I have trying to write this post all summer. Each time I try, I want it to be more focused. Yet each time I revisit this idea I feel there are more things to add! So here we are, with the cumbersome number of 13 thoughts on math teaching as we enter the 2021 school year. Some of these may turn into additional posts, and please let me know if I should link to the writing of others in any category.

The idea of “learning loss” is deficit-focused, somewhat nonsensical, yet we cannot escape other kinds of loss. Loss that has permeated our collective lives in the last year and a half. Students have lost those dear to them. Students have lost time with friends, teachers, families. For many kids and families who attended very little school in person last year, it feels like the last year almost didn’t exist (for more on loss and our kids last year). I have heard my own child call last year “a lost year.” Kids had very different experiences, some attending school that felt like any other year, others visited their school in person maybe never, maybe a few times. Some experienced engaging Zoom classes, others not.

The first thing we need to consider is how these disparities in access and experience play out in equity. Math is already the most inequitable subject, with unfair outcomes based on demographics. What in the system will further penalize those who already suffered too much? This is a time to advocate for de-tracking, for elimination of standardized tests that determine opportunity. This is a great time to rethink grading practices that unfairly penalize some of our students for their lack of opportunities last year.

In teaching and learning mathematics, teachers face an old problem with a new twist. There have always been variability in our students, in their prior knowledge, in how they engage in mathematics, in their beliefs about their own selves as mathematicians. But these divergent experiences last year will make the variability greater. Teaching mathematics across this kind of variability is not easy, but it is both possible and necessary. And perhaps this year we will embrace what needs to be done to create a community of mathematical learners that is accessible to all.

Let us provide what students need without rushing to remediation for all. Yes, we might see that many students are behind. Many might score below a cut score on a screener (cut scores that were created pre-pandemic by a corporation). That does not mean that we take these students out of core mathematics instruction, that we focus on what they don’t know so much so that they don’t get a full chance to learn this year’s content. Instead, we need to welcome all kids into accessible, engaging math classrooms. Yes, we will need to provide extra supports for some, and opportunities to learn the concepts that they have not yet been exposed to, but we need to keep the train moving.

Resist remediation, resist making mathematics into a ladder in which kids cannot move on until they know everything ever taught in past years. Disability Studies scholar Alison Kafer writes about how disability is seen through a lens of “the curative imaginary”- she notes that disability is often seen only as something to fix, not as an identity, or as a set of strengths as well as challenges, or as a community, or a natural part of humanity that does not need to be fixed. Just as something to fix. She writes that the “curative imaginary, an understanding of disability that not only expects and assumes intervention but also cannot imagine or comprehend anything other than intervention”(Kafer, 2012, p. 27). Resist this. Do not look at your kids as data points, or they might see themselves that way. Resist the urge to think of your kids as a collection of “gaps.” The metaphor of gaps assumes that mathematical knowledge is some kind of perfectly filled in space or track or ladder. I don’t think that is true for almost anyone. No student has gaps, or we all have gaps. Math is not a ladder, it is a web. This means we can do intervention through big ideas, making connections through concepts. Yes, this is a crisis, but I think it is a crisis whose solution is increased access, not a rush for massive remediation.

Building on these ideas, here are my 13 thoughts for teaching math to all our students in Fall 2021

1. Dismantle barriers that further punish those who experienced the worse of learning in the time of COVID. Make sure that the barriers that exist are dismantled (are kids being punished/excluded for time lost in COVID? Can we relax grading standards? Can we detrack?) Advocate for our kids in this moment.
2. Begin with a well-designed, engaging curriculum designed around grade level standards. Should be:
   1. Concept-driven (develops big ideas in well sequenced ways, through rich tasks and connected representations)
   1. Visual (mathematically important representations that are connected together)
   1. Gives kids tons of opportunities to DO MATH (engage in the SMPS)
   1. Built around rich, multi-leveled tasks (low floor, high ceiling)
3. Consider starting with a really fun/engaging unit. It will be better for kids to re-engage with math in an accessible unit rather than beginning the year with everything they didn’t get the year before. Weeks and/or months of boring review is a sure way to re-ignite trauma. Starting with something engaging and new (like geometry, a unit on casino games and probability, a culturally relevant unit on social issues).
4. Collect data on your students so you can understand what they do know (without over-assessing) know them in their complexity, and in different contexts. Use data you are mandated to use (like screeners) as a part of the puzzle, not as some kind of divine data that is not to be questioned. Really effective intervention builds on what students know, not what they don’t know. I suggest beginning with classwide assessments (simple, focused on concepts) with follow-up short interviews for students you want to learn more about their thinking.
5. Create a community of learners who support each other, take risks, and engage in joyful mathematics. Gently re-engage your students in collaboration, mathematical talk, etc. Remember that some of them might have “forgotten” how to. Be patient, provide scaffolds (like group roles, or explicit guidance on how to do what you ask).
6. Develop relationships with students that will help them persist when it gets hard.
7. Explicitly teach/model growth mindsets and a positive mathematical identity. Important messages:
   • Mathematicians take time. We can take time.
   • Being fast is not all that in math
   • Math takes different ways of thinking
   • Each of you is a mathematician
   • We learn through mistakes
8. Scaffold so that all students can engage in grade-level curriculum. Build on-ramps (Fritzgerald, 2020) into mathematics so that all students are with you. I use Universal Design for Learning as a way to frame this kind of accessibility. You can read more here (and an upcoming paper in Teaching and Learning Mathematics K-12), but here are a few critical ideas:
   • Focus on core concepts- big ideas. This is where instruction should be focused. If a kid doesn’t understand the concept of multiplication, teach them that. If they are inefficient in multiplying, and you are moving on to other work, hand them a calculator. Spend valuable time on concepts.
   • Provide multiple ways to engage in these big ideas. Lots of chances to get information multiple ways (and refer to it later). This includes multiple representations, providing visuals/models, and providing more than one way to access content.
   • Provide choice in how kids engage. Provide a mix of collaborative work and time for thinking alone. Teach kids to understand what works best for them in what situations.
   • Make content accessible by providing tools for all.  Calculators, multiplication charts, notes that remind students of procedures or ideas, a class note-taker. Things that in the past might have been accommodations for some can be accessible for all.
   • Coach kids in being math students and developing metacognition. Develop students ability to understand their own learning, to self-regulate and self-assess. We need meta-cognition in this moment.
   • Build in lots of useful feedback for kids (not just grades)
   • Provide additional support through student choice. After you launch a lesson, ask if anyone wants to hear it explained it again, come to this table. Have sign-ups for peer tutoring in particular topics. Get kids to understand what they need to work on, and teach them to advocate for themselves.
9. Build in opportunities/routines to build student understanding in unfinished learning
   • Focus on core concepts- big ideas.
   • Map out connections between those concepts. Use assessment data to make a list of the critical unfinished learning in earlier grades. Make goals to provide opportunities to revisit these concepts where they fit well.
   • Incorporate instructional routines that blend conceptual learning with procedural fluency. Number strings are an example of this. But there are plenty! Make short instructional routines a cornerstone of your instruction and a regular way to work on prior content.
   • Judicious use of technology. For some kids the right program could be very useful in addressing work they may have not had the opportunity to engage in before.
   • Games! Maybe once a week you have a Game Day, giving you a chance to work with small groups, do some assessment, while students practice fluency through games.
10. Excessive homework will compound inequalities. Don’t expect kids to catch up because you load them up with homework. What can you do with homework that will support engagement, enthusiasm, and provide practice in new and prior learning?
11. Some kids will need more supports. Design/advocate for a RTI/MTSS system that has responsive ways to decide which kids need more targeted instruction in small groups (Tier 2 and 3). Responsive means that assessment is at the heart of this practice, and we are collecting multiple sources of data on what works and what does not for these students (not just screeners). And all kids receiving Tier 2 and 3 services are still fully included in Tier 1/Core Instruction.
12. Move away from rigid grading, towards useful feedback and self-reflection.
13. And for us teachers, work on your own beliefs. All kids can learn mathematics, all kids can engage in deep mathematical thinking. Resist the urge to think of your kids as a collection of gaps. As Andy Gael and myself have written, our kids are not swiss cheese!

Fritzgerald, A. (2020). Antiracism and Universal Design for Learning. CAST, Inc.

Kafer, A. (2013). Feminist, Queer, Crip. Indiana University Press.