Reframing Interventions in Mathematics Education: Emerging Critical Perspectives


To be presented at PMENA 2016 November 3-6 in Tucson, AZ.  Registration is online now at:

If you are interested in attending the working group, please comment here so we can send you further information.

James Sheldon, University of Arizona

Kai Rands, Independent Scholar

Rachel Lambert, Chapman University

Paulo Tan, University of Tulsa

Elizabeth De Freitas, Adelphi University

Nathalie Sinclair, Simon Fraser University

Katherine E. Lewis, University of Washington

Jeremy Stratton-Smith, Middlebury College


Mathematics interventions have proliferated within the field of mathematics education as schools are under increasing pressure to raise the mathematics test scores of low-achieving students, particularly students of color and students with disabilities.  These interventions target individual students and are based on a deficit model; the problem is located within the individual student rather than in the social, discursive, political, or structural context.  These interventions also tend to focus primarily on rote algorithms and calculation skills rather than the solving of rigorous, high cognitive demand problems.  Our working group is composed of researchers and teachers who draw upon critical theories, such as Disability Studies in Education, Critical Race Theory, and DisCrit, in order to offer an alternative vision of mathematics education based around a different type of intervention.  Rather than making an intervention into the deficits of an individual student, our working group suggests that we need to make an intervention into classroom practice, utilizing models like Complex Instruction (CI) and Universal Design for Learning (UDL) to create classrooms in which all students are able to access the curriculum in meaningful and rigorous ways.


Keywords: Classroom Discourse, Equity and Diversity, Instructional activities and practices

Rationale:  Framing the Problems/Questions of the Working Group

The title of this working group, Reframing Interventions in Mathematics Education, Emerging Critical Perspectives, is intended to evoke a double meaning.  It can be read as an intention to critique the practice of intervention in the field of mathematics education; alternatively, the title can be read as inviting critical interventions into mathematics and mathematics education.  By pursuing both paths simultaneously, we intend to stimulate productive discussions and lay the foundation for future projects during our work in the span of three working group sessions.


Mathematics Intervention

Intervention programs have become ubiquitous within mathematics education as teachers and schools are under pressure to raise mathematics test scores.  These programs utilize service delivery models such as Resource Specialist Programs (RSP) and Response to Intervention (RTI) and techniques such as Progress Monitoring in order to identify students in need of intervention and deliver interventions.  These interventions rarely focus on increasing student participation in classroom discourse; they instead focus primarily on basic fact acquisition and algorithmic fluency.  Most districts use older models that measure mathematics students against normative standards of development, with instruments such as the Woodcock-Johnson, the Wechsler Individual Achievement Test (WIAT), and the KeyMath being used to diagnose areas in which students’ “achievement” fails to match what IQ tests show as their “ability.”  Some districts use newer models such as RTI for diagnosis, which claim to identify and classify students based on their response to “scientific”, “evidence-based” interventions.  Progress monitoring techniques such as AIMSweb focus less on testing of “ability” and instead focus on repeated assessment of students’ mathematical skills, but the data collected still tends to focus myopically on basic calculation skills.  The problem, our working group believes, is not with the instruments being used to assess, but with the very concept of intervention itself.


The Problem with Intervention

To better understand the concerns we are raising about the concept of intervention, we invoke the history of the term, finding that the very etymology of the word points to some problematic assumptions imbedded within.  The English word “intervention” comes from the Latin “inter,” meaning “between,” and “venire,” meaning “to come.”  Etymologically then, intervention implies “coming between.”  Two core assumptions are embedded in the concept of intervention.  The first assumption is that there is something wrong with the situation at hand that needs to be changed.  The second assumption is that it is someone or something from outside the situation that must “come into” the situation and make the change.  Often, in education generally and in mathematics education in particular, the need for intervention is taken-for-granted.  However, acknowledging the assumptions upon which the concept of intervention rests raises numerous questions about the idea of intervention in education, and specifically in mathematics education.  The critique that we are offering asks questions such as:

To what extent is “intervention” necessary or desired in the situations in which it is currently used?  Necessary for what and to whom?  Desired by whom and for what purpose?

What aspects of the situations are taken as “wrong” and requiring intervention?

Who benefits from interventions, and in what ways?

What are the implications of the fact that the concept of intervention is based on the assumption that someone from outside must “come in” to make changes?

What counts as “intervention”; are interventions only narrow, technical methods used to correct problems with a particular student or can we expand the concept of intervention to create meaningful change within classrooms?

In our current historical moment in the United States we believe it is important to consider the way that “interventions” are used for low-achieving students (especially students of color and students with disabilities) and to offer critical alternatives to the practice and philosophy of intervention.


Drawing upon Theory

Gathering together a group of researchers, graduate students, undergraduate students, and classroom teachers interested in developing an alternate paradigm around intervention, we have begun to explore the different theoretical frameworks that we can use to analyze and change this situation within mathematics education.  Heeding Lather’s (1986) call for researchers to utilize multiple theoretical schemes in their work, our working group believes that this work requires the participation of multiple paradigms of critique.  Our working group draws upon critical theories such as disability studies, critical race theory, and other poststructural theories (including queer studies and trans studies) in this analysis.  A commonality among these perspectives is that each problematizes normativity.  We welcome the participation of those with other perspectives as well.  In the following sections, we describe a sampling of these perspectives in order to frame the work of the group.


Critical Theories

Although the notion of critique dates back to antiquity, the phrase critical theory originally referred to a body of work coming out of the Frankfurt School and Institute for Social Research in the late 1920s through the early 1940s.  Critical theory seeks to reshape reality, not merely explaining things.  As Karl Marx (1845) wrote almost a century earlier, “The philosophers have only interpreted the world, in various ways; the point is to change it.”   Critical theory has come to mean not just the work of the original critical theorists, but any theory that seeks to transform rather than merely explain society.  The Stanford Encyclopedia of Philosophy gives three main criteria for a critical theory, that “it must explain what is wrong with current social reality, identify the actors to change it, and provide both clear norms for criticism and achievable practical goals for social transformation.” All of the theoretical perspectives that our working group draws upon are in some ways “critical theories.”


Disability Studies and Disability Studies in Education

Many of the members of our working group utilize disability studies (DS) and disability studies in education (DSE) as a mode of inquiry in order to questioning the taken-for-granted assumptions and practices in mathematics education and the intervention paradigm.  DS and DSE provides a framework for exploring questions such as: who is labeling, who is being labeled, and how do we advance more equitable practices for all students.  Disability studies calls into question the medical/individual model of disability in which disability is seen as a deficit within an individual that requires “curing.”

In contrast to the medical model, many disability studies scholars and activists have adopted a social model of dis/ability, which locates dis/ability in an inaccessible environment.  Those who adopt the social model of dis/ability make a distinction between impairment, as any physical or mental limitation, and disability, as the “social exclusions based on, and social meanings attributed to, that impairment” (Kafer, 2013, p. 7).  Kafer (2013), however, argues that such a sharp distinction between impairment and dis/ability is unhelpful because it “fails to recognize that both impairment and disability are social” (p. 7).  In the book Feminist Queer Crip, Kafer suggests the term “political/relational model” to refer to perspectives recognizing that both impairment and dis/ability are socially constructed.

In educational settings, this construction of dis/ability manifests in the double education system that splits general education and special education. Scholars have traced the ways in which special education “serves as a vehicle for preserving general education in the midst of ever increasing diversity” (Reid & Valle, 2004, p. 468, paraphrasing Dudley-Marling, 2001; also see Skrtic, 1991, 2005).  Rather than using research-validated frameworks like Universal Design for Learning (UDL) and Complex Instruction (CI) to deliver rigorous, high-cognitive demand instruction to all mathematics students, the system of special education shunts certain students (especially students of color) into an inferior, segregated mathematics education, thus providing a band-aid to a broken general education system and preventing larger, more systematic changes. One line of research pursued by working group members involves developing understanding and theorizing the research divide between special education and mathematics.

Institutional schooling practices such as writing Individual Education Plans (IEPs) construct certain students as having disabilities; however, from a disability studies perspective, “the label of students with IEPs [can be viewed] not as an inherent and static determinant of individual ability, but as a school-based designation which reflects and recreates differential ability within the classroom” (Foote & Lambert, 2011, p. 250; also see Dudley-Marling, 2004; McDermott, Goldman & Varenne, 2006; Skrtic, 2005).  Certain students are chosen for this assessment and intervention, and this selection process is not objective and often singles out those students who are not from a dominant cultural background.

Returning to the assumptions inherent in the concept of intervention, a disability studies perspective problematizes the taken-for-granted assumption that what is “wrong” with the situation requiring intervention is a pathology or deficit within students.  Instead, the problem is located in the inaccessibility of the environment; in other words, what needs to be changed is not the student, but rather the environment to allow access for students who differ from one another.  As Reid and Valle (2004) assert, “the responsibility for ‘fitting in’ has more to do with changing public attitudes and the development of welcoming classroom communities and with compensatory and differentiated instructional approaches than with individual learners (Shapiro, 1999).  In other words, our focus is on redesigning the context, not on ‘curing’ or ‘remediating’ individuals’ impairments” (p. 468).  A related line of research of working group members involves conceptualizing interventions into participation rather than content.  That is, what interventions might contribute to more equitable participation and deeper engagement across students in mathematics classrooms?  For example, one of the working group members has conducted empirical research focused on equitable participation in a Cognitively Guided Instruction algebra routine.  Moreover, a political/relational model suggests that inaccessibility is embedded in the context of power relations.  Finding ways to “intervene” to make the environment accessible, then, also requires analyzing the power relations involved in maintaining inaccessibility.


Critical Race Theory and DisCrit

Critical race theory (CRT) is another theoretical framework that informs the work of the group.  According to CRT, racism is ‘normal’ rather than an anomaly in U.S. society (Delgado, 1995).  Critical race theorists assert that the U.S. was founded on property rights, and specifically the fact that enslaved African Americans were considered property, rather than civil rights (Ladson-Billings & Tate, 1995).  CRT reveals the way race and racism continue to structure U.S. society.  In relation to educational interventions, critical race theorists have addressed the issue of over-representation of students of color in special education.

Often, however, these analyses leave ableist assumptions in place; similarly, DS perspectives often fail to adequately consider race.  DisCrit is a perspective that acknowledges that racism and ableism are both “normalizing processes that are interconnected and collusive.  In other words, racism and ableism often work in ways that are unspoken, yet, racism validates and reinforces ableism, and ableism validates and reinforces racism”  (Connor, Ferri, & Annamma, 2016, ch. 1). Studies of administrators’ and teachers’ perceptions related to overrepresentation of students of color in special education have revealed that their perceptions tend to be rooted in “deficit thinking and infused with racial and cultural factors” (Connor, Ferri, Annamma, 2016, ch. 1; also see Abram et al., 2001 and Skiba et al, 2006).  DisCrit perspectives, therefore, identify the individual problematic attitudes of teachers and administrators as one “accessible entry point for intervention” (Connor, Ferri, Annamma, 2016, ch. 1).


Summary of the Problem

This working group will investigate the problem of interventions in mathematics education.  Using multiple theoretical frameworks, the working group participants will analyze current practices in mathematics interventions, including the power relations involved, and develop and elaborate on alternatives.  The working group participants will also plan ways to evaluate these alternatives in various educational settings and contexts.


Plan for Active Engagement of Working Group Participants


Prior to Session 1

The organizers will choose 2-3 articles or book chapters from different perspectives related to the theme of the working group.  The organizers will send out the list of readings to participants who have expressed interest in the working group.


Session 1

In the first session, the organizers will introduce the rationale for the working group and the current state of related research.  Participants will share related projects in which they are involved.  The group will collaboratively refine the goals of the working group.  The organizers will share the list of chosen readings with any participants who did not previous have access to them.


Session 2

In the second session, participants will discuss the chosen readings in relation to the goals refined in the first session.  Participants will discuss the ways in which the readings relate to ongoing projects and possible future collaborative projects.


Session 3

In the second session, participants will discuss the chosen readings in relation to the goals refined in the first session.  Participants will discuss the ways in which the readings relate to ongoing projects and possible future collaborative projects.


Plan for Sustainability: Anticipated Follow-up Activities

The working group sessions during the conference are designed to enable the participants to develop concrete plans for collaborative work beyond the end of the conference timeframe.  Specifically, the third session is allotted for developing specific plans for future collaborative work.


Annamma, S., Connor, D.J., & Ferri, B.A. (2013). Dis/ability critical race studies (DisCrit): Theorizing at the intersections of race and dis/ability. Race Ethnicity and Education. 16(1), 1-31. DOI:10.1080/13613324.2012.730511

Cohen, E., & Lotan, R. (1995). Producing equal-status interaction in the heterogeneous classroom. American Educational Research Journal, 32(1), 99-120.

Cohen, E. & Lotan, R. (Eds.)(1997). Working for equity in heterogeneous classrooms. New York: Teachers College Press.

Connor, D., Ferri, B., Annamma, S. (2016). DisCrit: Disability studies and critical race theory in education. New York, NY: Teacher’s College Press.

Delgado, R. (Ed.) (1995). Critical race theory: The cutting edge. Philadelphia: Temple University Press.

Dudley-Marling, C. (2001). Reconceptualizing learning disabilities by reconceptualizing education. In L. Denti & P. Tefft-Cousin (Eds.), New ways of looking at learning disabilities (pp. 5-18). Denver, CO: Love.

Dudley-Marling, C. (2004). The social construction of learning disabilities. Journal of Learning Disabilities, 37(6), 482-489.

Ferri, B.A. (2012). Undermining inclusion? A critical reading of Response to Intervention (RTI). International Journal of Inclusive Education. 16(8), 863-880. DOI:10.1080/13603116.2010.538862

Ferri, B.A., Lackie, P., Metzger, B.J., & Phillips, C. (1998). Tumbled identities: Negotiating invisible disabilities and sexual orientation. Disability Studies Quarterly, 18(3), 182-189.

Foote, M. Q., and R. Lambert. (2011). I Have a Solution to Share: Learning through Equitable Participation in a Mathematics Classroom. Canadian Journal of Science, Mathematics and Technology Education, 11(3), 247-260. doi: 10.1080/14926156.2011.595882

Gabel, S.L. (2005). Disability studies in education: Readings in theory and method. New York: Peter Lang Publishing.

Gutiérrez, R.  (2007).  (Re)defining equity:  The importance of a critical perspective.  In Nasir, N.  and Cobb, P.  (Eds.) Diversity, equity, and access to mathematical ideas, pp. 37-50.  New York: Teachers College Press.

Gutiérrez, R. (2010). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 42, 1-32.

Jackson, H. G., & Neel, R. S. (2006). Observing mathematics: Do students with EBD have access to standards­ based mathematics instruction? Education and Treatment of Children, 29, 593.

Kafer, A. (2013).  Feminist Queer Crip. Bloomington, IN: Indiana University Press.

Ladson-Billings, G. & Tate, W. (1995). Toward a critical race theory of education. Teachers College Record, 97(1), 47 – 68.

Marx, K.  (1845).  Theses on Feuerbach.  Retrieved February 20, 2016 from <>

McDermott, R., Goldman, S., & Varenne, H. (2006). The cultural work of learning disabilities. Educational Researcher, 35(6), 12-17.

Reid, D. & Valle, J. (2004). The discursive practice of learning disability: Implications for instruction and parent-school relations. Journal of Learning Disabilities, 37(6), 466-481.

Shapiro, A. (1999). Everybody belongs: Changing negative attitudes toward classmates with disabilities. New York, NY: Routledge Falmer.

Siebers, T. (2008). Disability Theory. Ann Arbor: University of Michigan Press.

Skovsmose, O., & Borba, M. (2004). Research methodology and critical mathematics education. In P. Valero & R. Zevenbergen (Eds.), Researching the socio-political dimensions of mathematics education: Issues of power in theory and methodology (pp. 207-226). Norwell, MA: Kluwer Academic Publishers.

Skrtic, C. (1991). The special education paradox: Equity as the way to excellence.  Harvard Educational Review, 61(2), 148-206.

Skrtic, C. (2005). A political economy of learning disabilities. Learning Disability Quarterly, 28(2), 149-155.

Union of Physically Impaired Against Segregation (1975). Fundamental principles of disability. London, England: U.P.I.A.S.

Van Garderen, D., Jackson, C., Hampton, D., & Scheuermann, A. (2009). Supporting the collaboration of special educators and general educators to teach students who struggle with mathematics: An overview of the research. Psychology in the Schools, 46, 1, 56-77.