**Bowties and Durags LIterature Review**

Infiltrating the mathematics classroom is, in essence, a socio-political objective. Many exchanges between stakeholders have exemplified this trend: the “new math” curriculum discourse within the context of the Cold War’s politicization of STEM education and schooling (Phillips, 2014); the “math wars” of the 1980s between “traditional” and “reform” camps over math approaches and curriculum (Boaler, 2015, p. 31-38); and efforts to mitigate inequities in access to quality math education for underrepresented minorities (URMs), for example. The notion that a strong mathematics education for the populous is instrumental for and within the U.S. economy underlies much of the interest. For example, Robert P. Moses and Charles E. Cobb Jr. (2001) argue that “[t]he most urgent social issue affecting poor people and people of color is economic access. In today’s world, economic access and full citizenship depend crucially on math and science literacy.” (p. 5). Their assertion aligns with a great deal of literature and stakeholders that focus on the math outcomes of students from under resourced communities and those with marginalized identities.

Discrepancies exist between different conceptualizations of a teaching and learning mathematics for social justice (TLMSJ) approach. Still, I argue that a TLMSJ approach lie at the heart of the intersecting interests of education stakeholders and their hopes for fostering more achievement and success in mathematics. Some scholars posit that TLMSJ can act as a motivating factor for minority students to engage with mathematics and others insist that addressing social justice issues should be a primary goal for all education,

There appears to be two discernable camps. One camp envisions social justice as enabling or creating access, socioeconomically, and another camp conceptualizes social justice as a fundamental critical consciousness raising endeavor (Larnell, 2017, p. 20). These two “poles” that, sometimes, emerge may be unnecessary. In fact, Ilana Seidal Horn (2012) suggests that the fundamental visions of both camps may reinforce each other. She lists four principles for equitable mathematics teaching: learning and achievement are related, but not the same; “achievement gaps often reflect gaps in opportunities to learn;” all students, including high achieving students, can learn mathematics more deeply; and students need to see themselves in mathematics. She implies that student connection to the content and mathematics classrooms aligning with the home cultures of students increases their engagement (p. 13-17).

Perhaps, a mathematics education can both provide students with the mathematics instruction that will create access to the current educational and economic landscape and allow students to see themselves in their mathematics through confronting social dilemmas (Bartell, 2013, p. 129-130). Nevertheless, much of the literature that engages with the notion of TLMSJ complicates the traditional approach to mathematics with students collaborating, discussing their problem solving, and being active learners. Jo Boaler (2015), especially, critiques and calls attention to the ineffectiveness of mathematics teachers that encourage passive learning: teachers demonstrating methods at the front of the class while students copy them down and emulate those methods in near-identical problems. She insists that “students taught through passive approaches follow and memorize methods instead of learning to inquire, ask questions, and solve problems.” Consequently, some students develop a disinterest because it posits rote memorization as critical to achievement and allows no room for questioning (p. 38-40).

With that being said, some teachers have reported difficulty or concern reconciling the tensions between introducing mathematical goals and social justice goals into lesson designs with balance and coherence (Bartell, 2013, p. 140). Teachers fear or report that the lesson plans lead to one goal undermining the other or causing a disjointed lesson. Perhaps, a disjointed classroom period is a risk worth taking if the outcome could potentially engage more students and empower them to actively improve their classroom culture and interpersonal interactions. Regardless, there are a growing number of resources and examples of educators working to align social justice and mathematical goals into a coherent and single lesson plan. Eric Gulstein (2016) uses social justice examples from the real world in his twelfth grade mathematics class in a low-income Chicago public neighborhood high school:

Gulstein’s approach to mathematics is definitely inspiring to me, but it is not entirely unique.

Problems that draw inspiration from the real world are common place in mathematics. In fact, Jo Boaler (2015) criticizes the suspension of belief that most mathematics problems necessitate. For instance, trains travel toward each other on the same tracks, people paint houses at identical speeds all day long, or people run tirelessly around tracks at the same distance from the edge at constant speeds. She concludes that this undermines the perceived usefulness of mathematics for some people, reducing their interest and engagement in the subject. Instead, they learn to ignore the less than believable context and work only with the numbers, detrimental to any real-world problem solving or professional situation (p. 50-52). With that being said, TLMSJ and efforts to make mathematics more equitable and accessible to broader populations should not be reduced to a mere effort to include social justice lessons into an already tight curriculum or to simply increase the number of social justice examples that students will work through silently at their desks or at home.

Lastly, a great deal of literature and studies relate the learning environments of mathematics classrooms to disparities in learning and achievement outcomes. It is well-documented that classroom climate informs students’ experiences and STEM persistence in college. In addition to rigor and discouragement due to low grades, the competitive STEM culture and unwelcoming atmosphere of STEM courses have also been identified as factors that influence why undergraduates leave STEM majors (Dagley, 2015, p. 168). The literature on STEM retention programs, self-efficacy, and STEM persistence provides insight that peer interactions and faculty interactions are instrumental to students’ success and perception of their own abilities to thrive.

Often times, interventions and programs for URM students are premised on proactively combatting the negative, potentially isolating experience of STEM programs in post-secondary institutions. In conjunction with student affairs programming, they attempt to introduce students to support resources and help students adapt to the rigors of STEM curricula and the expectations of their faculty (Palmer et al, 2010, p. 442). In fact, many of the programs, such as the EXCEL learning community, have both residential and curricular components to foster underrepresented minority students’ integration into the social and academic parts of campus (Dagley et al., 2015, p. 170).

Apprehension that more student-centered approaches to mathematics will sacrifice rigor acts as an obstacle to changes in mathematics instruction and practices (Boaler, 2015, p. 1-2). The Bayer Corporation (2012) survey polled 413 STEM department chairs at the nation’s top 200 research universities. Fifty-seven percent of the chairs

We must ask ourselves why we accept supplemental support for students in STEM that are as innately social and collaborative as they are academic, if we remain subdued by apprehension from opponents of more student-centered approaches to mathematics pedagogy and curricula. Objections that rely on rigor also seemingly complicate more calls to bring different teachers into the mathematics teaching fold. Perhaps, this helps make sense of the resistance I encountered trying to actively shape my teacher education in ways that would allow me entry into mathematics classrooms. Ultimately, rigor seemingly becomes discursively synonymous with rigid.

Discrepancies exist between different conceptualizations of a teaching and learning mathematics for social justice (TLMSJ) approach. Still, I argue that a TLMSJ approach lie at the heart of the intersecting interests of education stakeholders and their hopes for fostering more achievement and success in mathematics. Some scholars posit that TLMSJ can act as a motivating factor for minority students to engage with mathematics and others insist that addressing social justice issues should be a primary goal for all education,

*including*mathematics (Leonard et al, 2010, p. 261). Yet, TLMSJ is an umbrella term that encompasses a wide variety of ideas and definitions. In fact, some scholars prioritize intervening on behalf of URM students over structural overhauls of mathematics curriculums and pedagogy. TLMSJ is thought of as entailing all or some of the following by different parties: access to high-quality mathematics instruction for*all students;*using mathematics as a tool to understand social life and oppression; curriculum and pedagogy focused on the experiences of marginalized students; and the use of mathematics to transform society into a more just and equitable one (Leonard et al, 2010, p. 261- 262).There appears to be two discernable camps. One camp envisions social justice as enabling or creating access, socioeconomically, and another camp conceptualizes social justice as a fundamental critical consciousness raising endeavor (Larnell, 2017, p. 20). These two “poles” that, sometimes, emerge may be unnecessary. In fact, Ilana Seidal Horn (2012) suggests that the fundamental visions of both camps may reinforce each other. She lists four principles for equitable mathematics teaching: learning and achievement are related, but not the same; “achievement gaps often reflect gaps in opportunities to learn;” all students, including high achieving students, can learn mathematics more deeply; and students need to see themselves in mathematics. She implies that student connection to the content and mathematics classrooms aligning with the home cultures of students increases their engagement (p. 13-17).

Perhaps, a mathematics education can both provide students with the mathematics instruction that will create access to the current educational and economic landscape and allow students to see themselves in their mathematics through confronting social dilemmas (Bartell, 2013, p. 129-130). Nevertheless, much of the literature that engages with the notion of TLMSJ complicates the traditional approach to mathematics with students collaborating, discussing their problem solving, and being active learners. Jo Boaler (2015), especially, critiques and calls attention to the ineffectiveness of mathematics teachers that encourage passive learning: teachers demonstrating methods at the front of the class while students copy them down and emulate those methods in near-identical problems. She insists that “students taught through passive approaches follow and memorize methods instead of learning to inquire, ask questions, and solve problems.” Consequently, some students develop a disinterest because it posits rote memorization as critical to achievement and allows no room for questioning (p. 38-40).

With that being said, some teachers have reported difficulty or concern reconciling the tensions between introducing mathematical goals and social justice goals into lesson designs with balance and coherence (Bartell, 2013, p. 140). Teachers fear or report that the lesson plans lead to one goal undermining the other or causing a disjointed lesson. Perhaps, a disjointed classroom period is a risk worth taking if the outcome could potentially engage more students and empower them to actively improve their classroom culture and interpersonal interactions. Regardless, there are a growing number of resources and examples of educators working to align social justice and mathematical goals into a coherent and single lesson plan. Eric Gulstein (2016) uses social justice examples from the real world in his twelfth grade mathematics class in a low-income Chicago public neighborhood high school:

I wrote the numbers on the board as class wound down. Students silently and soberly stared at 150,000 – 291,000 = 92,000 (an “equation” derived from a recursive function, modeling a mortgage). I talked as I wrote: “You’ve paid two hundred and ninety-one thousand dollars on a one-hundred-and-fifty-thousand-dollar mortgage, and you still owe ninety-two thousand dollars. Check that math out. One hundred and fifty thousand minus two hundred and ninety-one thousand equals ninety-two thousand.” I paused as students looked and mumbled to themselves and neighbors. “Think about that. Hey! You started with a hundred and fifty—you paid two ninety-one—and you still owe ninety-two thousand dollars. What’s going on here?” Antoine: “They’re taking your money.”1 Daphne: “The bank is taking advantage of you.” Mr. Rico:2 “This is legal—this is how banks loan money and make money.” Silence. I paused and repeated slowly. “This is legal—this is how banks loan money and make money.” I paused again. As class ended, I asked, “What are some questions you could ask here?” Renee said, “Why is it legal?” and Daphne asked, “Why don’t more people look into it so they don’t end up in the same situation?” (p. 454)I wrote the numbers on the board as class wound down. Students silently and soberly stared at 150,000 – 291,000 = 92,000 (an “equation” derived from a recursive function, modeling a mortgage). I talked as I wrote: “You’ve paid two hundred and ninety-one thousand dollars on a one-hundred-and-fifty-thousand-dollar mortgage, and you still owe ninety-two thousand dollars. Check that math out. One hundred and fifty thousand minus two hundred and ninety-one thousand equals ninety-two thousand.” I paused as students looked and mumbled to themselves and neighbors. “Think about that. Hey! You started with a hundred and fifty—you paid two ninety-one—and you still owe ninety-two thousand dollars. What’s going on here?” Antoine: “They’re taking your money.”1 Daphne: “The bank is taking advantage of you.” Mr. Rico:2 “This is legal—this is how banks loan money and make money.” Silence. I paused and repeated slowly. “This is legal—this is how banks loan money and make money.” I paused again. As class ended, I asked, “What are some questions you could ask here?” Renee said, “Why is it legal?” and Daphne asked, “Why don’t more people look into it so they don’t end up in the same situation?” (p. 454)

Gulstein’s approach to mathematics is definitely inspiring to me, but it is not entirely unique.

Problems that draw inspiration from the real world are common place in mathematics. In fact, Jo Boaler (2015) criticizes the suspension of belief that most mathematics problems necessitate. For instance, trains travel toward each other on the same tracks, people paint houses at identical speeds all day long, or people run tirelessly around tracks at the same distance from the edge at constant speeds. She concludes that this undermines the perceived usefulness of mathematics for some people, reducing their interest and engagement in the subject. Instead, they learn to ignore the less than believable context and work only with the numbers, detrimental to any real-world problem solving or professional situation (p. 50-52). With that being said, TLMSJ and efforts to make mathematics more equitable and accessible to broader populations should not be reduced to a mere effort to include social justice lessons into an already tight curriculum or to simply increase the number of social justice examples that students will work through silently at their desks or at home.

Lastly, a great deal of literature and studies relate the learning environments of mathematics classrooms to disparities in learning and achievement outcomes. It is well-documented that classroom climate informs students’ experiences and STEM persistence in college. In addition to rigor and discouragement due to low grades, the competitive STEM culture and unwelcoming atmosphere of STEM courses have also been identified as factors that influence why undergraduates leave STEM majors (Dagley, 2015, p. 168). The literature on STEM retention programs, self-efficacy, and STEM persistence provides insight that peer interactions and faculty interactions are instrumental to students’ success and perception of their own abilities to thrive.

Often times, interventions and programs for URM students are premised on proactively combatting the negative, potentially isolating experience of STEM programs in post-secondary institutions. In conjunction with student affairs programming, they attempt to introduce students to support resources and help students adapt to the rigors of STEM curricula and the expectations of their faculty (Palmer et al, 2010, p. 442). In fact, many of the programs, such as the EXCEL learning community, have both residential and curricular components to foster underrepresented minority students’ integration into the social and academic parts of campus (Dagley et al., 2015, p. 170).

Apprehension that more student-centered approaches to mathematics will sacrifice rigor acts as an obstacle to changes in mathematics instruction and practices (Boaler, 2015, p. 1-2). The Bayer Corporation (2012) survey polled 413 STEM department chairs at the nation’s top 200 research universities. Fifty-seven percent of the chairs

*did not*report that they felt a significant change to their introductory courses was necessary in order to retain and attract more URM STEM students. Ironically, there was a general consensus that “weeding out” introductory STEM courses that are extremely rigorous are harmful and, especially, harmful to URM students. Rather, seventy-one percent of them believe that increasing academic support for students, mentoring, and informal faculty engagement are methods that post-secondary institutions should employ to retain more STEM students (p. 321-322).We must ask ourselves why we accept supplemental support for students in STEM that are as innately social and collaborative as they are academic, if we remain subdued by apprehension from opponents of more student-centered approaches to mathematics pedagogy and curricula. Objections that rely on rigor also seemingly complicate more calls to bring different teachers into the mathematics teaching fold. Perhaps, this helps make sense of the resistance I encountered trying to actively shape my teacher education in ways that would allow me entry into mathematics classrooms. Ultimately, rigor seemingly becomes discursively synonymous with rigid.

References

Bartell, Tonya G. (2013) “Learning to Teach Mathematics for Social Justice: Negotiating Social Justice and Mathematical Goals.”

Benjamin, Gower. (2015) “Teaching Mathematics for Social Justice.”

Bayer Corporation. (2012). Bayer Facts of Science Education XV: A View from the Gatekeepers—STEM Department Chairs at America's Top 200 Research Universities on Female and Underrepresented Minority Undergraduate STEM Students.

Boaler, Jo. (2015).

Bristol, Travis J. (2018). Policing and Teaching: The Positioning of Black Male Teachers as Agents in the Universal Carceral Apparatus.

Bristol, Travis J. and Mentor, Marcelle. (2017). “To Be Alone or in a Group: An Exploration Into How the School-Based Experiences Differ for Black Male Teachers Across One Urban School District.”

Brockenbrough, Ed. “The Discipline Stop:” Black Male teachers and the Politics of Urban School Discipline.

Covington, M., Chavis, T., & Perry, A. (2017). A scholar-practitioner perspective to promoting minority success in STEM.

Dagley, M., Georgiopoulos, M., Reece, A. and Young, C. (2015), “Increasing retention and graduation rates through a stem learning community”, Journal of College Student Retention: Research, Theory & Practice, Vol. 1, pp. 1-16.

Gassaway, Jermaine. (2017)

Griffith, Amanda L. (2010). Persistence of women and minorities in STEM field majors: Is it the school that matters?.

Gulstein, Eric. (2016) “Our Issues, Our People—Math as Our Weapon”: Critical Mathematics in a Chicago Neighborhood High School,”

Horn, I. S. (2012

Klopfenstein, Kristin. (2008). Beyond Test Scores: The Impact of Black Teacher Role Models on Rigorous Math Taking.

Lachner, A. & Nückles, M. (2016). Tell me why! Content knowledge predicts process-orientation of math researchers’ and math teachers’ explanations.

Larnell Gregory V. et al. (2017). “Rethinking Teaching and Learning Mathematics for Social Justice from a Critical Race Perspective,”

Leonard, Jacqueline et al. (2010). “The nuances and complexities of teaching mathematics for cultural relevance and social justice.”

Litzler, Elizabeth, Samuelson, Cate C., and Lorah, Julie A. (2014) Breaking it Down: Engineering Student STEM Confidence at the Intersection of Race/Ethnicity and Gender.

Moses, Robert P. and Cobb Jr., Charles E. (2001).

Palmer, R.T., Davis, R.J. and Thompson, T. (2010), “Theory meets practice: HBCU initiatives that promote academic success among African Americans in STEM”,

Price, Joshua. (2010). The effect of instructor race and gender on student persistence in STEM fields.

Strayhorn, T. (2010). The Role of Schools, Families, and Psychological Variables on Math Achievement of Black High School Students.

Toshalis, Eric & Nakkula, Michael J. (April 2012). “Motivation, Engagement, and Student Voice.”

Bartell, Tonya G. (2013) “Learning to Teach Mathematics for Social Justice: Negotiating Social Justice and Mathematical Goals.”

*Journal for Research in Mathematics Education, 44(1), 129-163.*Benjamin, Gower. (2015) “Teaching Mathematics for Social Justice.”

*Mathematics Teaching., 1(245), 6-9.*Bayer Corporation. (2012). Bayer Facts of Science Education XV: A View from the Gatekeepers—STEM Department Chairs at America's Top 200 Research Universities on Female and Underrepresented Minority Undergraduate STEM Students.

*Journal of Science Education and Technology,**21*(3), 317-324.Boaler, Jo. (2015).

*What’s Math Got to Do With it? How Teachers and Parents Can Transform Mathematics Learning and Inspire Success. New York, New York: Penguin Books.*Bristol, Travis J. (2018). Policing and Teaching: The Positioning of Black Male Teachers as Agents in the Universal Carceral Apparatus.

*The Urban Review, 50, (2),*218-234.Bristol, Travis J. and Mentor, Marcelle. (2017). “To Be Alone or in a Group: An Exploration Into How the School-Based Experiences Differ for Black Male Teachers Across One Urban School District.”

*Urban Education, 54 (3),*334-354.Brockenbrough, Ed. “The Discipline Stop:” Black Male teachers and the Politics of Urban School Discipline.

*Education and Urban Society, 47 (5),*499-522.Covington, M., Chavis, T., & Perry, A. (2017). A scholar-practitioner perspective to promoting minority success in STEM.

*Journal for Multicultural Education, 11*(2), 149-159.Dagley, M., Georgiopoulos, M., Reece, A. and Young, C. (2015), “Increasing retention and graduation rates through a stem learning community”, Journal of College Student Retention: Research, Theory & Practice, Vol. 1, pp. 1-16.

Gassaway, Jermaine. (2017)

*Unopened Books: Multiplying the 2%.*Jermaine Gassaway*.*Griffith, Amanda L. (2010). Persistence of women and minorities in STEM field majors: Is it the school that matters?.

*Economics of Education Review, 29(6),*911-922. https://doi.org/10.1016/j.econedurev.2010.06.010.Gulstein, Eric. (2016) “Our Issues, Our People—Math as Our Weapon”: Critical Mathematics in a Chicago Neighborhood High School,”

*Journal for Research in Mathematics Education, 47(5), 454-504.*DOI: 10.5951/jresematheduc.47.5.0454Horn, I. S. (2012

*). Strength in numbers: Collaborative learning in secondary mathematics.*Reston, VA: National Council of Teachers of Mathematics.Klopfenstein, Kristin. (2008). Beyond Test Scores: The Impact of Black Teacher Role Models on Rigorous Math Taking.

*Contemporary Economic Policy 23(3)*, 416-428.Lachner, A. & Nückles, M. (2016). Tell me why! Content knowledge predicts process-orientation of math researchers’ and math teachers’ explanations.

*Instructional Science, 44(3), 221-242.**https://proxy.library.upenn.edu:2101/10.1007/s11251-015-9365-6*Larnell Gregory V. et al. (2017). “Rethinking Teaching and Learning Mathematics for Social Justice from a Critical Race Perspective,”

*Journal of Education, 196(1) 19-29.*Leonard, Jacqueline et al. (2010). “The nuances and complexities of teaching mathematics for cultural relevance and social justice.”

*Journal of Teacher Education, 61(3), 261-270.*Litzler, Elizabeth, Samuelson, Cate C., and Lorah, Julie A. (2014) Breaking it Down: Engineering Student STEM Confidence at the Intersection of Race/Ethnicity and Gender.

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*Radical Equations: Civil Rights from Mississippi to the Algebra Project*. Boston, Massachusetts: Beacon Press.Palmer, R.T., Davis, R.J. and Thompson, T. (2010), “Theory meets practice: HBCU initiatives that promote academic success among African Americans in STEM”,

*Journal of college student development*, Vol. 51 No. 4, pp. 440-443.Price, Joshua. (2010). The effect of instructor race and gender on student persistence in STEM fields.

*Economics of Education Review, 29(6),*901-910. https://doi.org/10.1016/j.econedurev.2010.07.009.Strayhorn, T. (2010). The Role of Schools, Families, and Psychological Variables on Math Achievement of Black High School Students.

*The High School Journal,**93*(4), 177-194. DOI: 10.2307/40865058Toshalis, Eric & Nakkula, Michael J. (April 2012). “Motivation, Engagement, and Student Voice.”

*The Students at the Center Series.*