Are “bad” conversations worthwhile?

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Karen Wootton, Director of Curriculum & Assessment, karenwootton@cpm.org

Last fall, at the NCTM Regional Conference in Seattle, I attended Steve Leinwand’s session on quality lessons. During his presentation, he made a comment that, due to my bad memory, I cannot remember, but prompted me to record this in my notes: “Are bad conversations worth as much as good conversations? Mistakes!” After the conference when I was reviewing my notes, I realized I needed to know more about what Dr. Leinwand had said. In particular, I had a pressing need to know since I was (and still am) in the process of reading feedback on the pilot course developed to support students who might be struggling in the Core Connections, Course 3 class. Piloting teachers had expressed concern over students not always getting the right answers. A few teachers expressed their frustration over students working for 45 minutes on a problem and not being “successful.”

Personally, I would be celebrating students who would work 45 minutes on math, particularly when they are not arriving at the “right” answer! Talk about perseverance! But while I might be thrilled with this, how valuable is it for the students? I wrote Dr. Leinwand, about this. Specifically, I asked if it was worthwhile for students to spend a year in a support course, if they never mastered anything.

Dr. Leinwand replied to my email, saying he thought it worthwhile to be working on math whether or not the students were getting the right answers. He said “I base my approach on two views: 1. That good math begins with answers – often a wrong answer – and the key is justifying these answers, and 2. That mistakes are to be expected and honored because often, more is learned from mistakes than from correct answers.”

I was still somewhat hesitant to embrace this completely, and worried that I might be considered the math equivalent of Harold Hill, the con man from The Music Man. If you are unaware of the plot of this musical, Professor Hill claims that by using the Think method, anyone can learn to play a musical instrument. He sells the instruments to all the families of the children in the small Iowa town, claiming they will learn to play by thinking about the music. When I expressed this concern to Dr. Leinwand, he replied “Yes, Harold Hill was a con man and usually just telling someone to think doesn’t work, but getting students to actually think productively is 3/4 of the battle. And yes,… the struggle [is] essential.”

He went on to say “I often think about writing as a way to think about math. There is never an on-off switch where suddenly you can write, but with the right experiences your writing always gets better. Same with math.

I do not think this means we should be content when students have incorrect answers, but rather we have to help them understand WHY the answers are incorrect, and then guide them to form correct ideas. These “bad” conversations are the rough draft talk that leads to correct thinking. And by going through the process, having “bad” conversations, or conversations that contain misunderstandings and incorrect pieces, students make sense of the mathematics.

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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.