“Moving Forward: Mathematics Learning in the Era of COVID-19”

According to (Dubiel, 2020) is split into three sections each describing a separate area
with implications for high-quality teaching and learning. Each section provides
considerations or lists of resources as well as lists of questions for stakeholders to
think about. The major take-aways are grounded in research and there are
recommendations for resources that can help with implementation of the action items. 

The Structures section suggests ideas that are pertinent at the school level. Ideas
include a recommendation for grade school teachers to loop up with their students and
a call to eliminate ability grouping of students for different teachers. Rather, students
with a variety of strengths should be encouraged to work together to complete rich,
complex tasks. Teachers should be allowed to participate collaboratively in
professional development on a variety of topics that will promote student learning..
Above all, structures need to be in place that support teachers in creating high-quality
learning opportunities for all students.

The section on Teaching Practices contains four parts that focus on actions in the
classroom that can promote equitable access for high quality teaching and learning.
The first part is a call to identify essential learning for students per grade-level or
course. Teachers should work together to examine standards and agree on the
essential learnings for their grade level and courses. Considering how the standards
for the current grade level or course connect to previous or subsequent courses is
imperative to identify key topics and understandings. So, collaborating not only
within but across grade levels is important to identify essential learning.   

The second and third parts of this section are about determining prior knowledge and
introducing new learning. Talking with teachers of prior grade-levels or classes can
help identify the topics and skills for which students may need additional support. If a
topic was taught during remote learning, some students may be less familiar with it.
Determining prior knowledge through instruction and assessment allows for a focus
on the most pertinent topics. Be intentional about using formative assessment that
supports next instructional steps. 

The final part of the Teaching Practices section is about using the most effective
teaching practices advocated by Principles to Actions (2018) by NCTM. These
practices reinforce good teaching strategies like establishing goals, using purposeful
questions, supporting productive struggle, and eliciting and using evidence of student
thinking. If you read only one piece of the original document in full, it is this part of
the Teaching Practices section found on pages 9-10. This particular section of the
document is full of resources that teachers can use to promote equitable and high-
quality instruction for all mathematics learners. 

The third section of the document is on Advocacy. We need to continue to work with
multiple stakeholders in education to promote equitable and high-quality teaching and
learning for all students. Budgetary changes will need to occur in these uncertain
financial times, but we need to minimize any potential negative impact on quality
education. We need to revisit our use of large scale assessments that reduce
instructional time and consider instead the use of formative assessment tasks for the
classroom. We also need to advocate support for teachers with professional learning
and with social-emotional needs. 

While the “Moving Forward” joint statement is full of ideas and questions to consider,
there are some common themes that thread through the sections of Structures,
Teaching Practices, and Advocacy. I want to highlight three of these themes that are
applicable for teachers of all levels. 

Collaborate
Throughout the “Moving Forward” joint statement there are references to teachers
collaborating. Teaching is a surprisingly lonely profession. You are around people all
day long, but constantly in an authority role. It is necessary to take the time to talk
with fellow teachers - plan together, get ideas, and simply check in as we could all use
some social-emotional support. 

Identifying essential understandings for grade levels and courses is a task that needs to
be undertaken collaboratively. Groups of teachers work together to analyze standards
and create common goals allows for greater equity among students by keeping
expectations the same across teachers. Collaboratively designing instructional
experiences and common formative assessments also supports high quality and
equitable experiences for students. Teachers need to be allowed to have time, within
the school day, to work with other teachers. Stakeholders in education need to
advocate to protect and promote collaborative time for teachers.

Indeed, teachers want to collaborate. In a survey for teachers on professional

development (PD) preferences, Heather Wolpert-Gawron found that one of the
highest-ranking engagement strategies was “let us talk and collaborate.” Ideally,
professional development requires the use of professional learning communities
(PLC) where groups of teachers work on a common goal. The best PD opportunities
are also job-embedded where teachers are required to try out the ideas in their own
classrooms followed by reflection on the implementation process. 

Moving Forward: Mathematics Learning in the Era of COVID-19

Mathematics teachers and leaders must continue to speak to and support the development and
implementation of educational policies and practices to promote high-quality, equitable mathematics
teaching and learning for every student (NCTM 2014; NCSM 2020a).

Mapping the Reality of Mathematics Teaching and Learning During COVID-19 The shift to a virtual
platform across K12 necessitates the availability of technology remotely to facilitate lesson delivery
and ongoing communication among students, teachers, parents, and other stakeholders (Government of
Ontario, 2020). Initially, making sure that teachers, students, and parents have access to technological
devices was a challenge (Statistics Canada, 2019); therefore, local school boards in Ontario offered
technology pick-ups for laptops, iPads, and tablets for those in need, which ensured access for all
(Strong, 2020). Furthermore, to help students make sense of abstract mathematical concepts using
concrete materials (e.g., measuring sticks, snap cubes, and geoboards), teachers and parents improvised
by using household items, finding links to online manipulatives, or using statistics/graphs about the
pandemic (Skarky, 2020).

Developing a growth mindset (Boaler, 2016; Dweck, 2008) among students is vital for learning
mathematics. It requires consistent and regular guidance from teachers through collaborative
opportunities with peers that allow students to witness multiple solutions (Boaler, 2016). This was re-
envisioned by creating collaborative teams in the form of breakout groups, where students connected
using social platforms/apps.

This section mapped some of the ways mathematics education was reimagined from face-toface to
virtual delivery. As we continue grappling with the COVID-19 situation, we turn to an enactive approach
and propose a contemplative space to make sense of the constraints caused by the pandemic and the
opportunities for reimagining research in mathematics education.

Examining the Co-evolving Mathematics Education Environment and Community:

An Enactive Approach

We find enactivism helpful for understanding how the mathematics environment and

community continue to co-evolve during this time of crisis, recognizing that any pregiven

formula to create a mathematics environment and community limits viability.

Enactivism is an approach to cognitive science which challenges theories of mind that continue

to perpetuate the dualistic views of mind, such as knowledge/action, human/world, and

mind/body binaries. Enactivism claims that cognition emerges from a network of interactions

among agents and their environment. From the enactivist perspective, a mathematical

community does not simply react to an existing pandemic environment around them; the

community and the environment co-emerge. The shift from face-to-face to online teaching and

learning environments cannot be seen as a pre-given problem for the community to react to,

but rather as an opportunity for the community to “pose the relevant issues that need to be

addressed at each moment” (Varela et al., 1993, p. 145) and to reimagine mathematics

education within the constraints related to the pandemic. The mathematical community, then,

brings forth the world of significance (e.g., mathematics) on a moment to moment basis

through their actions and interactions with others and with their environment (Varela et al.,

1993), which in our view makes enactivism a relevant lens to study the emerging mathematical

environment and community.

Drawing from complexity and an enactive approach, Davis and Simmt (2003) describe the

conditions that promote an emergence of a mathematical community, including (a) internal

diversity (the members of a community contributing in different ways), (b) redundancy

(duplication and excess of the features that are necessary for the emergence of an intelligent

collective), (c) decentralized control (no one seems to be in charge of the community and the

community organizes itself as if coordinating agents are present at its centre), (d) organized

randomness (a structural condition that helps to determine balance between redundancy and

internal diversity among members), and (e) neighbour interactions (agents within the complex

system affect one another’s activity). We use these conditions to understand the emergence of

the co-evolving mathematics environment and community in the present context of COVID-19.

The constraints caused by the COVID-19 pandemic provided an opportunity for policy makers,

teachers, students, and parents to work together, exchanging ideas, views, experiences, and

knowledge. Every member of the community contributed towards meeting the common goal

(redundancy) of teaching and learning mathematics. The differing experiences and ideas

brought forth by stakeholders created an internal diversity, which in turn allowed for innovative
ways to learn and teach mathematics. The online platform offered opportunities for

neighbouring interactions within the mathematical community to bounce ideas about teaching

and learning. Switching to technology in the form of video lessons or situating math problems

in real-world contexts were instances where stakeholders interacted with each other.

From an enactivist lens, turning to an online platform was not about adapting face-to-face

pedagogical strategies by simply following a prescribed curriculum towards some optimal goal

through a prescriptive logic; that is, “what is not allowed is forbidden” (Varela et al., 1993, p.

195). It was, rather, about finding other pedagogical strategies while maintaining the viability of

the mathematics education system and moving towards the proscriptive logic—“what is not

forbidden is allowed” (Varela et al., 1993, p. 195). Understanding that what is not forbidden is

allowed opens a space of opportunities for reimagining mathematics education. The online

platform prompted education stakeholders to reimagine possibilities for teaching and learning

mathematics as well as structuring the learning environment.

In the context of the pandemic, turning to online teaching practices needed to be done quickly

with teachers who may have had little experience with online teaching. Through an enactivist

lens, a viable mathematics education system was reimagined. This points to the need for

further research to document and conceptualize this phenomenon. Likewise, education

researchers need to rethink methodologies and theoretical frameworks in order to understand

the emerging educational realities in the context of the COVID-19 pandemic.

According to the U.S. National Council of Teachers of Mathematics (NCTM) and

the National Council of Mathematics Supervisors (NCSM) 2020, during the
pandemic, the urgency to change the way mathematics is taught has become
apparent. According to both agencies, math instruction needs to be more
equitable, so it is essential to plan what math classes will look like before
returning to school in the coming months.

Planning is key
The document focuses on three critical areas for planning, namely, structural
considerations, teaching practices, and advocacy. These topics challenge district
leaders and schools to think about who should be in the conversation, what
supports are needed, and what questions should be asked before moving
forward.

Three critical areas for planning a mathematics program

1. Structural considerations: These include support strategies for students to
update them after the quarantine period. Institutions and teachers must
differentiate the support, think out interventions, and rework school
schedules to focus more on mathematics. The NCTM and NCSM also
recommend approaches such as joint teaching or team teaching to help
instructors coordinate their school grade content with what came before
and what follows. Both agencies stress the importance of teachers
working together to determine what is prioritized before teaching math in
the new school year.
2. Teaching practices: These refer to educators using educational strategies
that focus on formative assessment to know how well they are learning.
Adjustments should be made if necessary. Being flexible is critical.
According to the document, there are eight practices for equitable and
effective teaching of mathematics that serve to provoke students to think.
These practices focus on formative evaluation. They serve to obtain and
use evidence of the students' mathematical thinking and to help the
students feel valued. To implement them, the teacher needs to ask
questions, analyze the assignments and activities, and observe them.
These eight effective practices are:
o Set math goals that focus on learning.
o Implement tasks that promote reasoning and problem-solving.
o Use and link mathematical representations.
o Facilitate meaningful problem-solving course.
o Ask questions with a purpose.
o Develop procedural fluidity that comes from conceptual
understanding.
o Support the productive struggle in learning mathematics.
 o Obtain and use evidence of students' mathematical thinking.
3. Advocacy: This point refers to not limiting mathematical reasoning to the
classroom. The purpose is to make the students see how math is
everywhere, from their devices to politics and finance.

The National Council of Mathematics Teachers also notes that it is essential to

get students to participate in meaningful mathematical discourse inside and
outside the classroom. It is of paramount importance to promote mathematical
reasoning and purposeful questions.

To be successful, the NCTM advises using an approach based on the teacher-

student relationship's strengths and skills and building and maintaining a positive
identity and disposition toward mathematics. They also encourage improving
relationships with families and the community to get them involved. Finally, the
Council recommends ensuring that all students are given the same learning
opportunities, and they advise educators to be on guard not to diminish these
possibilities.

Both agencies' most significant concern is to alert educators to the problems of

inequality that have existed in education for several years. They point out that the
problem comes from the curricular structure. They caution to avoid any unequal
practices, such as the grouping of students by mathematical skills, that divides
the class according to the student's abilities. One example of this is putting
together students perceived as slow learners and leaving them with that label
throughout their student lives.

Analyzing the structure of curricula, being flexible, motivating students to see

mathematics as useful and exciting, and planning to continue facing the
pandemic's challenges are some actions that will help to have more equitable
teaching of mathematics. Paulette DelgadoJuly 24, 2020