Faculty in many kinds of programs, especially those designed for professional careers, need to articulate outcomes and curriculum features that will produce Level 4 knowledge, also referred to as working expertise. Failure to do so results in graduates with knowledge deficiencies that impede successful practice in work settings. Developing higher level knowledge requires careful instructional design to build both learner capacity for handling more interacting elements of knowledge and learner ability to transfer knowledge to multiple contexts. This module includes a description of Level 4 knowledge, a profile of the characteristics of Level 4 learners, and an educational model for developing Level 4 knowledge that is theoretically sound and also practical for the classroom educator. A basic assumption is that learning performance assessment and evaluation (4.1.2 Distinctions Between Assessment and Evaluation) must be based on a clear understanding of a learner’s problem-solving capacity in relation to the complexity of the problems and contexts involved in learning experiences, whether in the classroom or in life situations.

Characteristics of Level 4 Knowledge and Level 4 Learners

The original resource for defining levels of knowledge is Bloom (1956). However, Pacific Crest’s adaptation of Bloom’s taxonomy introduces changes in the levels beyond Level 3, “application,” by using new terminology that emphasizes a problem solving and research focus (2.2.1 Bloom’s Taxonomy—Expanding its Meaning). In Pacific Crest’s adaptation, Level 3 remains similar to Bloom’s application level, i.e., ability to apply knowledge to new contexts. Level 4, working expertise, is defined as ability to use knowledge flexibly in multiple contexts. Level 5, “research,” and Level 6, “assessment” are additional knowledge levels in the Pacific Crest model that enhance Bloom’s “synthesis” and “evaluation” levels.

The most substantive indication of Level 4 knowledge is attainment of greater capacity for learning in complex contexts. Building knowledge beyond Level 3 includes careful regulation of problem complexity, usually by an expert, to provide predictable increases in difficulty and context that best meet the developmental needs of students.

Level 4 learners demonstrate the following characteristics:

The ability to integrate knowledge with learning skills to produce a generalized problem solution
The ability to solve complex problems by applying many kinds of knowledge and integrating these with processes and tools to produce a quality problem solution
The ability to produce general solutions that can be reused and transferred to similar situations with minimal adjustments

An “expert” in a particular field will demonstrate all of the above characteristics within his or her discipline or field. This expertise is the goal for most educational programs, but the concept of even more generalized types of expertise is valid as well. Some of the greatest minds have produced striking changes in the paradigms of knowledge used by experts across many fields.

A Model of Level 4: Working Knowledge

The capacity to solve problems at Level 4 is a complex topic that is receiving increasing amounts of attention from cognitive and educational researchers (e.g., Van Merriënboer, Kirschner, & Kester, 2003; Renkl & Atkinson, 2003). In order to facilitate students’ ability to achieve working expertise, educators must recognize two significant interactions: the interdependence of problem complexity and learner capacity, and the interdependence of learner capacity and the problem context.

The level of difficulty of a problem-solving task is a function of three major interacting variables that are discussed in the following sections. These variables are

Problem complexity
Individual learning capacity of the learner
Problem context

Problem Complexity and Levels of Difficulty

The complexity of a problem is characterized by the following criteria:

Number of knowledge items involved
Number of schemas crossing discipline boundaries
How recently the knowledge area has been practiced
The extent of direction or guidance provided
Clarity of problem definition and of key issues
Subtlety of the assumptions
The availability of information or misinformation
Resource constraints
Difficulty in validating solutions either through estimation or alternative solutions
Large-scale integration of information
The complexity of the relationships among aspects of the problem
The ease of partitioning the problem into sub-problems
The extent of the history of efforts to resolve a problem
The level of emotional commitment or involvement

Table 1 contains a classification of the levels of difficulty of problem-solving tasks. This general rubric is a guide for selection or design of learning tasks that fit the current level of knowledge and experience of learners in a course or program.

Table 1 Levels of Difficulty of Problem-Solving Tasks

Difficulty Level		Description
1	automatic	Can perform a task without thinking
2	skill exercise	Is consciously involved, but experiences minimal challenge using specific knowledge
3	problem-solving	Finds the task challenging but possible with current knowledge and skills through a strong problem-solving approach
4	research	Requires additional knowledge that currently does not exist within the learner’s current capacity to effectively accomplish the task
5	overwhelming	The task cannot be accomplished without a significant increase in capacity, most likely by bringing in additional expertise.

Learner Capacity

Capacity refers to an individual’s ability to solve problems. It represents a combination of traits, including the following:

Past problem-solving and critical thinking experience
The ability to apply a variety of concepts across boundaries
The internalization of the problem-solving process
A portfolio of problem solving techniques and models
A personal attitude that includes persistence, coping, recovering from failure, etc.
Adventurousness, including playfulness, creativity, open-mindedness, etc.
Access to additional capacity as needed to expand beyond the learner’s current limits
The ability to remain objective
The understanding of the significance of the problem

Problem Context

The context in which a problem is presented also influences the ability of a learner to address it. Bransford et al. (2000) comment that “Learners do not always relate the knowledge they possess to new tasks, despite its potential relevance.” Therefore, a learner’s familiarity with the context significantly enhances his or her ability to effectively and efficiently employ conceptual knowledge in concert with appropriate processes and tools to produce an intended outcome. Moving a problem to an unfamiliar context will make it more challenging for learners, even if no new tools are needed.

An example illustrates how perceptions of context can change problem-solving success for learners at lower levels of capacity. Transferring the principles from a statics problem, initially illustrated with trusses, frames, and simple tools, to the skeletal system of a living organism is a change of context that many students will find disorienting at first. However, once they recognize the transferable elements and principles, they are much more ready to apply the laws of mechanics to other situations. The educator’s goal is to expand the learner’s ability to recognize the universality of principles that were first learned and applied in a narrower context.

Interdependence of Problem Complexity and Learner Capacity

Figure 1 illustrates how, at a low level of problem complexity and high individual capacity, the problem-solving experience is merely a skill exercise without any additional development toward working expertise. As the complexity of the situation increases, a boundary is crossed and a skill exercise develops into a problem-solving situation that can assist in the development of working expertise. However, if the complexity continues to increase further, additional boundaries are crossed, and the problem-solving challenge can become utterly overwhelming for the student, and fruitless as a learning experience.

Figure 1

Interdependence of Learner Capacity and Problem Context

Figure 2 represents the interdependence between problem complexity, ranging from simple skill exercises to challenging research, and problem context. Although the learner’s problem-solving capacity (the success and speed at which he or she finds a solutions) may be very strong for familiar contexts, the addition of more varied contexts will create challenges that will require substantial growth, especially in one’s ability to integrate knowledge in more complex ways. Often, direct experience in varied contexts is the most effective way to facilitate growth from using mainly lower- level knowledge to consistent use of Level 4 knowledge.

Figure 2

Generalizing Knowledge

A critical issue in Level 4 knowledge development is the facilitation of the learning process so that it will generalize across multiple contexts. Typically, learners first need to explore a series of examples in order to build a conceptual model that allows them to recognize that it is possible to apply knowledge in varied contexts. Experts must recognize when knowledge should not be transferred, even if it is technically possible.

Classroom Application

Educators can use the concepts and tools presented in this module to adjust the level of complexity in problem solving to provide sufficient challenge to elevate student knowledge to Level 4. By controlling the factors of problem complexity and context, educators can design the learning experience so that it is more than simply a skill exercise but not overwhelming for individual learners. A specific example follows to illustrate the ways in which a problem can be modified to adjust its level of complexity.

Problem Statement: You are visiting a car dealership with a friend who is ready to purchase a car. The dealer and your friend have agreed upon a purchase price of $10,000. As your friend is completing the purchase agreement, the sales manager offers a choice between a $1,000 rebate and a 3.9% interest rate. Your friend asks for your expert problem-solving assistance to decide which is the better choice. What advice would you give?

This is a complex problem with some missing information that must be filled in by the learner. For example, some assumptions will have to be made about current and future inflation rates, the time period of the loan, how and when the interest charges are calculated, and the size of any initial payment. It would be a significant undertaking to solve this problem completely for multiple situations covering a wide range of variables. However, depending on the learning level and experience of the students, an instructor might make the following modifications to reduce the complexity, rendering the problem tractable for less experienced learners:

complex	Specify only the time period for the loan
difficult	Provide an example of a comparison loan including a repayment schedule that has already been fully worked out
medium	Specify what comparison to calculate
easy	Define the problem fully and ask for a computational solution
simple	Define the problem, provide the formula, and ask for a computation

Table 2 suggests how the level of learning challenge can be adjusted to fit overall learner capacity. By starting with the most complex problem statement, and then by simplifying it step by step, educators can guide learners to recognize how the difficulty level is being scaled back as more information and structure is provided. Students should be continuously challenged to work at the most difficult level they can manage.

Table 2 Levels of Problem Complexity

Complexity Level		Description
1	complicated	Minimal or no assumptions and constraints provided
2	difficult	Provide an example of the solution to a similar problem
3	medium	Specify the assumptions and constraints to be placed on the problem
4	easy	Define the problem fully and ask for a solution
5	simple	Define the problem, provide a detailed problem-solving method, and ask for a solution

Techniques for Shaping Growth to Level 4, Expert Knowledge

General techniques are offered below for facilitating the movement of learners to the level of working expertise:

Generalize understanding. Ask learners to write paragraphs about applying their knowledge in a familiar context (e.g., current and voltage analysis of an electric circuit in a homework problem); applying their knowledge in an unfamiliar context (e.g., flow and pressure analysis of a fluid piping network, or series and parallel combinations of mechanical spring elements); and generalizing their knowledge by describing similarities and differences between the two contexts, identifying common underlying principles.
Categorize problems. Develop proficiency in problem classification by asking colleagues, mentors, and students to tackle problems in a variety of contexts. Have faculty and students rank these problems by level of difficulty, justifying their reasoning. This activity can give insight about the range of problem-solving capacity present in the classroom and give students a better idea how a particular course builds toward the working expertise of a professional.
Practice formulation and estimation. Instead of having learners invest time in implementing a single, formal solution, ask them to explain alternate solution paths and provide an estimate of the answer.
Use self-assessment. Grow self-awareness and self-control of problem-solving skills by having learners document and assess their problem-solving performance by identifying strengths, areas for improvement, and insights (4.1.9 SII Method for Assessment Reporting).
Use a problem-solving methodology. Unquestionably, the best means for a learner to tackle a potentially overwhelming problem is through the use of a methodology. A solution is more likely when learners move through the necessary steps of a problem solving process.
Assess the use of the problem-solving methodology. By examining how well a methodology for a complex process is employed, (as opposed to evaluating the solutions themselves), you provide links with complementary teaching and learning processes, such as information processing, critical thinking, teamwork, and communication.
Validate problem solutions. Ask students to write a paragraph describing how to validate their solutions. The paragraph should identify the most important assumption made and explain how the result might change if that assumption were changed.
Holistic development. In order to fully build Level 4 proficiency or working expertise, other aspects of personal development should also be considered. In particular, the learner’s affective skills need to be enhanced in order to counter learner frustration as the complexity of the problem-solving situation goes up and the comfort level decreases.

Concluding Thoughts

Educators who can recognize and assess Level 4 knowledge, i.e., working expertise, will be in a better position to create effective learning experiences to facilitate growth to this level. Three major variables interact to create the complexity involved in expert knowledge: learner capacity, problem complexity, and variations in context. If educators accurately assess the threshold at which learners are frustrated by any combination of these variables, they will avoid a substantial amount of the unproductive frustration that impedes learning.

References

Bloom, B. S., Engelhart, M. D., Furst, E. J., Hill, W. H., & Krathwohl, D. R. (1956). Taxonomy of educational objectives: The classification of educational goals. Handbook 1: Cognitive domain. New York: David McKay.

Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.

Renkl, A., & Atkinson, R. K. (2003). Structuring the transition from example study to problem solving in cognitive skill acquisition: A cognitive load perspective. Educational Psychologist, 38, 15-22.

Van Merriënboer, J. J. G., Kirschner, P. A., & Kester, L. (2003). Taking the load off a learner’s mind: Instructional design for complex learning. Educational Psychologist, 38, 5-14.