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.
- 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.
- 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?"
- 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.
- 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.
- 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.
- 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.
- 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?