The Impact of Identify in K-8 Mathematics: Rethinking Equity-Based Practices

Written by Julia Aguirre, Karen Mayfiled-Ingram, and Danny Bernard Martin

Reflection written by Whitney Christenson

Brief Overview:

            The focus of this book is aimed at three essential questions: 1. What is mathematics? 2. Who is if for? And 3. What is the purpose of math? The purpose of this text is to invite educators into a conversation about first recognizing our own identity in mathematics, and then moving into how we may respond to students by encouraging positive labels and reframing negative ones within their own mathematical and other identities.

Part one focuses on inviting educators into the conversation about recognizing their own identify. Part two focuses on an educator’s response to students’ math identities. And part three focuses on the “we” response, bringing into light the village that it takes to raise a child: teachers, parents and community stakeholders.

A Closer Look:

Part one: Rethinking Mathematics Learning, Identify and Equity

This section lays a clear illustration of how teachers perpetuate stereotypes, both the ones that lift students up, that they claim as their identities and are proud of of, and the ones that seem derogatory and hold negative connotations. We perpetuate them.

Everyone has multiple identities that play off one another: gender, social class, socio-economic class, heritage, language, hobbies, and so many more. As educators with our words and our actions we must be sure that we recognize in the classroom that equitable does not mean equal…

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One way to cultivate a positive mathematical Identity in ourselves and in our students is to first define it: “Dispositions and deeply held beliefs that students develop about their ability to participate and perform effectively in mathematical contexts.” (Aguirre, et. al., 2016, p. 14) The agency that students have over their identities allows for them to be active participants in these declarations over their lives.

Another way to press into our math identities is to look at our identity among five strains (or types) of logical thinking that the authors illustrate. (Though these strands are actually provided by the National Research Council in correlation with the Mathematical Practice Standards K-12 (CCSS)). In this book,  Aguirre et al., recognize these five strands to be braided among one another as students are experimenting and using math daily, instead of a hierarchical approach. You can see their thinking below:

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When students begin, or even when we as educators begin to adopt identities regarding mathematics, we must do so in relationship with each of these strands. As educators we also must be sure to keep the focus on reframing identities by focusing on the learning rather than on labeling. Factors are not forcers! And, in turn we must highlight the positive identities we adopt and polish, or reframe, the negative ones.

Think about your math story, if someone asked you: “What was your experience with math like as a student.” what would you say?

When I first read this I thought about my math elevator speech: I have always enjoyed math, and I have been pretty good at it my whole life. In fact, I was that kid in high school who took math as an elective. The thing I struggled with most in elementary school was fractions but once I had that lightbulb moment happened it was smooth sailing until high school calculus. I enjoyed algebraic concepts more than geometry. Overall, I had a strong math identity, and that was rarely shaken throughout school.

Again, the definition of Identity is: “The stories that people tell about themselves and what they view as important to them: their understanding of their place in the world and their core beliefs.” And, the definition of math identities is: “Dispositions and deeply held beliefs that students develop about their ability to participate and perform effectively in mathematical contexts.” (Aguirre, et. al., 2016, p. 14)

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Part 2: Rethinking Equity-Based Practices

“We believe that the work of most teachers intrinsically includes elements of each of the five practices. However, tying these practices to mathematical learning and identity may be a new challenge.” (Aguirre, et. al., 2016, p. 44)

There are five practices Aguirre, et. al, recommend for teachers to use. You can see the practices along with brief example of how to incorporate each into your classroom below:

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Through researching these 5 Equity Practices I have come to agree with the authors when they say, most good teachers see elements of each of these in their classroom. The largest strength my teaching attests to is Leveraging Multiple Math Competencies. I pride my classroom of meeting the need of all students through differentiation of content, process, product, and environment.

An example of this how we are reviewing our standards for the year. Content: Students who have mastered a standard get the choice to work on Odyssey, MobyMax or join another center for that work station time. Students who need additional assistance have the choice of working with a student who has mastered that standard (with teacher check ins), or being in a small group with myself or the teaching assistant.

The process for centers is generally times, however some students need additional time given. Students are able to work up to 5 minutes over the time given in order to complete their tasks. I also give students the option to stop by at recess or activity for additional assistance. It is prefered that I am made aware that they take on this agency prior to leaving my class so that I may plan accordingly.

Product is differentiated by the supplies students use: type of paper, pencils or crayons. At some centers they are able to explain in words or draw pictures for the strategies they select.

Lastly, differentiating environment in my classroom looks like provide space for privacy folders, table groups, individual desks, students on the carpet and in the hallway, headphones, etc. As long as they are learning and being safe, I do not mind how they are working.

The area of the 5 Equity Practices I believe I can have the greatest area of growth in would be Challenging Spaces of Marginality. I currently bring student interests and names into word problems, however there are much larger areas I could engage them in real-world relevancy. One way is creating word problems that students will be engaging with during summer and on the weekends, real world/community issues. One specifically could be related to “do you have enough money?” If not, how could you save the money for this item that you want/need?

Chapter Six goes on to discuss how assessment is related to these five equity-based practices. Some of the mindsets, questions and topics of conversation that you may continue to chew on after reading chapter 6 are: Do you teach for learning or for testing? Is our current testing system honestly meeting best practice recommendations and differentiating for our students’ needs? Are multiple choice standardized test really the best end all data we can gather? And are we giving our students the most meaningful feedback possible on their assessments?

            Part 3: Rethinking Engagement with Families and Communities

This final section allows for teachers to reflect on the roles that parents and community organizations can play in deepening mathematics learning for students and reinforcing students’ positive math identities (Aguirre, et. al., 2016, p. 85).

In fact, the authors, “encourage a paradigm shift in thinking regarding the roles and participation of parents and community organizations in a student’s math education. In-class and out-of-school examples can assist teachers in developing true partnerships with parents and community groups to support students’ success in math.” (Aguirre, et. al., 2016, p. 86).

These final chapters share artifacts from two different classrooms that allow teachers to recognize how to better communicate with parents about visions. One way they do so is through classroom math newsletters. Classroom newsletters allow for important information about classroom activities and upcoming events to be shared. It allows for connections to be made about student learning goals, values, expectations and visions from classroom to home as well. There are opportunities to help parents know tricks and strategies used in the classroom. Classroom newsletters may also provide meal time conversation topics for families to engage in. All in all, this fosters additional trust between parents and teachers, and vise versa.

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My Takeaways and Implementation:

Currently in our classroom we provide a daily space where students engage in spiralled review and introduce new concepts through songs and games. (I teach second grade math). We call this time: “Math Meeting”.

For those of you who are unfamiliar with spiralled review, this is a time that allows for teachers to engage students in concepts they have already learned. At the beginning of the school year this allows them to activate prior knowledge from their previous classes or grade level. As the year moves on this allows teachers to engage students in relevant word problems with concepts taught in earlier months. One example of this in my classroom is the March calendar patterns. We focus on clocks and adding and subtracting time by ten minutes. This engages a standard that expects students to be able to mentally add and subtract ten to any number. This review engages students in a way that makes their number sense, base ten, and order of operations concepts relevant.

We call this time Math Meetings because it is a time that we meet as a whole class and talk about things we are doing well. We review things we need to do better with and prepare for new concepts: this time is centered around discourse: sharing ideas, critiquing ideas and providing relevance to show that math is meaningful to our everyday lives. You can see an example below of how some of the elements of the five equity-based practices are ingrained already into our math meeting below:

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One way I would like to dig a little deeper in this Math Meeting next year is to continue to have a word problem of the day that centers around relevant issues to my students real lives. For example, next year I would like to make telling time and adding/subtracting time more relevant to my students in relationship to scheduling sports games and school assignment time limits. I also would like to make measurement relevant by its regards to cooking and rearranging rooms.

Now, many of you teach in upper elementary or secondary math classrooms. If you are a pre-algebra or algebra teacher there are ways of implementing a math meeting at your student’s level. One book that may be a good resource to utilize storytelling or new activities is called Kiss My Math by Danica McKellar. This book gives weight to many different aspects of algebra in an enticing way while recognizing common mistakes students may make. One of my favorite chapters goes on to explain the distributive property through the story of a costume party, or another is talking about integers in relationship to mints and/or Bertie Bott’s Jelly Beans from Harry Potter.

Remember, the purpose of a math meeting is to quickly activate prior knowledge while engaging students with current content. In a secondary classroom, this may look like reading an excerpt of having a real-world scenario of the week. Students then have to work together to solve the rigorous problem while small hints are given each day. Math meeting are also a great time to invent 10 minute games with you students.

Another takeaway for next year is revamping my current parent letters. I am a huge advocate for having family investment in the classroom, not just student investment. Below you can see how I currently communicate with parents:

Next year I would like to create this to be more of a comfortable classroom newsletter that students hope to take home and share with their parents. That way, parents always know what standards we are working on. This newsletter would be able to demonstrate strategies we are working on in class as well as have conversation starters or problems their students can teach them how to do. This is where I will begin implementing the research I have done form The Impact of Identify in K-8 Mathematics: Rethinking Equity-Based Practices.

Lastly, you can find the resources discussed attached in this google drive folder for continued research. There are some resources regarding a lower elementary math meeting and documents with parent bi-weekly letters like you saw above.

Many of the math meeting resources that I use are not editable. If you have questions or want guidance on ways to implement a math meeting, feel free to reach me at whitneychristenson@gmail.com .

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