Hands-On Workshops to Assist in Students' Conceptual Understanding of Heat Transfer

Heat transfer is part of the core of the Mechanical Engineering curriculum and its concepts can be found throughout science curricula. Given the importance of heat transfer in modern society, it is most troubling that recent research shows that students have a limited understanding of heat transfer principles even after the completion of one or more heat transfer courses [1]. Specifically, students have shown (i) a significant lack of conceptual understanding of heat transfer principles, (ii) an inability to transfer knowledge to subsequent courses and out-of-context problems, and (iii) an insufficient transformation from novice to “competent practitioner.”

Heat transfer is traditionally taught using a deductive instructional style. Deductive instruction is characterized by an instructor presenting and defining a general concept, providing examples that demonstrate the idea, giving students practice in solving similar problems, and finally, testing their ability to do the same tasks on exams. This “skill-and-drill” approach allows students to approach learning passively, and does not challenge them to modify their prior understanding. Little attention is paid to the physical phenomena that the concepts explain or what types of practical problems that they can be used to solve [2]. Consequently, traditional lecture style courses are limited in how well they can convey abstract concepts such as those encountered in a heat transfer course. While they stress important ideas such as setting up control volumes and energy balances, they do not provide opportunities for students to see or feel heat transfer. This results in a lack of understanding of the underlying concepts of heat transfer, which are vital for real learning.

Although other engineering and science curricula can make similar claims, these problems are usually overcome by introducing measurement sensors and instruments to easily quantify and demonstrate the associated phenomena. For example, in electrical engineering, most engineers are introduced to voltmeters and ammeters during their education to measure voltage and current. Conversely, although temperature measurements are common for students, heat transfer is rarely if ever measured. The lack of heat flux or heat transfer measurements in undergraduate labs is rather amazing given that heat transfer is the subject of the course. Moreover, heat transfer labs are typically taught with a deductive structure where students follow “cookbook” instructions with a known outcome [3]. Thus students have no opportunity to challenge and modify their existing knowledge framework.

Consequently, despite completing several courses in thermal and transport sciences, a significant number of students have remaining misconceptions about simple heat transfer processes [4–6]. Through the development of the “thermal and transport concept inventory” (TTCI) test [7], it has been observed that students possessed “robust misconceptions” about the differences between

• heat, energy, and temperature;

• rate and amount of transfer (e.g., heat transfer, momentum transfer, mass transfer);

• steady-state and equilibrium processes [8].

In their experiments with Chemical Engineering senior students, it was found that one-third to one-half of the students had misconceptions about these concepts as recorded by the TTCI [9]. The above three concepts, however, are specific to students in chemical engineering and include ideas from thermodynamics as well. Since heat transfer is taught differently to mechanical engineering students, a new list of six concepts specific to mechanical engineering students in heat transfer is proposed. This list is shown below in Table 1.

This work reports on the results of research to integrate challenge-based workshops (CBW) that utilize actual heat flux and temperature sensors into existing heat transfer courses. This provides hands-on activities with real-world challenges to help the students relate heat transfer to their conceptual framework. The effects on both student misconceptions and retention of basic concepts are evaluated.

Inductive pedagogies such as CBW that promote discovery and conceptual connections to observed and measured physical phenomena are centered in student engagement. A survey of neurological and psychological research found strong support for these approaches, specifically showing that (i) students understood information better when they were forced to link it to their existing cognitive structures, (ii) students were more motivated to learn when they could see the potential for impact, (iii) there was a greater chance of knowledge transfer, and (iv) students' problem-solving skills were improved [10]. Conversely, the deductive learning mode does not reflect what we know about how people learn—following the constructivist learning theory, it is known that students form knowledge representations of new information by building on their previous knowledge and experiences [11]. If the new information has few connections to what they already know, learning will not occur nor will students be motivated to learn [12]. Thus, effective instruction must provide experiences in which students actively construct knowledge by adjusting, rejecting, or modifying their prior beliefs and understanding based on their experiences [2].

The authors' CBW approach is grounded in an existing pedagogy that blends inductive and deductive processes: challenge-based instruction (CBI). CBI begins first with an inquiry or challenge (i.e., a question to be answered or a hypothesis to be tested). Following the principles of the legacy cycle of instruction, the students are then (i) asked to formulate their initial thoughts, (ii) receive expert perspectives, (iii) research and revise their solution to the challenge, and finally, (iv) present a final conclusion via presentation, report, or examination [13]. This cycle presents a blended inductive and deductive mode to instruction: the need for learning is motivated by an authentic problem; the challenge causes the students to continuously iterate their conceptual understanding of the domain by consulting the expert (through small lectures), and discussions with their teammates. CBI modules [14] were created [15] with support from NSF for a variety of topics in bioengineering [16]. The method was shown to improve students' performance with open-ended problems [17–19]. Inquiry-based learning approaches, such as CBI, have been found to be “more effective than traditional science instruction at improving academic achievement, and the development of thinking, problem-solving and laboratory skills” [2], and to enhance understanding of critical engineering concepts [20,21].

The integration of hands-on activities into courses has shown significant learning gains for students across several domains. Faculty have used interactive learning in small groups with hands-on demonstrations to enhance fluids and heat transfer learning in the Chemical Engineering curriculum [22–25]. Rensselaer Polytechnic Institute has instituted mobile studios, consisting of a suite of instruments that are connected to a personal computer for observing and testing electrical theories [26]. A similar approach (Technology Enabled Active Learning) has been instituted at Massachusetts Institute of Technology for freshmen physics classes with positive results [27]. Virginia Tech has created a “lab-in-a-box,” which is an inexpensive set of instruments and a bread-board to allow students to perform electronic experiments themselves [28].

The heat transfer workshops in this study are modeled after the CBI pedagogy and are designed specifically to target students' common heat transfer misconceptions. The workshops are heavily focused in providing hands-on experiences and allowing students to explore connections between theory and the physical world. As such, the workshops feature state-of-the-art sensors that measure both temperature and heat flux (heat transfer per area). These sensors have recently been made commercially available at a low cost for education purposes by FluxTeq.

This paper consists of a 2-year study on the use of two different types of hands-on, heat transfer workshops. Different students participated each year.

1. (1)

   The first year consisted of having the students use heat flux and temperature sensors to take data for different situations and scenarios that related to topics from the lectures. Students were encouraged to physically explore basic concepts and thus facilitate learning through the active reconfiguration of their cognitive structure. There were 12 workshops given throughout the semester covering each major topic introduced in the lectures. The workshops were given the week before the lecture covering the topic, thus, the students had no prior knowledge of the material going into each workshop.

2. (2)

   The workshops were restructured for the second year of the study by using videos of the experiment containing real-time data and plots. The physical setup, however, was still given to the students so that they could emulate the experiment while simultaneously watching the videos without worrying about acquiring good data. The workshops were consolidated down to only six to focus on the most important concepts and topics and they were given a few days after the topics were introduced in the lecture.

The first year workshops were offered in place of the third lecture each week for one section of a 3-h junior level heat transfer class. The experimental workshop section consisted of 68 students. A group consisting of 58 students taking the traditional lecture class without the workshops was used as a control group. Students chose classes normally between five sections of the course and three instructors. Aside from the workshops in the experimental section, all other aspects of the two classes were the same, including instructor, tests, weekly quizzes, and homework. Monday and Wednesday lectures were the same between the experimental and control sections. Friday lectures covered the same material for the control group as the workshops.

The 65 student experimental section was split into three groups of equal size (about 21 students per group) so that they could have more individualized attention during the workshops. Within those groups, students were split into teams of two or three to perform the workshops so that each student could touch the materials and feel the heat transfer processes individually. Teaching assistants and/or instructors were available to help and answer questions.

Unlike traditional lab classes, CBWs were given to the students in a format that included a challenge question and five step approach to guide the students in the direction of both solving the challenge question and understanding the underlying concepts. The challenge every week consisted of a hypothetical scenario intended to make the students imagine that they were engineers working in industry trying to solve a problem for their employer.

Students worked to solve the challenge question via research and experimentation through the following five step process inspired by CBI pedagogy:

1. (1)

   The first step was to generate ideas about the problem and a hypothesis to predict what was going to happen.

2. (2)

   Step two provided some background information to the students which related to the challenge question they were attempting to solve.

3. (3)

   In step three, the students were asked to show which equations they were going to actually use and how they were going to use their heat flux sensors and thermocouples to perform their experiment.

4. (4)

   Step four was the measurements and evaluation of the results including answering the initial challenge question.

5. (5)

   Step five was reflection about the concepts that were stressed during the workshop.

Every workshop consisted of a physical arrangement using thermocouples and heat flux sensors. The sensors were connected to a data acquisition instrument provided by National Instruments and the software: LabVIEW, also by National Instruments, was used to collect and graphically display the heat flux and temperature measurements from the sensors in real time. The students then would run a prewritten matlab program which would take the data and output any relevant plots and values the students would use for their particular experiment. A wireless printer was available with each measurement system to obtain hard copies of data and plots. This helped the students to focus on the concept questions and the corresponding calculations of important quantities needed as output for the graded workshops. An introduction to the sensors was given in the first workshop.

The workshop topics were chosen to be those presented in the lectures the following week. Each workshop was intended to address specific misconceptions associated with the topic at hand. This approach provided students the opportunity to gain physical experiences with heat transfer phenomena first as a means for motivating their learning of the theoretical principles and relationships. A list of the workshop topics in order of the weeks they were given is presented in Table 2 along with the specific concepts stressed as listed in Table 1. Workshop 9 was a computer simulation as a comparison to test the student response relative to the hands-on experimental workshops.

Workshop 2 is presented in detail here to provide an example of a CBW. The objective of this workshop was for the students to learn what a fin is and how it affects heat transfer. In this workshop, the students were also introduced to the idea of convective heat transfer coefficients. The challenge presented was to determine the convective coefficient, overall heat transfer, and efficiency of the given fin. Provided for the students was a piece of metal heated at the base to act as a fin, a fan with low and high settings to provide different heat transfer coefficients, thermocouples, and a heat flux sensor attached to the fin, and data software and instructions on how to run the experiment.

Step 1: The students were asked to generate ideas about what a fin is, how it works, and what purpose it provides. They were asked questions to help lead them in the right direction.

Step 2: The students were provided information about fins and the relevant equations associated with them. All of the terms in the equation were provided.

Step 3: The students then revised their earlier ideas about fins with the new information.

Step 4: The experiment was conducted by the students. In this particular workshop, they created low and high fan air speeds on the fin and watched real time data of temperature across it using the LabVIEW software. A screenshot of the LabVIEW program is shown in Fig. 1(a) with the actual computer output. Students then ran a matlab code which gave plots and the heat flux values to assist them in calculating convective coefficients, total heat transfer, and efficiencies. Examples of the output data from the matlab program are shown in Figs. 1(b) and 1(c).

Step 5: For the final step, the students answered reflective questions related to what they learned. They were asked general questions about fins and how their performance changes based on the convective coefficients.

The goal of this workshop was for the students to learn the basics of convective and conductive heat transfer and how they are related to temperature gradients. The unique challenge-based and hands-on approach is implemented using a heat flux sensor combined with thermocouples. For example, using the results in Fig. 1 the heat flux of q″ = 722 W/m² was at the x = 10 cm position, giving a calculated heat transfer coefficient of h = q″/(T_s − T_∞) = 95 W/m² K. Most importantly perhaps, this workshop gave students the opportunity to actually put their hands on the fin and feel the change in temperature from the fin's base to its tip. This, combined with the plots of the measurements, provided a new and innovative learning experience for fin heat transfer.

In order to evaluate the effect that the workshops had on the students, a concept inventory test was given to them at the beginning and end of the semester. The pretest featured five questions from the TTCI and was given not only to compare against a post-test, but to ensure that the control and experimental groups' understanding at the beginning of the study could be considered equivalent. At the end of the semester, the entire 19 question TTCI was given to each section to see if the workshops played a role in helping the students better understand the basic concepts in heat transfer. The questions were taken from both the Heat Transfer section of the “Thermal and Transport Concept Inventory” by Ron L. Miller, the “AIChE Concept Warehouse,” and the authors. They were all multiple choice with typically four to six options presented. The questions from both the pre- and post-tests featured a mix of ones specific to the six concepts from Table 1 in Sec. 1 and control questions focused on thermodynamics ideas rather than heat transfer. A statistical analysis software package, jmp 11, was used to examine statistical differences between the performances of the two groups of students. Statistically significant differences were assumed at a significance level (α) of 0.05.

The results from the pretest showed no significant difference between the class sections for any of the five questions. Because student selection for the class was made at random, it can be assumed that the two sections started off without any advantage or prior knowledge regarding heat transfer concepts. The scores on the five question pretest for both groups along with the standard errors and p-values is displayed in Table 3.

The results from the 19-question concept inventory given at the end of the semester show a statistically significant difference both in overall scores between the two sections and for certain individual questions. Values for the test overall as well as those questions that showed a statistical significance are listed in Table 4. The results for each question are shown in Fig. 2 grouped into the six categories corresponding to the list in Table 1. The experimental group outscored the control group on 17 of the 19 questions The questions showing statistically significant differences were 1, 10, 16, and 17.

Question 1 tested the concept of temperature versus heat and energy by asking why a tile floor feels colder than a carpeted floor. The reason for the discrepancy in scores directly links back to the workshops one and four where the students felt the difference between a steel plate and plastic plate and watched how the corresponding surface temperature and heat flux responded over time. They saw higher heat flux and lower temperature change for the metal, because the metal has less thermal resistance than the plastic.

Question 10 tested the concept of radiation for different emissivity and reflectivity values of two different surfaces at the same temperature. During the workshop on radiations, students measured heat flux from the black plate and felt that it was warmer than the low emissivity plate, even though the two plates were heated to the same temperature. While 85% of the students in the experimental class answered this question correctly, only 59% of the control group got it right.

The last two questions that showed statistically significant differences were 16 and 17 and had to do with heat transfer in a heated pipe maintained at a constant temperature hotter than the incoming water. The two questions asked what would happen to the average temperature of the water at the exit and overall heat transfer to the water, respectively, if the mass flow rate was doubled. This question, much like the radiation one, stresses the different nature of heat flux and temperature. While the total heat transfer to the water will increase with an increased flow rate, the outlet temperature will decrease. In workshops 6 and 7, the students directly measured the heat flux and temperature on the inner and outer surfaces of a metal pipe being cooled on the outside by a fan and having hot air flow through it. In addition, they felt the surface temperature down the length of the pipe.

Aside from the concept inventory scores, it is worth looking at how the students performed in the class in general based on their quiz and test scores. Unlike the concept inventory scores, the grades on the quizzes and tests showed no significant difference between the experimental and the control group. Certain test questions were even intended to focus more on the fundamental principles than simply solving problems, but the scores on such questions failed to show any significant difference between the two sections. Students do not seem to connect their conceptual knowledge with their problem solving.

A survey was given to the students in the experimental section at the end of the semester to gauge what they thought of the workshops from a qualitative standpoint. Fifty-four students responded. Looking at the survey results as a whole, the general consensus was very positive. Many students mentioned the benefit of being able to see and feel the modes of heat transfer to apply the concepts they learned in class into physical experiments. Students felt they were able to remember the actual workshops better than the traditional lectures themselves. They also pointed out the benefit of being guided through the workshops by the teaching assistants/instructors, and they liked how the workshops involved real-world scenarios.

Looking at what the students disliked about the workshops, some of the students pointed out that some of the number crunching was tedious and excessive when they were required to calculate values based on their measurements. Students also mentioned how they would sometimes get bad or unreasonable values from their data acquisition. This caused them to try and retake the data or to be confused by what was physically happening.

Overall the hands-on, challenge-based workshops in the first year did a good job addressing the main misconceptions in heat transfer and helped the students to improve their understanding of the concepts. Looking at the statistically significant results in particular, it is worth noting that the concept questions showing significant difference relate to the topics that had two workshops made for them as opposed to one. The students had two workshops on conduction and thermal resistance, two on radiation, and two on internal flow. These results stress the importance of not only hands-on, active learning, but also of repetition of a topic to better engrain the concept. The workshops failed, however, in helping the students to apply the concepts for solving problems on their quizzes and tests. The students who took the workshops seemed to be unable to translate the concepts they learned into solving traditionally formulated heat transfer problem sets. This is an important conclusion that will be addressed in future work.

The retention of the students' conceptual understanding was tested in classes in the following semester, after summer break. Seven concept questions (similar to previous concept tests, but not repeating) were given as a quiz to all of the students who had taken heat transfer the previous year. The quiz was given on their first day of class in the Fall semester of 2014 and they took the heat transfer class in the spring semester of that same year or earlier. This left a gap of at least 3 months since the students had last taken the heat transfer class. These students came from five different sections of heat transfer taught by four different professors, including the control group and the experimental group who took the class with the workshops.

The results of the quiz showed only a slight difference in the total scores between all the sections with the experimental workshop section attaining the highest score. The bar chart showing the total scores between all of the sections is shown in Fig. 3. None of these results, however, yielded any significant difference and not a single section averaged above 3.4 out of 7 on the quiz (48.6%). The first six questions on the concept retention quiz were multiple choice questions focusing on concepts 1, 2, 3, 4, and 6 from Table 1. None of these questions yielded any statistically significant differences comparing the experimental section with the other sections using an alpha value of 0.05.

The seventh question was a simple surface energy balance problem involving conduction, convection, and radiation with a quantitative answer. Students needed to account for the direction and magnitude of the specified heat fluxes and determine the appropriate surface temperature. No “plug and chug” equation was provided. As shown in Fig. 4, a much higher percentage of students from two of the sections answered this question correctly than the other sections. However, less than one-half of the students retained this fundamental skill over the summer. Most of those who missed this question did not even attempt to perform an energy balance using a control volume. The two sections that performed the best were the experimental and control groups taught by the professor who gave the workshops. In these classes, a strong emphasis was placed on the concept of modeling and using an energy balance versus calculating numbers from a multitude of equations. This focus on fundamental concepts (in this case, the concept of using an energy balance) appears to be vital to how well students can retain what they learned.

The second year involved restructuring the workshops to focus more on data analysis and less on data acquisition. The number of workshops was reduced from twelve to six to reduce the teaching load requirements. Each workshop replaced one of the assigned homework problems the week given and appeared as a 1-h additional assignment in lab. Consequently, the experimental section returned to the standard three-lecture a week format. Table 5 lists a brief summary of all six workshops given to the students throughout the semester. Videos were created to guide the students through the experiment and demonstrate the data acquisition. The students then followed along with the video and performed the same experiment but watched the data being taken on the video itself instead of taking the data themselves.

The workshops still included the five-step challenge-based instruction method just as in the previous year, but the challenge-based approach was relaxed to help the students focus more on what was physically happening rather than making sure they were performing the experiment correctly. It should be noted that in each workshop, the students were required to physically feel the different heat transfer processes taking place and fully interact with the physical equipment in the lab. The concept numbers are included in parenthesis and match up with the concepts listed in Table 1.

Before the first workshop, a video was provided to the students which introduced the heat flux sensors and thermocouples and how to use them to take data. Sample screen shots from this introductory video are provided in Fig. 5.

In addition, for this year, a step was added that showed a diagram of a control volume and thermal resistance for the physical setup in each workshop. These were provided to help the students relate their experiment with the problem solving process and the very important concept of using a control volume and energy balance. Example control volume and thermal resistance diagrams for the first workshop are displayed in Fig. 6.

The videos with each workshop showed someone doing the experiment with a split screen showing real time plots of the temperature and heat flux measurements. The video included audio with subtitles to guide students through the process. With this method, the students were able to feel the materials, while watching the real-time plots without getting concerned with how their data looked. The students then answered some questions about the plots which were geared to help them think about the concepts. The last step was a reflection step where the students were asked questions to help them think about what they did.

Just as in the previous year, two sections of the junior level heat transfer course were used for analysis. Both sections were taught back-to-back with the same instructor using the same quizzes and tests. The second class was given traditional lectures and was used as the control group consisting of 69 students, while the first class was the experimental section consisting of 65 students which was given the same lectures along with the six hands-on workshops. Instead of having a workshop every week like in the first year, a workshop was taught every two to three weeks throughout the semester. It took the place of one of the homework assignments to keep the same required workload. A short concept inventory quiz consisting of six questions was given to all of the students in both sections at the beginning of the semester before the first lecture. These questions were hand-picked to include a few that tested the six concepts from Table 1 and a few that were more specific to thermodynamics in order to act as a control.

To gauge the progress of the students' conceptual understanding for both the experimental and control groups throughout the semester, certain concept-specific questions were also given on tests and quizzes during the course. The questions always had to do with concepts from a specific workshop and were asked on quizzes the week after the workshop was performed. The two tests for the course consisted of five concept questions in addition to textbook style problems that the students needed to solve.

As a final evaluation, instead of giving a stand-alone concept quiz at the end of the semester like in the previous year, ten concept questions were given on the final exam. These questions included a few from the previous year's 19 question concept test as well as new questions more focused on concepts specific to the course topics and workshops.

An initial concept inventory quiz given at the beginning of the course again showed that the two sections were nearly equal in terms of their misconceptions. Four individual quizzes during the semester had at least one concept-specific question relating to the topic and workshop being taught. Each quiz was taken 3–4 days after the workshop on that specific quiz topic was performed. None of the concept specific questions on the quizzes yielded statistically significant differences between the groups.

Two tests were given during the course with five concept questions on each. On the first test the experimental group with the workshops did significantly better on one of the questions, which related to the thermal resistances emphasized in each of the workshops. On the second test, however, the control group did significantly better than the experimental group on one of the questions. There did not appear to be an overall effect of the workshops as in the previous year.

At the end of the semester, nine concept questions were given on the final exam for both the experimental and control groups testing all six of the critical heat transfer concepts. Of the nine questions, one was focused on the topic of radiation, two were about internal flow, and six focused on ideas of thermal resistance and the difference between heat and temperature. The question on radiation (question 1) was the only one that showed a statistically significant difference between the groups. The results from this question, along with the average scores of the nine questions total are shown in Table 6. The performance is surprisingly low, but typical for concept questions for current engineering students.

Unlike the previous year, the average scores on the final concept assessment for the experimental section were not significantly higher than the control group as seen from the averages and p-value. The workshops had little if any effect on the students' performance and conceptual understanding.

One reason for this could be attributed to the fact that the videos placed the students in a passive state of mind. In the first year, the students were forced to use the data acquisition software, take the data, and perform the experiment. Their data directly reflected how well they performed the experiment. This cause and effect method forced the students to think more about the plots and data being displayed in real time. If they made a mistake in the experiment, they would be forced to think about why certain heat flux or temperature values did not look right, thinking back to the underlying concepts. In the second year, the videos were mistake free. The cause and effect structure was removed since the students were no longer taking the data. They just passively watched the videos as if they were just another lecture. This passive mindset disengaged the students and took away from the whole hands-on experience

Just as in the first year, a survey was given to the students to gauge the benefit of the workshops from a qualitative standpoint. The same survey was used as in the previous year, but a different format resulted in fewer students completing the survey. Of the 16 students who took the survey, 15 students mentioned that the workshops were helpful in understanding the material, five believed they learned the concepts better during the actual workshop than the lecture, 12 believed the workshop sessions contributed significantly to their understanding of heat transfer concepts, 13 believed the hands-on nature of the workshops contributed significantly to their learning of the concepts, and 14 would recommend the workshops be offered to future versions of the class. So while the results from the concept questions reveal otherwise, the students believed that the workshops were beneficial to their understanding of the difficult concepts. This is worth noting because it is possible that the workshops have intrinsic value that cannot easily be measured quantitatively. While the students' problem solving skills can be assessed through textbook test problems linking to their homework and examples in class, conceptual understanding is much harder to assess. It is possible that the concept questions or even the concepts themselves do not reflect how students think about heat and temperature. In addition, if the students have positive memories of the course, this will help guide them to consider this field of interest, particularly when considering graduate school and working in heat transfer laboratories.

The addition of hands-on workshops for undergraduate students in Mechanical Engineering heat transfer classes has been demonstrated to improve their conceptual understanding of some of the material. This was true when the students were required to perform the actual experiments and record the data themselves. Conversely, the use of video-enhanced instruction did not provide the effect even though the students thought that it helped their understanding of the material. The students particularly liked being able to visually observe and measure heat transfer. In addition, repetition of the workshop topics seemed to help the students overcome their initial misconceptions. The problem solving skills of the students, however, were not improved with the current format of the workshops. The students appeared to be unable to link the concepts they learned to the problems they had to solve on tests and quizzes. Research needs to continue to find ways to help students combine conceptual understanding with problem-solving skills and to retain the gains in understanding after they have finished taking the class. One promising possibility to test is to provide each student individually with their own workshop heat flux hardware for the entire course. This allows each student to record measurements on their own computer as part of their normal homework, potentially combining the hands-on benefits with their own problem solving.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

• Directorate for Education and Human Resources, National Science Foundation under the Transforming Undergraduate Education in Science, Technology, Engineering and Mathematics (TUES) program (1254006).