## Unit 3-Group Research Report

Daniel Griepp

Zeyad Saleh

Stefanie Reichman

Christina Moawad

5/14/2013

The Examination of Verbal and Problem Solving Skills Demonstrated by Prospective Engineers

## Abstract

Our team of four conducted a research project consisting of a prompt, a mathematical task, and lines to describe the computation of the mathematical task as described in the prompt. Information gathered from the surveys comprised of name, year, gender and major. We gave the worksheets out to willing third and fourth year engineering students in Steinman Building at the City University of New York. We did not begin the research with a direct hypothesis because we could not infer what types of correlations our data would draw. We were mainly interested in trends between explanations of males versus females, and among different majors of engineers. To evaluate the various explanations, we divided them into two categories, general or specific. We did not find any correlations among different engineering majors as to who explained “better” because roughly the same percentages were noticed in each category. We did find a more interesting result, however, in the gender analysis as we found that 80% of women simplified the problem before solving it, 85% of women used the Quotient or Product rule and 85% of female engineers left the problem in a non-simplified format, as opposed to 30% males. We hope to take our study in a different direction by limiting some of the variability we unintentionally allowed for.

## Introduction

Engineers are the inventors, problem solvers, and designers in our society. They are responsible for developing some of the most useful objects we use daily and as a result, we owe the convenience of daily life to them. Because many engineers gravitate towards concepts, ideas, formulas, and math, despite their genius, they are criticized for lacking verbal abilities and social skills. In our project, we hoped to discover how different types of prospective engineers would explain a simple calculus derivative problem in paragraph form and the differences in the way that they solved it. To further examine differences that different prospective engineers would display, we decided to compare the different methods used between male and female prospective engineers. Our prospective engineering student subjects were broken up into 3 groups of Mechanical and Civil, Chemical and Bio-Medical, and Electrical and Computer Engineers. We were interested to learn if different types of engineers would solve and explain the problems differently; we also hypothesized that we would notice a pattern of female engineers explaining how to solve the problems in more detail then the males.

## Methodology

First, we composed a sheet which described a hypothetical situation of a first year calculus student having trouble solving calculus problems such as the one given on our sheet. The prompt asked the participant to solve the problem given, and then describe the solution with words to the first-year student. For control purposes, there were no variations of math problems or written prompts; there was only one math problem and one prompt given to all participants.

To gather our data, we went to the Steinman Engineering Building to find willing 3rd and 4th year prospective engineers that fit into any of our categories. Our members split up on different floors of the Steinman Building to find participants. All prospective engineers were approached randomly and asked what field of engineering and what year they were in. If they met our qualifications, they were asked if they were willing to participate in a five minute study. If they were willing, they would be given our sheet with our prompt and simple derivative. Each subject was given as much time as they needed to solve and explain the problem. All male engineers were approached by males and all female engineers were approached by females. Our goal was to find an equal amount of five engineers in each category totaling thirty engineers: fifteen male and fifteen female.

Once we acquired enough data, we examined the different methods used to solve each problem and the explanatory skills which the prospective engineers demonstrated. We compared the differences and similarities of their technique in the context of different fields of prospective engineers first and then in the context of different genders. All the problems were graded as either incorrect, not simplified, or correct. A problem labeled as “incorrect” was simplified but had a wrong final answer. A problem labeled as “not simplified” was set up as if the person was going to complete it but was not finished or simplified. A problem labeled as “correct” simplified completely and had the correct final answer. Once the problems were graded, all the explanations were categorized as either specific or general. A specific explanation included specific terms used in the problem such as “x.” A general explanation did not include specific terms in the explanation, was relatively short, or just listed the rules which were used to solve the problems. All data was graded and then classified as either general or specific using these methods. This enabled us to consolidate our results and find a correlation between a certain group, either gender or prospective engineer, and their style of writing and problem solving.

## Results

When comparing different engineers in their respective categories, we found that they all seemed to correctly complete, not simplify, and incorrectly do the problem at relatively equal ratios. When comparing the methodology of different engineers, we found that they each seemed to use Quotient/Product Rule and simplify at similar ratios. When we compared the explanations given, we found that 67% of Mechanical and Civil engineers explanations were specific in their explanations while only 22% of Biomedical and Chemical engineers and 11% Computer and Electrical engineers gave such explanations.

When comparing different genders of prospective engineers, we found that male engineers correctly solved the problem 50% of the time while zero female engineers solved the problem correctly. When considering the methods which each males used, we found that 80% simplified the problem before deriving it. When considering the women, we found that 85% of women used the Quotient or Product rule. Additionally, 30% of males left the math problem in a non-simplified format while a 85% of female engineers left the problem in a non-simplified format. When comparing the explanations given with respect to gender, we found that 55% of males explained their work specifically while only 15% of females gave specific explanations.

## Data

Answers(Engineers vs. Engineers):

Mechanical/Civil (15) | Biomedical/Chemical (9) | ~Electrical/Computer (9) | |
---|---|---|---|

Correct | 5 | 3 | 2 |

Not Simplified | 7 | 4 | 4 |

Incorrect | 3 | 2 | 3 |

Methods(Engineers vs. Engineers):

Mechanical/Civil (15) | Biomedical/Chemical (9) | ~Electrical/Computer (9) | |
---|---|---|---|

Quotient/Product Rule | 7 | 4 | 4 |

Simplification | 8 | 5 | 5 |

Explanations(Engineers vs. Engineers):

Mechanical/Civil (15) | Biomedical/Chemical (9) | ~Electrical/Computer (9) | |
---|---|---|---|

General | 5 | 7 | 8 |

Specific | 10 | 2 | 1 |

Answers(Male vs. female):

Male Engineers (20) | Female Engineers (13) | |
---|---|---|

Correct | 10 | 0 |

Not simplified | 6 | 11 |

Incorrect | 4 | 2 |

Methods(Male vs. female):

Male Engineers (20) | Female Engineers (13) | |
---|---|---|

Quotient/Product Rule | 4 | 11 |

Simplification | 16 | 2 |

Explanations(Male vs. female):

~Male Engineers (20) | ~Female Engineers (13) | |

General | 9 | 11 |

Specific | 11 | 2 |

## Discussion

After going through all our results, it was clear that many correlations could be made using our data. The easiest way to discuss these results was by separating them into engineer vs. engineer and then look at the results from the gender differences.

### Engineers vs. Engineers

Going into this project we did not really have a set hypothesis or knew exactly what we were looking for. We were hoping to come up with these as the experiment was being done. From the results we gathered, we can come up with some correlations.

Overall we found similar results in the amount of problems that were graded as correct, incorrect, or not simplified in all three categories of engineers. We found that most people that used the product or quotient rule tended to have answers that were not simplified. This is mainly because this method required a lot of work and terms and it became rather difficult and time consuming to simplify the whole expression. Consequently, students who simplified first and then took the derivative didn’t have the opportunity to be stumped by a long answer that was hard to simplify. In the biomedical and chemical engineer group, 56% percent of the students simplified. 56% of the electrical and computer engineers simplified, and of the mechanical and civil engineer students 53% simplified. Though civil and mechanical engineers ranked lowest as far as simplifying they ranked highest in specific explanations at 67%. The other two categories gave specific explanations 22% of the time for biomedical and chemical engineers and 11% of the time for computer and electrical engineers.

We saw that in the engineering vs. engineering category, there were not any correlations that can be made. All that can be said is that mechanical and civil engineers had more specific explanations. It is not a surprise that civil (and mechanical) engineers did the best with explanations since they are known to do more writing in general than an electrical engineer. While the statistics for the percent simplified was close between groups, there is a much bigger gap in the percentage of explanations between these engineering groups. Therefore something has to be said for the curriculum of civil and mechanical engineering students since it seems that they are the best at explaining things as specifically as possible. What is meant by specific, is that the student’s answer can be used to specifically guide a person through that specific problem. Rather than a nonspecific answer that can really be applied to any differentiation problem. Some key words or terms that we were looking for in the specific answers was “x”’s and equations of sorts.

### Male vs. Female

In this second part of our results, we split up our data based on gender alone. The results we found were quite surprising, and also the opposite of what we were expecting. We originally thought that female engineers would be able to give the most specific explanations. However, our data proved otherwise.

We started by separating the females and males into the number who simplified the problem. This was done using the same measure that we did for engineer vs. engineer. Of this, we found that 80% of males simplified the problem while only 15% of females simplified the problem. As previously stated people who used the quotient or product rule tended to have a much harder problem to later simplify. It seemed that by a vast majority, most women used these rules. Therefore, though some females may have gotten it right, it was not simplified all the way and therefore we don’t know whether or not they would have a correct answer. Men on the other hand tended to right away look for the easiest way of doing it, while the females wanted to stick to the rules.

We saw that more men than women simplified the problem before taking the derivative. We also saw that more men had the correct answer, with 0% of women giving the right answer. Therefore, simplifying a problem will more likely get you to the right answer than by using the quotient/product rule. We also saw that most men who used simplification also gave specific explanations. Of the male subjects, 55% of them gave specific explanations. However, most women who used product/quotient rule, gave a general explanation. Therefore, simplifying the problem can make it easier to write down exactly what you did to answer the problem and will lead to specific explanations. On the other hand, the messy quotient/product rule made it rather difficult to go back to and follow and therefore, forced the engineer to give a general explanation.

## Conclusions

We do recognize that the correlations we were able to draw may vary if our experiment was conducted in a different manor. Through the analysis and breakdown of our results we were able to target these areas to improve for future directions we may choose. One of the main problems we faced in the accumulation of our data was the definite lack of female engineers. Although this issue was foreseen, finding female engineers that fit our criteria was a greater problem then we accounted for. This being the issue, we ended up not having equal number of males and females, but rather relied on percentage. A more accurate experiment would have standardized this aspect, allowing for precise results.

Another problem we faced was the multitude of external variables that affected our research. If we had done a more intensive screening process of our subjects, we would have better understood our results. Through this process we could have correlated a specific survey to a specific person, and with more background we could have been able to provided probable explanations for trends. This was important because not each engineer had the same level of intellect, and without a better screening process, we cannot be sure results were not due to this. Also, the situation the engineer was in at the moment of the quiz varied. Some students were in a hurry, some had class, and some were relaxed at lunch. The state the individual was in could have also affected their performance on completing the task to the best of their abilities.

To improve the experiment we could take many different routes to ensure more accurate results. One plausible measure would be to use a larger variety of prospective engineers from not just City College, but also other universities. We could also involve actual engineers in the respective fields to see if there are any changes in our results as opposed to prospective engineers. Lastly, we could administer the mathematical task and prompt to all of the test subjects at one time, standardizing the state- of-mind the engineer is at the time of completion.