• Jay Martin, University of Wisconsin Madison
• John Mitchell, University of Wisconsin Madison
• Ty Newell, University of Illinois Urbana–Champaign
• Tony Jacobi, University of Illinois Urbana-Champaign

In contrast to the approach followed for the Fluid Mechanics Concept Inventory and following the lead of Krause and others working on concept inventories, development of a Heat Transfer Concept Inventory (HTCI) began with students. Faculty members at the University of Illinois Champaign–Urbana and the University of Wisconsin Madison worked with students to identify essential concepts and alternate conceptions. They also worked with students in developing and evaluating questions used on the HTCI and on the answers to the questions, as students assisted in the identification of key false-positive answers. This was done through focus-group activities, including videotaping of student discussion of concepts and questions and guided reflection on concepts led by faculty members.

The goal for the HTCI is to be an assessment tool for

• determining student understanding of concepts as opposed to mastering skills
• identifying student misunderstandings
• providing feedback to instructors as a guide to areas for improvement
• evaluating the student gains in a heat transfer course

HTCI should be one piece of a package that would help instructors make the learning of heat transfer more effective. The complete package would include an HTCI as described above, a large set of concept discussion questions that could be used in class, and a set of concept test questions that could be used to evaluate the level of mastery of concepts in specific topic areas (e.g., conduction heat transfer). An instructors' guide to concept-based instruction would be an integral part of this package. Ultimately, the heat transfer package would be part of a larger set of similar teaching materials in the thermal sciences (thermodynamics, fluid mechanics, and heat transfer).

Faculty members discussed the lack of understanding of concepts that undergraduate students have. Although they know that most students have a poor grasp of the basic concepts in a course, the absence of quantitative data has reduced the impetus to change teaching approaches. Preliminary results from concept testing and discussions with students have forced some faculty members to acknowledge the deficiencies of current teaching methods. Support and guidance are necessary for implementing change in how courses are taught. The concept-based instruction materials provide that support.

Developing a HTCI involves both students and faculty members. The faculty team is listed above. The students involved are from the same universities as these faculty members. The faculty team developed a set of concepts that students need to understand to be proficient in heat transfer:

• Fundamental ideas (properties, control volumes and surfaces, modes of energy transfer, and conservation statements)
• Conduction (Fourier’s law, and multidimensional, steady state, and transient applications)
• Convection (Newton’s law of cooling, conservation equations, boundary layers, internal flow, laminar and turbulent flow, nondimensional parameters)
• Radiation (radiative processes and properties, black and gray body concepts, emission/absorption/reflection/transmission, radiative exchange)

This list of concepts provides the structure for student input and question development.

Six University of Wisconsin students (four men and two women, average GPA of 3.3) participated in the HTCI development. The initial assignment was for each student to go through the course syllabus and make a list of (a) the top 10 topics/concepts of which he/she was most confident that he/she thought are important and (b) the top 10 topics/concepts of which he/she is least confident that he/she thought are important. In subsequent assignments, they provided a set of statements that demonstrated their understanding of the concepts of which they were confident and developed a set of questions that, if they had the answers to them, would allow the students to understand the concepts of which they were not confident.

The University of Wisconsin faculty members collated the student input and developed concept questions for the students to discuss in videotaped sessions. Questions asked included

1. What are the differences between conduction and convection?
2. What are the differences between conduction and radiation?
3. What is a temperature gradient?
4. What is a thermal resistance?
5. What is Fourier’s law?

The group at the University of Illinois consisted of six students (three women and three men, average GPA of 3.0). Two had completed the heat transfer course, two were currently enrolled, and two had not yet taken the course. Three discussion sessions were held—two with a pre-heat-transfer student and a current enrollee and one with the two students who had completed a heat transfer course. Each discussion lasted a little less than an hour; the faculty members participated by asking questions and probing student responses.

Questions were developed from the earlier written exercises and sometimes used simple props. For example, two geometrically identical pieces of material—one metal and one plastic—were presented to the students; they were asked which was colder. As another example, the students were asked if they knew about the Greenhouse Effect and to explain it if they could. The input from these sessions with the students helped in (a) understanding the level of understanding that students had and (b) developing concept questions that would elicit discussion and understanding of concepts.

A draft set of 54 potential heat transfer questions that could be included in an HTCI has been developed. The team is evaluating this set for coverage, in terms of the concepts previously identified. One complicating factor in this subject is that each concept question combines more than one concept, as listed above. This is probably true of the material covered in most upper-division (junior and senior) courses. The relevant physical phenomena naturally draw in several concepts.

A typical question for the draft HTCI is given below.

For steady state, onedimensional conduction in a composite wall with uniform properties in each material and no generation, circle the letter of the temperature profile that can occur: