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Mathematics Preparations for 2020-2021

Latest Guidance from NCTM and NCSM for 2020-2021

In June of 2020, the National Council of Teachers of Mathematics (NCTM) and NCSM: Leadership in Mathematics Education jointly released Moving Forward: Mathematics Learning in the Era of COVID-19. This document was organized around three major areas to consider when planning for the 2020-2021 school year:

  1. Structural considerations (What are the equitable structures that will best support students?)
  2. Teaching practices (What planning and teaching practices will best support students?)
  3. Advocacy (How can we humanize mathematics teaching and learning?)

The main points of Moving Forward are summarized below, but in no way should this list replace reading and carefully considering all the major points, guiding questions, and recommendations from the original 18-page document.

Structures Supporting Mathematics Teaching and Learning

In Moving Forward, the key recommendations for structures to support mathematics teaching and learning are:

  • Detrack students into heterogeneous ability groups, both within and across classes.
  • Create strategically mixed groups of students with a variety of strengths and give them tasks that require and encourage collaboration and the production of work in a variety of media, including digital and print.
  • Prioritize mathematics teaching and learning by providing additional time for planning and implementing intervention plans.
  • Detrack teachers so those teachers with most success or experience teach students of all abilities and levels.
  • Provide regular professional learning opportunities for teachers that focus on effective and flexible instruction.

Teaching Practices Supporting Mathematics Teaching and Learning

In Moving Forward, the key recommendations for teaching practices that support mathematics teaching and learning are:

  • Determine the essential learning of each grade level so that the majority of instructional time and effort is focused on the most critical topics.
  • Determine necessary prior knowledge and what may have been missed or taught previously under remote learning and then strategize to provide just-in-time support for students if necessary.
  • Determine what students know through formative assessment practices using rich mathematical tasks instead of typical pretesting and posttesting.
  • Support teachers in learning and using effective mathematics teaching practices so they may provide high-quality instruction regardless of instructional setting.

Advocating for Teachers, Students, and Humanizing the Development and Implementation of Education Policies and Practices

In Moving Forward, the key recommendations for advocacy and policy-making are:

  • Plan for contingencies related to school closures, moving back and forth to remote teaching, or modified schedules.
  • Humanize the situation with stakeholders so everyone understands the human impact of fiscal decisions.
  • Promote the allocations of time and resources to ensure every student is provided to meaningful, grade-level content and high-quality teaching.
  • Speak and find support for crucial positions that support teachers, such as instructional math specialists, coaches, and other instructional leaders.
  • Consider and grapple with the systemic impacts that affect the validity and reliability of large-scale assessment and data collection.
  • Protect instructional time by only using assessments demonstrably connected to content and resulting in actions.
  • Create a culture that promotes professional learning, increasing teacher capacity, and teacher collaboration.

Other National and State Guidance

Recommended Reading: TNTP's Learning Acceleration Guide advocates for accelerating learning in 2020-2021 and recommends many of the same actions suggested in Moving Forward by NCTM and NCSM. They stress the importance of planning over the summer of 2020 for adjustments to instruction that will be required throughout the next school year and absolutely do not recommend "pausing" grade-level instruction for remediation or re-teaching of previous content. CCTM members can watch a recording of a webinar presented by Mary Pittman (CCTM President-Elect and TNTP Project Manager) where she discussed the report and its implications for mathematics teaching and learning in 2020-2021.

Student Achievement Partners' 2020-2021 Priority Instructional Content in ELA/Literacy and Mathematics advocates for a deep understanding of mathematics standards and how major work of the grade is organized in multi-year progressions of learning. While CDE's stance for all of its standards is "All Students, All Standards," we realize that meeting the goals of each standard does not take the same amount of instructional time nor necessarily have the same impact on students' progress. This document from SAP is not advocating for only teaching some of the standards, so do not interpret it that way. Instead, use it to guide curricular planning and instructional decisions so that allocations of instructional time and effort are optimized to have the greatest possible positive impact on student learning and growth. This document is complementary to the Council of Great City Schools (CGCS) framework Addressing Unfinished Learning After COVID-19 School Closures, which carries similar messages as the guidance from TNTP, but focuses more on transitions between particular grade levels. This focus on some grade-level transitions and not others is a peculiarity of CGCS's work and has no basis in the Colorado Academic Standards, so readers of CGCS's document should not interpret that aspect as a recommended practice or perspective by CDE's Office of Standards and Instructional Support.

CDE's Planning for the 2020-21 School Year: A Framework and Toolkit for School and District Leaders does not necessarily contain advice specific to the teaching and learning of mathematics, but teachers of mathematics may want to be familiar with the toolkit to better understand the context in which their district or school is making decisions and/or to better inform themselves so they may more strongly advocate for decisions that benefit the teaching and learning of mathematics.

Coherence Maps and Coherence Gaps

Curriculum planning in mathematics, like what is represented by scope and sequence documents, requires great care and skill to get the right topics for the right duration and in the right order. When instruction is interrupted, those plans will need to be adjusted. To avoid the negative consequences of interruptions and unfinished learning, two tools may be particularly helpful:

  • The Coherence Map from Student Achievement Partners. This dynamic view of the Common Core State Standards and associated resources allows educators to quickly see what standards are prerequisites for learning others.
  • The Coherence Gap spreadsheet from CDE. This spreadsheet uses the coherence information from the Coherence Map but adds in instructional time estimates so that educators can better understand the consequences of uncovered or partially covered content. This page includes a 12-minute video tutorial that quickly reviews the use of both the Coherence Map and the Coherence Gap spreadsheet.

Teaching and Learning in the Era of COVID-19 and #blacklivesmatter

The current circumstances of a global pandemic and reignited awareness of the inequities faced by the Black and African American communities have created space for many of us to think about issues of human health, safety, and dignity. Part of that thinking broadly applies to our roles as humans and citizens, but more narrowly that thinking applies to our role as teachers and learners of mathematics.

The organization TODOS: Mathematics for ALL released a position statement titled The Mo(ve)ment to Prioritize Antiracist Mathematics: Planning for This and Every School Year in June of 2020. This position statement reasserts TODOS's 4 Essential Actions in the current context of COVID-19 and structural racism: (1) eliminating deficit views of mathematics learning, (2) eradicating mathematics as a gatekeeper, (3) engaging the sociopolitical turn of mathematics education, and (4) elevating the professional learning of mathematics teachers and leaders with a dual focus on mathematics and social justice. From this, TODOS identifies four key areas in need of most attention:

  1. Prioritizing meeting the social and emotional needs of students
  2. Careful consideration of when and how to assess mathematical knowledge in ways that account for social and emotional needs of students
  3. Radically restructuring the parent-school relationship to position parents as central to student learning
  4. Assess, evaluation, and design of technology for distance and hybrid learning

TODOS: Mathematics for ALL is planning to release additional commentaries addressing these key areas as schools prepare for the 2020-2021 school year. TODOS also hosts a series of webinars, called TODOS Live!, many of which have focused on equity issues during this pandemic. In addition to TODOS Live!, TODOS co-hosted four sessions of NCTM's 100 Days of Professional Learning, offering the following webinars:

  • Amplifying Langauge in Sense-Making Routines (Grades 3-5) by Nichole Lindgren (July 6)
  • Supporting ELs through Mathematical Inquiry and the Discursive Assessment Protocol (Grades 6-8) by Richard Kitchen (July 7)
  • Translanguaging to Persevere: Exploring Latinx Bilingual Students' Collective Problem Solving (Grades 8-10) by Hector Morales, Joseph DiNapoli, and Craig Willey (July 8)
  • Humanizing Online Mathematics Teaching: Possibilities and Resistance (General Interest) by Mary Raygoza, Kelsey Macias, and Nima Harirchian (July 9)

Considerations for Implementing the Mathematics Teaching Practices in Non-Traditional Instructional Settings


CDE defines four different instructional settings:

  • In-Person Learning: Face-to-face instruction within a building.
  • Remote Learning: Education that happens away from a school building in response to emergency situations like the COVID-19 pandemic or a natural disaster.
  • Hybrid/Blended Learning: A combination of in-person learning and remote learning.
  • Online-Only Learning: Education from a designated online school that offers online courses on a full- or part-time basis, with students who are either enrolled in an online school or supplementing their in-person coursework with an online course.

Even with these definitions, there are variations. For one, in-person learning with and without a need for social/physical distancing (to prevent transmission of illnesses) is a different kind of teaching and learning environment. Synchronous and asynchronous lesson delivery and participation in remote or online environments are also very different environments for teaching and learning. While the definitions may not be perfect or cover every possible scenario, having these and other arrangements in mind is important when planning instruction for the 2020-2021 school year.

Implementing Mathematics Teaching Practices

Both the effective mathematics teaching practices and the equity-based mathematics teaching practices were written with typical classroom settings in mind. However, that does not mean that these practices don't apply to online or other non-traditional instructional settings. Taking these practices in mind when choosing or designing curriculum, instructional tools, and lesson plans can help make teaching more effective. Consider the following:

  • Establishing Goals: There's no reason a teacher can't focus goals on learning in an online or hybrid setting just as well as they can for in-person instruction.
  • Implementing Tasks: Computers can be very good at presenting students with practice problems and instantly telling students if they have a right or wrong answer. Just because computers are good at this doesn't mean that this represents good math instruction. Don't default to low-demand tasks; instead, teachers should push themselves to find and implement tasks with higher levels of cognitive demand.
  • Use and Connect Representations: Computers can be very bad at allowing for the wide range of symbols and shapes we use to represent mathematical ideas. Don't let these constraints limit the kinds of representations students are expected to engage with in non-traditional settings. Some platforms use virtual manipulatives, which can be a great substitute for the real thing. If students are fighting the technology, sometimes it's easiest to have them get out pencil, paper, and/or whatever else they need to represent their ideas, do the work, and then send the teacher a photo of it afterward. If the teacher needs to watch them work as they problem solve, consider collecting video while students talk through their thinking.
  • Facilitate Discourse: Teachers' ability to facilitate discourse outside of a traditional classroom settings depends on the particulars of the environment. Is engagement with students synchronous or asynchronous? Do all students have the technology they need to be equal participants in a video chat? Can the teacher manage small group instruction? How are students able to show and represent their ideas to other students? Teachers need to keep all these things in mind as they do their best to facilitate discourse in their instructional setting.
  • Pose Purposeful Questions: It is good practice for teachers to think about and plan questions in advance of the lesson, anticipating where students may struggle or how best to push their thinking to higher levels. Teachers in non-traditional settings may find this preparation is especially important, as it may not be as easy to be as nimble in prompting and re-prompting students with questions in an online environment as it is in a classroom.
  • Build Fluency from Understanding: This is a difficult practice to implement even under normal circumstances, as it depends as much on long-term curriculum planning and coherence as it does the quality of implementing individual lessons. Don't just assume in a hybrid/blended learning setting that conceptual understanding can be done in face-to-face moments and that technology will support procedural fluency. That may be how it's supposed to work in theory, but it takes care to make the two halves work together in a cohesive way that truly supports the student, rather than just providing a convenience for the teacher. Also, teachers need a good working relationship with parents, who may be imposing their own goals for fluency while lacking the conceptual understanding to back it up.
  • Support Struggle: A lot of teachers need to support productive struggle is inherent in other practices: good goals, good tasks, good discourse, good questions, and good feedback. The degree to which teachers can do all those things online or remotely will have a lot to do with their ability to support productive struggle. But so will their relationships with students, which may take more effort and intent by a teacher working with students remotely than one who sees their students every day in person. Some students may prefer the indepdendence of working remotely so they can build confidence in their work while feeling fewer pressures of a traditional setting.
  • Use Evidence: Assessment is challenging in non-traditional settings. First, teachers have to trust that students are doing their own work, which means making space for eliciting students' understanding in more direct and formative ways than simply having students submit work online. Also, not all feedback needs to be immediate. In fact, when computers (or teachers) give immediate feedback, it tends to be short and evaluative in terms of right or wrong. A better teacher (or better computer) will be more patient and seek to really understand a student's thinking before jumping to respond. The effort it takes to provide such quality feedback in a timely fashion in a non-traditional setting can be intense.