The Power of Reflection

Sharon Rendon, Director of Professional Learning,

It seems like school years continue to go by faster and faster.  It is already March and many of you are about to turn the corner, entering the fourth quarter of the year. Now is a great time to take some time to reflect and consider the opportunities you are providing for students to make sense of mathematics.

If you are in your first year of implementing, you are probably just now seeing the beauty of the connections and the learning over time that is happening with students. And those of you in your second year or beyond continue to see the beauty of mathematics unfold over time. I remember the first year I started teaching I was thrilled when my student arrived at the factoring quadratics section and they could see many of the previous concepts connected.

This year the professional learning department has made a concentrated effort to use the Implementation Progress Tool to provide some language and descriptors during support visits.  However, this tool is also useful beyond the first few years of implementation. Many of you have not had the opportunity this year to engage with this document, and you may not be aware of this tool or the ways in which it could be used.

The tool is aligned with the three pillars behind CPM’s design. The first section describes the foundational idea of the pillars. The second and third sections provide powerful opportunities for reflection. Section two focuses on student learning. Think about your lessons this past week and identify where your students are having success. What evidence are your students providing of high quality learning? You might also consider the areas your students need more support or structure to be successful in their learning. Maybe you and your colleagues could identify a goal that you work on collectively.

Section Two: Features of desired student learning when the pillars are in place.

Collaborative LearningProblem-Based LearningMixed, Spaced Practice
Students read and make sense of problems together.Student thinking at varied depths of conceptual understanding are openly shared and valued.Student work through lessons at an appropriate pace.
Students are able to listen to the ideas of others and communicate their own ideas both in teams and during whole class discussions.Students demonstrate and value both conceptual and procedural knowledge.Students understand that mastery takes time, effort, and support.
Students listen carefully to the thinking of others and respond with clarifying questions or extensions of their own.Students look for, compare, and connect multiple models and solutions strategies.Students are aware of learning targets and periodically self-assess their progress towards those targets.
Students engage in productive mathematical discourse, justifying answers, creating viable arguments, and critiquing the reasoning of others.Students recognize that incorrect work cn be a stepping stone to learning and are wiling to share and investigate their thinking.Students solidify learning as they work on Review & Preview problem sets daily as intended.

The third section provides some language about teacher actions. The language included in these descriptions is similar to the eight teaching practices found in the book Principles to Actions, published in 2014 from the National Council of Teachers of Mathematics. Use this tool to identify a goal for the fourth quarter of the school year and put some action items into practice.  If you have not read the publication, put this book on your summer reading list.

Section Three: Instructional strategies evident when the pillars are in place.

Collaborative LearningProblem-Based LearningMixed, Spaced Practice
Teachers creat an environment of collaboration and consistently provide feedback on studens’ progress towards effective collaboration.Teachers us the lesson launch to connect to prior learning and clearly communicate the learning target.Teachers plan and pace lessons as intended, based on a thorough understanding of the learning progression of each chapter and the course as a whole.
Teachers use a variety if classroom modes (whole group, study team, partner, individual) at appropriate times within each lesson.Teachers circulate purposefully to interact with all teams, monitoring and questioning the thinking of students.Teachers anticipate common misconceptions and consider varied levels of understanding to differentiate and move all students towards stated learning targets.
Teachers use Study Team and Teaching Strategies (STTS) and Team Roles with purpose.Teachers use questioning to uncover student thinking, and then provide opportunities for that thinking to be shared.Teachers provide timely feedback on student practice of previously introduced skills and on beginning understandings of developing concepts.
Teachers hold students individually accountable within the team environment.Teachers formatively assess student needs and take appropriate action to support accessibility.Teacher elicit students’ informal ideas and leverage them towards developing formal mathematical vocabulary and procedures at appropriated times in the course,
Teachers are aware of and take status issues into consideration when managing teamwork,Teachers design and facilitate lesson closure that provides opportunities for students to make connections between various solutions and key mathematical ideas.Teachers use varied assessments that are based on mastery over time and assess both conceptual and procedural knowledge.

Don’t wait any longer or let any more of the school year go by without taking the time to reflect on the learning happening in your classroom. Gather a couple of colleagues and spend some time celebrating your successes and identifying some next steps.

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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.