Journal of Urban Mathematics Education

December 2016, Vol. 9, No. 2, pp. 11–28

©JUME. http://education.gsu.edu/JUME

BRIAN R. LAWLER is an assistant professor in the Department of Secondary and Middle

Grades Education at Kennesaw State University, 1000 Chastain Rd., Kennesaw, GA, 30144; email:

blaw@kennesaw.edu. His research interests include power and privilege in mathematics education,

and system change toward humanizing and equitable mathematics practices in schools.

RESPONSE COMMENTARY*

To Rectify the Moral Turpitude1 of

Mathematics Education

Brian R. Lawler

Kennesaw State University

First, I must confess that over the past few years I have been gravely disappointed with

the white moderate. I have almost reached the regrettable conclusion that the Negro’s

great stumbling block in the stride toward freedom is not the White Citizen’s Council-

er or the Ku Klux Klanner, but the white moderate who is more devoted to “order”

than to justice; who prefers a negative peace which is the absence of tension to a posi-

tive peace which is the presence of justice; who constantly says: “I agree with you in

the goal you seek, but I can’t agree with your methods of direct action;” who paternal-

istically believes he can set the time-table for another man’s freedom; who lives by the

myth of time and who constantly advises the Negro to wait until a “more convenient

season.” Shallow understanding from people of goodwill is more frustrating than abso-

lute misunderstanding from people of ill will. Lukewarm acceptance is much more be-

wildering than outright rejection.

– Dr. Martin Luther King, Jr., 1963

rofessor Danny Bernard Martin delivered a different talk at the National Coun-

cil of Teachers of Mathematics (NCTM) Research Conference in April 2015

(published by JUME later that year); he established an important concern that few

in the room would soon forget. Martin, like King (1963), was not interested in wait-

ing for a more convenient season to achieve a positive peace in mathematics educa-

1 The notion of “moral turpitude” is a legal concept, referring to conduct that is thought to be

against community standards of justice or morality. I do not claim here that any person or formal

organization ought to be brought to justice; however, it is certain that the current practices of

mathematics education are unjust and fail even its own moral standards.

*EDITOR’S NOTE: In the Spring/Summer 2015 issue (Vol. 8, No. 1) JUME published, as a

Commentary, Dr. Danny Bernard Martin’s invited plenary address delivered at the NCTM Re-

search Conference April 2015 in Boston, Massachusetts (Martin, 2015). In the Fall/Winter 2015

issue (Vol. 8, No. 2), JUME published a Response Commentary, authored by Drs. Diane J. Briars,

Matt Larson, Marilyn E. Strutchens, and David Barnes (Briars et al., 2015). The Response Com-

mentary here continues this important discussion; we invited others to keep things going while

they are still stirring (see “Contributing a Commentary to JUME: Keeping Things Going While

They Are Still Stirring”).

http://education.gsu.edu/JUME
mailto:mailto:blaw@kennesaw.edu
http://ed-osprey.gsu.edu/ojs/index.php/JUME/article/view/308/193
http://ed-osprey.gsu.edu/ojs/index.php/JUME/article/view/308/193

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 12

tion. Speaking truth to power (Rustin, 2012), he questioned whether NCTM could

be the organization to create the reform needed to change the conditions of the col-

lective Black (Bonilla-Silva, 2003) in mathematics education. Or is NCTM, the

“public voice of mathematics education” (NCTM, 2014, p. ii), this White moderate,

seeking an absence of tension, more dedicated to order than to justice.

In his invited talk, Martin (2015) expressed his disappointment with the

“White moderate” position that NCTM has taken. He recognized that a nearly thir-

ty-year history of documents, policies, and position statements from NCTM reflect

a nearly static concern with standards for mathematical content, instruction, and

assessment (Berry, Ellis, & Hughes, 2013), yet there has been little if no reduction

of dehumanizing practices or positive impact on inequities in student achievement.

Our profession, mathematics education, seems to lack the will to shift from an ori-

entation toward mathematics and mathematics education that systematically op-

presses, or fails to reduce the inequities of the larger society.

Representatives of the NCTM leadership (Briars et al., 2015) authored a re-

sponse to Martin on behalf of NCTM, set as a call to action. In that response, they

restated the many efforts toward more equitable mathematics education that have

been part of its recent history, and recognized there is more work to do—as they

had done previously: “Over the past twenty-five years, we have learned that stand-

ards alone will not realize the goal of high levels of mathematical understanding by

all students. More is needed than standards” (NCTM, 2014, p. vii). In this call to

action, NCTM (i.e., Briars et al., 2015) invited the mathematics education commu-

nity to participate in the conversation to consider what more is needed, committing

to using its role to strive for improvement. I commend the organization for this

stance; it is my intent to use this forum to take them up on the invitation to consider

action.

While there is great complexity in the challenge for NCTM to end its partici-

pation in the stratification of society, I focus in this paper on three core issues: what

counts as mathematics, explicit pedagogical attention to how mathematics works in

society, and revaluing mathematics as human activity. These three issues could be

considered ontological, epistemological, and axiological concerns; fundamental

structures or underlying worldviews of the mathematics education community that

in their present state obstruct the pursuit of a more just mathematics education. To

forge a liberatory and re-humanized mathematics education, I suggest each of these

core issues must be addressed. The changes I propose to each issue, while seeming-

ly radical, are insights recognized for decades within our own field.

Prior to the discussion of these three issues, I elaborate concerns raised by

Professor Martin (2015) then respond, reflecting on my 25-year career in mathe-

matics education. Following elaboration on the three issues, I argue that a new or-

ganization must emerge to speak back to NCTM, wholly convinced that the nature

of NCTM as an organization could never direct nor condone the work that would

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 13

radically change the collective conditions of African American, Latin@, Indigenous,

poor, queer, and otherwise underserved students.

A Consistent History

Of the core ideas in Martin’s (2015) invited talk, several resonated strongly

with me. First, the various standards for content and practice, teaching and profes-

sionalism, and assessment are far more similar than different over a nearly thirty-

year history. This lack of advancements in ways of thinking about content, peda-

gogy, and assessment suggests an inadequate interest for a positive peace. Second,

standards and similar documents reflect a particular ideology of what counts as

mathematics and mathematical ways of thinking. This ideology is presented as both

non-negotiable as well as necessary for a successful life after schooling. Yet many

adults find happiness and comfort in life, but do not have a level of mathematical

literacy called for in these standards (Ernest, 2000). And third, given the lack of

significant progress on equity targets in mathematics education, it strikes me that

very different ideas and very different voices are essential to make change.

The points raised by Martin (2015) are not entirely new (cf., Bishop, 1990;

Frankenstein, 1983); mathematics education functions in a manner to preserve itself.

Foucault (1981) recognized, “any system of education is a political way of main-

taining or modifying the appropriation of discourses, along with the power and

knowledge they carry” (p. 64); mathematics education is no different. For example,

Martin’s remarks during the talk provide an analysis of Principles to Actions: En-

suring Mathematical Success for All as an exemplar of “Race, Racial Projects, and

Mathematics Education” (Martin, 2013), an essay published in the NCTM periodi-

cal Journal for Research in Mathematics Education. As Martin notes in that essay,

questions such as Whose interests are served by mathematics education? persist,

having been considered by critical mathematics educators for several decades. It is

curious why now NCTM responds. More importantly, an honest analysis of this

condition would likely be important to understanding how impactful changes can

be achieved, what alternate voices might be heard.

NCTM’s mission charges it to be the public voice of mathematics education.

While NCTM is to be commended for publications that reflect many voices repre-

senting the diverse perspectives of mathematics educators, its stance as the public

voice remains problematic. As Martin (2011, 2013, 2015; see also Martin, Gholson,

& Leonard, 2010) argues, there is a need for NCTM as this public voice to recog-

nize and then interrogate its position as an institutional space of whiteness serving a

majority White audience. This status is likely not by design, rather a historical

product of a deeply racist society and educational system, a product of both physi-

cal and psychological colonization by European settlers and Western thought. The

danger of this status is that NCTM is unlikely to recognize possibility that lies out-

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 14

side its paradigm. Furthermore, because of its responsibility to its members (recall,

“the voice of mathematics education”), NCTM is unlikely to take a stance that

would not be readily embraced by the (predominantly White) mathematics educa-

tion community. Because of its status, NCTM is unlikely to advocate for children

over mathematics. Because of its incorporation, survival of the business is the first

priority. Ultimately, NCTM operates in service to the White majority: its economic

desires, its rationalities and sensibilities, its benevolence. Martin (2015) claims that

given this frame, gains for the collective Black can only come hand in hand with

benefits for Whites. His is not a singular perspective; modern sociology recognizes

these conditions as the present operations of racism in modern day America, where

not only the criminal justice system but also the educational system is creating a

new Jim Crow (Alexander, 2010; Thomas, 2013), a uniquely American approach to

ensuring a caste social system.

The Need for Introspection

NCTM’s actions since the late 1980s occurred within a larger neoliberal eco-

nomic, political, and social context, generally a turn toward free market ideology

and individualism.2 For example, NCTM’s policies typically came with a message

that there are many ways a teacher can support students to achieve the standards;

we will not prescribe any particular pedagogical strategy. Furthermore, the context

has allowed for schools to view the student as “being solely responsible for the con-

sequences of the choices and decisions they freely make” (Thorsen, 2006, p. 208).

These actions fail to interrupt (if they do not create) a bifurcated educational

experience that works more insidiously than to create simple discrepancies such as

achievement gaps. In its present form, mathematics education operates as a Centaur

state (Wacquant, 2014), liberal at the top and punitive at the bottom. The enterprise

of mathematics education flouts egalitarian ideals, evidenced by cries for Mathe-

matics for All and strong support for equity—as seen routinely in conference pro-

grams as an “equity strand.” Attention to mathematical processes, habits, or prac-

tices value problem solving, discourse, and the conceptual-oriented thinking of

mathematicians. Yet for students of the collective Black, they are more likely to

experience mathematics classrooms that focus on procedures and memorizing (Da-

vis & Martin, 2008), skills for employability or servitude. All the while, classrooms

that include children of society’s more privileged focus on higher order reasoning,

problem solving, and discourse (Anyon, 1980; Ladson-Billings, 1997; Lubienski,

2002).

2 Liberalism is generally a strategy toward the prevention of social conflict. Neoliberalism has

emerged as economic policy grounded in ideas of free market capitalism and the glorification of

individualism.

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 15

Sociologist Loïc Wacquant (2014) argues that neoliberal policies for address-

ing inequalities experienced by marginalized populations, as we see in mathematics

education, leads to the “criminalization” of poverty (i.e., the creation of the collec-

tive Black). An example of this sort of educational criminalization is the deficit ori-

entation to the learner, an ideology baked into our discourse. Further examples of

neoliberalism in mathematics education include brutal assessment policies, which

work to disproportionately hold children of the collective Black further and further

behind;3 policies that emerged from the federal Elementary and Secondary Educa-

tion Act of 2002 create shutdowns or takeovers of a disproportionate number of ur-

ban schools (Sunderman & Payne, 2009); research programs yield pedagogical

strategies focused on deficit, such as student misconceptions (e.g., Smith & Stein,

2011); and the notion that certain families do not value education (Aguirre, May-

field-Ingram, & Martin, 2013) allows for lessened expectations. This criminaliza-

tion of children leads to heighted punitive results such as increased suspensions

(Advancement Project, 2007) and more years repeating math classes (e.g., Fong,

Jaquet, & Finkelstein, 2014), leading to our grave awareness of the efficiency of the

school to prison pipeline (Amurao, 2013) for children of the collective Black. The

centaur state of mathematics education creates liberal ideals with minimal oversight

for those at the top, and repressive practices with strict controls for those at the bot-

tom. This mathematics education is systematically failing all our children—whether

by oppression or by creating a false sense of righteousness.

Martin (2015) argues well that the negative outcomes experienced in mathe-

matics education by the collective Black serve to support larger economic, social,

and political agendas. In NCTM’s role as the public voice of mathematics educa-

tion, I expect the recognition of and calls to action against such injustices. These

calls, however, are not enough; Martin has challenged NCTM with introspection, to

consider how it may be complicit.

A Liberatory Mathematics Education

The present centaur state of mathematics education serves to sediment the ne-

oliberal (and neocolonial) standardization agenda. The particular mathematics

knowledge and ways of knowing put forth by NCTM is to format (Skovsmose,

1994), or fabricate (Lawler, 2012), the child. Here I suggest shifts in three princi-

ples foundational to mathematics education, necessary, yet not sufficient for a radi-

3 For example, “The achievement gap between children from high- and low-income families is

roughly 30 to 40 percent larger among children born in 2001 than among those born 25 years ear-

lier” (Reardon, 2011, p. 91).

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 16

cal4 change that may allow for a liberatory and re-humanized mathematics educa-

tion. The first is ontological—the status of mathematical knowledge; the second,

epistemological—an interrogation of how mathematics education is complicit in

racism; and the third, axiological—what a re-humanized mathematics education

should value.5 I point to these underlying philosophical principles that have invisi-

bly guided mathematics education to its present state of moral turpitude.

Rethink the Ontological Status of Mathematics

The present ontological status given to mathematics reflects Western logic; a

way of thinking that arose during the Age of Reason. This current status reflects the

realist (or Platonist) tradition, which emerged from rationalists of 17th century Eu-

rope. They claimed that all knowledge could be acquired on the power of reason

alone; mathematics is the model for such knowledge. Furthermore, this mathemati-

cal knowledge is considered to exist independent of human experience. The realist

orientation to knowledge allows for metaphors such as discovery for learning, and

guidance or facilitation for teaching (Davis, Sumara, & Luce-Kapler, 2015)—

metaphors common to present mathematics education.

This ontological perspective persists for several reasons. Among them is that

many working mathematicians are mathematical realists. They see their work as

discovery of naturally occurring objects, not the products of their humanity or con-

structions of their mind. Davis and Hersh (1981) suggested, “The typical mathema-

tician is a Platonist during the week and a Formalist on Sundays” (p. 321). That is

to say, mathematical objects are real, they exist “outside the space and time of phys-

ical existence” and “quite independent of our knowledge of them” (p. 318).

A second force maintaining this ontology is how it has so successfully sorted

and ranked our current society by defining levels of intelligence (Lakoff & Núnez,

2000; Lawler, 2005); mathematicians are often thought of as brilliant, having at-

tained the highest form of knowing. An example of this societal belief can be found

in our print media: “One reason why people who learn more mathematics earn

more is because doing maths makes you smarter and more productive” (Schrager,

2009, ¶3). As a result, those who possess knowledge in the domain (i.e., the disci-

pline of mathematics) are “more aligned with communities of practice that hold

more power” (Nasir, Hand, & Taylor, 2008). This sort of status bestowed upon the

nobles precluded them from alternate considerations of the ontological status of

mathematics that have the potential to remove them from the court.

4 A shift in these foundational principles may reflect the notion of violence summoned by Martin

(2015).

5 For the purposes of this article, I bend the epistemological argument to attend to how the noetic

emphasis of a realist ontology sharply limits what counts as mathematics, and thusly can be used

to sediment hegemony.

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 17

This present, persistent ontology afforded to mathematics produces innumer-

able iniquities, one being that it allows for deficit language in mathematics; we fo-

cus on misunderstandings—not possessing the correct, enlightened way of knowing.

Foucault (1965) writes that this sort of deficit orientation to forms of discourse,

knowledge, or ways of knowing pathologizes not only the discourse but also the

person. Mathematics educators are so steeped in the dominant, realist, “standard-

ized” mathematics (Gutiérrez, 2007) that we can no longer imagine, let alone have

the ears to hear, our students’ subjugated knowledges (Foucault, 1980)—

mathematical ways of thinking and knowing that are left out, opposed, or ignored

by the dominant culture. We can only not hear the brilliance of the collective Black.

What is needed is a counter-discourse, oppositional to the standard system of

mathematical knowledge and knowing. This counter-discourse must reveal how the

accepted knowledge is built on exclusion and confinement. It is within these hidden

forms of knowledge that we may recognize the limits of the knowledges that dis-

qualify them.

This sort of disruption of Western ontologies already exists within mathemat-

ics education. One example is in the ethnomathematics tradition; the dominant view

of mathematics is recognized as only one of many (see Powell & Frankenstein,

1997). Similar perspectives emerge in relational (Belenky, Clinchy, Goldberger, &

Tarule, 1986; Thayer-Bacon, 2003) and indigenous epistemologies (Battiste, 2013;

Sarra, 2011). In some of these perspectives, the learner is characterized as a mathe-

matical author (Povey, Burton, Angier, & Boylan, 1999). Povey and colleagues ar-

gue that this shift in perspective on “author/ity amongst teachers and learners will

support a renegotiation of the relations of dominance embedded within current con-

ceptions of the nature of mathematical knowledge” (p. 244), a disruption that has

the potential to revalue whose mathematics counts.

There is a second, ignored tradition in mathematics education that interrupts

the realist ontology of the dominant orientation to mathematics—the constructivist

orientation to knowing and learning that arose in mathematics education just prior

to NCTM’s first standards. Smock and von Glaserfeld (1974) posited that

knowledge is not passively received through the senses or by communication; ra-

ther the cognizing subject actively builds it up. In other words, knowledge is the

result of a self-organizing process, a human construction generated in interaction:

“Coming to know is a process of dynamic adaptation towards viable interpretations

of experience. The knower does not necessarily construct knowledge of a ‘real’

world” (von Glaserfeld, 1990). Constructivism suggests an ontology in which

“knowledge is not the commodity the tradition of Western philosophy would have

us believe” (von Glaserfeld, 1988, p. 83).6 Unfortunately, the radical ontological

6 Quoting Montaigne, “La peste de l’homme, c’est l’opinion de savoir” or “Mankind’s plague is

the conceit of knowing” (von Glaserfeld, 1988, p. 83).

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 18

notions of constructivist epistemologies that briefly enamored the profession (Davis,

Maher, & Noddings, 1990) failed to take hold.7 Presently, many applications of

constructivist theory emphasize the activity of the learner, but fail to shift the ontol-

ogy (Lawler, 2014).

Since constructivism’s explosion and quick departure in mathematics educa-

tion, there have been others whose work disrupts the ontological status of mathe-

matics from a sociocultural and sociopolitical orientations (see, e.g., Gutiérrez,

2013; Nasir et al., 2008) rather than psychological. Yet these, too, have yet to find

traction.

The implications for the proposed ontological shift from one to many mathe-

matics are systemic. Fundamentally, it demands a re-humanization of both mathe-

matics and mathematics education. Could the institution and pedagogies of mathe-

matics education recognize many mathematics and many ways of being mathemati-

cal? Such an ontological shift suggests a pedagogy focused on listening8 rather than

telling, a move away from authority and control, evoking new relations of power.

Teachers listen to form conjectures of student conceptions, serving to generate for

the teacher a tree of potential new ways of knowing for the child. The teacher’s role

becomes to design an environment that may occasion the emergence of new math-

ematical ways of knowing (Davis, 1996). The child leads, the teacher follows.

Confront the Role of Racism in Mathematics (and Mathematics in Racism)

The second foundational shift I propose is for mathematics education to be

explicit about the consequences of and its complicity in racism and similar oppres-

sion, an epistemological emphasis on how mathematics functions. At present, the

field is nearly silent on the roles of racism in mathematics (cf., DiME, 2007; Powell,

2002; Spencer & Hand, 2015) and mathematics in racism (Bishop, 1990; Franken-

stein, 19839). Much that I have documented above demonstrates the ways in which

the racist American society propagates itself through a particular mathematics—that

racism flourishes is in part through this mathematics’ ability to create a centaur

state.

Others have demonstrated mathematics’ functions in racism. For example,

through the use of counting and emphasis on hierarchal relationships, mathematics

provides a colonizing power to administer and govern (Foucault, 2009). Davis and

7 A notable exception is the idea of enactivism (Davis, 1996), still present in some research pro-

grams outside the United States, Canada in particular.

8 Davis (1997) proposes a hermeneutic listening, which “is intended to imply an attentiveness to

the historical and contextual situations of one’s actions and interactions” (p. 370).

9 “Traditional mathematics education supports the hegemonic ideologies of society” (Frankenstein,

1983, p. 328).

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 19

Martin (2008) argue how the subordination of Blacks is built on scientific methods

of mathematical measures to support and validate racist beliefs. Frankenstein (1983)

suggests, “the hegemonic ideology of ‘aptitudes’—the belief, in relationship to

mathematics, that only some people have a ‘mathematical mind’—needs to be ana-

lyzed” (p. 329). Furthermore, Popkewitz (2004) argues that modern pedagogies in

mathematics serve to “divide, demarcate, and exclude particular children from par-

ticipation” (p. 4). Mathematics, as a colonizing force historically and presently, is

thought to represent the highest forms of Western thinking, and is assumed better

than any indigenous mathematical systems or ways of knowing.

This second recommendation is that not only must our profession recognize

and embrace the colonizing and formatting power of both mathematics and mathe-

matics education, but also the study of these issues must become a required element

of the K–12 mathematics curriculum. Again, the ethnomathematics tradition may

offer a start toward this alternative epistemology. Powell (2002) notes that ethno-

mathematics “departs from a [Western] binary mode of thought and a universal

conception of mathematical knowledge that privileges European, male, heterosexu-

al, racist, and capitalistic interests and values” (p. 17); it disrupts the notion of a

singular mathematics. The mathematics classroom could include study of others’

mathematics, and include questions like Where do degrees come from? and Who

decided we will measure angles with degrees? Given that answers to questions like

these are along the lines of “because some people determined it should be that

way,” such a pedagogy can allow students to begin to recognize mathematics has a

cultural history (Bishop, 1990), another re-humanizing move.

Similarly, the traditions of criticalmathematics (Frankenstein, 1983; Powell,

2002) and mathematics for social justice (Gutstein, 2005; Leonard, Brooks, Barnes-

Johnson, & Berry, 2010) offer frameworks for examining as well as teaching a dif-

ferent mathematics, such as Gutstein’s (2005) call to embrace classical, community,

and critical mathematics. Furthermore, there is a wealth of strategies and materials

available for use in the classroom, and a broad community of mathematics educa-

tors embracing this approach (Gutstein & Peterson, 2005; Wager & Stinson, 2012).

Critical and social justice mathematics offer different pedagogies, yet as Martin

(2013) has noted, the perspectives have not been consistent in explicitly attending

to issues of racism. Culturally relevant pedagogy (Ladson-Billings, 1995; Leonard

et al., 2010) offers this missing element, calling for a critical pedagogy of cultural

critique, to attend to “political underpinnings of the students’ community and social

world” (Ladson-Billings, 1995, p. 477).

Often a critical or social justice approach to mathematics teaching is rejected,

arguing such topics lie outside the discipline (Beck, 2014; Ravitch, 2005). NCTM

could elect to impact this rationale; in fact, it already has a rich history of embrac-

ing interdisciplinary approaches to mathematics education—often connections to

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 20

scientific or economic topics. Seeing mathematics as a product of human activity

offers a seemingly natural interdisciplinary fit with humanities and social studies.

Mathematics has been used for great evils including the creation of ranked so-

cial structures and the validation of racist beliefs. It would be incomplete to not rec-

ognize it as also been used for great good, and can be used to disrupt injustices

(Gutstein, 2005). A critical social and historical understanding of the role of math-

ematics in people’s lives would create better understanding of the roles mathemat-

ics has contributed socially and politically historically, the way it operates presently,

and how it can be harnessed to fight injustices and create a better world

(D’Ambrosio, 2007). The recognition that mathematics works in particular ways,

including to stratify society and perpetuate racism, and that how it works can be

changed, leads to a need for consideration or the moral code underlying the field of

mathematics education.

Highlight the Humanity of Mathematics

A third foundational element of mathematics education in need of examina-

tion is its moral code, an axiological consideration. Mathematics is not neutral (Na-

sir et al., 2008) nor value free (Frankenstein, 1983); mathematics and mathematics

education are the products of human activity (Davis & Hersh, 1981; Kilpatrick,

2012), “math needs people” (Gutiérrez, 2013, p. 48). What is the kind of behavior

we aspire to? Why do we teach mathematics, to what end?

Several years ago I interviewed Laurie Reyes Hart and George M. A. Stanic

(Lawler, 2005), two mathematics educators whose careers focused on issues related

to equity. The interview was grounded in their review of research focused on dif-

ferential achievement in mathematics based on race, sex, or socioeconomic status

(see Reyes & Static, 1988). I asked both Why should we teach mathematics?—a

question Stanic (1984) traced historically for his doctoral dissertation; a question

usually assumed to be so self-evident that we as a field forget to ask. Yet that math-

ematics seems complicit in both benefits and iniquities10 compels contemplation of

the justification question.

In their response, both Hart and Stanic (see Lawler, 2005) questioned argu-

ments about the utility of mathematics; they frequently ignore that most people

function well in their daily lives without a profound level of mathematics.11 Fur-

10 I intentionally use iniquity, a term to indicate a gross injustice, or wickedness. My use was

prompted by Stanic in my interview, in which he expressed his notion of equity “as the opposite of

iniquity, as the opposite of something evil. So that it’s more than the kind of gentle word than we

think of it as.... When you start thinking of it as that which is the opposite of iniquity, suddenly

you seem to have more responsibility” (Lawler, 2005, p. 36).

11 There is a “simultaneous objective relevance and subjective irrelevance of mathematics in socie-

ty” (M. Niss, as cited in Ernest, 2000, p. 3).

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 21

thermore, both dismissed the justification that we must teach mathematics so future

citizens can contribute to the economy. Hart surmised that mathematics should be

taught for access to power and resources, as well as awareness of mathematics as a

tool of oppression. Stanic added that mathematics seems to be “this interesting phe-

nomena that has arisen among human beings, and thus worthy of study because it’s

such an important part of human life, historically” (p. 35).

Stanic (see Lawler, 2005) suggested that not only is humanity defined in part

by our mathematics but also the study of mathematics is in part a study of our hu-

manity. Beyond the shift to recognize mathematical ideas are generated by people

and in cultures, there is an onus to examine ethics of mathematics, and mathemati-

cal ways of knowing. What are the responsibilities that come with learning mathe-

matics? What are the responsibilities that come with knowing a particular mathe-

matics? What are the responsibilities for using mathematics? Furthermore, what

might it mean to develop a mathematics education with a project to erase inequities

between people, mathematics, and the globe (Gutiérrez, 2007)? Gutiérrez (2013)

argues a key aspect of equity is for the mathematics education community to “be-

come experts at supporting learners to maintain a sense of wholeness while doing

mathematics” (p. 61). Classroom and professional foci such as those indicate in the

questions above would contribute not only to the development of robust children’s

mathematical identities (Aguirre et al., 2013), but also to those of our professional

community.

Similar to a study of the sociohistorical productive and destructive uses and

impacts of mathematics as previously encouraged, a broader study of the humanity

of mathematics would begin to achieve an ethical imperative to humanize the disci-

pline. The stories of mathematicians, wide-ranging biographies, may become part

of the curriculum. Some stories may be of a particular problem that puzzled this

person, serving to pose a problem for classroom study. The effort could extend to

the study of peoples, in which once again the ethnomathematics tradition offers

many examples.

Over these past 30 years, NCTM has asserted standards for mathematical

practices and identified habits of a mathematician. These human aspects of doing

mathematics and the development of mathematical identity (Aguirre et al., 2013),

however, seem to be largely ignored. During the same time period, epistemologies

that embrace a critical orientation to the intersection of mathematics and society,

and postmodern shifts in ontology have also been ignored in the practices of math-

ematics education, as well as in the policy statements and other actions of the

NCTM. The three recommendations suggested above are radical, in the sense they

call for difficult shifts in mathematics education. Of course there are recommenda-

tions offered by others that I have not recognized here, such as a modernized and

germane content, culturally relevant tasks, a diversity of teachers that match that of

students, and an end to the accountability rhetoric (Suspitsyna, 2010) and the testing

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 22

regime. It is my sense that each of those is secondary to the changes I have argued.

That is, making those shifts are predicated on the three I suggest, and are not suffi-

cient to change the experiences of students to be something other than schooling as

a colonizing experience into the White, upper-middle class value system and ways

of knowing.

What NCTM Did Not (Could Not?) Hear

I have suggested three recommendations fundamental to a liberatory and re-

humanized mathematics education. These recommendations are not new; they are

already represented in numerous traditions and research programs within the larger

Mathematics Education community. Yet they remain unfulfilled. Important ques-

tions to ask: Why has the field of mathematics lacked political will to enact re-

humanizing recommendations? Where is the moral outrage? (Spencer, 2015) Mar-

tin (2015) suggests that the current state of affairs affords not only NCTM as an

organization but also its leadership and its members social, economic, and political

privileges. It is certain that the mathematics education community is a conservative

force (Kilpatrick, 2012), lacking the will to disrupt this current state of affairs. As it

operates now, the mathematics education project writ large benefits from the status

quo. There are large sums of money to be garnered for research programs that rely
on seeing the collective Black as deviant (Berry et al., 2013), and potentially greater

dollars to be made peddling equity-themed products and professional develop-

ment—all in the guise to improve the lives of the collective Black. Furthermore, as

mathematicians and mathematics educators, our status is conferred by a particular

view of mathematics; it is not in our interest to disrupt this enlightened, ordained

form of knowledge. Kilpatrick (2012) notes: “Teachers of mathematics may derive

considerable status from presiding over a subject that others find difficult or even

impenetrable. Why should they lower it from its elite pedestal?” (p. x). These

changes are messy, imbued with power and ego, requiring mathematics educators

to “reject a view of their subject that may have been a mainstay of their scholarly

identity” (p. x).

From my perspective, the NCTM response (see Briars et al., 2015) ignores

significant aspects of Martin’s (2015) critique. This non-response was predicted by

Kilpatrick (2012); it is the product of the organization’s conservative drive to main-

tain the present state of affairs in mathematics—the decades-long, persistent cry for

equity. NCTM’s response seems to not recognize two critical concerns voiced by

Martin: (a) to redefine the goals of the mathematics education enterprise to escape a

colonizing orientation, and (b) to wonder if NCTM is capable of leading such

change.

Martin (2015) states that the mathematics education community, in general,

and NCTM, in particular, has not made significant progress in addressing the op-

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 23

portunity gap; that is, it has not made significant progress in changing “the condi-

tions of African American, Latin@, Indigenous, and poor students in mathematics

education” (Martin, 2015, p. 22). NCTM either refused to hear, could not hear, or

ignored Martin’s intent with this passage. NCTM remains muddled in the notion of

an opportunity gap, but Martin has no interest in this framing of an opportunity gap;

it leaves unquestioned the Eurocentric and colonizing form of mathematics educa-

tion indisputed, undisturbed. At present, mathematics education functions to per-

petuate the ideology of the dominant view of mathematics. The emphasis on an op-

portunity gap for NCTM is to improve the opportunities for the collective Black so

as to assimilate to the dominant view, in effect to become white washed.12 As Mar-

tin (2015) puts it, NCTM seems unable to get beyond an orientation to equity for

the collective Black “to enjoy contingent benefits of the system, [a system] that is

not set up for them or by them” (p. 22).

Martin (2015) characterizes the change necessary to the status quo of mathe-

matics education as violent, a change that would put the last first. This language is

strong, yet “decolonization is always a violent phenomenon” (Fanon, 1968, p. 35).

As a White heterosexual man, quite successful in a system set up for me,13 I can

empathize with the anxieties this sort of language brings. If the collective Black

were to become those who succeed, people like me could be repositioned as the re-

current failures. It is clear that such a result does not sit well for neither me nor oth-

ers; but the fierceness in which we refuse such a solution seems not to be matched

in our duty to correct the contemporary reverse injustices.

The present iniquitable outcomes of mathematics education are evidence that

the Eurocentric mathematics of schools serves as a colonizing force to the minds of

children, possibly all children, but certainly those whose cultures do not align to the

dominant American (U.S.) culture. The last 27 years suggest that relying on the

White benevolence of NCTM will not achieve the kinds of equity called for.14 For

correction to be other than an incremental change, the history of mathematics edu-

cation suggests that some form of impassioned, vigorous, violent—in the sense of

total—action must be taken. This is not the violence of bloodshed, but the overhaul

of a colonizing institution and belief system about what counts as mathematics, and

what is valued in a mathematics education. It is to be a violence on the level of the

12 To understand the trauma associated with this sort of experiencing of the Eurocentric mathemat-

ics school culture, consider, for example, Stinson (2006).

13 I owe “the fact of [my] very existence… to the colonial system” (Fanon, 1968, p. 36).

14 Gutiérrez (2007) proposes a redefinition for equity goals in mathematics education. She sets the

target for equity to be three-fold: (a) to be unable to predict achievement and participation based

solely on student characteristics; (b) to be unable to predict ability to analyze, reason about, and

critique the knowledge and events in the world based solely on student characteristics; and (c) to

erase inequities between people, mathematics, and the globe.

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 24

routine psychological, social, and institutional violence perpetrated on the collective

Black.

Mathematics education incurs a psychological, not physical violence; it is a

psychological colonization (Fanon, 1968). The decolonization project must liberate

the colonized mind from the effects of alienation and dehumanization. It is certain

to be an intense, sociopolitical contention in which race and class-based struggle

play a key role. In this struggle, NCTM is a political organization representative of

the colonial bourgeoisie. It is not in their interest to oversee a removal of the system

that has created their dominance: “Is NCTM the kind of organization that is capable

of facilitating the kind of violent reform necessary to change the conditions of Afri-

can American, Latin@, Indigenous, and poor students in mathematics education?”

(Martin, 2015, p. 22). I suspect the institution, the voice of mathematics education,

can only imagine a reform entailing tweaks and modifications. NCTM will promote

compromise, a non-violence. The question I see unasked in Martin’s comment is

What violence is necessary?

I suggest the violence necessary is embedded in three shifts I have recom-

mended here, actions that reclaim and humanize the ontological, epistemological,

and axiological roots of the present mathematics education. It is my hope that these

recommendations could result in a liberation of the consciousness, reverse the ef-

fects of alienation and dehumanization for both students and educators, build soli-

darity in the struggle for liberation, and reconstitute the structures and social institu-

tions of the present mathematics education.

To close, I call for a movement to rise, possibly from within mathematics ed-

ucation, that not only strives to improve the condition of the collective Black but

also conceives further to disrupt the status quo in such a way that moves the last to

first, 15 to decolonize mathematics education. This movement cannot become a

pawn or affiliate of the NCTM, “it is the colonist who fabricated and continues to

fabricate the colonized subject” (Fanon, 1968, p. 2). Based on nearly thirty years of

equity rhetoric and little action, NCTM’s content adherence to “myth of time”

(King, 1963, p. 10), that “the very flow of time will inevitably cure all ills” (p. 11),

suggests that NCTM “paternalistically believes [it] can set the timetable for another

man’s freedom” (p. 10). The colonized subject must break from NCTM and create

a counter-organization to express its own voice. This new community must emerge

to counter the conservative institutional force of NCTM. We cannot afford the

mathematics education that presently exists under our watch.

15 It is my sense that in a new ontology, all can be first—an absence of hierarchy, a postcolonial

heterarchy.

Lawler Response Commentary

Journal of Urban Mathematics Education Vol. 9, No. 2 25

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