Collaborative groups can be difficult to cultivate in a classroom, but students benefit from knowing what roles and behaviors make groups function well. The following exercise, which lasts a full class period, helps students develop solidarity and awareness of group leadership and behavior, especially when paired with instructional units on group communication and leadership.
Materials needed for the exercise: Small tables or desks and chairs, a whiteboard or chalkboard, dry-erase markers or chalk, four index cards, pencils or pens, an analog wall clock, two pairs of scissors, two small stacks of construction paper, eight six-sided dice, (optional) eight 12-sided dice.
Right before class: Organize the classroom into four group work areas — two on the left side, two on the right. On the two left-side tables/desks, place one pair of scissors and one stack of construction paper on each table. On the two right-side tables/desks, place four six-sided dice and four 12-sided dice on each table. Put the wall clock in a visible location apart from the work areas. As students enter the classroom, ask them about their math proficiency, and, maintaining some measure of equal group size between tables, sort them into groups seated with generally low self-reported proficiency on the left and high self-reported proficiency on the right.
Give preliminary instructions to the class explaining that, working cooperatively, they will be given a math problem to solve. After solving it, they will need to plan how to present it to the class. They are assuming their audience has very little knowledge about how to solve the particular problem their group has solved.
Place an index card on each table. The author of this exercise prefers to then ask, “At each table, who feels the least like talking today? Raise your hand.” Choose one person at each table to be the “Judge.” They will record each group member’s name on the index card and, during the course of the activity, score a point for each group member whenever they contribute, or do something to further the group’s goals.
This represents an opportunity to ask the class for their preconceptions: “What counts as ‘contributing?’” Supply them with a few examples, such as the following:
- Sharing ideas about how to solve the problem.
- Providing materials, such as calculators or notebooks.
- Asking questions or encouraging input from group members.
- Drawing a diagram of the problem.
Give the class about a minute for the “Judges” to record all names. Assure “Judges” that they, too, may contribute to the group if they feel the need.
Then, hand out each table’s particular instructions. Inform them that, as soon as they receive instructions, they have about 10-15 minutes to solve their problem and devise a way to present it to the class. Be sure to remind them while they are working that all items in the classroom may be used in their presentation. Lecturers may find it necessary to remind groups that they need to plan for their presentation after solving the math problem. They need to make decisions on how to present: Do they use the visual aid materials? Do they present as a group or assign one member as presenter?
The particular math problems are as follows:
- For the low math proficiency side:
On a clock face, the minute hand and hour hand are right on top of each other at 12 p.m.
How many minutes must pass between that time and the next time the minute hand and hour hand are right on top of each other?
Explain the solution to the rest of the class assuming that they have never told time on a traditional (analog) clock face. Your presentation should not exceed 5 minutes.
- For the greater math proficiency side:
If you roll a 6-sided die, and another person rolls a 6-sided die, what are the odds you will roll a higher number than the other person?
If both of you roll 12-sided dice instead, will the odds be the same? Why or why not? How will the odds be different?
Explain this clearly to the rest of the class, assuming they have only a vague understanding of probability. Your presentation should not exceed 5 minutes.
Be forgiving with the time limit. It is likely the low-proficiency groups will be finished first, so have them present first. Also, be forgiving with the math. It is not unusual for some groups to reach incorrect solutions.
(The solution to the time problem is 65 minutes and 25 seconds, as both the hour and minute hands must move slightly past the 1 mark on an analog clock. The solution to the dice problem is 2.5/6 or 42% chance for six-sided dice and 5.5/12 or 46% chance for 12-sided dice; the key is to determine number of possible outcomes and then eliminate outcomes that do not show your die being higher.)
After each group presents, ask the following questions:
- Which elements of the presentations made them easier to understand?
- What was done with the visual aids that made the presentations more effective?
- What could have been done with the visual aids that wasn’t done?
- Normally, time problem groups don’t think to use the wall clock. Additionally, it’s sometimes effective (and entertaining) to use one shorter student standing in front of a taller student, moving their arms to simulate the movement of a clock.
- Probability groups may not think to distribute dice to the other tables, allowing listeners to see first-hand how the dice rolls work.
- Probability groups also get bogged down in their own ways of solving the problem. It is always good to draw out the problem in a matrix of outcomes on the whiteboard or chalkboard.
- Who do you feel contributed most to the group? How did they do that? Who did the “Judges” record as contributing the most?
- What role did you play? Were you doing the math? Drawing out the problem? Keeping the atmosphere light? Reminding members of the time limit? Checking the accuracy of the work? Taking charge of the presentation? Sharing opinions about the audience’s possible reaction?
- Who would you say was the group leader? What did they do to make you think of them as the leader? Were they the only ones exhibiting traits of leadership?
The exercise should result in students’ easy recall of practical definitions of leadership traits and emergent leadership roles, having allowed them to think critically and react to concrete stimuli before diving into the course material. The lecturer is able to reference this day’s activity going forward. Additionally, the exercise leaves students with an experience of informal and generalized (as opposed to the more commonly formal and individual, hence anxiety-inducing) feedback regarding their presentations, especially concerning visual aids usage.
In the author’s experience, the day of this exercise often represents one of the students’ favorite days in class.