5 Ways to go Beyond Recitation

By E. Fuller, WVU Mathematics (guest blogger)

Students at almost every institution of higher education will encounter a recitation as part of their mathematics class at some point, part of the class time set aside to repeat foundational mathematical equations. Graduate teaching assistants (GTAs) are frequently called on to lead these smaller groups of students through the basics of finding the roots of a quadratic equation or computing derivatives using the chain rule. Recitation time is often left for practice of the techniques students learn in lecture. But what if we could do more during this class time? What would that look like?

Here are a few approaches you can take to change your students’ experiences during recitation.

1) Focus on getting students to do the work instead of doing it for them. Homework problems are great and it’s sometimes easiest for us to go to recitation prepared to work out many variations of problems we‘ve done ahead of time. The problem is that we already know how to do them. We are better served, as are the students, by providing the space to let them work through the content with guidance. This is perhaps the easiest way to stay true to the content of the class while creating student-focused time. Use inquiry and questioning to get students to tell you how to do the problems instead of the other way around.

2) Incorporate group work into your sessions. Build teams and leverage peer instruction (a method that allows students quick to understand a method or solution to help his or her peers through the problem) so that they can become teachers themselves. Empowering students is always a good thing.

3) Get students to communicate what they understand to each other and to the class. Research shows that students need to explain what they understand to really master a topic. This practice forces them to rethink concepts as they try to convey knowledge to someone else. Writing prompts such as ‘Explain why this procedure works…’ or ‘Evaluate this solution and determine if there are errors’ force students to think through ideas and develop reasoning to support conclusions.

4) Have students relate mathematics to their own experiences. To develop a connection with mathematical ideas, students can investigate how mathematics is related to their futures or how multiple levels of mathematics show up in their day to day experiences. Connecting ideas like contour maps to real world activities like hiking can bring even more advanced concepts into life.

5) Cultivate an environment where failure is ok and experimentation is encouraged. Students need to learn that trying is important even if it doesn’t lead to the (correct) answer the first time. Making your classroom safe for exploring ideas (even incorrect ones) helps support a growth mindset among the students, especially important if the classroom is student-centered and they are doing and explaining the mathematics that is happening.

It’s important to keep in mind that you can start small - you don’t need to do these things in every meeting. You can pick some manageable topics to try something new with and build from there. It can be hard work and takes time and practice, but your students will benefit from it, and you will find that those recitation sessions can lay the groundwork for some pretty amazing mathematical discoveries for the students.

Language matters: 5 Ways Your Language Can Improve Your Classroom Climate

Rachel Levy, Contributing Editor, Harvey Mudd College

The language we use in our classes extends beyond mathematical content. We communicate subtle (and not so subtle) messages about who belongs in the classroom and in our profession. Signals transmit through our level of enthusiasm, quizzical looks at incorrect or convoluted statements, and focus of our attention through eye contact, time to speak, and personal interactions. To avoid perpetuating our unconscious biases through language, we can recognize them and find ways to reduce their impact on our students.

Even when we are careful, at some point our language will likely cause unintended ouch for one of our students. Hopefully we can create feedback mechanisms and classroom environments where they can let us know. But as long as we give grades and write letters of recommendation, the power dynamic in the classroom is unavoidable. This may make it hard for students to speak up and let us know. We hold the responsibility to create a welcoming environment for all of our students.

Here are five ways you can modify your language to improve your classroom climate:

1. Convey explicitly in your syllabus that you believe that mathematics belongs to everyone and that everyone can be a math doer. Share with your students that making and discussing mistakes are a normal part of learning (and being human). See this tool for surveying your syllabus and course design for examples of inclusive syllabus language.

2. Be intentional about encouraging questions. Pay attention to which students in the class feel empowered to speak and provide a variety of ways for students to communicate with us and with each other. Many of the Teaching Tidbits have concrete suggestions, such as ways to engage your students through reflective writing; your responses to incorrect answers; office hours; and inquiry-based learning.

3. When they suggest an answer to a question, ask students to justify that answer, whether is it right or wrong. For example, let students know if they don’t provide a justification you will ask “And why would you say that?” This is a technique common in Russian pedagogy. It allows you to better see how your students are thinking and where they might have gone awry. Students may also sort out their own errors as they argue their point.

4. Avoid perpetuating mathematical language that fails to acknowledge the challenge of learning, such as "clearly, " "only” and “obviously.” These words tend to cue the audience that the speaker thinks the work is trivial. The problem is that even when ideas are taught well, they may not be at all simple for new learners. They also may carry an underlying assumption that all students have had access to the same prerequisite information. Since students enter with a range of previously acquired knowledge and experience, it can be more welcoming to say “the rest requires algebra” instead of “the rest is *just* algebra.”

5. Aim to use inclusive and unbiased language. For example, privately request students’ preferred pronouns and preferred names and use them. Pay attention to how you use humor, encouragement and analogies while teaching. Small comments can have a big positive impact. For example, “When a mathematician approaches this problem, she…”. or “When you explain it like that, you are really thinking like a mathematician.”

Unintended ‘ouch’ happens. What one person finds funny, another finds offensive. What one person finds welcoming, another finds off putting. We are not perfect and we can’t please everyone all the time. But my hope is that when we establish a constructive classroom climate with opportunities for feedback, students will let us know when they experience an ouch because of some way we communicated.

Related Links Karp, Alexander, and Bruce Ramon Vogeli. Russian mathematics education: Programs and practices. Vol. 2. World Scientific, 2011.