Final answer:
The best type of discontinuous measurement to track engagement during a class lesson is quantitative discrete data, as engagement can be counted through specific occurrences such as questions asked or participation in discussions.
Step-by-step explanation:
To track engagement during a class lesson, a type of discontinuous measurement that would be best is quantitative discrete data collection. This is because engagement can be recorded in distinct, separate occurrences such as hand raises, contributions to class discussions, or instances of active participation. An effective way to measure these discrete events is by using a tally system or a clicker to record each occurrence of student engagement in real time.For example, a tutor might note every time a student asks a question, responds to a question, or provides commentary during a lesson. These counts can then be analyzed to assess the level of engagement. Engagement is not something that is measurable in a continuous sense, like time or weight, but rather in the actual acts of participating, making quantitative discrete data the main answer to this question.In conclusion, engagement is best tracked as a series of observable, countable events, making quantitative discrete the most appropriate metric. Such data provide clear and actionable insights into the frequency of student engagement during a class lesson.