Filling the Gaps, Plugging the Holes, Stopping the Slip

Karen Wootton, Odenton, MD

My inbox is filled with solutions to our country’s serious problem: students falling behind. Each email claims to be able to fill the gaps in students’ knowledge, plug the holes created by missed classes, or stop students’ scores from slipping further. With almost a year of virtual learning, many things have suffered. But students’ knowledge, missed classes, or slipping scores are not where we should be focusing our attention.

The pandemic has caused trauma for many students and teachers. Loss of socializing, loss of jobs, and loss of life far outweigh the loss of some perceived level of learning. Remember that grade-level standards are completely arbitrary. We introduce place value in second grade, develop understanding of fractions in third grade, and measure angles in fourth grade, not because there is something about 7-year-olds, 8-year-olds, and 9-year-olds that makes them ready and able to learn those standards. Those topics are placed there because they are the next step in the development of the standards, not necessarily the development of the child. Students are not “falling behind” anything but an arbitrary marker. If the marker is arbitrary, then should we be worried?

I suspect to see more emails claiming to have the solution to students falling behind. Already school districts are talking about a summer school filled with remediation. If your district is already starting these discussions, here are some questions you should ask.

  • With students missing about a year of the socialization piece of schooling, how might students view schooling right now? Would it be the view you would want them to have?
  • Do you think after a year of virtual learning students will be more or less anxious about math class?
  • How will a summer math class emphasizing “catching up” or “filling gaps” affect students’ anxiety levels in a positive or negative way?
  • If you do not think an emphasis on “catching up” or filling gaps is the best way to address the last year of fuzzy learning, what else could you do?

Perhaps there is a need for some in-person summer school, but not with the focus of catching up. What if instead, in-person summer school could be used to remind students of the joys of learning with and interacting with their peers? What if students could just engage in some interesting math tasks with no worries about being graded? Could students be allowed time to wallow in the pleasures of discussing interesting mathematics with their friends? Why not let students play with math while the teacher also addresses social-emotional learning or growth mindset?

If your district is thinking about in-person summer learning, guide them to something that could be truly valuable to the whole child. Share with students the humanity of mathematics by letting them play and talk. The benefits of this will far outweigh any filled gaps or plugged holes.

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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.