DCV (Directed, Convergent, Divergent) Questions

Context: You are designing an activity or assignment with questions for students to answer.


Problem & Forces: Questions can guide students in many ways, and it can be difficult to design the right set of questions. If there are too many questions, students may get discouraged; if there are too few, students may miss key connections. If questions are easy, students gain confidence but might get careless; if questions are difficult, students might struggle and get discouraged. Students often want the “correct answers”, but also need to consider open-ended questions to Climb Blooms Taxonomy. With a mix of easy, hard, closed, and open questions, students may struggle to allocate the right time and effort to each question.


Solution & Consequences: Therefore, use a combination of DCV (Directed, Convergent, Divergent) questions. Directed questions are based on prior knowledge or provided information and are rarely difficult to answer. Convergent questions require more effort, but most students or teams will reach the same answer, or one of a few answers. Divergent questions also require more effort, but students and teams will often reach very different answers and explore broader issues. Help students identify the effort and sort of answer needed with cues such as wording (e.g. “recall”, “look up”, “jot down”, “discuss and agree”), the space for an answer (e.g. cell in a table, blank line to fill in, or half a page) or a suggested amount of time (e.g. 1 min, 5 min).

Discussion: DCV Questions are related to but distinct from the phases in EIA (Explore, Invent, Apply) Learning Cycles. Exploration questions are often directed with a Simple Answer, but may be convergent or even divergent; invention questions are often, but not always, convergent; and application questions are usually either convergent or divergent, Open Ended Questions. Directed and convergent questions are useful for Misconception Assessment; convergent and divergent questions are useful to Challenge Understanding.

Examples: Each POGIL activity model pattern contains sample DCV (Directed, Convergent, Divergent) Questions.

A sample activity uses a Hi-Lo number guessing game to introduce concepts in algorithm analysis. It begins with directed questions to ensure that students understand the rules, such as “How many different responses can player A give?” and “How does the game end?” Defining possible strategies seems divergent, but is usually convergent, since most teams reach a similar set of strategies. Describing other examples of the speed-complexity tradeoff is divergent. Finding the maximum and average number of guesses for each strategy is convergent, since it requires effort but there is a single correct answer.

Author: Clif Kussmaul

Publication: C Kussmaul. 2016. Patterns in classroom activities for Process Oriented Guided Inquiry Learning (POGIL). HILLSIDE Proc. of Conf. on Pattern Lang. of Prog. 23 (October 2016).

Contributors to this page: Clif Kussmaul .
Page last modified on Sat November 11, 2017 12:15:04 EST by Clif Kussmaul. (Version 9)