AAEE2018 CONFERENCE Hamilton, New Zealand

Spatial skills and their correlation with engineering problem-solving

Sheryl A. Sorby1; Gavin Duffy2, Norman Loney1, Lance Perez3. 1 University of Cincinnati, 2 Dublin Institute of Technology, 3 University of Nebraska-Lincoln Corresponding Author Email: [email protected]

STRUCTURED ABSTRACT CONTEXT Well-developed spatial skills have been shown to be important to success in engineering and engineering students have the highest spatial skills among those across many college majors. Unfortunately, of all cognitive processes, spatial skills continue to show the most robust gender differences which could contribute to the underrepresentation of women in the engineering profession.

PURPOSE In this research, we examined the spatial skills of students enrolled in a chemical engineering program. We then asked the students to solve a number of typical problems encountered in their studies, to determine if there was a link between scores on a spatial instrument and the number and type of problems solved correctly.

APPROACH The Mental Cutting Test (MCT) was administered in a common 3rd year course for chemical engineering students—Thermodynamics. The test is a timed test that assess a person’s spatial skill level. In a second session, students were given a set of 12 problems to solve. The problems were selected from typical chemical engineering textbooks. Both instruments were scored and statistical analyses were performed on the data.

RESULTS A strong positive correlation (R=0.59, p<0.00001) between spatial skills test scores and the number of problems successfully solved by the students was found. Problems where spatial skills appear to play a role were identified and will be further described in the presentation.

CONCLUSIONS Findings from this research confirm the link between spatial skills and engineering problem-solving. Further research will involve using EEG data to examine the brain activity of students who are low and high visualizers to determine if there are neurological differences between the two groups.

KEYWORDS Problem-solving, gender differences, spatial skills

This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http s://creativecommons.org/licenses/by/4.0/legalcode Context Spatial Skills in Engineering Spatial visualization is defined as the process of apprehending, encoding, and mentally manipulating three-dimensional spatial forms (Carroll, 1993). Tasks related to spatial visualization include the ability to predict how three-dimensional forms correspond to their two- dimensional representations. For example, recognizing a two- dimensional cross-section obtained by slicing a three-dimensional object requires spatial visualization skill. There is evidence that spatial visualization skill predicts course selection and success in physics (Kozhevnikov, Motes, & Hegarty, 2007), chemistry (Wu & Shah, 2004), engineering (Sorby, 2001) and geology (Kali & Orion, 1996; Orion, Ben-Chaim, & Kali, 1997). There is now strong evidence linking spatial skills to success in STEM (Shea, Lubinski, & Benbow, 2001; Wai, Lubinski & Benbow, 2009), creativity and technical innovation (Kell, Lubinski, Benbow & Steiger, 2013) and in computer programming (Jones & Burnett, 2008). A longitudinal study following 400,000 high school students 11+ years later found that adolescent spatial reasoning skills were predictors for choice of STEM majors and careers, above and beyond the effects of verbal and math abilities (Wai, Lubinski, & Benbow, 2009). Spatial ability emerged as a consistent and statistically independent predictor of selecting STEM related courses, graduate study, and other measures of STEM attainment. It is well-documented that the 3-D spatial visualization skills of men are superior to those of women, especially for 3-D mental rotations (Linn & Petersen, 1985; Tartre, 1990; Voyer, Voyer, & Bryden, 1995). More recent studies have found that sex differences in spatial skills persist (Ganley & Vasilyeva, 2011; Tarampi, Heydari, & Hegarty, 2016; Sorby et al, 2013). Geiser, Lehmann, and Eid (2008) found that sex differences existed at all ages between 9 and 23, and that differences increased with age. In an examination of 14 years of data, Veurink and Sorby (2011) found significant gender differences among engineering students for each year. Although it appeared that the gender gap was narrowing slightly over that time period, the gap was never eliminated altogether. In addition to significant gender differences in spatial skills, Levine et al. (2005) found that the spatial skills for students from low Socio-Economic Status (SES) groups were significantly lower compared to those from middle or high SES groups. Casey et al. (2011) also found significant differences in spatial skills, favouring students from affluent SES groups. According to the Children in Poverty report by the Kids Count Data Center in the U. S. (2018), 34% of American Indian, 12% of Asian, 34% of African American, and 28% of Hispanic children are living in poverty, compared to 12% of White children. Thus, minority children are over-represented in the low SES groups, meaning that poorly developed spatial skills for students from low SES backgrounds could have serious implications for improving diversity in STEM, particularly engineering. Sorby has developed the Developing Spatial Thinking (DST) curriculum that consists of a workbook and software that helps students to develop their 3-D spatial skills through funding from the National Science Foundation in the U. S. The one-credit intervention course at the university level that uses this curriculum is aimed at first-year engineering students with weak spatial skills. The spatial skills intervention course has been adopted at a number of colleges of engineering across the U. S. Longitudinal studies have shown the efficacy of the curriculum with the following key outcomes (Sorby & Baartmans, 2000; Gerson et al, 2001; Sorby, 2001; Sorby, 2005; Sorby, 2009): • The spatial skills of the students who participated in the course increased significantly. • Increases were uniform for both the males and the females. • The students who participated in the course went on to earn higher grades in their introductory engineering, calculus, chemistry, computer science, and physics courses. • More students graduated from engineering. This was particularly true for women students. [In one study the engineering graduation rate for women in the intervention was 77% compared to 47% for women not in the intervention.] Sorby’s intervention has shown improved success rates in terms of grades and retention for engineering students who have participated in the course; however, it is unclear what the mechanism is that leads to greater success for these students. One theory is that improved spatial skills leads to improved problem-solving ability. Since problem-solving is central to an engineering education, it seems that improving problem-solving (through spatial skills intervention) could contribute to improvements in overall success. The study outlined in the remainder of this paper is aimed at examining this phenomena in more detail.

Proceedings, AAEE2018, Hamilton, New Zealand Problem-solving Clement (1982) highlighted how apparently simple word algebra problems can be extremely difficult for engineering students to solve. For example, the success rate on the following problem was only 27 %: “Write an equation using the variables C and S to represent the following statement: At Mindy’s restaurant, for every four people who ordered cheesecake, there are five people who ordered strudel. Let C represent the number of cheesecakes and S the number of strudels.” (Clement, 1982, p. 17) Why did over two thirds of the 150 freshman engineering students fail to correctly translate this word statement? Carelessness was considered but Clement ruled this out because he found that a large cohort, approximately two thirds of the incorrect group, provided the same (incorrect) answer. He believed this reflected focused, careful thinking about the problem but a thinking that resulted in a different translation of the word statement. Where the answer should have been 5C = 4S, about half the participants wrote 4C = 5S A result of what Clement labelled as ‘word order matching’. Even when the underlying mathematics is very simple, engineering students can have great difficulty in solving word problems despite careful thinking and analysis. Since then some work on word problem solving in mathematics has focused on its relationship to spatial ability, a primary factor in several models of intelligence and cognition. Hegarty & Kozhevnikov (1999) measured a large and significant correlation (r(31) = .52, p < .01) between a set of math problems and a test of spatial ability among 6th grade boys (12 years old). They also found some evidence to suggest that high spatial ability was associated with the use of schematic spatial representations which facilitated higher rates of success in problem solving. In other words, high spatial students were more adept at creating visualisations from the problem statements that were schematic and accurate and very useful to the problem solution. However, visualisation quality did not account for all of the spatial – problem solving correlation in this and a similar study (Boonen, van Wesel, Jolles, & van der Schoot, 2014) and, for those who teach engineering students, it’s not clear if finding from studies of this age group transfer to engineering students who have passed through several years of adolescent growth and development. We examined the relationship between spatial ability and math problem solving among engineering students. At a large Midwestern university in the U. S. all incoming first-year engineering students are required to take a math placement test (MPT) and the Purdue Spatial Visualization Test: Rotations (PSVT:R; Guay, 1977). The MPT contains 25 questions with multiple choice answers; only one question is presented in the form of a word problem. While a small correlation was measured between the two tests (r(1051) = .21, p < .01) the word problem revealed the largest effect size with spatial ability (Duffy et al, 2017). In another study, we administered several word problems in mathematics to a small sample of teaching assistants at the university and found a large and significant correlation (r(11) = .79, p < .01). Hence, among engineering students there is evidence to suggest a strong relationship between spatial ability and word problem solving in mathematics. Factorial models of intelligence tend to limit the role of spatial ability to tasks associated with the generation and manipulation of visualisations from well-structured images (e.g., Carroll, 1993; Linn & Petersen, 1985; McGee, 1979). However, word problems that do not contain well-structured images also require spatial ability in order to be represented even when visualisation is not necessarily apparent. Thinking about problem scenarios is cognitively challenging and those with a particular cognitive ability profile in which spatial ability is augmented are well suited to such challenges. Many students struggle in this regard; they do not possess a cognitive ability profile that is matched with the cognitive demands of engineering education. In order to better prepare the next generation of engineers we should seek ways to transfer research on spatial cognition into practice to provide students with opportunities to develop not just verbal and mathematical abilities but their spatial abilities too. We believe this will transfer to enhanced performance in a wide range of tasks that not only require visualisation but also require thinking through non-routine problems and forming mental representations from ambiguous problem statements.

Purpose The purpose of the research presented here was to determine if findings from math problem-solving with regards to spatial skills transferred to other engineering disciplines. In particular, we were

Proceedings, AAEE2018, Hamilton, New Zealand interested in the relationship between spatial skills and problem-solving in chemical engineering. A secondary objective of this research project was to identify problems from chemical engineering where spatial skills appeared to play a role. Once appropriate problems have been identified, they can be used in further studies examining the link between spatial skills and chemical engineering problem- solving.

Approach Students enrolled in a 3rd year course in a Chemical Engineering program at the University of Cincinnati were administered a test of spatial cognition, the Mental Cutting Test (MCT; CEEB, 1939). A sample problem from the MCT is given in Figure 1.

Figure 1: Sample Problem from the MCT (Correct Answer is D) Students then solved problems based on concepts learned in a prerequisite course. Some of the problems utilized typical chemical engineering concepts re-framed with “everyday” examples and other problems were taken directly from chemical engineering textbooks. Examples of these two types of problems are given in the following: • One vegetable oil contains 8 % saturated fats and a second oil contains 26 % saturated fats. In making a salad dressing from these two oils how many ounces of the second must be added to 10 ounces of the first in order for the dressing to have 14 % saturated fats. • One thousand kilograms per hour of a mixture of benzene and toluene containing 50% benzene by mass is separated by distillation into two fractions. The mass flow rate of benzene in the top stream is 450 kg/hour and that of toluene in the bottom stream is 475 kg/h. The operation is at steady state. Calculate the component flow rates in the output streams

Results Average score on the MCT were computed and disaggregated by gender and by domestic/international status. Table 1 includes the results from this analysis. The maximum score on the MCT is 25. Average MCT score Group Sample Size Significance (std deviation) 11.48 Overall 63 N.A. (4.74)

12.12 Males 43 (4.55) p=0.0910; 9.95 Cohen’s d=0.46 Females 20 (4.91)

11.87 Domestic 54 (4.59) p=0.0699; 8.78 Cohen’s d=0.64 International 9 (5.04)

Althought gender differences on average MCT scores were not statistically significant at the p=0.05 level, there was a small-medium effect size. Similarly, the difference between domestic and international students on the MCT was not significant, the effect size of the difference was medium. Problem sets were administered during a class period in Thermodynamics, a third-year course in the Chemical Engieering program, but the topics tested in the problems are typically covered in a second- year course in chemical engineering. Since the students were all given the same amount of time, those who were better at problem-solving would likely solve a larger number of problems compared to weaker students. Figure 2 shows the correlation between the number of problems correctly solved and scores on the MCT.

Proceedings, AAEE2018, Hamilton, New Zealand 12

10

8

6

Correctly 4

2 y = 0.2789x + 2.0596 Number of Problems Solved 0 R² = 0.34435 0 5 10 15 20 25 Score on the MCT

Figure 2: Scatter Plot with Results from Chemical Engineering Problems

A strong positive correlation (R=0.59, p<0.00001) between spatial skills test scores and the number of problems successfully solved by the students was found. In addition to the overall performance on the chemical engineering problem-solving, we also examined the individual problems to determine which specific ones were most reliant on spatial skills. In this analysis, the average score on the spatial skills test for the students who answered the problem correctly was computed and compared to the average score for those who go the problem incorrect. Table 2 includes the analysis from this portion of the study.

Table 2. Analysis of individual problems from chemical engineering Problem # Avg MCT n Avg MCT n Incorrect Correct #1 10.42 14 10.11 28 NS #2 9.47 17 10.72 25 NS #3 9.5 4 17.44 9 p<0.0001 #4 9.3 21 12.5 34 p=0.0169 #5 4.8 5 11.88 52 p=0.0014 #6 7.71 7 11.94 47 p=0.0334 #7 11.54 22 15.17 12 p=0.0168 #8 11.14 22 15.43 6 p=0.077 #9 12.0 13 12.58 19 NS #10 11.77 13 13.07 14 NS #11 8.87 8 13.0 24 p=0.0403 #12 12.11 9 14.33 3 NS #13 11.25 4 21.5 2 p=0.0261

As can be seen from the data presented in Table 2, a little less than half of the chosen problems seemed to have a “spatial factor.” For these problems (1, 2, 8, 9, 10, and 12) the spatial skills of the students who got the problems correct were not different from the spatial skill levels of the students who got them incorrect. For reference, the salad oil problem given earlier in this paper is problem #3 in this table and the benzene and toluene problem is problem #4. Problem #9, which did not show a difference in spatial skills between those who got it correct and those who didn’t is given below:

Proceedings, AAEE2018, Hamilton, New Zealand 9. Given the dehydrogenation of ethane in a steady-state continuous reactor where the following reaction

C2H6 →C2H4 +H2

occurs. If one hundred kmol/min of ethane is fed to the reactor, and the molar flow rate of H2 in the product stream is 40 kmol/min, calculate the amounts of C2H6 and C2H4 in the product stream. One significant difference between problem #3 and problem #9 is that chemical reaction equation is given and students who understand the equation can likely pull the information out of the problem itself to “plug” values in as appropriate. Whereas, in problem 3, no equations are given and students must be able to determine which equation to use, how to apply it, and how the information given “fits” into their selected equation.

Conclusion Previous research has shown the importance of well-developed 3-D spatial skills for overall success in engineering, but little work has been accomplished in the specific areas of engineering where spatial skills play a role. Solving ill-defined problems is central to engineering and it appears that spatial skills are important to successfully solving this type of problem. When presented with a problem where an equation is given and students need only to determine which quantities are needed to be input into the equation, students, regardless of spatial skill level, can solve it. However, when students are presented with a problem where they need to determine the relevant equation and also determine how the given quantities are used in the equation, then students who have good spatial skills have a decided advantage over those who do not. Further study is required to determine if these findings are generalizable across other engineering disciplines.

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Proceedings, AAEE2018, Hamilton, New Zealand Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817-835. Wu, H.K & Shah, P. (2004). Exploring visuospatial thinking in chemistry learning. Science Education, 88(3), 465-492. Acknowledgements This material is based upon work supported by the National Science Foundation in the U. S. under grants number DRL-1535307 and DRL-1818758. 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.

Proceedings, AAEE2018, Hamilton, New Zealand