Page 105 - International Journal of Process Educaiton (Special Issue)

Figure 3 The First Three Levels of Learner Knowledge and Critical Thinking Questions

Directed Questions

Level I The answers can be found by examining the model presented in the activity, using the information resources
Information listed, or by drawing on personal experience and prior knowledge and activities. Such questions have a
definite answer and build the foundation for more challenging questions.

What is…? Who were the main…? Can you list the three …?
Where is…? Which one…? Who was…?
When did…? Can you recall…?
What facts or ideas show…? Can you select…?

Convergent Questions

Level II Build Level 2 knowledge and help students elevate their knowledge to Level 3. Students need to organize,
Conceptual interpret, analyze, and synthesize. They may have more than one correct answer, and the level of difficulty
Understanding progresses within a sequence of questions. A good convergent question makes important connections,
links concepts together, leads to better understanding, and requires that students reach conclusions.

How did… happen? How would you state or interpret in your own words…?
How would you compare or contrast…? What is the main idea of…?
How would you describe…? Which statements support…?
How would you summarize…? Can you explain what is happening…?
How would you show an understanding of…? What is meant by…?

Level III Divergent Questions
Application
Divergent questions send students in new and interesting directions. They often have no right or wrong
answer, but require students to ponder, explore, generalize, and expand their current knowledge.
Divergent questions require the highest level of thinking and produce outcomes and conclusions that vary
among learning teams and individuals. They help identify holes in knowledge and test understanding by
challenging the knowledge structure that was built.

How would you use…? What other way would you plan to…?
What examples can you find to…? How would you apply what you learned to develop…?
What would result if…? How would you structure an argument to show…?
Can you make use of the knowledge to…? What elements would you choose to change…?
What approach would you use to…? What questions would you ask in an interview with…?

of learner knowledge (Hanson, 2007). Figure 3 pulls explored in the Faculty Guidebook module Self-Validation
together the pertinent Levels of Learner Knowledge with of One's Learning (Armstrong, 2007) and implemented
information about how each level corresponds to the practically in Foundations of Mathematics with a section
sequencing of critical thinking questions. called "Identify and Correct the Errors" (Fremeau 2005).
As the sample problem from this section in Chapter 3
The Problem Solving section discusses the use of makes clear, this innovation asked students not only to
problems in curricula to elevate learning to the level of demonstrate that they had learned by showing the “correct
problem solving. From the perspective of scholarship, this process” but to validate that learning (see Figure 4).
elevation was the focus of the Problem Solving Across the
Curriculum Conferences (Kramer & Beery, 1990), as well Validation is included as a critical aspect of learning to
as Learning Through Problem Solving (Apple, Beyerlein learn in other active learning curricula published by Pacific
& Schlesinger, 1992), Foundations of Problem Solving Crest (see Figure 5):
(Myrvaagnes, 1997), and Developing Working Expertise
(Level Four Knowledge) (Nygren, 2007). Additionally, students at any of the quantitative Learning
to Learn Camps (e.g., Algebra Learning to Learn Camp),
Validation of Learning are required to validate each answer as part of the process
of showing their work in order to receive credit for having
A key facet of learning to learn is that learners must the correct answer.
develop the ability to validate their own learning; they
must be able to know that they have learned. This idea is

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