Power of Feedback

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Karen Wootton, Director of Assessment karenwootton@cpm.org

Previously, I wrote about the debate on whether feedback should be opinion or fact. I advocated that we should share not just the facts but also our wisdom and guidance when providing feedback to students. If we do not value the teacher’s opinion, we might as well just place students in front of a screen and let them “learn” that way.

Feedback is a strange beast, and I realize that what I see as feedback may mean nothing to another. Recently at a conference, I conducted a session on assessment, and in introducing the topic of feedback I read a passage from a book, Pictures of Hollis Woods, by Patricia Reilly Giff.

This picture has a dollop of peanut butter on one edge, a smear of grape jelly on the other, and an X across the whole thing. I cut it out of a magazine for homework when I was six years old. “Look for words that begin with W,” my teacher, Mrs. Evans, had said.

She was the one who marked in the X, spoiling my picture. She pointed. “This is a picture of a family, Hollis. A mother, M, a father, F, a brother, B, a sister, S. They’re standing in front of their house, H. I don’t see one W word here.”

I opened my mouth to say: How about W for wish, or W for want, or W for “Wouldn’t it be loverly,” like the song the music teacher had taught us?

But Mrs. Evans was at the next table by that time, shushing me over her shoulder.

I asked the participants two questions. First, did Mrs. Evans give Hollis feedback? And second, do you think Hollis received the feedback that Mrs. Evans intended to give? Typically, the answer to the first question is an easy “Yes!” and then we go on to discuss what sort of feedback Mrs. Evans gave, and whether or not it was what she intended. At my last conference, however, I had a participant say that Mrs. Evans really did not give any feedback, just answers. After some discussion, this participant said she would concede that some information was given, but since it was unrelated to teaching, it was irrelevant.

Irrelevant? This comment struck me, and I have thought about the implications. Maybe I am showing my age, but I hope I am not alone in believing education is about the journey, not the destination. Is anything we do in the classroom irrelevant? My response is “no;” everything, no matter how small, is relevant.

One thing I think math teachers take for granted is that at some point in time, math must have had a terrific lobbyist working on its behalf. Think about it: even though we all say math is important – learning to think critically and be good problem solvers – how many of our students will actually ever use the math we teach them? Won’t the bulk of our students never use more than arithmetic, or if slightly more advanced, won’t they still be within the realm of what a calculator could do? How is it that we have the country, if not the world, convinced that every student should take at least through algebra 2, if not through calculus? And if not calculus, then statistics! Don’t get me wrong: I LOVE math, and in my ideal world everyone takes three hours of math every day and loves it. But, my ideal world is a fantasy. Yet, even politicians jump on the “Do more math!” bandwagon. Math is seen as necessary to everyone because learning math is learning to think critically and be good problem solvers.

While I agree that in our math classes we have ample opportunity to develop critical thinking skills, is it more so than in an English class where the students are critically analyzing the meaning of a novel? And, yes, we allow students to grapple with situations to improve their problem solving techniques, but any more than a student in a technical class figuring out why a motor does not run? Don’t other classes provide these opportunities as well? Is it just that math reasoning and problem solving is better than other types?

So while I hope my students improve their problem-solving capabilities, enhance their critical thinking, and love math, I am always aware of what else I can do for my students. Feedback and learning can take many forms. Does a student need someone else to read his essay? Sure, I will do that. Does a student need someone to hear about her fight with her BFF? I am available. Does a student need verification that there is someone in the world who values this student as a human being? I hope I am lucky enough to give that feedback.

You never know when these events of non-math learning will take place, what form they will take, or where they will lead. Mrs. Evans’ interaction with Hollis will probably stay with Hollis for a long time. Recently a student I had in class in 1985 sent me a Facebook message. It said, “You may have been new to the game when I was in your class, but you were there for us, intellectually and emotionally, and made geometry interesting and fun! (I still have the hall pass you gave me when I was having a bad day – it’s one of my favorite mementos from high school).” Who would have thought that a hall pass would have so much meaning to a student? Who would have thought that just letting this student out of math class—missing that all-important math class—for a bit would have a positive, lasting benefit?

Almost thirty years later, I received some very worthwhile feedback from this student. It is a fact that I gave her a hall pass. It is my opinion that she needed the time away from geometry for her well-being. She took the time to let me know this seemingly small incident was not irrelevant at all. Is her feedback fact or opinion? It does not seem to matter to me.

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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.