Building an Effective In-Class Learning Environment, Part 2: Student Presentations

In this series, I explore the questions: What are some advantages and disadvantages of group work and student presentations? How can students be held accountable for learning in groups and from student presenters? What defines a good balance of group time with whole class presentations? In Part 1, I focused exclusively on group work.

In Part 2, I focus mainly on student presentations. Finally, in Part 3, I will discuss considerations involved in balancing time allocated to each of these modes of classroom organization, and balancing the strengths and weaknesses of the two modes against each other.

 

Advantages and disadvantages of student presentations to the class:

Student presentations are a way to bring important ideas to the entire class. Presentations focus the entire class on one piece of work. This enables the instructor to monitor the mathematics more easily in comparison to students solving problems in small groups, and to bring up questions to ensure the entire class has the opportunity to grapple with and resolve the key issues in a problem. Student presentations are a good opportunity for the instructor and the class to get an understanding of the presenter’s thinking about a problem. This is especially helpful when a problem has stumped most of the class, so that everyone has a chance to see an idea or tactic that resolves a roadblock. Additionally, individual presentations give the instructor an opportunity to praise a student for sharing his/her thinking about a problem and its solution. Student presentations also enable individual ownership of the mathematics, as the class may later refer back to “Carmen’s solution,” or “Manuel’s way,” etc.

A major disadvantage of student presentations is that fewer students will participate in a discussion of the solution or proof. This happens not only because the group is larger, but also because many times the audience is afraid to trip up the presenter with a question. Moreover, students are sometimes embarrassed about bringing up their questions in front of the class. Another difficulty is that in a class of more than 20, students sometimes do not work enough outside of class on the problems because of the low probability that they will need to present them. 

Individual accountability during student presentations:

To combat the tendency for fewer students to participate in a discussion of a student presentation, there are a few strategies that can be used.

1. Call on students in the audience randomly. To ensure equitable participation, call on students randomly. This combats the common problem of having just a handful of students who are willing to comment or ask questions. Students can be asked to paraphrase particular parts of a solution, to identify key pieces of the solution, to identify the type of argument used, or to summarize an entire solution. While it may not increase the number of contributions, calling at random does help to ensure that over the course of a week or so, most students will have a chance to participate in the discussion.
2. Use think-pair-share. One way to generate more discussion is to have students first review the solution/proof on their own, and then pair up to discuss the work of a presenter. Students can be tasked to come up with a question about the presenter’s work, or to provide further explanation for a part of the solution. The instructor then randomly selects some individuals to report on what they discussed with the partner. It is also worth noting that students often have an easier time answering the question, “What did you discuss?” rather than, “What do you think of this solution?” or, “What question do you have?"
3. Let the presenter sit before discussion begins. There can be advantages to letting the presenter moderate the discussion, but if students are shy about putting the presenter on the spot, it may be helpful to let the presenter sit. This does not absolve the presenter from having to answer questions about his or her process in producing a solution, but it often reduces anxiety if the presenter is not standing uncomfortably at the front of the room.
4. Emphasize the importance of discussing ideas, not people. Whether or not the presenter remains in front of the class during discussion of his or her work, it can be helpful to remind the class that suggestions and questions are not personal attacks against the presenter. Instead, emphasize that everyone is learning, and that the presenter would like the feedback now, rather than to find out later that he or she has been making a consistent error. Moreover, if the class finds flaws or makes corrections, the flaws are in the solution, not in the presenter.

To reduce the tendency of students to spend too little effort outside of class, here are some ideas.

1. Although this was also mentioned in the post on group work, check homework at the beginning of class to ensure that individuals already have a record of their own attempts and solutions before discussing their ideas with others. This lets students know that they are being graded for making their own attempts on assigned work outside of class. 
2. Again repeating a suggestion, use colored pens in class. This strategy gives the instructor the power to discern what students are completing on their own time as well as what they are doing in class. As an added benefit over the early homework check, the instructor can encourage students to keep good records in class by commenting on the notes when the assignment is collected, and by giving full credit to assignments that show that all problems were attempted individually AND show corrections and notes that reflect work done in class.
3. Do not accept volunteers for presentations. Typically, at the beginning of a course, it is helpful to let students volunteer. However, shortly thereafter, perhaps by the second week, it is often wise to keep a list of students that have yet to present (and later, the students with the fewest presentations), and to call on those students first. While students will often have significant breaks between presentations, calling on students with the fewest presentations ensures that students know that they are all expected to contribute. 

While all of these strategies reduce the tendency of students to disengage from presentations, I find that in practice, a mix of group work and presentations works best. In the final post in this series, I will examine considerations involved in using a combination of group work and individual presentations.

Readers, do you have other ideas about how to get the most from students before and during student presentations?

The instructor's role in an IBL class, Part 1

In discussing inquiry-based learning (IBL) with college faculty and K-12 teachers, I find that one of the difficult things to do is to communicate what the instructor’s role is, as opposed to what it is not. Many people are familiar with such mantras as, Teaching is not telling, or, Don’t lecture. These are helpful, but then instructors are left wondering what to do. In this post, I want to briefly describe a few important duties of an instructor in an IBL classroom. The roles I am going to describe are not mutually exclusive categories, but interwoven threads. Nonetheless, I call these out because I think they capture some critical aspects of the flavor of teaching an IBL course. These duties are: managing expectations, managing emotions, keeping the students engaged, finding out what students know, and fitting the problems to the students. In this post, I will deal with the first three aspects, and deal with the last two in my next post.

Managing expectations is a primary duty in an IBL classroom. Students come to class, and especially, come to math class, with expectations, including unconscious ones, about what is going to happen. These expectations are often something like, "The teacher will show me a formula and examples, and I just have to memorize and repeat what the teacher does on similar examples." In contrast, in an IBL classroom, students are expected to bring their ideas to problems for which the path to solution may not be clear. Students are not used to being asked to think things through for themselves in math class, and this leads to frustration. The teacher’s first duty is to make it clear to students that they will need to bring their own ideas, and that they will often not know what to do, or they will do things that turn out not to work, but as a class, they will make progress in understanding the mathematics. In class, the IBL instructor can say things like, “This is going to be different, but you will learn a lot,” or, “You’re going to experience mathematics the way that mathematicians do,” or, “You will get stuck a lot in this class. That’s ok. You can even write ‘STUCK!’ on your work when that happens. The important thing is to learn from what you try, both what works and what doesn’t."

In tandem with managing expectations is managing emotions. As mathematicians, we experience frustration as we search for a solution, and we take wrong turns, or the path to the solution is longer than we hoped. Students feel this frustration. If you are managing expectations properly, then students should know that frustration is normal and expected. However, there is more to the instructor’s role than that. If the entire class is boiling over with frustration, the instructor has a duty to respond. If the students are left to flounder, a mutiny can begin to brew. The instructor may say things like, “It seems like this problem/theorem is really stumping us. Let’s brainstorm how we can find new ways to attack it,” or, “I am glad to see everyone is showing persistence on this problem. Sometimes the best way to get past a roadblock is to go around it. So why don’t we look at this {example, related theorem, special case} for now and then come back to the main problem,” or, “This problem is really giving us a rough ride. Let me tell you a quick story about this time when I was frustrated and how I got through it…”

Keeping the students engaged is a multifaceted task. I have written on this blog before about a specific engagement strategy, and about how to reach out to students who are reluctant to participate. I will add to what I’ve written before by mentioning the importance of managing classroom participation. When there is a student presenting work to the class, the instructor’s role is to ensure that the rest of the class is engaging with the presenter and/or the presenter’s work. This can be done in several ways. One of them is to give the students question/comment stems and to call on students to use the stem to offer a question or comment. Some of my stems include, “I like how you…” “What led you to think of…” “I’m not sure I follow how you got from … to …” Another way is to have the presenter pause and to do a check for understanding or a think-pair-share. When the presentation is done, the instructor then pushes the students to ensure that they agree with all aspects of the mathematics, and also see to it that they understand insofar as possible how the student came up with that solution. When students are working in pairs or small groups, the instructor should make sure that all group members are contributing to the conversation. When necessary, this can be actively managed when the instructor inserts him or herself into a group conversation to make statements such as, “I see that Ann and Bob are sharing their ideas. Carol, is what they’re saying making sense to you?” or, “I appreciate that you’re all giving Darryl your attention. Could someone else try to restate what Darryl has shared so far?” or, “It seems like this group has spent some time working independently, each person with his or her own ideas. I think now would be a good time to share some of your progress and see what you can learn from each other’s approaches to this problem."

In the next post, I will take up the other two aspects of the instructor's role.

Let me know your thoughts or other aspects of the instructor's role I have left out.

The Calculus of (Instructional) Variation

As a professor, I take a lot of professional pride in my teaching. As part of that professionalism, I am always looking for ways to improve the learning experience for my students. In this post I am going to describe how some small changes have made a really noticeable impact in one of my classes. (That's where this post title comes from: a little variation has added up to a big change.)

Before I can describe what I did, I should give a little background about what happens in my classes. For now, I am going to focus on my Transition to Proof course. I teach via inquiry-based learning (IBL). As part of that approach, I use student presenters a lot. This means that students come to class having worked on problems (mostly proofs) at home, and they come to class knowing that for most of the problems, someone will have an opportunity to present their proof attempt in front of the class.

This semester, one of my goals is to improve the quality of the discussions that follow a student's presentation. To achieve this goal, I made a couple of changes. In the past, I collected work from everyone at the beginning of class. Then, a presentation proceeded through the following steps:

1. A student wrote their work on the board 
2. The student explained their work.
3. The class proceeded through a Think-Pair-Share: They were asked to look at the work in silence, then share ideas with a partner, and finally ask questions or make comments to the presenter. 
4. During this entire time, the presenter remained standing to answer questions about their work. 

This term, I started in a small classroom with a small chalkboard and a projector screen fixed in place in front of the chalkboard, so that using (most of) the chalkboard was only possible if I unhooked the screen from the wall and set it on the floor. This was part of the inspiration for a new presentation procedure:

1. I photograph student work and upload it to NotesPlus, and project the student work via iPad. 
2. The student explains their work, but sits down immediately, rather than waiting for questions. 
3. The class proceeds through a Think-Pair-Share: They look at the work in silence, then share ideas with a partner, and finally ask questions or make comments, BUT now the presenter is not on the spot during the discussion, as he or she is sitting down.

In addition, I have changed from collecting work at the beginning of class to collecting at the end of class. During class, students used colored pens (Thanks Clark Dollard and Dana Ernst!) to annotate their work, so that I know what was completed before class. Therefore, students are able to compare their work to the work being presented.

These changes are minor, just changing the medium of the presentation, letting the presenter sit during Q&A, and letting students keep their work in front of them for comparison. But the discussions have been stronger for the four weeks of this semester than in years past. My hypothesis is that the students feel more comfortable asking questions with me at the front, even though I am still directing questions back to the class or to the presenter. The class no longer feels like it is putting the presenter on the spot when they raise issues.  Moreover, they are able to ask questions based on their own efforts that they now have in front of them. I am sure there are other factors involved in the improved discussions, including the fact that cohorts of students vary, and this group seems to have a number of people willing to share. Still, it is amazing how small changes can have such a visible impact.