social justice in her classroom community over her second goal -educating her students about social justice issues and finding a solution of the problem of exclusion together.To address the problem of systematic exclusion and her two major pedagogical goals, Paley employed very creative pedagogical approaches by:  (Paley, 1992, p. 27) 18 .
However, she did not reply to her own self-challenges as if she was suppressing her own internal voice challenging her ideological position of pedagogical authoritarianism.Paley did not want to reply to her own challenging questions nor to challenging questions about her problematic pedagogy raised by Matusov and Smith in their personal email communication with her.After reading a draft of their critical essay, she replied to them, "Thanks also for inviting me to comment on your paper, but I prefer to let you carry on your own investigations and come to your own conclusions" (Matusov, 2009, p. 272).Matusov and Smith shared their and her own challenges of Paley's publicized pedagogical actions but she apparently refused to take responsibility for her pedagogical deeds by not responding to these challenges in her book and in her reply.Matusov and Smith called this phenomenon of being aware of challenges to one's own deeds without replying to them "awareness without responsibility" (Matusov, 2009, p. 261).
In sum, we argue that in the first phase of her pedagogy, Vivian Paley promoted justice and education about justice in her preschool classroom by successfully establishing a public forum for a critical dialogue of internally persuasive discourse.However, together with other critics, we challenge the intellectual limitations of this critical dialogue.Paley did not guide and did not allow her young students to explore the complexity of exclusion, constituting the crux of any special relationship.
In the second phase, when she radically changed her class' pedagogical regime by executing her coup, the situation was more complex.In contrast to Ana (see above), Vivian Paley had the urgency in experiencing the injustice of the systematic exclusion of minority children caused by the play bosses almost every moment of her classroom time.She felt responsible to stop it as soon as possible.We are sympathetic to Paley's concern about the continuation of horizontal peer oppression via systematic exclusion of minority and/or working-class unpopular children from play and friendship.However, we challenge her abrupt ending of the critical dialogue and the shift to her authoritarian pedagogical regime of "you can't say you can't play."The shift transferred her pedagogy of children's collective critical examination of the self, life, world, and society honestly assisted by the teacher into children's socialization into "the goodness" defined by the authority.We argue that this shift, or better to say, coup, was guided by Kantian universal rule-based justice making people mutually replaceable and circumstances universal.However, even with our critique, the question remains open of whether her classroom after the coup became more just than before for previously excluded children on a systematic basis and the other children.Is vertical oppression by the authority, which involves promoting forced integration at the expense of special exclusive relationships of freedom, still better than horizontal peer oppression of systematic exclusion or not?One can argue that Paley's pedagogical move of coup was similar to the US

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forceful racial desegregation of public schools, leading to imposed busing of children from one racially segregated neighborhood to a school, located in another racially segregated neighborhood, in order to mix racially diverse children.Although imposed busing may not be without its flaws and critiques, one can convincingly argue that on average, a situation of forced racial desegregation is better than a situation of forced racial segregation.
Alternatively, one can compare Paley's coup with the Bolshevik revolution in Russia in 1917, where forced equality was imposed on the country.Like in the case of Paley's coup, the Bolshevik revolution required suppression of all public discussions and elimination of all alternative approaches (in contrast to the forced racial desegregation in the US).This raises a possibility that Paley's regime was not only authoritarian but may also have been totalitarian in nature.
Of course, to address the question of whether the situation became more just before or after Paley's coup, it can be helpful to access Paley's children's subjectivities and ask them.Unfortunately, Paley did not do that and probably could not do that as a regime of free discussions was eliminated in her classroom.Finally, we wonder if Paley's lack of responsibility in replying to her own, her children's, and other people's challenges of her pedagogy is part of the pedagogical and social justice authoritarianism, if not totalitarianism, that she has committed.We wish that Paley wanted to reply to our criticism 19 …

Educational justice of the replaceable and measurable in the Bakhtinian dialogic ethics framework
Above, we discussed diverse approaches to the immeasurable notion of justice in educationi.e., justice, which is applied to unique people and unique educational processes.What about measurable justice?For example, money and many material things can be mutually replaceable and, thus, measurable.Thus, how can they be distributed justly?In our epigraph quote, David Graeber argues that when things are replaceable and measurable to be just they have to be divided equally, "…since there's no basis for ranking such unique individuals on their merits, everyone deserves the same amount of those things that can be measured: an equal income, an equal amount of money, or an equal share of wealth" (Graeber, 2013, p. 301).For example, in an educational context, this principle probably means having the same funding expenditure for each student.We want to take issue with this equality-based approach to measurable justice.
Although one can argue that economic exchange-value of a $20 bill is the same regardless of who has it 20 , its meaning for the person, for his/her particular needs, wants, and interests -its use-valueis rather unique and, thus, irreplaceable and immeasurable.A twenty-dollar bill has the power to affect lives of different people differently depending on their needs, their affluence, desires, interests, and so on.In educational context, we know that the same expenditure for "regular" students and students "with disabilities" may be highly unjust.As above shows, an evenly leveled floor does not guarantee that all people can see the game.This is the problem of the exact equal distribution of measurable things to people.Of course, as we have already discussed, equity -unequal distribution of measurable resources to achieve the same outcome -is highly problematic in its own right.In general, in our view, Graeber is 19 Sergeiy Sandler, who kindly provided us with his feedback on a pervious draft, raises an interesting question of how our harsh criticism of Paley is different from our Ana's treatment of Sarah.In our view, there are many differences.In contrast to Ana who wanted to change her behaviorist student, we do not try to change Paley in any way.Rather we honestly want to know her reply to her own and our challenges to her pedagogy.Also, Paley is not our student -we do not serve her self-education as teachers.She is our colleague.We do not need to assume a teacher orientation toward her.Our dialogue with Paley is out of educational context.There are other less important differences as well (e.g., institutional authoritarianism). 20Of course, in practice this is a questionable assumption since access to the global market and availability of goods are always local and particular.

Beyond equality and inequality in education
Eugene

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too optimistic, cavaliering the problem of measurable justice.The main problem we see is that although sometimes resources can be mutually replaceable, exchangeable, and measurable, their meaning and use value for unique people with unique goals situated in unique circumstances becomes unique in itself.Thus, exchangeable resources are measurable but they are also always unique.This creates a selfcontradiction in measurable things and, thus, in measurable justice.Karl Marx (1972) emphasized this self-contradiction of the notion of economic value as a mutually constitutive self-contradiction between exchange-value, which is always measurable and replaceable, and use-value, which is always unique and immeasurable.
But, how can unique people with unique goals, interests, and needs being in unique circumstances be supported by measurable resources in a just way?When these resources are unlimited or abundant enough for all of the participants in education, this is not a problem, of course.In this case, people can take as much resources for their education as they need and want.The problem starts when these measurable resources, having unique use-value for each participant, are not enough for all participants -how can they be split in a just way?
Our Bakhtinian dialogic ethics approach leads us to realize that there is no satisfactory formula for solving this problem.Thus, we reject Kantian Modernistic formulaic preset approaches based on equality, or equity, or lottery (i.e., luck of equal opportunity), and so on.Together with Bakhtin, we argue that justice and its criteria do not pre-exist the problematic situation but rather emerge from the problematic situation and the participants' creative deeds addressing it.Thus, we argue that the so-called measurable justice is not much different from the immeasurable justice situations discussed above.Participants' authorial deeds, their justifications, and replies to challenges of these deeds and justifications (i.e., taking responsibility) will ethically define these deeds and these participants for others and themselves in their unique circumstances in critical dialogue.Paraphrasing Thomas Jefferson's declaration that "all men are created equal," we argue that "all people are created unique." Having said all that, any society faces a problem of a just allocation of measurable resources in advance, without fully knowing the unique people with their unique goals, interests, and needs in their unique circumstances.Thus, in education, different public and private funding agencies have to allocate their funding in advance, knowing rather stereotypically about possible unique educational goals, interests, needs, and circumstances and not at all about emerging ones.The Bakhtinian dialogical ethics of responsibility reaches a limit in addressing this problem.In our view, it has to compromise with a Kantian formulaic approach.Recently, we have introduced such a proposal making a compromise between Bakhtinian dialogical ethics and Kantian formalism (Matusov & Marjanovic-Shane, 2016).
In our approach, we want to minimize unavoidable educational injustice coming from the limitation of resources, their unique effect on and unique value for unique participants, and the preset nature of the allocation process.We propose the minimum necessary monetary funding (i.e., measurable resources in the form of educational vouchers given directly to students 21 ) that can promote good quality education, where good quality education is defined heuristically and impressionistically by students.The formula for minimum funding is based on a statistical comparison of the surveyed quality of education between "poor" and "rich" students."Poor" students are those whose education is only funded at the public level."Rich" students are all those whose educational funds exceeds the public ones.If the comparison of the medians shows that "poor" students' satisfaction with their education is statistically lower than the educational satisfaction of "rich" students, the public funds have to be increased until the difference is not statistically significant.Thus, "rich" students define the minimum necessary resources for "good enough

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education" for all.This idea is based on the principle of "good inequality," promoting the future, described by Sci-Fi writer William Ford Gibson on the radio show Fresh Air (NPR, August 31, 1993), "The future is already here -it's just not very evenly distributed."Good inequality drives creativity and innovation and sets new goals for distributive justice.
The Kantian aspect of our proposal for funding justice in education involves: 1) a formula of funding, equalizing unique students, 2) statistical modeling, "regression to the mean," 22 and 3) surveying students' educational satisfaction, ranking unique values and definitions of education.The Bakhtinian aspect of our proposal involves unique students uniquely defining their goals, values, quality, and criteria of their education, calling for the pluralism of education philosophies, and the recursivity of the funding allocation process.Of course, our proposal is possible only when there are enough resources to support good enough education for all where "good enough for all" is defined statistically, -and there is societal commitment to that.As the overall measurable resources of the society grow and "rich" students consume more and more for their education, the statistically defined good enough education will require more resources.Thus, we expect that the minimum necessary public funding will grow as well (of course, if there is a political will for that).Because of that, our proposal for the societal allocation of public educational resources can be called "the maximin for good enough education as a basic universal right." The society maximizes that what it can afford and politically wills to allocate for the minimum universal basic income.

Conclusions: Just educational practice
In conclusion, we want to discuss how a just educational practice may look like from the perspective of the definition of educational justice based on Bakhtinian dialogic ethics.A just pedagogical practice does not guarantee educational justice but rather it promotes it by creating favorable conditions for justice.Bakhtinian dialogic ethics, described above, focuses on the uniqueness of people and their voices, on authorial transcendence of the given, on recognition of this transcendence by others and the author, on consciousnesses with equal rights, on internally persuasive discourse, on no-alibi in being, and finally on personal responsibility (Bakhtin, 1986(Bakhtin, , 1991(Bakhtin, , 1993(Bakhtin, , 1999)).Applied to education, this framework puts the learner in the center of educational practice as the author of this practice.Only when the learner is the full and final author for his/her education, supported by others as needed by the learner, is the educational practice just in the Bakhtinian dialogic ethics framework.We operationalize the favorable conditions for the learner's full and final educational authorship as the learner's multidimensional academic freedoms.These multidimensional academic freedoms and rights involve:

I
started thinking, but is it really true that two plus two always equals four regardless what one counts?Does what one count matter for the result?Rather quickly, I came to the following five paradoxical examples: Beyond equality and inequality in education Eugene Matusov, Ana Marjanovic-Shane Dialogic Pedagogy: An International Online Journal | http://dpj.pitt.eduDOI: 10.5195/dpj.2018.236| Vol.6 (2018) Matusov, Ana Marjanovic-Shane Dialogic Pedagogy: An International Online Journal | http://dpj.pitt.eduDOI: 10.5195/dpj.2018.236| Vol.6 (2018) Neither a correct nor an incorrect answer exists outside of the social context of the question.This context continues evolving and being evaluated.Correctness or incorrectness is always temporary until the next flip of meaning changes it: (in)correct for what, for whom, and under what circumstances?That makes people in dialogue poor Beyond equality and inequality in education Eugene Matusov, Ana Marjanovic-Shane Dialogic Pedagogy: An International Online Journal | http://dpj.pitt.eduDOI: 10.5195/dpj.2018.236| Vol.6 (2018) [I] was very concerned that Sarah, […] would remain ignorant and continue harming [her] students by [her] behaviorist pedagogical techniques without understanding how bad [it] what [she was] doing [was].[.
Beyond equality and inequality in educationEugeneMatusov, Ana Marjanovic-Shane Dialogic Pedagogy: An International Online Journal | http://dpj.pitt.eduDOI: 10.5195/dpj.2018.236| Vol.6 (2018) E23 and the learner's educational desires.I introduced the "Magic Wand" metaphor to the students on the class online forum, and in the next class meeting -as an open inquiry about, … what do I want to achieve and in what way with my students.If there were a Magic Wand that I could use to make all my students behave and study exactly as I wanted them to do, would I use it?When would I use it?Isn't ABA (behavioral management) something like a magic wand, to help me as a teacher achieve exactly what I want, with all my students?… Let's examine different real and imaginary scenarios and test the limits of our own beliefs about behavioral management techniques.[Let's examine] different difficult and problematic educational situations for all of us to think through whether to use or not to use behavioral management.What are the pros and what [are] the cons?…[ Beyond equality and inequality in education Eugene Matusov, Ana Marjanovic-Shane Dialogic Pedagogy: An International Online Journal | http://dpj.pitt.eduDOI: 10.5195/dpj.2018.236| Vol.6 (2018) schools' institutional pressures to control children's behavior.Nor did the class participants agree on the legitimacy of behaviorism to make children "sit still and focus on learning what they need to learn."The boundaries Beyond equality and inequality in education Eugene Matusov, Ana Marjanovic-Shane Dialogic Pedagogy: An International Online Journal | http://dpj.pitt.eduDOI: 10.5195/dpj.2018.236| Vol.6 (2018) Matusov, Ana Marjanovic-Shane Dialogic Pedagogy: An International Online Journal | http://dpj.pitt.eduDOI: 10.5195/dpj.2018.236| Vol.6 (2018) Beyond equality and inequality in education Eugene Matusov, Ana Marjanovic-Shane Dialogic Pedagogy: An International Online Journal | http://dpj.pitt.eduDOI: 10.5195/dpj.2018.236| Vol.6 (2018)

Beyond equality and inequality in education Eugene
undermining her ontological, Matusov, Ana Marjanovic-Shane Dialogic Pedagogy: An International Online Journal | http://dpj.pitt.eduDOI: 10.5195/dpj.2018.236| Vol.6 (2018) If you are using the same kind of techniques based on behavioristic learning theory on children, are you really keeping them [young autistic children], in some way, hungry?And what do you think about that?"Some of my other students picked up on my moralizing tone and vocally joined in the critique of using behaviorism with young autistic children, while other students openly or tacitly took Sarah's side.Sarah became incredibly disturbed as this situation made her confront her own professional ethics.Our discussion in class resulted in Sarah's dramatic protest, … Sarah burst out in protest and defended her position.In a shaky voice, holding back tears, she explained in a distressed and angry tone, addressing primarily [the] Professor …, that in her practice, based on ABA [behaviorist techniques of shaping children's behavior], she was "not cruel to my students!!! On the contrary!…You don't know what you are talking about!You don't know much about ABA! How can you judge it?!I love my students -I feel like a mother to them!You don't know my day-to-day problems!Enough of this!!!"(Marjanovic-Shane, 2016, p. A61)

Beyond equality and inequality in education Eugene
(Bakhtin, 1999)e is evidence that she knew perfectly well what she was doing, although this evidence is very indirect.We can hear another, almost alien, voice violently entering Paley's self-reflections in her book.It usually comes into very sensitive moments of Ms. Paley replying to children's urgent questions.It sounds like a voice of Paley's double(Bakhtin, 1999)who vigorously argues with her in her internal dialogues.Paley's double is not nice to her.It comments on her own statements with brutally-honest evaluations denouncing her own hidden manipulation with the children 17 , "Angelo wants to know what else I don't tell the children."I try not to tell you what thoughts or opinions to have," is my less than honest answer, at a time when I am singlemindedly pushing new attitudes about play Matusov, Ana Marjanovic-Shane Dialogic Pedagogy: An International Online Journal | http://dpj.pitt.eduDOI: 10.5195/dpj.2018.236| Vol.6 (2018)