Reflections are Transformative

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Stephanie Castaneda, Round Rock, TX,

To reflect an image is to move many points across a line of reflection. Not all of the points move the same distance, but collectively they accomplish the same goal. Teaching a social justice lesson requires a great deal of reflection. In some instances, we have a lot of work to do, and in other instances we are not too far from where we need to be. In the end, we look the same but we are in a different place than where we started. I challenge you to engage in reflective practices to become a more effective facilitator of social justice lessons and an advocate for social justice on your campus.

Use reflective practices to get to know yourself.
Reflection is a great way to get to know yourself. Your beliefs send messages to students about who is valued and who is not valued. How do you know if you are sending subtle messages to your students? Make a list of your core values and beliefs. Then ask yourself, Why are these my values and beliefs? Where do they come from? To answer those questions, interview family members and research your family history. The more you know about the origins of your family traditions and roles, the better you will understand your values and beliefs.

This is a time-consuming process intended to help you connect with the greater world and people from other cultures. Consider this an informal autoethnography. Most people have heard of research, but an autoethnography is mesearch, a process of getting to know yourself and your culture through interviews and reflection. For a greater understanding of yourself, recruit colleagues of different backgrounds to go through this process with you. Check in periodically to share and discuss your findings. If you choose to engage in this process with others, you must be willing to listen without judgement. The purpose of the conversations is to better understand yourself and to develop a greater understanding and appreciation of others.

Use reflective practices to improve your interactions with students.
Periodic student surveys allow you to compare the classroom environment you want to create to your students’ perception of the environment. Keep your surveys short and questions direct. Sample questions include: Do you feel valued? Explain. and How are you able to share your voice and perspectives in class?

A trusted colleague or supervisor can also perform an observation for non-evaluative purposes. For example, you might want to compare your interactions with Black and White students. Consider a simple observation form. Instruct your colleague to look for specific interactions and provide constructive feedback.

Influence campus reflection.
Opportunities for campus-wide reflection include:

DateNumber of InteractionsWho initiated?
Teacher Responses
White MaleS


White FemaleS


Black MaleS


Black FemaleS


  • Encourage campus administrators to engage teachers and staff in a book study of critical race theory (CRT). This theory challenges your ideas about what role race plays in the education system. Critical Race Theory in Mathematics Education by Julius Davis and Christopher Jett is a starting point for you and your math department.
  • Call for administrators to consider restorative discipline. This practice turns the focus away from punishment and moves toward identifying the problem and uses relationships to establish an inclusive community and resolve conflicts. 
  • Identify and meet the needs of your students with action research. Action research leverages local data and human capital to identify opportunities for improvement. After an action plan is developed, data analysis and regular reflection are vital in making necessary improvements to the plan. If you have never heard of action research, watch this short video. This is one example of how a school in Maryland used action research courtesy of Edutopia.

Social justice is not a lesson or a series of lessons. It is a mindset shaped by critical reflections.

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Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.