*By **Saúl A. Blanco**, School of Informatics and Computing, Indiana University*

For several years I’ve been incorporating active-learning and inquiry-based learning activities in my teaching. There is ample documented evidence of the benefits of these approaches for students, but equally as important, they make teaching and learning more fun! Shifting class time from lecturing to having students work on problems, present their solutions to the class, and explain answers to each other has a dramatic effect: students become more engaged, learn communication skills, and gain confidence. These soft skills are in high demand in the job market. In this article, I will describe my use of these approaches and my experience teaching in a classroom designed for collaborative learning.

So far I’ve mostly been doing these active learning activities in traditional classrooms, but for smaller classes of about 25 students I’ve used collaborative classrooms with great success. The main difference between a “traditional classroom” and a “collaborative classroom” are (A) the seating arrangement; and (B) the presence of integrated technology. In a collaborative classroom, students usually sit around tables, often facing each other, which facilitates working in small groups. Many collaborative classrooms do not have an obvious “central location” where the instructor can stand, so teaching in such as classroom requires getting used to (see picture below). The main hesitation I had with using a collaborative classroom is this lack of a central location from which to lecture. I normally don’t use slides when lecturing so I wanted a way of emulating writing on a blackboard. I used a tablet computer with writing software to project what I would write on overhead screens. It ended up working very well. Students took notes as I wrote them, and I made the notes available to them after class. As can be seen from the pictures, collaborative classrooms tend to have many screens so students can see at least one of them easily.

As instructors, we are aware that “traditional classrooms” can come with different seating arrangements. Some have individual desks that one can move around, some have tables that are fixed and chairs that can be moved, some have multiple tables and chairs that cannot be moved, and some have a typical auditorium setting. I have taught in all of these types of classrooms and I have tried to incorporate active learning techniques with different degrees of success. It is significantly harder to have students work on a problem collaboratively if they can’t really face each other in a natural way. Collaborative classrooms, on the other hand, are designed to foster discussion by having multiple tables where one can move chairs as needed. For the particular classroom I was using, the tables were distributed in such a way that it made it easy for the instructor and the teaching staff (composed mostly of undergraduate students who had done well in the class in prior semesters) to circulate in the room to answer questions and address students.

Many of these collaborative classrooms also have multiple screens where the instructor can project information in a way that all students can see easily, without rearranging the way they are seated. So, a collaborative classroom accomplishes two goals: it allows students to work in groups, thus allowing the teaching staff easy access to every student, and allows for multiple displays so that the entire class has an easy view of what the instructor is projecting. There is no need to rearrange the seating every time one transitions from group-work time to “instruction” time and back.

This past summer I had the opportunity to teach in a collaborative classroom for a larger class of 59 students. This class was a proof-based introductory discrete mathematics course that emphasized logic, proof techniques, and both oral and written communication of mathematical ideas. The class did better overall than the same class in the regular semester. I was happy about how things went, and I decided to share my experience in case other instructors are considering utilizing more collaborative approaches to teaching. To take advantage of the collaborative space, I incorporated the following components.

**Course staff helped me answer questions while students worked during class.** To make this process work, it was important to have more than one teaching staff member in the classroom. To accomplish this, I recruited a few undergraduate students who had taken the class previously and had done exceptionally well. When it was time to work on the worksheet problems, we had about five people walking around (one instructor and four undergraduate instructors), answering questions, and talking to the students about the class material. These undergraduate instructors also held office hours, so we ended up having about 13 office hours every week.

Choosing the right undergraduate instructors is extremely important. I selected students who I knew could do the job, understood the material reasonably well, and were able to express mathematical ideas. Seeing them work with students was also a rewarding experience, as I was able to notice a significant improvement in their mathematical ability since they had taken the class. There is no better way to learn a topic than to teach it! We also had graduate assistants, who were in charge of grading homework, but in my experience undergraduate instructors do an excellent job understanding student questions, even if they are not perfectly formulated. There is something about talking to a peer that makes everyone, student and teaching assistant, more comfortable.

**Reading quizzes, both individual and team-based.** The idea of these reading quizzes comes from team-based learning (TBL), where instructors assign a reading before class, and at the beginning of the class they give an individual quiz (referred to as an individual readiness assessment test, or iRAT) and a team-based quiz (referred to as team readiness assessment test, or tRAT). Both the iRAT and tRAT for a given day have the same questions. At the beginning of the term, students were placed in teams according to a brief survey asking them about their level of comfort with teamwork as well as with logical and mathematical thinking. Then groups of four were formed according to their answers in such a way as to have “balanced teams.” These teams were used for the team quizzes and in-class work. For the reading quizzes, I assigned a specific section from the textbook for each class, and then gave a quiz on that section before it was officially covered in class. For many students, the idea of being asked questions before seeing a topic in class is preposterous. Nonetheless, reading comprehension is an important skill to develop. So that it wouldn’t greatly affect the students’ grades, the topics were carefully chosen and these quizzes didn’t count for a large portion of the final grade (but did count for something, as otherwise students might not be motivated enough to do the reading). The students would first do the quiz individually, and then would get together in their teams and work on the team quiz. Not surprisingly, students did better in the team version of the quiz than in the individual version. I witnessed many spirited discussions as members of the same team were choosing their answers: students were indeed teaching each other!

**Worksheets containing a summary of the major concepts for a given class, along with problems to test student knowledge.** I prepared a worksheet for every class that included the basic definitions, and then several problems for students to work on. Students were given time to work on the problems while the teaching staff walked around, answered questions, and discussed the problems with students (without giving them the answers). Most of lecture time was spent clarifying concepts from the reading, and providing examples that would inevitably bring more questions. But I tried to avoid talking continuously for more than 10 minutes and would provide several “breaks” where students would work on the problems provided in the worksheets.

**Opportunities for students to explain their work to others.** After several students had worked on a problem, we selected someone to present the solution to the rest of the class. We utilized a document camera to project students’ work on an overhead screen, and had the student walk us through their solutions. Sometimes the instructor or other students would ask questions. I would often compare the work of multiple students, which was a great way to highlight the fact that there are multiple correct ways of solving a problem or proving a proposition. I would also show work that wasn’t quite complete and correct, but without revealing the student who had made the work, and I would ask the class how to fix the mistake or how to complete the problem.

Overall, teaching in a collaborative classroom was a great experience. I will be politely requesting these kinds of rooms to the powers-that-be for all my future classes!