This paper deals with the mathematics courses offered to the engineering students at the United Arab Emirates University (UAEU). The paper focuses essentially on the level of achievement by the students of the outcomes of the mathematics and how this reflects on the satisfaction of the engineering ABEToutcomes. Mapping between the course outcomes of the different math courses offered at UAEU to engineering students and the engineering ABET criteria ((a)–(k)) was made. It is found that most of the ABEToutcomes are to a great extent inline with the outcomes of our mathematics courses. This encourages us to use the achievement of the courses outcomes as an assessment tool for the engineering ABEToutcomes. We considered both direct and indirect assessment tools to assess the level of satisfaction of the math courses outcomes. The performances of the students according to both methods are then used to assess the achievements of the ABEToutcomes. The results generally show very good level of achievement of the outcomes, although few ABEToutcomes were not achieved well according to our performance criteria. Accordingly, we provide some comments and recommendations aiming at the improvement of the program.
In any engineering program mathematics comes as an essential component that every such program must fulfill adequately. Mathematics helps and represents a tool engineering graduates can use to understand and apply engineering concepts. Hence, the graduates of engineering programs must clearly and explicitly demonstrate good ability to apply knowledge of mathematics in the different phases of their engineering study. This is what well recognized accreditation bodies for engineering education strongly and clearly emphasize [
The College of Engineering at the United Arab Emirates University (COEUAEU) is keen to meet international standards in the delivery of their curricula for all departments in the college [
In this paper we try to highlight the experience of math courses in the engineering curricula of the five different departments at the COEUAEU, namely, architectural, chemical and petroleum, civil, electrical, and mechanical engineering, and the level of satisfaction of the outcomes of these courses by the engineering students of these five departments and how these outcomes are linked to the ABET criteria ((a) through (k)). Towards this end, data on the students’ performance in these math courses have been collected and analyzed for three consecutive semesters and discussions and conclusions have been drawn from them. The different assessment tools used to assess the performance of students in these courses and the results collected based on these are also presented and discussed in this paper. Some emphasis is also put on the “students opinion” as an indirect assessment tool and how this can be used as helpful feedback towards the goal of boosting the learning process in these math courses. Hereby the study draws conclusions not only from the direct data collected on students’ performance in the math courses we offer based on exams of different kinds and other course activities such as projects, homework assignments, and quizzes, but also based on the feedback collected from students through surveys conducted at the end of each semester, as part of the assessment tools used in the process. Hereby it is important to see how students judge their level of satisfaction for the courses outcomes, as they see it, aside from the learning assessments mentioned above. This kind of feedback obtained from the students is looked at as a means of improving the way the scientific material is delivered and a feedback to the instructor to ensure that students who at the end and foremost are partners and major constituent in the learning and teaching processes are active and really receiving the doze of material the courses target instilling in them.
The results of this study and the conclusions and recommendations drawn from the analysis of the presented data aim at contributing to the continuing efforts that target keeping up the level of math courses delivery at UAEU at highest level possible, as well as meeting the worldwide well recognized ABET standards. Moreover, as part of our commitment towards the international community, we publicize and share hereby our mathteaching experience with the peers in the field internationally to add to the literature in this vital area and to invite hereby contributions from peers in that direction that are expected to enrich the educational experience at the global level.
The math courses offered at the COEUAEU, are
MATH1110: Calculus I for engineers,
MATH1120: Calculus II for engineers,
MATH2210: differential equations and engineering applications,
MATH2220: linear algebra and engineering applications.
Details on the mapping of the course outcomes for the above courses with the ABET criteria ((a)–(k)) as well as details on the statements of these course outcomes, the outcome assessment tools used in these courses to assess level of satisfaction of the outcomes, data on the level of satisfaction of the course outcomes judged based on the assessment tools adopted are all presented and discussed in the subsequent sections.
The ABET identifies 11 outcomes for engineering programs, and they are listed below:
an ability to apply knowledge of mathematics, science, and engineering,
an ability to design and conduct experiments, as well as to analyze and interpret data,
an ability to design a system, component, or process to meet desired needs,
an ability to function on multidisciplinary teams,
an ability to identify, formulate, and solve engineering problems,
an understanding of professional and ethical responsibility,
an ability to communicate effectively,
the broad education necessary to understand the impact of engineering solutions in a global and societal context,
a recognition of the need and an ability to engage in lifelong learning,
a knowledge of contemporary issues,
an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.
Course outcomes, mapping with ABET and students direct assessment tools for the course MATH1110Calculus I for engineers.
Relevant ABET outcomes  Course outcome number  MATH1110 course outcomes  Assessment tools  

Assignment  Quizzes  Labs  Misc  Exams  
(a), (b), (e)  1  Sketch and analyze the graphs of functions and interpret the results  ✓  ✓  □  □  ✓ 


(a), (e), (k)  2  Find derivatives of different functions  ✓  ✓  □  □  ✓ 


(a), (e), (k)  3  Understand the conceptual foundations of rate of change, slope of tangent line, and their application to engineering problems  ✓  ✓  ✓  □  ✓ 


(a), (c), (e), (k)  4  Learn how the derivatives can be used to model engineering problems  ✓  ✓  ✓  □  ✓ 


(a), (b), (c), (i)  5  Demonstrate ability to think critically in analyzing engineering problems  ✓  □  ✓  □  □ 


(d), (f), (g)  6  Work effectively with others  ✓  □  ✓  □  □ 


(a), (e), (k)  7  Able to integrate (to find the antiderivative of) different functions  ✓  □  □  □  ✓ 


(a), (e), (k)  8  Able to use the integration to find the areas under or between curves, displacements given the accelerations, and work done by a particle or so  ✓  □  □  □  ✓ 
As can be seen from Tables
Course outcomes, mapping with ABET and students direct assessment tools for the course MATH1120Calculus II for engineers.
Relevant ABET outcomes  Course outcome number  MATH1120 course outcomes  Assessment tools  

Assignment  Quizzes  Labs  Misc  Exams  
(a), (b), (c), (i)  1  Show the ability to think critically in analyzing engineering problems  ✓  □  □  □  ✓ 


(a), (e), (k), (b)  2  Parameterize a curve  ✓  □  □  □  ✓ 


(a), (d), (g), (k)  3  Use computers to enhance visualization and solve calculus problems in several variables  ✓  □  □  □  □ 


(a), (e), (k)  4  Understand the properties of vectors and know some of their applications  ✓  □  □  ✓  ✓ 


(a), (b), (e)  5  Identify the equations of common surfaces such as sphere, cone, and paraboloid  □  □  □  ✓  ✓ 


(a), (e), (k)  6  Calculate partial derivatives, the rate of change, and the extrema of function of several variables  ✓  □  □  □  ✓ 


(a), (c), (k)  7  Use multiple integrals to get the areas, volumes, and center of mass for different configurations  ✓  □  □  ✓  ✓ 


(a), (k)  8  Realize which system of coordinates is more convenient to describe a physical situation  □  □  □  ✓  □ 


(a), (e), (k)  9  Calculate line integrals  ✓  □  □  □  ✓ 


(a), (k), (e), (j)  10  Understand the notion of the curl and divergence of a vector field  □  □  □  □  ✓ 
Course outcomes, mapping with ABET and students direct assessment tools for the course MATH2210differential equations and engineering applications.
Relevant ABET outcomes  Course outcome number  MATH2210 course outcomes  Assessment tools  

Assignment  Quizzes  Labs  Misc  Exams  
(a), (e), (j), (k)  1  Analytically solving firstorder differential equations  □  ✓  □  □  ✓ 


(a), (e), (j), (k)  2  Analytically solving second order differential equations both homogenous and nonhomogenous  □  ✓  □  □  ✓ 


(a), (e), (j), (k)  3  Analytically solving differential equations using the Laplace transform  □  ✓  □  □  ✓ 


(a), (c), (e), (k)  4  Modeling thermal systems  □  □  □  □  ✓ 


(a), (c), (e), (k)  5  Modeling translational mechanical systems  □  ✓  □  □  □ 


(a), (c), (e), (k)  6  Modeling rotational mechanical systems  □  □  □  □  ✓ 


(a), (c), (e), (k)  7  Modeling electrical systems  □  ✓  ✓  □  ✓ 


(a), (d), (k)  8  Using MATLAB in the solution and analysis of differential equations  □  □  ✓  □  ✓ 


(a), (d), (k)  9  Using MATLAB in the solution and analysis of transfer functions  □  ✓  □  □  ✓ 


(a), (f), (d), (i)  10  Working and writing a report on a term project  □  □  ✓  □  □ 


(a), (f), (d), (i)  11  Step response analysis  □  □  □  □  ✓ 
Course outcomes, mapping with ABET and students direct assessment tools for the course MATH2220linear algebra and engineering applications.
Relevant ABET outcomes  Course outcome number  MATH2220 course outcomes  Assessment tools  

Assignment  Quizzes  Labs  Misc  Exams  
(a), (e), (j), (k)  1  Find the reduced form, the row and column spaces, and the rank of a given matrix  □  ✓  □  □  □ 


(a), (e), (j), (k)  2  Solve a system of homogeneous or nonhomogeneous linear equations  □  ✓  □  □  ✓ 


(a), (e), (j), (k)  3  Find the inverse of a matrix and the solution of a nonsingular system using determinants  □  ✓  □  □  ✓ 


(a), (e), (j), (k)  4  Find the eigenvalues, eigenvectors and and diagonalize a matrix  □  ✓  □  □  ✓ 


(a), (e), (j), (k)  5  Analyze orthogonal and symmetric matrices  □  ✓  □  □  ✓ 


(a), (e), (j), (k)  6  Analyze power series, exponential, and trigonometric complex functions  □  ✓  □  □  ✓ 


(a), (e), (j), (k)  7  Analyze complex logarithms and powers  □  ✓  □  □  ✓ 


(a), (e), (j), (k)  8  Find the integral of a complex function over a closed path using Cauchy's theorem  □  □  □  □  ✓ 


(a), (e), (j), (k)  9  Find the singularities and analyze the residue theorem  □  □  □  □  ✓ 


(a), (k), (e), (j)  10  Some applications of the residue theorem  □  ✓  □  □  □ 
As can be seen from Tables
The ABET criterion “(h),” which is not mapped to any of our four math courses is related to the broad education necessary to understand the impact of engineering solutions in a global and societal context, and this is something traditionally difficult to fulfill in a math course at this level in the curriculum. Fulfilling this ABET criterion, however, is a very important and essential requirement in the other courses that are more of a basic science nature and in the subsequent parts of the engineering curricula of the different programs in the COE, which students will be exposed to after they get specialized after finishing the required doze of ERU courses.
Moreover, ABET outcome “g” is related to communication skills and it is addressed here in the math courses only at a small scale where it is only mapped at this moment to the first two of our math courses and is assessed in activities like labs which in this context comes under common tutorial and problems solving sessions and homework assignments where in part students use computers to work on some certain task together as a team.
A collective summary of the course outcomes of the four different math courses as mapped to ABET criteria ((a)–(k)) is given in Table
ABET outcomes versus math courses outcomes.
ABET outcomes  MATH1110  MATH1120  MATH2210  MATH2220 

(a)  O1–O5, O7, O8  O1–O10  O1–O10  O1–O7 
(b)  O1, O5  O1, O2, O5  
(c)  O4, O5  O1, O7  O4–O7  
(d)  O6  O3  O8–O11  
(e)  O1–O4, O7, O8  O2, O4–O6, O9, O10  O1–O7  O1–O7 
(f)  O6  O10, O11  
(g)  O6  O3  
(h)  
(i)  O5  O1  O10, O11  
(j)  O10  O1–O3  O1–O7  
(k)  O2–O4, O7, O8  O2–O4, O6–O10  O1–O9  O1–O7 
The course that the least maps to ABET criteria is the fourth course (MATH2220: linear algebra and engineering applications). Nevertheless, it at least maps well to the three ABET criteria (a), (e), and (k) that are highlighted above to be major outcomes relevant for a typical math course. Moreover, this linear algebra course is a higher level and inherently more specific and specialized course than the other three courses and as such is expected to map to a lesser number of ABET criteria. Nonetheless, it should be noted that generally not all of the courses in a curriculum need to address all ABET criteria to the same extent, but the whole curriculum of a program needs of course to show strength and well balanced mapping in the different courses of the curriculum as a whole, a requirement that is well fulfilled by our four math courses and by the whole ERU curriculum as a whole unit; going through the details of the whole curriculum of our ERU is out of the scope of this paper.
In this section, we provide a learning assessment of the level of satisfaction of the outcomes of the different mathematics courses and based on the mapping between these outcomes and ABET criteria, we can indirectly judge the performance and the level of satisfaction of the ABET criteria in our math courses offered by the ERU at UAEU. The assessment tools, as given in Tables
A major purpose of this study is to assess the part of the curricula of the engineering programs that is related to the mathematics courses offered for engineering students at the UAEU and to see the extent of the satisfaction of the ABET criteria ((a)–(k)) in this part.
This study is designed for the College of Engineering students at the UAEU who are taking the mathematics courses offered by the ERUUAEU. This study is based on the feedback from two different kinds of assessment tools, direct and indirect tools. A direct tool is the one that gives a direct measure on the student performance through exams, homework assignment, project report, and so forth, while the indirect tool is the one that gives feedback on the student performance based on surveys and opinions in questionnaires and in this study this is taken based on feedback received from students’ surveys. The students’ opinions collected in surveys conducted at the end of each semester aim to see how the students judge their fulfillment of the course outcomes, regardless from their actual scores based on the direct assessment tools used. It should be noted that the score the students give in these surveys is not considered as part of the overall score the students attain in the course and is used solely as feedback to guide the improvement of the course material delivery. One of the purposes of collecting this indirect feedback from the students in each course is to see any possible discrepancy and mismatch between the actual learning direct assessment and the way how students see themselves fulfilling the course. This would help the instructor to better prepare their course material and the way they design the direct assessment tools for their courses in the subsequent semesters; the course is offered so that a better and more representing assessment of the course can be done.
The data collected based on the two assessment tools types described above (direct and indirect) that are reported in this paper cover a period of three consecutive semesters. These data are provided by the ERU/UAEU.
A sample of the questionnaire used to collect the indirect assessment results in the form of students’ opinion is given in Table
Sample for the indirect assessment students’ survey used in the course MATH2210differential equations and engineering applications.
Course intended outcome 
Very low 

Very high  

1  2  3  4  5  

□  □  □  □  □ 
( 
□  □  □  □  □ 
( 
□  □  □  □  □ 
( 
□  □  □  □  □ 
( 
□  □  □  □  □ 
( 
□  □  □  □  □ 
( 
□  □  □  □  □ 
( 
□  □  □  □  □ 
( 
□  □  □  □  □ 
( 
□  □  □  □  □ 
( 
□  □  □  □  □ 
The level of satisfaction of the different course outcomes of the four math courses under consideration is discussed in this subsection based on the direct assessment measures adopted in these courses. Table
Learning assessment of course outcomes based on the direct measures given in Tables
Course  Sem.  # 
O1 
O2 
O3 
O4 
O5 
O6 
O7 
O8 
O9 
O10 
O11 

MATH 
Spring 2011  21  3.9 
3.5 
3.8 
3.6 
4.9 
4.9 
4.1 
4.0 
NA  NA  NA 
Fall 2011  29  4.0 
3.8 
4.0 
3.9 


4.0 
3.7 
NA  NA  NA  
Spring 2012  33  4.2 
4.1 
3.9 
3.9 
3.8 
3.8 
3.9 
3.8 
NA  NA  NA  
















MATH 
Spring 2011  29 


3.5 
3.5 






NA 
Fall 2011  17 


3.4 
3.5 






NA  
Spring 2012  32  4.3 
3.9 
4.4 
3.5 






NA  
















MATH 
Spring 2011  29  4 
3.8 
4 
4 
3.8 
3.8 
3.7 
4.2 
4 
4.3 

Fall 2011  20  4.00 
3.90 


4.40 
3.60 
3.50 
4.30 

3.80 
4.00  
Spring 2012  21  4.3 
4.10 

4.30 
4.50 
4.70 
4.50 
4.4 
4.50 
4.7 
3.7  
















MATH 
Spring 2011  17  4.5 
4.50 
3.70 
3.80 
4.00 
4.20 
3.80 


3.8 
NA 
Fall 2011  18  3.90 

4.20 
3.90 
4.10 
4.00 
3.60 
3.80 
3.80 
3.60 
NA  
Spring 2012  17  4.5 
4.5 
4.5 


3.7 
3.7 
3.90 
3.9 
3.5 
NA  













Figure
The average level of satisfaction of the course outcomes over three semesters for all math courses.
Although the level of satisfaction of most outcomes for MATH1120 is judged as “ability” and above, our target (as mentioned earlier) is a level of no less than 3.5/5 (70 percent) and so the result reported for most outcomes should be triggering the actions of the instructors teaching the course to do some action to improve the performance of students on these outcomes and/or to revise the way these outcome are assessed. This is considered as part of our commitment to continuous improvement efforts. The level of satisfaction of outcomes like O5 and O10 in MATH1120 (Calculus II), as judged based on the used direct assessment tools; although this should not be the only trigger for improvement actions by different entities and committees in the ERU, it can also attract the attention of the focus groups and the continuous quality committees in any of the five engineering programs in the COE and may cause these engineering programs to give their feedback to the ERU on the impact such a level of satisfaction of the outcomes might have on the subsequent courses in these programs.
According to Table
Figure
The level of satisfaction of the course outcomes over three semesters for the course MATH1110 (Calculus I for engineers).
In this subsection the data obtained based on the indirect assessment tool, namely, the students’ opinion, are presented and discussed. Table
Opinion assessment of course outcomes based on indirect measures “students survey” (NA: not applicable, Values in italic are below the outcomesachievement passing criteria).
Course  Sem.  # 
O1 
O2 
O3 
O4 
O5 
O6 
O7 
O8 
O9 
O10 
O11 

MATH 
Spring 2011  21  4.8 
5 
4.7 
4.4 
4.5 
4.7 
4.8 
4.9 
NA  NA  NA 
Fall 2011  29  4.45 
4.38 
4.59 
4.45 
4.21 
4.41 
4.45 
4.38 
NA  NA  NA  
Spring 2012  33  4.6 
4.5 
4.50 
3.90 
4.00 
4.2 
4.5 
4.5 
NA  NA  NA  
















MATH 
Spring 2011  29  4.11 
4 

4.5 
4.5 
4.3 
4.3 
4.2 
4.4 
4.2 
NA 
Fall 2011  17  4.2 
4.1 

4.4 
4.6 
4.4 
4.2 
4.1 
4.3 
4.1 
NA  
Spring 2012  32  4.5 
4.27 

4.38 
4.50 
4.12 
4.19 
3.85 
4.38 
4.35 
NA  
















MATH 
Spring 2011  29  4.4 
4.05 
3.9 
4.15 
4.1 
3.95 
4.42 
4.10 
4.42 
4.36 
4.57 
Fall 2011  20  4.00 
4.25 
4.25 
4.25 
4.63 
4.25 
3.50 
4.38 
4.13 
4.50 
4.00  
Spring 2012  21  4.44 
4.33 
4.39 
4.61 
4.44 
4.44 
4.17 
4.44 
4.06 
4.33 
4.0  
















MATH 
Spring 2011  17  5.00 
4.71 
4.64 
4.64 
4.43 
4.57 
4.50 
4.29 
4.21 
4.20 
NA 
Fall 2011  18  4.30 
4.40 
4.20 
4.60 
4.60 
4.00 
3.70 

4.60 
4.60 
NA  
Spring 2012  17  4.64 
4.45 
4.54 
4.54 
4.45 
3.91 
3.73 

4.00 
4.10 
NA  













As can be seen from Table
A comparison between the outcomes assessment results based on the different direct assessment tools used in the courses (see Tables
Overall average score for the outcomes of all math courses based on learning and opinion assessments.
A correlation analysis was performed to identify how the direct measures relate to indirect measures as follows.
For each outcome, two variables were considered.
V1 is the variable of the averages of the scores in the outcome obtained from the direct measure. For instance, for outcome O1, V1 can take the following values: 3.9, 4, and 4.2.
V2 is the variable of the averages from the indirect measure; for instance, for outcome O1, V2 can take the following values: 4.8, 4.45, and 4.6.
Correlations between direct and indirect measures.
Course  O1  O2  O3  O4  O5  O6  O7  O8  O9  O10  O11 

MATH1110  −0.4  −0.8  −0.6  −0.4  0.8  0.8  0.8 

NA  NA  NA 
MATH1120 



−0.9 

0.2  −0.4  −0.9 

NA  
MATH2210  0.6  0.9 

0.6  0.9  0.7  0.4  0.9  0.0 

−0.9 
MATH2220  0.9  0.6  −0.3  0.8  0.5  0.9  0.9 

0.0  0.0  NA 
One can see from Table
For the MATH1120 outcomes O1 and O2 and perfectly positively correlated while O3, O6, and O10 are perfectly inversely correlated. The correlation of outcome O4 is not calculated since the first variable is constant. For outcome O7, the direct and indirect measures are not correlated. For the MATH2210 as well as for the MATH2220, the direct and indirect measures are not correlated at all for outcomes O9. The two measures for the other outcomes are correlated. In fact, O3 and O10 from MATH2210 and O8 from MATH2220 are perfectly inversely correlated. The measures of O11 for MATH2210 are also inversely correlated and O3 from MATH2220 is slightly negatively correlated. The direct and indirect measures of the remaining outcomes are positively correlated.
In this subsection, we summarize and define a conclusive criteria based on which we judge the achievement of a certain course outcome. In addition, we relate the ABET outcomes satisfaction level to the satisfaction level of the courses outcomes.
The following outcomesachievement passing criteria are defined.
According to the learning assessment presented in Table
The only course among the four that according to the above adopted achievement criteria received almost no deficiencies is MATH1110. As for MATH 2210 and 2220, they received much less concerning scores, as compared to MATH1120. By relaxing the above criteria and considering the passing grade to be 65 percent; for example, much of the concerns above would be alleviated. However, justification to do so and feedback on detailed actions to improve the situation of outcomes achievements especially in MATH 1120 are required before attempting to relax the criteria.
When considering the scores presented in Table
The summary of the level of achievement of the different outcomes satisfaction according to the criteria adopted above is given in Table
Judgment on outcomes achievement based on adopted criteria for directly assessment outcomes (AC: achieved, NAC: not achieved, and NA: not applicable).
Course  Semester  O1  O2  O3  O4  O5  O6  O7  O8  O9  O10  O11 

MATH1110  Spring 2011  AC  AC  AC  AC  AC  AC  AC  AC  NA  NA  NA 
Fall 2011  AC  AC  AC  AC  NAC  NAC  AC  AC  NA  NA  NA  
Spring 2012  AC  AC  AC  AC  AC  AC  AC  AC  NA  NA  NA  


MATH1120  Spring 2011  NAC  NAC  NAC  AC  NAC  NAC  NAC  NAC  NAC  NAC  NA 
Fall 2011  NAC  NAC  NAC  AC  NAC  NAC  NAC  NAC  NAC  NAC  NA  
Spring 2012  AC  AC  NAC  AC  NAC  NAC  NAC  NAC  NAC  NAC  NA  


MATH2210  Spring 2011  AC  AC  AC  AC  AC  AC  AC  AC  AC  AC  NAC 
Fall 2011  AC  AC  NAC  NAC  AC  AC  AC  AC  NAC  AC  AC  
Spring 2012  AC  AC  NAC  AC  AC  AC  AC  AC  AC  AC  AC  


MATH2220  Spring 2011  AC  AC  AC  AC  AC  AC  AC  NAC  NAC  AC  NA 
Fall 2011  AC  NAC  AC  AC  AC  AC  AC  NAC  AC  AC  NA  
Spring 2012  AC  AC  AC  NAC  NAC  AC  AC  NAC  AC  AC  NA 
By considering the mapping between the course outcomes and ABET criteria ((a)–(k)) presented in Tables
Tables
Average ABET outcomes achievement level based on learning assessment tools (AC: achieved, NAC: not achieved, and NA: not applicable).
Course  (a)  (b)  (c)  (d)  (e)  (f)  (g)  (H)  (i)  (j)  (k) 

MATH1110  AC  AC  AC  AC  AC  AC  AC  NA  AC  NA  AC 
MATH1120  NAC  NAC  NAC  AC  NAC  NA  AC  NA  NAC  NAC  NAC 
MATH2210  AC  NA  AC  AC  AC  AC  NA  NA  AC  NAC  AC 
MATH2220  AC  NA  NA  NA  AC  NA  NA  NA  NA  AC  AC 
Average ABET outcomes achievement level based on the indirect assessment tool “students opinion” (AC: achieved, NAC: not achieved, and NA: not applicable).
Course  (a)  (b)  (c)  (d)  (e)  (f)  (g)  (h)  (i)  (j)  (k) 

MATH1110  AC  AC  AC  AC  AC  AC  AC  NA  AC  NA  AC 
MATH1120  AC  AC  AC  NAC  AC  NA  AC  NA  AC  AC  AC 
MATH2210  AC  AC  AC  AC  AC  AC  NA  NA  AC  AC  AC 
MATH2220  AC  NA  NA  NA  AC  NA  NA  NA  NA  AC  AC 
Overall average ABET outcomes achievement.
Course  (a)  (b)  (c)  (D)  (e)  (f)  (g)  (h)  (i)  (j)  (k) 

MATH1110  AC  AC  AC  AC  AC  AC  AC  NA  AC  NA  AC 
MATH1120  NAC  NAC  NAC  NAC  NAC  NA  AC  NA  NAC  NAC  NAC 
MATH2210  AC  NA  AC  AC  AC  AC  NA  NA  AC  NAC  AC 
MATH2220  AC  NA  NA  NA  AC  NA  NA  NA  NA  AC  AC 
Once more, the students’ judgment on outcomes leads to having ABET outcomes being achieved to a good extent in all four courses, but this is not enough to grant overall achievement of ABET outcomes based on direct and indirect tools where the one more conservative of these tools hence determinant, which is the one based on the direct assessment tools, will dominate the final judgment.
Overall, the results of this study are very good and promising. They show that the majority of the ABEToutcomes are “mathematically” achieved according to our criteria of performance. Nonetheless, it is clear from the previous section that we need to give more attention to the MATH1120 Calculus II for engineers, namely, outcome “O5” which is
offering more exercises and problems in class and as homework for the outcomes that help students to gain competency in autonomy, responsibility, selfdevelopment, and role in context such as
the ability to think critically in analyzing engineering problems (e.g., “O5” in MATH1110Calculus I for engineers and “O1” in MATH1120Calculus II for engineers),
the ability to work effectively with others (e.g., “O6” in MATH1110Calculus I for engineers),
using computers and new technologies to enhance visualization and solve calculus problems (e.g., “O3” in MATH1120Calculus II for engineers and “O8O9” in MATH2210differential equations and engineering applications),
increasing the assessment methods for the outcomes that help student to acquire knowledge in mathematics, especially for the MATH1120Calculus II for engineers where almost all the outcomes were 70%unachieved, while for the others courses the results were good.
This paper gives a representative sample of data and based on that explains the methodology adopted in the COEUAEU for monitoring and controlling the educational and learning quality and performance in the MATH courses offered at UAEU for engineering students and the extent of satisfaction of ABET outcomes in these courses. Four math courses are offered at UAEU for general engineering students before they get specialized, namely, MATH1110: Calculus I for engineers, MATH1120: Calculus II for engineers, MATH2210: differential equations and engineering applications, and MATH2220: linear algebra and engineering applications. Mapping between the outcomes of these math courses and the engineering ABET criteria ((a)–(k)) showed that most of the ABEToutcomes ((a)–(k)) are to a great extent inline with the outcomes of our mathematics courses. This encourages us to use the achievement of the courses outcomes as an assessment tool for the engineeringABET outcomes. A course outcome achievement passing criteria is defined based on direct and indirect assessment tools that require the achievement of a score of 3.5/5 (70 percent) for each outcome for that outcome to be considered well realized. Hereby the indirect tools addressed are in the form of surveys conducted to take the opinion of the students on the level of outcomes achievement as seen by them. The direct tools used are the ones based on students’ scores in exams and any other learning activities such as homework assignments, quizzes, and course projects. Based on the data collected and analyzed in this study, it was found that most courses meet the passing criteria except MATH1120 (Calculus II), which was attributed to the high intensity of the course content that contains completely new topics to the students. As a part of the continuous improvement process, different improvement actions were suggested by the course focus group such as more tutorial sessions, extra worksheets, and modifying the course syllabus to meet exactly the needs of the students in the subsequent engineering courses.
On the other hand, this study shows that monitoring the performance of courses outcomes over a number of semesters is a means of showing a trend but some abnormalities in the results in some semesters and possible deviations from the general trend cannot be considered alone as a source of feedback to trigger quality improvement actions in isolation from other important factors such as the number of sections offered for the course and the number of students in the classes in the different sections over the semesters. The feedback obtained from the direct assessment tools used although is comparable to the feedback obtained from the indirect studentsopinionbased tool, the result of the students survey shows that the students evaluate higher their level of appreciation and satisfaction of the courses outcomes than what they achieve based on the direct assessment tools in reality. To bridge the gap between the results of the direct and indirect assessment tools, revisiting the direct assessment tools and perhaps the way the course material is delivered is required by the course instructor.
More stringent criteria on the ABET outcomes satisfaction are adopted and this shows that the course MATH1120 is most susceptible to lack of realization of ABET criteria. The other three courses meet ABET in a reasonable way according to the adopted criteria.
The authors declare that there is no conflict of interests regarding the publication of this paper.
All authors contributed equally to the writing of this paper. All authors read and approved the final paper.