Equity in Mathematics
Encouraging Math Talk For All Through A Social Justice Lens
Abstract
This paper will explore the possibilities of understanding how teaching mathematics with equity in mind will allow educators to reach, teach and educate all students from diverse backgrounds. The changing landscape of diverse populations in the Peel District School Board has furthered our need to bring to light our own positionality in the spaces we occupy in an effort to guide our moral compass towards a pedagogy of kindness in mathematics education. Going beyond a basic right for every student, an equitable mathematics education seeks to invite all teachers to challenge their mathematical teaching skills in ways that become accessible for all in order to lessen the achievement gap. The current discourse surrounding mathematics education should encompass a pedagogy of equity to meet the needs of all students whose identity is uniquely critically constructed. Each individual’s educational journey is highly contextual and should not be made to fit towards a certain standardization. In light of the current discourse on mathematics education, Social Justice Mathematics challenges dominant narratives in socially constructed mathematical problems and aims to extract the type of mathematics that is accessible for all students and to meet the needs of diverse learners.
The Student Work Study Initiatve in Peel
Student Work Study is a provincial initiative in its fifth year. Peel currently has seven SWST teachers; five in Elementary, and two in the Secondary panel. Presently, each teacher is working in four schools for a total of twenty-eight.
SWST's work together with classroom teachers through the process of collaborative inquiry to study student experiences to better understand what contributes to student achievement.
We observe student thinking, document student learning, analyze evidence of student learning, and reference research that supports our learning.
A digital monograph and supposition paper is written by each SWST and shared with the Superintendents, School Effectiveness Leads, School Administrators and the Ministry. The digital reports are currently housed at J.A. Turner professional library.
Further information about the impact of the SWS Initiative is detailed in the "Evaluation of Student Work Study Teachers Initiative Report" which was conducted by the Research, Accountability, School Success Planning Department.
SWS research has been used to inform ministry monographs, the Primary Reading Discussion Paper and various LNS Webcasts. SWS research informs and impacts our system through the sharing of our learning at staff meetings, Educator Resource Teacher and Regional Ministry Meetings.
Collaborating Teachers: Nicola Bailey Bennet Grade 8 Math & Bethany Lowe Grade 7/8 Math @ Darcel Senior P.S
Collaborative Inquiry
Questions We Asked:
- How might students use and learn multiple strategies to arrive at a solution?
- How might students be facilitators in groups to drive mathematical discussion?
- How might teachers improve questioning of mathematical concepts to drive large group discussion?
- How might students adopt a growth mindset in math to initiate solving and persevering with math problems?
Further Questions We Asked:
- Why were some students continuing to reject the initiation of solving mathematical problems?
- How might we make questions more contextual to students learning needs and style?
- Would social justice math provide the framework for students to engage and participate more in solving mathematical problems?
- How do we extract the mathematics when solving social justice questions?
Evolution of the Inquiry: Theory of Action
With a growth mindset, if we engage students in mathematical discussion by asking effective questions to provoke student thinking and deepen their conceptual understanding, then all students will persevere to solve mathematical tasks and demonstrate their thinking in different ways.
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If we carefully plan mathematical lessons to include a social justice lens, then students will engage more in solving mathematical problems that are contextualized and meaningful to their everyday lives.
Changing Mathematical Mindsets
Resources
Jo Boaler
Carol Dweck
Why Don't Students Like School?
A conversation about mindsets with student A
SWST: Are there math people?
Student A: Well my dad is a math person. My mom isn't. Not sure if there are math people or not. I wonder if Jo Boaler is good at math.
SWST: What about students? Are some math people and other not?
Student A: I guess it depends on if kids can go to school or not. Everyone has their own abilities.
SWST: What do you mean?
Student A: I think in some countries there are people who don't have the ability to go to school because of money or where they were born, so those people may have a hard time learning math or have good math lessons. But everyone can learn math if they try.
SWST: So math is important in your home is that correct?
Student A: Yes
SWST: How So?
Student A: My dad is actually a math and science teacher. He was in India.
SWST: What does your mom do?
Student A: She owns a banquet hall.
SWST: Do you think she is a math person?
Student A: No
SWST: So your dad is a math person and your mom isn't?
Student A: Yes, um.. no. I'm not sure.
SWST: If your mom owns a banquet hall she must be good at math since she handles a lot of numbers when operating the business. Would you agree?
Student A: I guess so, for her work she does. But she is not really a math person.
Setting Up Positive Norms in Math Class - Jo Boaler
Focusing on Mathematical Discussion
5 Practices
Margaret S. Smith
Mary Kay Sheri
Classroom Discussions
Asking Better Questions
Why Talk Math? - Marilyn Burns
Five Major Reasons That Talk Is Critical to Teaching and Learning
- Talk can reveal understanding and misunderstanding.
- Talk supports robust learning by boosting memory.
- Talk supports deeper reasoning.
- Talk supports language development.
- Talk supports development of social skills.
Open Ended Questions and Discourse
- Who is doing most of the talking in the class?
- Is the task rich enough to allow a good level of reasoning and conversation to happen?
Discussion Starters and Math Strategies to Use
Discussion Starters Anchor Chart
Discussion Starters for Groups
Math Strategies Poster
The 4 Step Problem Solving Model
Learning Goal and Criteria for Success in Problem Solving
Vocabulary Chart
Group Questions: Understanding Integers Using the 4 Step Problem Solving Method
A conversation about Accountable Talk with student B
SWST: Did you find this question hard?
Student B: No not really. At the beginning it was, but then I had a strategy. I used a table. I wanted to visually show it so I used a bar raph too. I thought we had to start from - to + but actually we had to do it the other way to show the increase in temperature. I'm finding a way to show my work is correct with an equation.
SWST: So what's going through your mind right now?
Student B: I'm trying to figure out an equation.
SWST: Do you think you should use a different strategy?
Student B: Yes, um....
SWST: What do you think will help you?
Student B: A class discussion to get more ideas.
SWST: How so?
Student B: I would share my strategy and ask other people how they answered the question. That helps me.
Student Work
De-Briefing with the Whole Class
Co-Analysis of the Documentation
Questions About Achievement and Student Success That We Had
Assessment of Learning - Doing the Math
First Question
Doing the Math
Tweeking
Student Responses
De-Briefing with the whole class What stategies did you use and why?
how do we reach all students?
A Conversation with Student c
SWST: Why don't you want to do this problem with your group?
Student C: Because I don't see what this has to do with me. I know that I will need to know math when I grow up and I will use it in the future. That is why I'm here.
SWST: Do you understand the question that you and your group are working on?
Student C: Yes, I understand it. I just don't want to do it. I know I will need it in the future, but I don't see how this question has anything to do with me.
Student C: I hate math and I'm better at other subjects.
SWST: Like which ones?
Student C: Social studies and Language
SWST: What if we blended some of the questions in math that you could relate to?
Student C: I still wouldn't want to do it
SWST: Why is that?
Student C: It's just not for me. I know that I will need it in the future and that makes me sad. I just don't want to do it now.
A conversation with student D
SWST: Do you understand what your group members are saying?
Student D: No, I'm so lost. I don't understand this type of math. It's hard.
SWST: What if you asked your group members to explain how they are figuring out the question?
Student D: No, it's no use. I just do get it. Whey they explain it, it doesn't make sense.
The Research
Equity Pedagogy and Multicultural Education in a Mathematical Context
Looking specifically at equitable practices in mathematics would have to include deconstructing who our students are. In an effort to understand diverse student populations, misconceptions of multicultural education has arrived at educations’ doorstep. In the past and to some extent even today, we see how many educational institutions seemingly try to encompass a multicultural attitude towards educating students about diversity. Critically understanding and teaching towards equity for all students begins with questioning assumptions, exploring dominant narratives and uncovering hegemonic practices. “Pedagogies that merely educate students to fit into and to experience social-class mobility within the existing structures of our society—which are characterized by sharp and pernicious social-class divisions and by racial, ethnic, and gender stratification-are not helpful in building a democratic and just society. An education for equity teaches students to master basic skills as well as to use those skills to become effective agents who work to create a just and democratic society.” (Banks, pg. 92) Students arrive to school every day with a backpack of knowledge. They bring with them an outlook based on a construction of ideas, thoughts and reflections of their unique lives that are deeply rooted, for some, on religious, cultural and ethnic beliefs. No person brings with them the same feelings, thoughts or ideas as every different individual views the world based on what is contextual to their unique lived experiences. “Equity pedagogy actively involves students in a process of knowledge construction and production. It challenges the idea of instruction as transmission of facts and the image of the teacher as a citadel of knowledge and students as its passive recipients. Equity pedagogy alters the traditional power relationship between teachers and students. Most importantly, it assumes an integral relationship between knowledge and reflective action.” (Banks, pg. 93) Students who see themselves as a part of the knowledge construction in schools rather than passive recipients of that knowledge allow for greater success.
The “banking” concept of education coined by Paulo Freire in his book Pedagogy of the Oppressed writes, students become containers to be filled by the teacher. (Freire, pg. 72) The teacher begins to educate students from their own construction of knowledge without considering what students bring with them to school every day. At times this furthers the oppression of some groups who see themselves as unconscious beings. Educators who view themselves as learners amongst students create an atmosphere that deconstruct dominant views of authority that aim to oppress students who are active agents in their own construction of knowledge. Educators who pose problems towards students and actively engage them in this construction of knowledge begin a process of breaking down hegemonic barriers that limit student success. Friere writes, “The students- no longer docile listeners-are now critical investigators in dialogue with the teacher. The teacher presents the material to the students for their consideration, and re-considers her earlier considerations as the students express their own.” (Friere, pg. 81)
Equity in Mathematics Education
How does this relate to mathematics? For many educators, the subject of mathematics is seen to be a standalone subject. The prospect of integrating ideas that affect the lives of students from marginalized communities goes unnoticed. As these communities struggle to achieve high standards in mathematics the achievement gap widens and makes it difficult for many to achieve higher paying jobs that require a solid understanding of mathematics. Schools need to raise expectations in at risk neighbourhoods and in high performing neighbourhoods, where there are diverse populations of English Language Learners (ELL) and encourage students to challenge the dominant discourse of an education built on traditional practices of teachers as all knowing and students as empty vessels ready to receive knowledge. Educators must begin to examine ways in which they can foster a partnership with students to learn amongst them and to broaden their views on how mathematics education is perceived. When mathematics is contextual for students they widen their abilities towards a growth mindset, where learning is grounded in using what they know and applying it to everyday experiences. Teaching mathematics with a social justice lens provides the backdrop of contextual mathematics and allows students to be active participants in constructing knowledge in a positive way. Students begin to see entry points and themselves in the discussion because they themselves know that the change they make in learning the math has a direct impact on their lives and the lives of others. Students also see themselves as having power as active citizens living in a democratic country where they may create change. They engage in critical thinking skills about the world they live in and construct meaningful change through a mathematics lens. For marginalized students who often don’t view themselves as mathematics learners simply because of their access to math and the standards that go along with the subject are limited, they shy away from it. Mathematics should be more than just rote memorization or repeating facts. It is about truly understanding the place that mathematics holds in our daily lives.
In Beverly Caswell’s Ph.d dissertation, Teaching Toward Equity Mathematics, she describes four themes that arise when speaking about equity and mathematics. First, she describes examining the achievement gap and why some marginalized groups fare poorly in math. Some people tend to “gap gaze” where marginalized students are seen as poor in math but seldom acknowledge what conditions led to this outcome. (Caswell, pg. 6) Some students do not do well on formal assessments. Careful consideration should be given to these students as there are many factors that influence how students perform on formal assessments such. These assessments that reflect a student’s ability to perform rather than focusing on learning, may not be a true reflection of a child’s competency in mathematics. It might be a question of considering rethinking our teaching and evaluation rather than students having to conform and perform to the curriculum. Secondly, students need to access high level mathematics in the school system in order to be held to high expectations. In addition, learning mathematics is a gatekeeper to higher paying jobs and many students need to be taught to advocate for themselves to access economic and academic opportunities. (Caswell, pg. 8) Thirdly, if we consider power issues in society and speaking about them through a mathematical social justice lens, then students can develop their own identities to have a voice in society. (Caswell, pg. 9) Lastly, students have to see themselves in the curriculum so that they connect their lived experiences to the mathematics. In turn they see themselves as “doers” of mathematics. (Caswell, pg. 10) Many students, aware that mathematics will be an important aspect of their everyday lives need to find practical ways of buying into learning the mathematics when they find it challenging and accept a place in the world of making sense of numbers.
References
Teacher As a Leader in Equity Through Social Justice Mathematics
Teachers need to rethink their role in the lives of students who learn mathematics as not just a teacher of mathematics, but also as a learner of themselves in mathematics and students who struggle to grasp concepts that would otherwise be known as “how does this apply to me?” We must begin to move away from seeing marginalized students as “deficits that resulted from their socialization within their families and community cultures.” (Banks, pg. 71) Students of colour bring many strengths with them to school. Banks writes, “They reject the idea that these students have cultural deficits and believe that the challenge for the school is to try to find ways to draw on the cultural strengths of these students and to make use of them in instruction.” (Banks, pg. 72-73) Keeping this in mind, all students, especially those of colour should be held to the same high expectations and be given the same opportunities to the type of math that is meaningful and full of rich discussion. Teachers who keep equitable practices by providing needs for all students despite their race allows a more reflective practice.
Social Justice mathematics is not a new concept in schools nor is it easy to try to implement in the mathematics classroom. It seems to be a subject that is largely misunderstood because of the implications of classroom discussions leading in often tumultuous waters. Teachers believe that the math component of social justice math may get lost in the discussion and diverges the practicality of doing the math. However, when thought out carefully, social justice math can have far reaching results for all students. When teachers teach math through a social justice lens, they are still teaching with the curriculum in mind, however the math that results from social justice issues provides students to analyze and make sense of their world by embedding context to the numbers. Students therefore become empowered by the use of learning math and engagement increases.
The problem that arises with teachers is the time it takes to really deconstruct global issues with students in a mathematical context. Careful planning must take place in order to fully realize the potential that social justice math needs. Teachers must really care about solving global problems and to create a sense of making a difference in their lives, the community and the world at large. In Lisa Delpit’s book, Multiplication is …. She writes, “We can and must build curricula that connect to our students’ interests, thereby allowing them to connect the knowns to the unknowns. We cannot allow an expectation gap to result in an achievement gap. Multiplication is for everyone.” (Delpit, pg.25) If connecting math to contextual everyday global ideas is so important, then why don’t educators implement these lessons in schools? Since understanding many of the issues that marginalized groups face, it is clear that many teachers would be ill equipped to truly realize the magnitude of what they simply don’t know about other cultures. To combat this issue, everything should be seen as a collaborative effort of minds coming together offering perspective. Nothing about global issues or reaching marginalized groups should be approached in isolation. It does perhaps take a deliberate step in the direction to learn about issues, and at the very heart of it, to care. Adapting one’s teaching towards a pedagogy of kindness, which in turn increases equitable practices in math would allow such powerful lessons to take place.
Education is linked to higher paying jobs and access to the type of wealth that is enjoyable for a thriving workforce. As educators, we need to invest in our students so they can compete in the global economy. Educators need to not only acknowledge their assumptions of marginalized groups, they need to shake their assumptions in order to stir the hearts and minds of students who don’t necessarily view themselves as math learners. Including a well thought out social justice practice could combat some of the issues related towards students who may or may not see themselves as those who don’t need to learn the math. A strong advocate to pushing the facilitation of these ideas can come from teacher leadership, however this must be fostered from an administration that believes, like Culturally Relevant Pedagogy in language is important, so should these ideas be included in the math that students will find themselves taking on later in life.
Social Justice math facilitates the type of discussion that allows students to deconstruct ideas that are associated with the economy and tied to their own ability to achieve later in life. As the inequalities of capitalism increase students need to be well equipped with understanding the numbers that are barriers to economic and personal growth.
Educators who evaluate their own personal narratives and shake their assumptions on the type of education that fosters a more contextual math curriculum begin equitable practices that improve achievement for all students. Students are not empty vessel that need to be filled. They are capable of more than we give them credit for and at times, instilling a belief that all students despite their situation can learn to appreciate a deeper conceptual understanding of the kind of math that is meaningful to their lives. Including a social justice lens may provide the type of math in classrooms that serve to demolish some of the oppression that holds some students behind and widen the achievement gap. The price is too high to look beyond including all students in a rich mathematics education that is contextual and rich in meaning. All students can engage in meaningful math if we examine teaching mathematics with equity.
How could we make learning mathematics contextual in order to increase student engagement?
We decided to use data in a Canadian context rather than using American data that might not have had the same impact.
Effective Questioning with Student Responses
- What information written or not jumps out at you?
- lots of numbers
- it goes highest to the lowest
- population goes from least to greatest
- the population is different for all three catagories
- population of females is bigger than males
- this report is from 2006
- how has the information changed from year to year?
- what are the differences between the numbers?
3. What are we comparing?
- dividing groups into three tables
Student of Mystery
Pedogogical Documentation
Students in Groups are looking at the data and thinking
Conversations in Groups
"I wonder if the employment data has changed throughout the years and why do females get more money."
Deluction: "More of the males have an education of a B.A or higher."
It was interesting to see some spark of interest from Matthew.
Large Group Discussion
- Our group discussed the different numbers and comparing the earnings of the different groups.
- We were looking at the males and the females.
- The earnings for Blacks were lower than other groups.
- The least employment rate was minorities and most with Blacks
- Females had the highest unemployment rate.
- Mrs. Bailey Bennett: What are some of the reasons for this? What contributes to this? Let’s make some connections.
- Maybe females don’t have a lot of opportunities to males.
- Women’s job is to take care of the children, they wouldn’t have the chance to get a job.
- They could be immigrants too.
- I’m adding on by saying it’s gender stereotyping, some cultures want women to stay home and not work.
- Blacks used to be slaves so they think they shouldn’t make as much.
- Its unequal rights.
Students Discussing what the data means
Students Needed to Self Identify
Asked the class which group they thought they belonged to and then started to deconstruct the vocabulary.
Students trying to understand where they fit in the data.
Many students made connections to seeing themselves in the data and why it is important to understand the numbers in the graph.
Student E: "When immigrants come to this country sometimes their education doesn't count so they have to do more here and have less education from the eyes of this country."
Student Work
In Conclusion
Social Justice Resources
By Sheila Sastri
Twitter: @SastriSheila