Feminist & Queer Framework for Evaluating Math Tasks
Feminist & Queer Framework for Evaluating Math Tasks
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Framework
Framework
The following framework was designed to aid in the design and evaluation of mathematical modeling(MM), integrated STEM(iSTEM), and mathematical social justice(MSJ) tasks.
Framework Design
Framework Design
Gender/Queer Representation
One way to evaluate learning materials is through analysis of the learning materials text (e.g. Ott, 2015; Parise, 2020). This is often accomplished through language analysis of the text by counting gender/queer identifying language and qualitatively analyzing how that language is used. For example, Ott found that there has been a shift in female/male proportional representation in German math textbooks over time, with historical ratios as high as 1 female: 9 male references. Additionally, Ott found that there was very little gender representation beyond the male/female binary. Moving to a more qualitative analysis, Ott found that male readers were offered a much wider range of professional occupations. Parise found similar representational issues in their analysis of US high school statistics books. Additionally, she identified there was often a lack of distinction made between sex and gender, as well as an a assumption of heterosexuality when relationships were depicted.
Rands (2009) describes four forms of gender education that can be used to evaluate how gender is being addressed in educational contexts. These include gender-stereotyped, gender-free/blind, gender-sensitive, and gender-complex. These forms of gender education can provide a lens for the evaluation on how gender issues are being addressed in mathematics.
Barker & Scheele (2016) identify a number of normativities that are assumed in modern culture. These normativities include: heteronormativity, monosexism, sexual imperative, mononormativity, and cisnormativity. Looking for the presence of these normativities can provide insight that can help designers of these tasks include varied representations.
Ott (2015) also summarized a list of considerations for gender sensitive design guidelines from interviews with publishers and authors. The list includes:
Stereotypical situations and job depictions are to be avoided
No stereotypical illustrations and themes
Balanced distribution of correct and incorrect solutions offered by male and female schoolbook characters
Gender-sensitive language in definitions of problems
Parity for terms for girls/women and boys/men
Uniform distribution of agency
As balanced representation of men and women amongst the authors as possible (pp. 54-55)
With these considerations in mind, as well as the findings from textbook analyses conducted by Ott (2015) and Parise (2020), there is a strong need for designers of math tasks to take into account the quantitative and qualitative representation of gender and queer identities.
Feminist Epistemology of Mathematics
Burton (2008/1995) presents a feminist epistemology of mathematics in order to critically evaluate the relationship between gender and mathematics. Burton’s promotion of a feminist epistemology is grounded in making mathematics more inclusive and open to a wider range of doing and understanding mathematics than the traditional male dominated view of mathematics. Burton identifies five ways of knowing mathematics that are built from the feminist literature:
its person- and cultural/social-relatedness;
the aesthetics of mathematical thinking it invokes;
its nurturing of intuition and insight;
its recognition and celebration of different approaches particularly in styles of thinking;
the globality of its applications. (p. 526)
These ways of knowing mathematics move beyond the traditional view of mathematics as rational, objective, and only for the select few who have enough innate talent. Feminist mathematical tasks should provide the opportunity for multiple ways that students can explore and demonstrate their mathematical knowing.
To define the aesthetics of mathematics a little more clearly, Sinclair’s (2004) three groups of aesthetic responses to mathematics are used. Sinclair identifies roles of aesthetics in mathematics that include: evaluative, generative, and motivational.
Critical Mathematics Education
Frankenstein (1983) uses Paolo Freire’s work to develop a critical perspective on mathematics education. A critical lens on mathematics supports a feminist pedagogy as it provides tools for the analysis and deconstruction of the traditional forms of power and oppression that feminist and queer pedagogy attempt to address. Frankenstein builds on Freire’s idea of critical consciousness. Challenging the status quo, promoting mathematical literacy, and providing opportunity for reflection are strategies that can be used.
Intersectionality
Crenshaw (1989) highlights the importance of intersectionality in the analysis of critical issues. Crenshaw claims that “because the intersectional experience is greater than the sum of racism and sexism, any analysis that does not take intersectionality into account cannot sufficiently address” (p. 140) the unique ways that people who identify with multiple minority identities are subordinated. Any feminist or queer perspective on mathematical tasks should also take into account how other intersectional identities are being represented, so that progress towards equitable gender and queer representation does not harm other minority identities.
References
Barker, M.-J., & Scheele, J. (2016). Queer: A graphic history. Icon Books Limited.
Burton, L. (2008). Moving towards a feminist epistemology of mathematics. ZDM, 40(4), 519-528. (Original work published 1995) https://doi.org/10.1007/s11858-008-0109-9
Cho, S., Crenshaw, K. W., & McCall, L. (2013). Toward a field of intersectionality studies: Theory, applications, and praxis. Signs: Journal of Women in Culture and Society, 38(4), 785-810. https://doi.org/10.1086/669608
Crenshaw, K. (1989). Demarginalizing the intersection of race and sex: A black feminist critique of antidiscrimination doctrine, feminist theory, and antiracist politics. University of Chicago Legal Forum, 1989(1), 139-167. https://doi.org/10.4324/9780429500480-5
Frankenstein, M. (1983). Critical mathematics education: An application of Paulo Freire's epistemology. The Journal of Education, 165(4), 315-339.
Ott, C. (2015). Innocent maths? Gender representation in German math books. In S. Mills & A. S. Mustapha (Eds.), Gender representation in learning materials (pp. 52-63). Routledge.
Parise, M. M. (2021). Gender, sex, and heteronormativity in high school statistics textbooks. Mathematics Education Research Journal, 33(4), 757-785. https://doi.org/10.1007/s13394-021-00390-x
Rands, K. E. (2009). Considering Transgender People in Education. Journal of Teacher Education, 60(4), 419-431. https://doi.org/10.1177/0022487109341475
Sinclair, N. (2004). The roles of the aesthetic in mathematical inquiry. Mathematical Thinking and Learning, 6(3), 261-284. https://doi.org/10.1207/s15327833mtl0603_1
Mathematical Modeling (MM) Tasks
Mathematical Modeling (MM) Tasks
Modeling Population Growth: Having Kittens
Modeling Population Growth: Having Kittens
Level: High School
Math Content: Exponential Functions, Modeling
Source: Mathematics Assessment Resource Service. (2015). Modeling Population Growth: Having Kittens.
Framework Analysis
Gender/Queer Representation
This task has some gender representation, but of cats primarily. This task is based on modeling population growth, and uses a claim about the number of offspring a single cat can produce in 18 months. While human gender and queer identity is minimally focused on in this task, there are certain normativities and assumptions that this task likely leads students to use. Because the task deals with reproduction and population growth, there is an assumption of female and male pairing for reproduction. Additionally, the assumptions that students make about the sex of the offspring kittens has potential for impacting the model that is created.
Additionally, there are 3 sample student responses for this task that students can evaluate. One sample response is attributed to Alice, a stereotypically female name, and 2 are attributed to Wayne and Ben, stereotypically male names. Along with having more male representation in the student samples, the sample response by Alice appears to be the least complex solution.
Feminist Epistemology of Mathematics
This task provides a context that is relatable to most people. It is also an open task that allows for students to approach the problem and create a model in various ways. Students have the opportunity to work individually and collaboratively to develop and revise a model to get a solution. Students are not limited to particular mathematics content, and can use their creativity and insight to approach the task.
Critical Mathematics Education
This task does not challenge any status quo, but does provide an opportunity for students to build their mathematical literacy. The main task asks the students to determine if a mathematical claim that a cat can have 2000 descentants in 18 months is true. By engaging in this task to mathematically justify whether this statement is true, the students' mathematical literacy is developed.
Intersectionality
Since this task is focused on kittens and not humans, there are almost no intersectional identities included. However, in the sample student responses the names used are Alice, Wayne, and Ben, which are traditionally Western sounding names. This provides no diversity in the representation of sample student solutions.
Polygon Paradise Park
Polygon Paradise Park
Level: Middle School
Math Content: Measurement, Equations, Optimization
COMAP. (2022). Polygon Paradise Park MidMCM Problem C.
Framework Analysis
Gender/Queer Representation
There is some gender representation through the 4 friends. Ming is a gender neutral name, Ishmael is a masculine leaning name, and Karine and Freya are feminine leaning names. No pronouns are used to refer to the 4 friends so there remains some ambiguity of the gender associated with each name. The descriptions of the 4 friends are relatively stereotype free. The image of the restroom on the map is the traditional female/male restroom images, and no acknowledgement of a gender neutral restroom. There is no discussion or acknowledgement of any relationship or queer identities. Gender appears to have been minimized in this task so that it is almost gender-free.
Feminist Epistemology of Mathematics
This task was designed to be interesting and relevant to middle school students by providing a context in an amusement park. The task also provides opportunity for students to approach the problem in multiple ways and be creative in providing a solution.
Critical Mathematics Education
There is no real challenge presented in this task to the status quo of society. By engaging with this task, students will be exposed to another way that they can use mathematics to solve problems. The task asks students to analyze (or reflect) on their work to identify strengths and limitations of their mathematical model.
Intersectionality
The names of the four friends are from diverse cultures providing diversity in representation. There is no direct mention of any disabilities, but there could have been a potential for including disability representation as part of the descriptions of the friends.
Integrated STEM (iSTEM) Tasks
Integrated STEM (iSTEM) Tasks
Storing the Sun
Storing the Sun
Level: High School
Math Content: Equations, Optimization
COMAP. (2021). Storing the Sun HiMCM Problem A.
Framework Analysis
Gender/Queer Representation
There is no gender or queer representation in this problem as it deals with solar energy.
Feminist Epistemology of Mathematics
This task provides a relevant real world context for a mathematics and science problem. The task also provides opportunity for students to approach the problem in multiple ways and be creative in providing a solution.
Critical Mathematics Education
This task does not directly challenge the status quo, but does potentially provide an entry point into discussions about environmental impacts of energy consumption and pros and cons of being part of the capitalist power grid. By analyzing the mathematics of these energy choices, students have the potential to develop mathematical literacy to help them engage in such status quo challenging discussions.
Intersectionality
There is no intersectionality as it does not deal with humans in the task.
Endangered Elements
Endangered Elements
Level: High School
Math Content: Linear and Exponential Functions, Modeling
Provost & Daniel. (2022). Endangered Elements.
Framework Analysis
Gender/Queer Representation
There is minimal gender and queer representation in this task as it is focused on the elements of the periodic table. Gender is only represented in the videos included that can be shown at the teachers' discretion to provide information to the students. One TED-Ed video is narrated by a woman, one Discovery News video is hosted by a man, and one video from the Royal Society of Chemistry is of a male professor. There are no representations of relationships or queer identities.
Feminist Epistemology of Mathematics
This task was designed to be relevant to students by connecting to their use of smartphones, and providing them an opportunity to think critically about how the materials that are necessary for the device are being consumed. There are different versions of the task that allow for various levels of scaffolding and support, or openness in the potential solutions. Students can use different strategies to create their models.
Critical Mathematics Education
This task highlights the potential for certain elements to be used up due to human consumption. By engaging with this task, students will degvelop mathematical literacy that they can use to address this potential issue. The task also provides students with an opportunity to reflect on the mathematics used in the modeling process.
Intersectionality
As this task is focused on elements and not humans, there is no intersectional identities represented.
Mathematical Social Justice (MSJ) Tasks
Mathematical Social Justice (MSJ) Tasks
Listen to GLSEN (Lesson 5.3)
Listen to GLSEN (Lesson 5.3)
Level: High School
Math Content: Matrices, Quantitative Reasoning, Mathematical Modeling, Units of Measurement
Meyer, B., & Staley, J. W. (2020). Listen to GLSEN. In Berry, R. Q. I., Conway, B. M. I., Lawler, B. R., & Staley, J. W. (Eds.) High school mathematics lessons to explore, understand, and respond to social injustice. Corwin Press.
Framework Analysis
Gender/Queer Representation
This task is centered on data from GLSEN about harassment and bullying that LGBTQ+ students face in school. There is little focus on gender specifically, as the main focus is on queer identities.
Feminist Epistemology of Mathematics
This task is a more guided and structured rather than an open ended modeling task that allows for varied student approaches. However, there is ample discussion on how the mathematics of matrices can be used to work with this data. Students are asked to reflect on how the data calculated with the matrices may be imperfect.
Critical Mathematics Education
This task heavily challenges the status quo by looking at actual data about a minority group's oppression. Students are encouraged to develop mathematical skills to help make a potentially abstract issue more relevant to themselves and their school community.
Intersectionality
The task encourages all students to reflect on times they have experienced harassment and bullying in order to build empathy for disadvantaged queer identities. This provides opportunity for discussions that connect other intersectional identities and how they may face similar oppression.
Intersectionality and the Wage Gap (Lesson 6.4)
Intersectionality and the Wage Gap (Lesson 6.4)
Level: High School
Math Content: Functions, Covariational Relationships, Solving Equations, Modeling with Functions
Jones, S.R., Gomez, C.N., Tanck, H., & Siy, E. (2020). Intersectionality and the Wage Gap. In Berry, R. Q. I., Conway, B. M. I., Lawler, B. R., & Staley, J. W. (Eds.) High school mathematics lessons to explore, understand, and respond to social injustice. Corwin Press.
Framework Analysis
Gender/Queer Representation
This task focuses on the wage gap, primarily based on gender, but on other intersectional identities of race and ability. The task includes activities that simulate gender differences in how people are paid by "paying" different students in the class with different amounts of candy based on an arbitrary factor such as shirt color. There is no focus on queer identities, as the task is focused on gender, ability, and race. The focus on gender is binary and there is no discussion of gender identities outside the female/male binary.
Feminist Epistemology of Mathematics
This task is a more guided and structured rather than an open ended modeling task that allows for varied student approaches. There is some opportunity for varied approaches, but most approaches would revolve around the construction of linear equations to model the relationships.
Critical Mathematics Education
This task provides many opportunities for discussion about the status quo of the wage gap, both for gender and other intersectional identities. This task provides students with the opportunity to develop mathematical literacy surrounding this intersectional issue of the wage gap. Students are also asked to reflect on their models and how well they represent the situation.
Intersectionality
This task is highly focused on the intersectionality of gender, race, and dis/ability in regards to the wage gap.
Hey Google, Who's a Mathematician? (Lesson 7.1)
Hey Google, Who's a Mathematician? (Lesson 7.1)
Level: Middle School
Math Content: Ratios, Percentages, Graphs
Lam, A. (2020). Hey Google, Who's a Mathematician? In. Conway, B. M., Id-Deen, L., Raygoza, M. C., Ruiz, A., Staley, J. W., & Thanheiser, E. (Eds.), Middle school mathematics lessons to explore, understand, and respond to social injustice. Corwin Press.
Framework Analysis
Gender/Queer Representation
While this task attempts to challenge what a mathematician might look like opposed to the traditional view of an "old, white, man", the focus on this activity is on race rather than gender. While the focus is on race, having students conduct actual Google searches and using some of the provided lists of mathematicians will potentially bring in more discussion of gender representation as well. There is no focus on queer identities. This task attempts to challenge the stereotypical representations of race and gender.
Feminist Epistemology of Mathematics
This task is a more guided and structured rather than an open ended modeling task that allows for varied student approaches. There will be some variation in the data that students collect when they conduct Google searches and do research on mathematicians. Students are encouraged to reflect on their own identities and how the mathematics reflects an new image of a mathematician.
Critical Mathematics Education
This task encourages students to question the status quo of who gets viewed as a mathematician. By searching and researching mathematicians, they will be exposed to mathematicians they have not heard of before. By using mathematical representations to visualize the ratios of mathematics, they can begin to challenge the picture of a mathematician.
Intersectionality
This task is primarily focused on race, but provides the opportunity for intersectional analysis of race and gender in picturing a mathematician.
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