{"id":2364,"date":"2020-05-12T01:30:19","date_gmt":"2020-05-12T01:30:19","guid":{"rendered":"http:\/\/hets.org\/ejournal\/?p=2364"},"modified":"2020-05-13T15:12:47","modified_gmt":"2020-05-13T15:12:47","slug":"mechanical-engineering-students-struggles-with-units-of-measure","status":"publish","type":"post","link":"https:\/\/hets.org\/ejournal\/mechanical-engineering-students-struggles-with-units-of-measure\/","title":{"rendered":"Mechanical engineering students\u2019 struggles with units of measure"},"content":{"rendered":"

By: Juan C. Morales Brignac, Ph.D., P.E.<\/a>,
\nMechanical Engineering Department Head
\nUniversidad Ana G. M\u00e9ndez, Gurabo Campus<\/p>\n

Abstract<\/strong><\/p>\n

The correct use of units of measure is a critical and fundamental skill that is often taken for granted.\u00a0 The fact that units are taught in high school leads to the expectation that university freshmen master these skills.\u00a0 Unfortunately, faculty often observe that students struggle with units.\u00a0 Although the literature is limited on the nature and extent of students\u2019 struggles with units, it is shown that all of it, without exception, points to a pervasive problem in STEM programs.\u00a0 This paper contributes to the literature by exploring the evolution in the performance of N=21 senior mechanical engineering students enrolled during the Fall 2019 semester in a 3-credit-hour, required course that prepares them for the NCEES Fundamentals of Engineering (FE) Exam.\u00a0 Students were given a unit-conversion quiz at the beginning each class session.\u00a0 It was corrected on the spot, with a score of either 1 or 0, followed by a discussion of the quiz.\u00a0 A score of 1 required a perfect solution.\u00a0 The performance on each quiz guided the decision on the content of future quizzes.\u00a0 The results show that 15 quizzes were required to get 100% of the students to push through their difficulties and achieve expertise.\u00a0 The paper includes the content of the quizzes, the solutions, the aggregated results for each quiz, and the nature of the mistakes.\u00a0 It also includes an algorithm to conduct unit conversions and a visualization scheme to use tables of unit conversions and tables of metric prefixes that were developed during the project.\u00a0 These greatly assisted students in overcoming their difficulties. \u00a0The experiment was repeated the following semester (Spring 2020, N=27) to test the effectiveness of an algorithm and visualization scheme developed by the author during the Fall 2019 semester.\u00a0 The time to achieve expertise was reduced to one third (5 quizzes vs 15 for the original group), thus confirming its merit.\u00a0 Part of the discussion section focuses on the benefit of the Scholarship of Teaching and Learning (SoTL) movement, of which this paper is an example, and its use in the ABET-required processes of outcomes assessment and continuous improvement. The paper also includes suggestions for further research.<\/p>\n

<\/p>\n

Introduction<\/strong><\/p>\n

The process of learning units of measures, particularly unit conversions, seems rather painless when compared to the level of frustration students typically undergo while trying to master Newton\u2019s laws of motion, the laws of thermodynamics, and the sequence of calculus courses, all of which are included in any ABET-accredited mechanical engineering undergraduate curriculum.\u00a0 The reason is because unit conversions only require low levels of math skills: simple knowledge of multiplication and division, along with addition and subtraction in some cases, such as converting temperature units. \u00a0Most engineering faculty expect students to absolutely master unit conversions due to its apparent lack of difficulty and because unit conversions are taught in high school. \u00a0However, in the author\u2019s experience, students do not master this skill.\u00a0 Although there is little research into the nature and extent of the struggles with units, all the available literature points to a pervasive problem that plagues engineering curricula, including senior students.\u00a0 The literature review section summarizes these findings.<\/p>\n

The lack of mastery of units of measure is worrisome given the fundamental and critical nature that units play in engineering projects.\u00a0 Mistakes with units are often grave and costly as evidenced by, for example, the loss of the $125 million NASA Mars Climate Orbiter spacecraft in 1999 [1].\u00a0 One team in the project used English units of measurement while the other team used the metric system for a key spacecraft operation.\u00a0 The spacecraft missed its intended orbit and disintegrated in Mars\u2019 atmosphere. \u00a0Similarly, in 1983 the fuel ran out midflight on an Air Canada Boeing 767 after a metric conversion error [2, 3].\u00a0 The error was caused by a confusion between pounds and kilograms and the plane took off with less than half the expected amount of fuel.\u00a0 The error was combined with the fact that the fuel gauges of the plane were inoperative.\u00a0 The pilots, who knew of the problem, worked around it and took off anyways. \u00a0Fortunately, the pilot was able to land the plane without casualties but with damages to the aircraft. \u00a0Regulations now require that fuel gauges be functional before flying.\u00a0 The changes in regulations solved half of the problem.\u00a0 The other half, a potential mistake with units, is unfortunately still very much present.<\/p>\n

It is also worrisome because, how can we expect students to master higher level engineering concepts if they exhibit a critical weakness in the most basic of the fundamentals?\u00a0 For example, students may be overwhelmed by the application of the ideal gas law in a thermodynamics course just because they are not able to input values with consistent units.\u00a0 Although the math is relatively simple (Algebra I level), ensuring that the units are consistent is apparently more difficult than many people would think.<\/p>\n

Viewed from a different perspective, this worrisome state may be turned into an excellent opportunity to conduct a wide variety of educational research projects on units of measure.\u00a0 Units combine both math and science and it does so at a relatively elementary level.\u00a0 Therefore, the difficulties in weaving together math and science can be explored at a level that is not very complicated.\u00a0 The science issues arise from the fact that the values obtained from scientific formulas (or measurements) are meaningless without units.\u00a0 Even if a quantity is non-dimensional, such as the Reynolds number used in fluid mechanics, it is still crucial for an engineer or scientist to know that the quantity is a pure number with no units attached to it.\u00a0\u00a0 When examined from a math perspective, the process of converting units is a straightforward mathematical operation at the Algebra I level.\u00a0 The potential gain from resolving this issue is immense because, if solved early, students could enjoy a much richer educational experience. \u00a0Students may still earn a few low grades in some courses due to the difficulty of the topics, but in terms of units, the students\u2019 performance should always be impeccable.<\/p>\n

This paper documents an experiment conducted in the Fall 2019 semester that focused specifically on the skill of converting units. No context nor applications were provided. \u00a0Students were simply given a quantity with specified units and were told to convert the quantity to another unit; for example, convert a speed of 65 miles per hour to meters per second.\u00a0 The objective was to isolate the skill of conversion of units (straightforward math skill) from other skills related to science such as a unit check of a specific formula.\u00a0 The students were mechanical engineering seniors enrolled in a required training course for the NCEES Fundamentals of Engineering Exam (FE Exam).\u00a0 The FE Exam only allows a calculator and a 250-page reference handbook [4].\u00a0 The handbook includes a table of metric prefixes (p. 1) and a table of unit conversions (p. 2).\u00a0 As the page numbers suggest, the examinees must master the fundamental skill of using metric prefixes and converting units before all others, if they expect to pass the FE Exam.\u00a0 The methodology section provides the full details of the experiment.<\/p>\n

The experiment was repeated the following semester (Spring 2020) to test the effectiveness of a conversion algorithm and a visualization scheme for tables of unit conversions and tables of metric prefixes.\u00a0 These were developed in the process of trying to assist students in achieving expertise and are presented in the Methodology section.\u00a0 Results for both are included.<\/p>\n

This paper includes the following sections: Abstract, Introduction, Research Questions, Literature Review, Methodology, Results, Discussion, Limitations, Further Research, and Conclusions.<\/p>\n

 <\/p>\n

Research Questions<\/strong><\/p>\n

    \n
  1. What is the extent of the struggles with unit conversions of mechanical engineering seniors enrolled in the course ENGI 478 Fundamentals of Engineering (Fall 2019)?<\/li>\n
  2. What is the nature of the mistakes made by students while converting units?<\/li>\n
  3. Can 100% of the students achieve mastery at converting units before the end of the semester? If so, how long does it take?<\/li>\n
  4. [Add on question after obtaining the results of the Fall 2019 semester.] If the conversion algorithm and visualization scheme of tables of conversions developed in the Fall 2019 semester are presented on the first day of class of the Spring 2020 semester (during the discussion of the first quiz), will it reduce the time to achieve mastery?<\/li>\n<\/ol>\n

     <\/p>\n

    Literature review<\/strong><\/p>\n

    Dorko and Speer (2015) [5] investigated unit use in computations of area and volume in a Calculus I course.\u00a0 It sampled N=198 students from a large public northeastern university in the USA.\u00a0 They found that 73% of the students gave incorrect units for at least one task.<\/p>\n

    Dorko and Speer also mention that there is little research into the nature and extent of students\u2019 struggles with units or why they exist; therefore, most of the evidence of the struggles is anecdotical.\u00a0 They cite four studies that evidence student difficulties with units in differential equations, physics and chemistry.<\/p>\n

    Redish (1997) [6] explores several aspects of student difficulties with math in the context of physics.\u00a0 Redish recognizes that students tend to want to put numbers into equations right away thus losing the possibility of doing unit checks for consistency (p. 10).\u00a0 On a similar line, Redish also points out the failure of many students to be able to parse equations, i.e., the ability to subdivide an equation into parts, to identify each of the parts, and to figure out their relations to each other.\u00a0 Therefore, if a student does not understand the equation immediately, they have no way of figuring out how to read it (p. 13).\u00a0 Also, many students fail to understand the role of mathematics as representing physical relations (p. 23).<\/p>\n

    Rowland (2006) [7] explored difficulties with units in a differential equations class by using quizzes.\u00a0 Only a few students were able to realize that the units of each term in the differential equation had to be the same.\u00a0 Also, only a few students were able to determine the units of a proportionality factor in a simple equation.\u00a0 He recommends instructors to not take the units knowledge for granted and that units be included explicitly in instruction.<\/p>\n

     <\/p>\n

    Saitta, Gittings and Geiger (2011) [8] report on an activity in a first-semester general chemistry course in which dimensional analysis was used as a tool to keep track of units and to guide students through calculations.\u00a0 The activity was motivated by their observations that many students have not mastered unit conversions by the time they enter college.<\/p>\n

     <\/p>\n

    Mikula and Heckler (2013) [9] conducted extensive testing and interviews of sophomore, junior, and senior engineering students at The Ohio State University and found that students struggle with many \u201cessential skills\u201d that were prerequisites, and that little to no instruction time was spent on them.\u00a0 Among these skills were dimensional analysis, using metric prefixes for various conversions, and operating equations when given variables in mixed units.\u00a0 They conducted an online training activity that, except for interpreting log plots and log scales, saw \u201clittle and insufficient improvement as a result of training, despite the basic nature of the skills\u201d.<\/p>\n

     <\/p>\n

    Dincer and Osmanoglu (2018) [10] administered a 14-question exam to n=73 prospective science teachers to examine their knowledge with unit conversions.\u00a0 The exam covered metric units for length, area, volume and mass.\u00a0 The findings indicated that \u201cthe performance was not satisfying in general\u201d.\u00a0 They also report that the major difficulties were related to the metric prefixes, i.e., converting gram to microgram, dm3<\/sup> into mm3<\/sup>, etc.<\/p>\n

     <\/p>\n

    Nguyen and Rebello (2011) [11] uncovered difficulties with units while conducting an experiment to determine the specific types of difficulties students might have with different kinds of representations of classical mechanics problems.\u00a0 The representations were of three types: all numerical, numerical and some graphical information, or numerical and some functional relationship.\u00a0 The issue of using wrong units was categorized as \u201cDifficulty with physical quantities\u201d in the article (p. 561).\u00a0\u00a0 The authors do not delve deeply into the difficulties with units in this article since their objective was to only develop a panoramic view of the difficulties.<\/p>\n

     <\/p>\n

    Although the number of articles is limited, all of them, without exception, clearly show that many students are confronting difficulties with units.\u00a0 It is a pervasive problem in STEM education.\u00a0 This paper aims to fill a gap in the literature by looking at the extent and nature of the mistakes, and by striving to get 100% of the students to push through their difficulties and achieve mastery in converting units.<\/p>\n

     <\/p>\n

    Methodology<\/strong><\/p>\n

    The experiments took place in ENGI 478 Fundamentals of Engineering, a required course for all mechanical engineering students at a private university in the Central-East region of Puerto Rico. \u00a0The goal of the course is to train students to pass the NCEES Fundamentals of Engineering Exam (FE Exam).\u00a0 The number of participants was N = 21 (Fall 2019) and N=27 (Spring 2020).\u00a0 The author is the instructor of the course.<\/p>\n

    In the Fall of 2019, a quiz on unit conversions was given at the beginning of each class, starting on day one of the semester.\u00a0 The students\u2019 performance in the first quiz provided a first glimpse at the answer to research question 1 (what is the level of mastery of students in converting units?).\u00a0 The total number of quizzes and their exact content was not preordained because it depended on the third research question (how long does it take for all students to achieve mastery?). \u00a0The students were told that daily quizzes would stop once 100% of the students showed mastery of conversion of units. \u00a0In terms of the quiz content, the performance in previous quizzes guided the decision on the content of future quizzes.\u00a0 This freedom allowed the author to focus on observed areas of difficulty (for example, the use of metric prefixes) and train the students until they resolved the issues.<\/p>\n

    A total of 15 quizzes, presented in Table 1, were required to achieve mastery of unit conversions.\u00a0 The procedure consisted of writing the quiz question on the whiteboard at the beginning of class and students answered it individually in their notebooks.\u00a0 The score on the quiz was either one or zero, which simulated the FE Exam methodology of not awarding partial credit.\u00a0 To earn a score of 1, the performance had to be perfect and the quiz completed within 3 minutes, which is the average time required to solve an FE Exam problem.\u00a0 The author walked around the classroom, observed what each of the students was doing, and scored the quiz on the spot.\u00a0 The author then solved the problem on the whiteboard and discussed errors he had observed while walking around the classroom.\u00a0 The entire sequence of events took approximately 15 minutes per quiz.\u00a0 The solutions to the 15 quizzes are given in Table 2.<\/p>\n

    The second experiment (subsequent semester, Spring 2020) used the same quizzes.<\/p>\n

    \"\"<\/a>\"\"<\/a><\/p>\n

    The author presented the process of conversion of units as a systematic algorithm that ensures consistency and reduces the potential for errors.\u00a0 The steps for the algorithm are explicitly shown below in Table 3.\u00a0 The steps are described in the left column and an example is provided on the right column (convert 40 ft\/s to m\/s).\u00a0 The solutions to the 15 quizzes shown in Table 2 use the algorithm.<\/p>\n

    \"\"<\/a><\/p>\n

    Results<\/strong><\/p>\n

    The results of the quizzes are provided in Fig. 1.\u00a0 The horizontal axis represents each of the 15 quizzes.\u00a0 The vertical axis provides the percentage of students that answered the question perfectly.\u00a0 The figure also includes a trend line (dotted blue line) which is a linear regression calculated with Excel.\u00a0 The legend includes the answers to all the questions as a quick reminder of the quiz content.\u00a0 Table 4 summarizes the errors committed by the students.<\/p>\n

     <\/p>\n

    \"\"<\/a><\/p>\n

    Fig. 1.\u00a0 Students\u2019 performance in the 15 quizzes required to achieve expertise (Fall 2019)<\/strong><\/p>\n

    \"\"<\/a><\/p>\n

    \u00a0<\/strong><\/p>\n

    Tab<\/strong><\/p>\n

    The results for the second experiment conducted the subsequent semester (Spring 2020) are shown in Fig. 2.\u00a0 The Fall 2019 group results are also shown to facilitate the comparison.<\/p>\n

    \"\"<\/a><\/p>\n

    Fig. 2.\u00a0 Spring 2020 students\u2019 performance in the 5 quizzes required to achieve expertise.\u00a0 The results of the Fall 2019 group are included to facilitate a comparison between the two groups.<\/strong><\/p>\n

     <\/p>\n

    Discussion<\/strong><\/p>\n

    (Fall 2019 Group) Experience throughout the 15 quizzes<\/em><\/p>\n

    In general, the trend line in Fig. 1 shows that the performance improved with respect to time.\u00a0 There were some issues throughout the experience but, by the last three quizzes, almost everyone had mastered the skill.\u00a0 Perfection was achieved in the last quiz (#15).\u00a0 The issues experienced throughout the 15 quizzes are discussed below.<\/p>\n

    The response to Q1, the first quiz (convert 65 mph to m\/s), immediately diagnosed that students were struggling with units.\u00a0 Only 55.6% of the students were able to answer Q1 correctly.\u00a0\u00a0 In addition, seven of the eleven error types were committed in this first quiz (the first 7 items in Table 4).\u00a0 With respect to the first research question (the extent of the struggle), the answer is that approximately 50% of the students in this class struggled with units in the first day of class.<\/p>\n

    Q2 (convert 1 MPa to psi) was selected because it included the two preferred units for \u201cstress\u201d (MPa and psi), as used in machine design.\u00a0 Q2 was also the first instance in which the use of metric prefixes was required.\u00a0 The performance dropped to 20% and uncovered the issue of struggles with metric prefixes (see items 8, 9 and 10 in Table 4).<\/p>\n

    Q3 delved deeper into the nature of the potential errors by requiring the conversion of volumetric units.\u00a0 The performance dropped even further to 16.7%.\u00a0 The most common error was that students did not cube the conversion factor (item 11 in Table 4).\u00a0 In addition, many students once again showed difficulties with the metric prefixes.\u00a0 The author observed that most students had difficulties in part 3d which required a conversion to cubic micrometers.<\/p>\n

    In Q4 (convert 40 mph to Gm\/s) students were once again pressed to deal with the issue of metric prefixes.\u00a0 The response was the lowest during the semester: 12.5%.\u00a0 At this point, the author realized that a stronger intervention was required and taught consistency to students by visualizing the tables provided by the NCEES in a different manner.\u00a0 The different visualization scheme is provided later in the paper as figures 2 through 5.<\/p>\n

    Q5 (convert 3 ft to nm) was a turning point in students\u2019 performance.\u00a0 It once again pressed them with the issue of metric prefixes and this time, 73.7% of the students answered correctly.\u00a0 The lecture on visualizing differently the NCEES tables seemed to influence students strongly.\u00a0 They started becoming consistent and systematic and, therefore, less error prone.<\/p>\n

    Q6 (convert 3 hp to \u03bcW) once again asked students to perform with metric prefixes but used units of power for the first time.\u00a0 The response was a more respectable, yet insufficient, 66.7% correct responses.<\/p>\n

    Q7 (convert 916 mbar to hPa and then to inches of mercury) included units of pressure used in weather reporting, familiar to all in Puerto Rico due to the frequent occurrence of hurricanes.\u00a0 Also, the hPa unit required the use of metric prefixes.\u00a0 Only 42.1% of the class answered it correctly.\u00a0 The drop in performance was mostly due to their inability to find a suitable factor to convert to inches of mercury.\u00a0 This is further discussed within item 2 in Table 4.<\/p>\n

    Q8 through Q12 continued pressing on the issue of metric prefixes with a variety of units used throughout mechanical engineering.\u00a0 Some quizzes required conversions into unusual units as a training exercise to ensure that they could convert units.\u00a0 The number of correct responses varied as can be observed in Fig. 1.<\/p>\n

    Q13 (convert 200 ft.lb to hJ) finally obtained a class response above 90% correct (94.7%).\u00a0 Q14 (convert 300 gpm to PL\/das) dropped to 84.2% but, finally, in Q15 (convert 6 ft2<\/sup> to cm2<\/sup>), a perfect response of 100% was achieved.<\/p>\n

     <\/p>\n

    Tables in the NCEES Handbook<\/em><\/p>\n

    The tables provided in pages 1 and 2 of the NCEES handbook (metric prefixes and unit conversions, respectively) were confusing to students.\u00a0 Fig. 3 shows part of the unit conversion table, including the heading.<\/p>\n

    \"\"<\/a><\/p>\n

    Fig. 3.\u00a0 Part of the conversion table given in NCEES handbook [4, p.2].\u00a0 It includes the headings \u201cMultiply\u201d, \u201cBy\u201d, and \u201cTo Obtain\u201d which favors a left-to-right unit conversion and created some confusion.<\/strong><\/p>\n

     <\/p>\n

    The format of Fig. 3 is useful if one, and only one, left-to-right, direct conversion is required; for example, convert from joule to Btu.\u00a0 If the conversion direction is reversed, from right-to-left (Btu to joule), the examinee must first decipher that they need to divide instead of multiply.\u00a0 This does not seem complicated; however, it requires additional thought and creates a source for errors. \u00a0\u00a0Also, in cases in which more than one conversion step is required, this format does not line up properly with the algorithm for converting units presented in Table 3.<\/p>\n

    It would be clearer and more useful to have a table that simply states the conversion as an equality, as shown below in Fig. 4.<\/p>\n

    \"\"<\/a><\/p>\n

     <\/p>\n

    Fig. 4.\u00a0 Proposed conversion table.\u00a0 It i<\/strong>s very similar to Fig. 3 except that the number \u201c1\u201d has been added as a coefficient in front of all the units on the left column, and an equal sign has been placed between the two factors (both emphasized with ellipses).\u00a0 In addition, the potentially confusing column headings (\u201cMultiply\u201d, \u201cBy\u201d, \u201cTo Obtain\u201d) have been eliminated (compare to Fig. 3).<\/strong><\/p>\n

     <\/p>\n

    With Fig. 4, the only required decision is to determine which side of the conversion belongs in the numerator and which one in the denominator.\u00a0 The algorithm shown previously (Table 3) explains how to make this decision systematically to minimize the potential for errors. \u00a0Also, although the coefficient \u201c1\u201d on the left column seems redundant, it is important to include it explicitly because it provides a magnitude.\u00a0 This lines up with the conversion algorithm which requires that the unit itself and its magnitude be treated separately (see Table 3).<\/p>\n

    The table of prefixes in page 1 of the NCEES handbook may also be similarly improved to minimize the potential for errors.\u00a0 Fig. 5 shows the entire table as it is presented in the handbook.\u00a0 It gives the multiple, the prefix and the symbol.\u00a0 It is valuable information, but students continually made mistakes while using it.\u00a0 It can be easily improved by treating the multiples as conversion factors.\u00a0 Fig. 6 shows such a proposed table.\u00a0 It contains the same information as Fig. 5 but organizes it differently.\u00a0 Fig. 6 is also consistent with Fig. 4 (unit conversions) by having the coefficient \u201c1\u201d on the left side of the equality, and the multiplier as the coefficient on the right side.\u00a0 This consistency in presenting the information was shown to minimize the probability of erring in such a fundamental issue.<\/p>\n

    \"\"<\/a><\/p>\n

     <\/p>\n

    Fig. 5.\u00a0 Metric prefixes table given in the NCEES Handbook [4, p.1].\u00a0 It contains all the necessary information; however, many students were not able to use it correctly.<\/strong><\/p>\n

    \"\"<\/a><\/p>\n

     <\/p>\n

    Fig. 6.\u00a0 Proposed table of metric prefixes.\u00a0 The multiples are presented as conversion factors, so it is analogous to Fig. 4.\u00a0 This visualization scheme assisted students in overcoming their difficulties.<\/strong><\/p>\n

    (Spring 2020 Group) Experience throughout the 5 quizzes<\/em><\/p>\n

    Fig. 2 shows the results of the second experiment.\u00a0 The objective was to answer research question 4, i.e., if the algorithm and visualization scheme are discussed in class after the first quiz, will it shorten the time to achieve mastery?<\/p>\n

    The results show that the time was shortened to one third (5 quizzes vs 15) which is very encouraging.\u00a0 The Spring 2020 group was bigger (N=27 vs N=21) which is even more promising for the algorithm and the visualization scheme of the tables.\u00a0 The improvement in quiz 2 was particularly significant because 90% (vs. 20% in Fall 2019) of the students correctly handled metric prefixes.\u00a0 This quiz was the first one after discussing the visualization schemes (Figs. 4 and 6).<\/p>\n

    However, the results of the first quiz for the Spring 2020 group (77% correct) was significantly higher than the Fall 2019 group (56% correct) which implies that it could be a \u201cbetter\u201d group of students.\u00a0 This may have had an influence in shortening the time to achieve mastery. \u00a0Nevertheless, the consistency involved in using the algorithm and the visualization of the schemes appears to be a step in the right direction for achieving expertise.<\/p>\n

     <\/p>\n

    Time to cover the syllabus<\/em><\/p>\n

    It has been made clear that students overcame their difficulties by providing proper training; however, there was a downside to conducting this research project. \u00a0The time that was spent on the 15 quizzes, and briefly discussing them in class, contributed to a reduction in the amount of material covered in class.\u00a0 Assuming each intervention consumed 15 minutes on average, the total amount of time diverted was equal to 225 minutes (3 hours and 45 minutes).\u00a0 This is equivalent to 8.33% of a typical 45-hour semester course.\u00a0 The third research question was answered but it came at the cost of covering less material. (Can 100% of the students achieve mastery at converting units before the end of the semester? Yes<\/em>.\u00a0 If so, how long does it take? 15 minutes of 15 class sessions for the Fall 2019 group and 15 minutes of 5 class sessions for the Spring 2020 group.<\/em>)<\/p>\n

    The issue of \u201ctime to cover the syllabus\u201d has been identified as a barrier to diffuse engineering education innovations in the classroom (Morales and Prince, 2019) [12] such as problem-based learning and project-based learning.\u00a0 This instance is no different.\u00a0 However, we must ask ourselves, is it worth it?\u00a0 The answer by this author is that it is certainly worth it if expertise can be achieved, as it was in this case.\u00a0 In the case of units, there is ample room to conduct the training at a much lower level, beginning at the high-school level and continuing in the introductory engineering courses.\u00a0 Students should master units before reaching this course.<\/p>\n

     <\/p>\n

    Scholarship of Teaching and Learning (SoTL)<\/em><\/p>\n

    As a final discussion point, the project described in this paper is an example of the movement of Scholarship of Teaching and Learning<\/em> (SoTL) in which post-secondary faculty approach teaching as a form of scholarly work with the goal of improving student learning and educational quality.\u00a0 SoTL starts with a question on student learning.\u00a0 The instructor must then determine how to address the question systematically through the teaching process.\u00a0 The University of Washington offers the following guidelines [13]:<\/p>\n

    Design:<\/u><\/em> What have others done to address similar questions (literature review)?\u00a0 What assignments or other activities can help address your question?<\/em><\/p>\n

    Evidence:<\/u><\/em> What indicators of student learning will be relevant for addressing your question? How can you systematically examine these learning indicators?\u00a0 How will you make sense of the student learning that you observe? How have others examined similar evidence of student learning?<\/em><\/p>\n

    Making it public:<\/u><\/em> Who can provide an informed review or critique of your observations (of successes as well as failures)?\u00a0 How can you make your work available for others to adapt or extend (options include developing course portfolios for others to review, presenting at campus forums or conferences, and writing for publication)?<\/em><\/p>\n

    Using this paper as an application example of the guidelines given above: the \u201cquestions on student learning\u201d that initiate the SoTL activity were posed as \u201cResearch Questions\u201d in this paper; the literature review section includes what others have done, and revealed that the issue of units is a pervasive problem in STEM programs; quizzes were used as the \u201cactivity\u201d that addressed the research questions; the results of the quizzes and direct observations were used as indicators of student learning; the process was made systematic by conducting a daily quiz until 100% of the students mastered the skill of unit conversions; the arguments made throughout this paper \u201cmake sense of the student learning\u201d that was observed; this methodology has not been used previously, to the best knowledge of the author, but the literature review section includes the methodologies used by others; and finally, the results were \u201cmade public\u201d through this publication.\u00a0 In addition, the publication will be shared with the faculty of the mechanical engineering program at this institution.<\/p>\n

    As a bonus, SoTL work offers a complementary deeper path to the outcomes assessment and continuous improvement processes required by ABET, in addition to typical processes which, unfortunately, tend to become perfunctory with time.\u00a0 At this university, SoTL was used for the first time last year to assess ABET outcomes \u201c1\u201d (complex problems), \u201c2\u201d (design – sizing), and \u201c7\u201d (acquire and apply new knowledge) based on a paper whose research questions revolved around the use of sizing existing machinery rather than an abstraction (a machine that is imagined) [14].\u00a0 The main concept is that a real, existing machinery provides a \u201csolution\u201d against which the students (and faculty) can critically compare the sizing results.\u00a0 This allows students to gradually develop expertise before embarking on a creative major design experience (capstone).<\/p>\n

    The results of this paper will be used as a continuous improvement strategy to achieve compliance with ABET outcome \u201c1\u201d (complex problems).\u00a0 An expected continuous improvement strategy for the program is that units will be included explicitly in the learning objectives of several engineering courses (this was also a recommendation by Rowland [7]).\u00a0 The specific courses will soon be chosen by the entire faculty of the department.<\/p>\n

    Hopefully, these examples of SoTL will also provide motivation to the faculty to start using it in their courses.<\/p>\n

     <\/p>\n

    Limitations<\/strong><\/p>\n