Math Instruction in the Age of the Coronavirus
(This is the first post in a four-part series.)
The new question is:
What does math instruction look like in the age of the coronavirus?
I've previously posted on Reading & Writing Instruction in the Age of the Coronavirus.
This week's series on math instruction continues looking at subject areas and will be followed by posts about science and social studies instruction in remote teaching.
The first and second posts in this series will feature commentaries by New York City high school math teachers Bobson Wong and Larisa Bukalov. They are the authors of The Math Teacher's Toolbox (Jossey-Bass, 2020) and recipients of the Math for America Master Teacher Fellowship.
For transparency purposes, I should point out that I am one of the co-editors of the Teacher's Toolbox series.
I'm adding this post to All Classroom Q&A Posts on the Coronavirus Crisis.
Core Beliefs About Math Instruction
Our teaching has changed in many ways as we've moved from in-person to remote instruction. However, our core beliefs about math instruction, pedagogy, and students remain unchanged. In this section, we describe four of these central beliefs and some of the steps we've taken to modify our instruction while maintaining them.
1. Students need to feel safe before they can learn.
If students feel threatened, their brains release adrenaline, which inhibits cognitive functions and any other activity that is viewed as unnecessary. Creating a well-organized classroom and a supportive relationship with students sets the foundation for successful learning and helps communicate high expectations. Such an environment encourages students to take chances and reduces their math anxiety, the feelings of fear and tension when doing math.
We find that creating a safe atmosphere is even more important now. Many students live in busy, stressful environments. Some take care of younger siblings or older relatives or share a small home with others. Tensions can be exacerbated when students and teachers are forced to stay at home all day. To maintain a stable environment, we establish clear routines and procedures in our online assignments and meetings so that students know what we expect from them. These routines not only benefit students but also benefit us by helping us manage our schedules.
We also work to maintain the sense of trust with students that we have worked to build throughout the school year. Research indicates that establishing an emotional connection supports learning since it frees up the brain for higher-order thinking. Even simple acts like checking in with individual students periodically can show that we care about them and counter students' feelings of alienation toward school. Building trust is an important part of culturally responsive teaching, the use of students' prior experiences to expand their learning capacity. Maintaining connections also prevents us from feeling isolated and maintains our spirits.
2. Math should make sense to students.
As we plan our lessons, we also make sure that the math we teach makes sense to students. Despite the limitations of remote instruction, we resist the temptation to reduce math to "tricks" and shortcuts. Such misguided attempts to save time or energy can quickly backfire if students see the work as pointless and refuse to do it. Although we can't do the cooperative activities that help students develop conceptual understanding, we incorporate smaller sets of questions that students can work through independently.
3. All students need access to rigorous math.
Students should solve challenging problems that deepen their thinking, not simply complete mindless calculations. Short self-guided discovery activities enable students to actively create knowledge. Recognizing our students' needs and hidden biases in our own thinking can also make our teaching more relevant and culturally responsive.
4. Teachers don't have to do everything to succeed.
Under normal circumstances, our classes usually consist of a daily in-class lesson, accompanied by a combination of assignments that include homework, tests, quizzes, and projects. Our students work in class under our supervision and outside of class with friends, with family, or by themselves.
In times like these, though, everyone's routines—both ours and our students'—have been seriously disrupted. As a result, we try to be flexible and mindful of students' limited time as well as our own. When we plan lessons, we make sure that students can complete it in a reasonable amount of time. We don't assume that students will be able to spend the same amount of time at home that they do in school, so we adjust our expectations and our assignments accordingly.
Most importantly, we remind ourselves that we can't do everything. The strategies we describe in these articles are not a checklist of everything that teachers must do to be effective. Instead, we see them as a collection from which we can pick to improve our instruction. Nowadays, we find that limiting our expectations for ourselves and others helps us maintain our sanity!
Designing Online Math Assignments
Without in-person meetings, our online assignments are the only interaction that we have with many students. As a result, we have to make these assignments as meaningful and manageable as possible. Here are some of the strategies that we use to do so.
Creating Unit Plans
As we do with our regular teaching, we organize our instruction by creating unit plans, documents that map out the major learning goals and the order of lessons for a unit. Unit plans don't have to be long, complex documents. They can be as simple as a pacing calendar.
Since our year-end goals have changed, we've changed our unit plans. In many cases, we've limited both the scope and content of our lessons. We omit topics that would be too challenging for us to explain remotely. Instead, we present new material only if it extends previously learned concepts. We occasionally give assignments like projects or other activities, which provide a welcome change to our routine. However, we limit these assignments to small activities that students could complete largely on their own with little or no research. The Desmos and Geogebra websites have many examples of online guided-discovery activities.
No matter what content we cover, we close the year with some type of year-end review, which helps to reinforce a sense of closure for the year and increases the likelihood that our students will remember the content.
Posting Online Assignments
Just as we have routines and procedures in our physical classrooms, we also establish them in our online assignments. Routines and procedures make classrooms more predictable, which helps students focus on learning.
To keep our online assignments more organized, we first simplify our work by giving no more than one assignment per day for each course or subject. Under normal circumstances, we would give both classwork and homework, but giving two or more online assignments per day can overwhelm students who are unaccustomed to managing all of their time at home. To make our work more manageable, we post one assignment every day. If we give larger assignments, we split it into smaller parts.
We post all of our assignments on a class website. When we post an assignment, we include the following:
- Title and due date: Numbering assignments helps us refer to them more easily. To communicate more clearly when assignments are due, we put due dates and the aim directly in the assignment's title, such as "HW #16: How do we solve quadratic equations by completing the square? (Due Wed. 4/15/20)." Grouping assignments by category or subject helps students find them more easily.
- Online resources: We include links to videos or websites that students can use to understand the lesson. These resources enable students to learn at their own pace and allow us to provide differentiated resources for English-language learners. However, we find that students often need additional help, so we also run online meetings.
- Directions: Instead of using pedagogical jargon ("In this assignment, students will be able to use the equation of a linear model to solve problems in the context of bivariate measurement data."), we prefer clear, simple language ("Today, we'll use linear equations in two variables to model real-world problems."). This enables students—and anyone else that may be helping them—to understand our directions.
- Template for student responses: To help students organize our thoughts and to make grading easier, we create templates containing the questions that we want answered and appropriate space for student work. Websites like DeltaMath that automatically grade student responses can simplify grading. We also give students multiple ways to submit their work. For example, if we want students to complete a worksheet, we allow them to type directly on the worksheet or upload written work on a printed copy.
We try to be flexible with assignment deadlines. Although we clearly (and repeatedly) state deadlines, we accept late submissions without penalty. If students consistently miss work, we reach out to see how we can help. In times like these, we find that compassion goes a long way.
Running Online Meetings for Math Classes
Online meetings with students are a critical part of our remote instruction. Simply posting assignments with videos or weblinks doesn't allow us to see how students react to our instruction. Even monitoring student responses through online forms (like Google Forms) or websites that automatically grade student work isn't enough—our students want more immediate feedback. Online meetings do more than provide a virtual version of an in-class lesson. They also enable us to talk to students in real time and give them more individual attention.
First, we think about what kind of classroom setup we need at home to run meetings. This can include items like a camera stand if we need to show things that aren't on the computer screen. If we turn on our cameras during online meetings, we also think about what background we have (such as a bookshelf, curtain, or a plain wall) and what we plan to wear.
We limit our online meetings to one per course or subject per day so students aren't overwhelmed. To make them more predictable, we schedule meetings at the same time every day. Our meetings usually run for about one hour.
Here's how we usually structure our online meetings:
- Introduction: We start our virtual meetings by greeting them individually as they log on. These measures reinforce the message that students matter to us and give us time to talk to them. (Sending a quick reminder to students right before the beginning of the meeting helps!) During this time, we encourage students to turn on their audio and video but only if they feel comfortable doing so. We also use this time to make announcements, such as reminders of upcoming assignments. If appropriate, we also share some personal updates about our own lives, which helps remind students that we're human!
- Mini-lesson: We then present a brief lesson—usually no more than five minutes—that summarizes important or especially tricky concepts. We ask students to turn off their audio and video (some apps allow the host to do this with one click). Doing so minimizes distractions from background noise, improves our sound quality by reducing the bandwidth, and protects student privacy if we record the lesson and upload it online. Students who want to ask questions can type comments in the online chat area or unmute themselves temporarily. To help students see what we're discussing, we share our screen with students so that we can display problems, relevant animations, or other helpful visuals.
- Feedback: We devote most of our online meeting to giving students time to ask questions and develop skills. Students who feel comfortable may discuss a solution or ask a question by sharing their screen, turning their video on, or typing in the online chat area. If we put problems on slides, we allow students to speak while we write on our slides for them. If students don't have any immediate questions, we allow them to work independently until they need help.
- Summary: We summarize our lesson with a question that enables us to gauge our students' understanding of the lesson. For example, we ask students to type their answer into an online form (such as a Google Form) so we can instantly collect and analyze student answers. We then review the question with students and remind them again of upcoming assignments, such as homework.
Although we consider these meetings important, we also recognize that many students aren't able to participate. Some of our students have told us that they have limited internet access, share a crowded and noisy home, care for younger siblings, or are grieving the loss of a loved one. To accommodate them, we edit and upload a record of our online meeting, such as a video recording or slide presentation. We may also schedule separate meetings with other students at another time. However, we try to put limits on these individual meetings since the time required to meet with individual students can quickly add up! Most importantly, we don't take students' lack of participation personally.
Thanks to Bobson and Larisa for their contribution!
You can see the second part of their commentary tomorrow, which will be followed by reflections from several other math educators teaching across the country.