Using Groupwork in Mathematics Recitations:

Some Guidelines and Considerations

  1. Motivation
  1. A body of research is being amassed (Hake, 1998; Mazur, 1997; Springer, Stanne, and Donovan, 1997; Redish, 1994; Redish and Steinberg, 1999; Smith, Johnson, and Johnson, 1991 ) that shows positive consequences for learning when students are actively engaged in the classroom.
  2. Many MIT faculty (e.g., Allen, Belcher, Boyce, Bradt, Bucciarelli, Carter, Hall, Waitz, Newman) and former math recitation instructors (e.g., Carlton, Lenart) have had positive experiences with groupwork.
  3. MIT students have a favorable response to groupwork judging from course evaluations from the above faculty.
  1. Basic Guidelines
  1. Make groupwork a norm in the classroom by beginning early in the semester. (Remember, this may be a different way of running a recitation than students are accustomed to.)
  1. Make the classroom a safe environment in which to make mistakes. (Tell students something about yourself; learn their names.)
  1. Determine purpose in giving specific problems; make this explicit to the students. (Write on the board the main topic[s] to be covered in class.)
  1. Problems should be solvable in 10-15 minutes.
  1. Use frequent feedback to gauge how groupwork is going.
  1. Specifics

Assigning the Problem

  1. Devise criteria for selecting the problem: representative of material covered in lecture? Similar to problems on quizzes or exams? Related to the hardest concept?

Doing the Problem

  1. Circulate among the groups after giving them a few minutes to work.
  1. Give students/groups who are having problems hints.
  1. Encourage students with questions to talk to one another.
  1. Give students who find the problem too easy, a harder one.

Reviewing the Problem

  1. Decide how you want students to report back (see “Considerations,” point f below).
  1. Focus on the key idea in solving the problem.
  1. Be open to all solutions, but remember all solutions are not created equal.
  1. Considerations
  1. Should you form groups or allow students to self select? Should students work together in the same group each week? How big should the groups be? Should you allow any student to work alone?
  1. How do you reconcile the fact that you will (probably) cover less

material using groups?

  1. Should the students work together for the entire class period? If not, what percentage of the class should be devoted to groupwork?
  1. What is no one says anything? What if someone gives the wrong answer? Will you cold call?
  1. How do you build in positive interdependence and individual accountability?

e. How do you manage the different levels of competence in the class?

f. Should students be called to the board to present problems?

g. Should the recitation instructor visit the groups as they are working?

h. How much, if any, information do you need to give students about

group process?

  1. What do you need in the classroom in order to support groupwork?
  1. Should the work students do in groups be counted their grades in

any way?

Addendum: Asking and Answering Questions

If you are asking a question:

  • Make sure everyone can hear the question that is being asked.
  • If no one answers: Wait. If still no one answers, rephrase the question, break it down into simpler parts, give a “hint” within another question, etc.
  • Make sure everyone can hear the answer.
  • Respond positively to a good answer
  • Make sure the students know if an answer is right or wrong.
  • Save face for the student answering the question incorrectly.

If you are answering a question:

  • Make sure you understand what the question is.
  • Make sure everyone else hears the question that was asked.
  • Check that you have answered the question.
  • Decide how you will handle questions that are too simple or too complex for the majority of the class. (But save face for the student asking the simple question.)

If you cold call:

  • Be fair in your calling patterns.
  • Think about instituting a “pass” policy.
  • Save face for students.