A Week of Amazing Mathematical Collaboration

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Alex Clayton, Johnstown, Colorado, 14ajclayton@gmail.com

“Everyone stand up and push your chairs in. Next, go touch three walls, two chairs, and one table. Find the closest person in your proximity.” “Take a card, and find the matching card at the table. This is now your new group.” “If you can hear me, clap once; if you can hear me clap twice.” “I hear three wonderful mathematical conversations. I now hear two wonderful conversations. And now I hear one fabulous conversation. Thank you for your great work.” These are many things that one would hear or observe in a day at the Academy of Best Practices (ABP). ABP is an amazing week of collaboration, practice, and development in becoming a better math educator. Thirty-two of us, who each have less than five years of teaching experience, spent one week at Seattle Pacific University bettering ourselves, bettering each other, and bettering our world.

We had three amazing facilitators: Mark, Sharon, and Karen. We also had two awesome mentors who are ABP alumni, Lucy and Mallory. These five were very organized and prepared. They executed many fantastic lessons. Every minute of our scheduled class time was filled with opportunity. Class was from 8:15  to 5:00 daily, and sometimes that was not long enough. We did some sort of collaborating ice breakers every day, and many days, we did two or three ice breakers, each time we changed teams. The most awesome part was that this week was all laced with math! It was awesome to have a week of ‘nerdy’ discourse. We could use a mathematical expression and binary numbers, without having to be embarrassed or explain ourselves! It was neat to collaborate with math teachers of so many different backgrounds and abilities; we had teachers of 6th grade math up to AP Calculus. There were so many great discussions about homework, grading, testing, direct instruction, group work, scaffolding, lesson planning, growth mindset, and so much more. Even when we were not in class, we were all discussing our methods and listening to each other’s ideas and experiences.

It was really neat to experience being a student under instruction that was perfected and smoothly ran. Learning under this type of instruction was so much fun. This is something that I have been wanting for my students. I want to make learning fun for my students. I am very excited to go about using the new tools that I now have.

Of the many guest speakers, Dan Myers, Eli Luberoff, and Aaron Brakoniecki were the most impactful to me. Dan Myers was awesome. He challenged us to teach math as if we were telling a story. He said, “DO NOT give away the SURPRISE, let the students discover the surprise.” I hope that I can do a better job and not spoil the mathematical surprises for my students. We also worked with Eli Luberoff, the creator of Desmos. Desmos is a FREE online graphing calculator. Let me say, if you have not worked with Desmos, you are missing out. There are some amazing tools, such as being able to graph any type of function, point, picture, and much more. There are also many lessons already created that you can use in your class. Go explore at teacher.desmos.com. I love that it has been created to help students discover the surprises of mathematics. Aaron Brakoniecki, a professor from Boston University, spoke about cognitive demand. He asked us to think about the type of tasks we are giving our students. Are they ‘high potential’ or ‘low potential’ tasks? In other words, we were challenged to think about our goals, and how we want the students to receive our message. I was very inspired by all three of these leaders. Thank you for the work you do in the world of mathematical education.

As we went through the week, we had to create an Action Plan. An Action Plan is taking a goal, putting these desires into words, words onto paper, and then sharing them with someone else. Our Action Plans targeted two goals in which we wanted to better ourselves this year. These Action Plans are detailed with dates, information, and with people who are to hold us accountable in achieving them. I now have 36 other teachers who are supporting me to be better at asking better questions and providing constructive feedback to my students. I knew I needed to be better at these things, and now I have a support system to help me achieve my goal.

I believe that every teacher needs to go through the ABP; however, this is impossible. So I want to leave you with a few things that I learned.

  1. Mark, Karen, and Sharon have had many years of practice. They learned many of their tools and practices over the years, so do not be afraid to try new things.
  2. “Change takes time” – Karen. We were told to just pick two things that we really wanted to change and make better this academic year. If we were all to focus on fixing and perfecting two teaching techniques every year, after a career of teaching, we would have so much knowledge to share. Also, make sure that you write your goals down.
  3. Share your knowledge and experiences no matter where you are in your teaching career. There are so many people in the world who want to know what someone else is doing in their classroom. Find ways to collaborate; it is how we grow.
  4. If you have questions, ask them. Search for information online. Chances are someone has already come up with and made an activity that you would like to implement. People will help you, but first, you must take a risk and ask.

If you are in your first five years of teaching mathematics, take a chance at bettering yourself. Apply! If you are farther along in your teaching journey, encourage a first year teacher to apply.

To Mark, Sharon, Karen, Lucy, and Mallory: thank you so much for all of the time and hard work that you have put in over the years into math education! I am very thankful that all of you have decided to share the experiences that you have learned over the years with others. Thank you for an amazing week of learning and bettering ourselves.

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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

This series contains three different courses, taken in either order. The courses are designed for schools and teachers with a minimum of one year of experience teaching with CPM curriculum materials. Teachers will develop further understanding of strategies and tools for instructional practices and assessment.

Building on Equity

In this course, participants will learn how to include equitable practices in their  classroom and support traditionally underserved students in becoming leaders of their own learning. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for implementing Chapter 1 that creates an equitable classroom culture and curate strategies for supporting all students in becoming leaders of their own learning. Follow-up during the school year will support ongoing implementation of equitable classroom practices.

Building on Assessment

In this course, participants will apply assessment research to develop methods to provide feedback to students and to inform equitable assessment decisions. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

This professional learning builds upon the Foundations for Implementation Series by improving teachers’ 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 rigorous, team-worthy tasks with all elements of the Effective Mathematics Teaching Practices.