Why Do Seemingly Insignificant Choices Have Significant Impacts?: What We Really Believe About Productive Struggle

October 2024

We hope you can name a time you really worked to learn something and that you remember the pride and satisfaction you felt when everything came together. Overcoming an obstacle is so powerful, we have no doubt you still remember what you learned. However, in this day and age, struggle is a struggle. Living through a pandemic was hard. In many ways, we are all trying to get back in shape to handle other challenges. And many of us are doing it in a culture that sends very mixed messages about the value of struggle. Athletes pour themselves into training until their weaknesses become their strengths. Parents nervously stand back to watch their children figure out how to ride a bicycle because, ultimately, they can only learn through the struggle of falling and getting back on the bike. But what about math students? Should teachers rescue their students when they get stuck? Are parents proud of their children when you call to say they are struggling? What does an educator mean when they talk about their “strugglers”? So often in schools, struggling is a weakness to be fixed. But what if struggling conveyed strength? What if the struggle was necessary, important, and expected?

Reflecting on Your Beliefs

Teachers in student-centered classrooms must believe that students can and should solve rigorous math problems. “By challenging them and supporting them through struggle, you can help them build the strategies and thinking they can carry with them into their futures” (SanGiovanni et al., 2020, p. 16).

We want to take a moment and invite you to reflect on some of your own beliefs.

“The fact is beliefs do matter, and what we actually do says more about what we believe than what we may say we believe” (Wells, 2024, p. 110). 

What might you say or do that will tell your students you want them to have the pride and satisfaction that comes from working through a good challenge?

Seemingly Insignificant Choices and Productive Struggle

Now that we have had time to reflect, let’s consider why seemingly insignificant instructional choices have significant impacts on productively struggling during learning. Grappling with this idea has led us to take action on our own student-centered instructional choices. Seeing learners as knowledgeable was our first idea to embrace. From there, it was about creating opportunities to share students’ knowledge in barrier-free ways. We implemented a Door Question every day. We asked questions like, “What is something you do right after school?” Learners might respond, “I like to go for a two-mile jog before beginning any homework.” In this case, it would turn out that running was a social connection between our learners and us, a connection formed in under 20 seconds. We paired this simple strategy with other student-centered strategies throughout the year to empower learners to transfer ideas while seeing their classmates as knowledgeable. 

Just as we become stronger through activities like a dedicated running routine, we recognize a need to nurture our classroom community with daily routines. We acknowledged that if we only completed a good stretch and committed to a light jog for the first two days of school in August or September, we would surely be unprepared to complete a marathon in May or June. The same was true for building a strong classroom community. To better support our learners in persevering and productively struggling, we need to collectively respect our personal setbacks, shared traumas, injuries, failures, and, yes, successes. At times in our teaching career, we failed to allow learners to share their negative (or positive) feelings about struggle. 

Supporting Openly Sharing Ideas with Prompts

We also recognized that learners lacked the prompts to share openly about their ideas. We found sentence and question frames to be highly effective as a student-centered strategy. 

Sometimes there were simple misunderstandings, such as learners leaving manipulatives and/or other resources out after an activity. One team member might become frustrated by unfairly cleaning the whole workspace. By providing a sentence frame like, “I will put away the _____, while you put away the _____,” we observed something very notable. Learners were more cooperative because they viewed it as a more equitable way to accomplish the task. At other times, we recognized that learners were being interrupted when communicating their ideas. Offering the question frame, “[ Name ] started to say something and did not get to finish. Can we hear more about what they had to say?” encouraged team members to help each other share more equitably, since it was no longer about who was fastest to respond. 

Too often, learners reported feeling unheard by their teammates. Providing general sentence frames (like these, adapted from CPM’s Inspiring Connections series) sustained discussions longer each period. 

  • What did you mean when you said _____?
  • [ Name ], you have been quiet. Do you feel excluded from the conversation?
  • I am getting frustrated. Will you help me _____?
  • I am not sure I am convinced yet. How do you know this is true?
  • My thinking was different because _____.
  • I want to hear more _____, but right now, we are working on _____.

Reinforcing Productive Struggle Throughout the Whole Year

After experiencing initial success early in the school year, we recognized that student-centered strategies needed to be reinforced throughout the whole school year as a routine to promote productive struggle in learning. Daily Door Questions reinforce that learning math is social; therefore, social connections are needed to productively struggle. Providing sentence frames reinforces a culture of discourse-based discussions. Once the discussions improved, the class gradually shifted the focus to assets rather than being stuck on deficits. We witnessed cycles of discussions and reflections about what they needed through rough draft ideas, team collaborations, independent reflections, and refinements. As the learners became more knowledgeable about how they learned, how they communicated their ideas, and the impact they had on others, they were also more supportive of helping their teammates be successful. 

 


 

References:

SanGiovanni, J. (2020). Productive math struggle: A 6-point action plan for fostering perseverance. Corwin. 

Wells, L. M. (2024). There are no deficits here: Disrupting anti-blackness in education. Corwin. 

Picture of  Jeremiah Morgan & Jocelyn Dunnack

Jeremiah Morgan & Jocelyn Dunnack

jeremiahmorgan@cpm.org (Eagan, MN)
joceylndunnack@cpm.org (Columbia, CT)

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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.