How much of the course is IBL?
- Level 0: All teaching is done by lecturing.
- Level 1: In addition to lectures, other presentations modes are used such as videos and the use of worksheets for the purpose of practicing rote skills. For example, the instructor shows students how to take a derivative of a trig function, and then provide some more problems similar to the shown example.
- Level 2: The instructor lectures for most of the time, but intersperses some interactive engagement, where students are asked questions and given mathematical tasks that require thinking and making sense, such as "Think Pair Share". Interactive engagement may take up a few minutes to anywhere up to approximately a third of class time, which may vary day-to-day or be based on weeks (e.g. lecture MW, problems on F). A key feature is that lectures remain a significant component of the teaching system. The instructor is the primary mathematical authority and validator of correctness.
- Level 3: The instructor lectures for roughly 1/3 to 1/2 of class time. Students do a variety of activities that focus on understanding of core ideas, problem-solving, generating ideas, evaluating arguments. The primary student-centered activities are higher-level tasks, such a problem-solving, categorizing, and understanding concepts. The instructor is not the only authority on the subject matter, and students share responsibility in validating mathematical facts.
- Level 4: All teaching is done via student-centered activities. Students are either presenting proofs/solutions, working in groups on problem-solving tasks. In this case, the instructor does talk for part of the time, often in the form of setting the stage for a new unit, facilitating discussions, or summarizing or pointing out important facets of a proof/solution after it has been approved by the class. The instructor and students primarily work together to form a consensus about the validity of solutions. Logic, reason, and mathematics are used to validate solutions.
In the next post, I'll make a list of questions for the purpose of self-evaluation.