Composing Your Symphony

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Sharon Rendon, Director of Professional Learning,

Have you ever stopped to consider what elements go into a masterful musical composition? Recently I had the opportunity to see the Broadway musical Hamilton and was amazed at the music, costumes, and acting. This experience got me thinking about how this relates to the math classroom. What components are necessary to create a mathematical masterpiece? Three necessary components that contribute to mathematical experiences for students are the score or piece of music, the conductor, and the musicians. However, a wonderful masterpiece does not just happen because those three elements are present. Let’s focus on two of those elements, the score itself and the actions of the conductor in relation to a math masterpiece.

A symphony will start with a great score. The foundation of a great math experience is to have a well-written progression of concepts and learning opportunities. CPM authors have provided this in the books. One of the most powerful examples of this is the development of linear relationships. Students have the opportunity to start with tile patterns and growth problems before moving to the more abstract concepts of slope and y-intercept. This set of tasks allows students to develop understanding and make connections over time.

It is critical that the conductors use the score as intended, with minimum adjustments. If the cognitive level or design of the tasks or progression is altered greatly, the masterpiece will be affected. Imagine a conductor deciding to play the reprise at the beginning and then move the prelude towards the end of the piece. Or if the conductor decides to have the trumpets play the flute parts, because it is too difficult for the flute section, the musical piece may not be as beautiful as intended. The conductor must carefully consider the effect changes to the score will have on the final production.

The second element necessary to produce a masterpiece is the actions the conductor might take to create an amazing experience for the instrumentalists. This is related to the mathematics instructor and their students. First, instructors must be learners themselves. There are always ideas and strategies to be learned and developed. There are many different venues to use in one’s learning path. Some of the best learning an instructor can have comes from observing their students. Many times students will be more creative problem-solvers and creative thinkers than their instructor. Another learning opportunity comes from CPM Educational Program, which provides teacher leaders who offer strategies and feedback through workshops, site visits, and coaching. An additional learning opportunity can be found in the power of collaboration with each other by creating collaborative work teams. Seek out a couple of colleagues that would be willing to learn alongside you. If you have a formalized “PLC” structure take advantage of that in order to impact both your practice and student learning. And finally, an instructor might participate in a book study or use the power of social media to facilitate their learning. Jo Boaler’s Facebook page, Twitter, and blogs provide a great opportunity to collaborate virtually with other instructors.

Becoming a reflective practitioner is also a key action a mathematics classroom conductor might take to produce a mathematical masterpiece. One method of reflecting is to ask a colleague to observe you. See #observeme for more ideas on how you might incorporate this strategy. Another fairly new strategy, called Pineapple Charts, allows teachers to post on a calendar when they will have lessons to watch or strategies they would like feedback on.

There is also the power of using a coach. If you have coaches in your building or district, reach out to them and ask them to collaborate with you to focus on an element of your practice. Working with a coach is a great way to focus on the next step in your journey as a practitioner. Coaches are not in the business of “fixing” teachers, just supporting them in taking risks and look at student learning.

Finally, mathematics instructors will be successful at creating masterful learning experiences when with they are committed to continual growth. This process will take time and require extended efforts. One of CPM’s guiding principles is that mastery takes time. This is not only true for students, but also for teachers as well. When you are in the midst of practices that do not sound great, that are messy, and you think are not working, you must remember that great results take work and practice. Stay committed to the process and continue to be committed to improving as time goes on.

Which of the ideas in this article need attention from you? How might you commit to making those actions happen? As you are continuing to craft your masterpiece and create sense-making, meaningful learning experiences, remember to take intentional actions toward improving your practice.

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Algebra Tiles Blue Icon

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.