Mathematical Competency of Engineers and Engineering Students

Soheila Firouzian Department of Educational Science, Mathematics and

Creative Multimedia Universiti Teknologi Malaysia

81300 Johor, Malaysia fsoheila2@live.utm.my

Zaleha Ismail Department of Educational Science, Mathematics and

Creative Multimedia Universiti Teknologi Malaysia

81300 Johor, Malaysia

Roselainy Abd Rahman UTM Razak School

Universiti Teknologi Malaysia Kualalampour, Malaysia

Yudariah Mohammad Yusof Science and Mathematics Department

Universiti Teknologi Malaysia 81300 Johor, Malaysia

Hamidreza Kashefi

Department of Educational Science, Mathematics and Creative Multimedia

Universiti Teknologi Malaysia 81300 Johor, Malaysia

Fariba Firouzian Mahani Department

Bahonar Universiti of Kerman Kerman, Iran

Abstract—Mathematics is considered a fundamental component of engineering education, thus it is important to determine the mathematical competencies (MCs) attained by engineering undergraduate students so that they will be able to use these competencies to support their professional engineering work. The MCs were identified based on Niss's work, namely; thinking mathematically, reasoning, problem posing and solving, modeling, representing, communicating, symbolism and formalism, using aids and tool. This research was done to explore MCs in engineering mathematics curriculum by conducting two studies; a study on engineers’ MCs requirements at the workplace and a study on the engineering students’ MCs acquirements at the university. In the first phase, 22 engineers from various industries in Malaysia responded to a set of open-ended questionnaires followed by interview session with 10 selected engineers. In the second phase, 41 engineering undergraduate students participated by answering a set of questionnaires with open ended questions The data of the research were analyzed qualitatively using schema coding approach as well as appropriate statistical analysis. The findings from both phases gave indication the MCs required should be the focus of engineering mathematics curriculum. Particularly it highlighted which MCs were actually attained by the undergraduate engineering students as compared to the MCs that were needed based on the demands at the workplace. The results gave suggestion that mathematics curriculum should also focus on MCs as outcomes besides the development of mathematical concepts and skills.

Keywords— Mathematical competencies; Engineering

mathematics curriculum; Mathematical skills

I. INTRODUCTION

This paper highlighted the requirements of the mathematical competencies in the workplace and consequently informed the mathematics curriculum for engineering undergraduates. Mathematical competencies are currently at the center of concern in developing the mathematics curricula in engineering education in Europe (see SEFI) studies in 2006, 2011 and 2013 [1-3]. Mathematical competency is the ability to apply mathematical concepts and procedures in relevant contexts which is the essential goal of mathematics in engineering education, that is, to help students to work with engineering models and solve engineering problems [4]. Following SEFI mathematics curriculum development for engineering students, the authors of this paper considered the amended set of eight mathematical competencies as defined by Niss (2003), namely; thinking mathematically, reasoning mathematically, problem posing and solving, modeling mathematically, representing mathematically, communicating mathematically, symbolism and formalism language, and using aids and tools [5]. This competencies were used for the first time in a study by OECD-PISA in 2003 and later in 2009 and in 2012 [6-8].

Previous work by authors of this paper has shown the importance of emphasizing mathematical competencies in engineering mathematics curriculum [9, 10]. It gave insight to

2014 International Conference on Teaching and Learning in Computing and Engineering

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DOI 10.1109/LaTiCE.2014.49

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the role of MCs and to a comprehensive conceptualization of MCs notion in the intended learning outcomes of mathematics courses in the OBE (Outcome Based Education) programs of engineering education in Malaysian engineering faculties. In another study done by the authors, results showed that there is a gap between the university education and workplace demand for mathematical competence of the engineers [11]. Accordingly, this research was conducted to see whether engineering students have the mathematical competencies required in the workplace so that their mathematics education can be further improve in this aspect. Here we will share some initial results of the status of MCs among the engineers and engineering students.

II. THE STUDY

A preliminary study was carried out to explore the MCs requirements of engineers’ at the workplace and later to determine the acquired MCs of final year engineering students at the university. The perceptions of the two groups were compared for conformity and the results can inform improvement to the mathematics curriculum. The data was analysed according to qualitative data analysis method following Creswell’s six steps of analysing and interpreting qualitative data [12]. The inference made from the data is supported with the work done by Alpers [4] and Cardella [13].

A. Study One: Workplace Study

The workplace study involved a survey and semi-structured interviews with engineers. In the survey the engineers responded to a set of open-ended questions. Interviews were conducted to answer questions about which mathematical competencies and skills were required by the engineers during workplace tasks and how mathematics is applied in their work. In addition, information on the kind of education or training that could improve their mathematical competencies related to their work is obtained. Suggestions as to how to improve the university education of engineers prior to their entrance in workplace were also requested. The interviews were video recorded and then transcribed. Later some words and phrases were highlighted in the transcripts of interviews as the data and the findings of the data were recorded.

B. Study two: University Study

The study of engineering students’ mathematical competency takes on a qualitative approach to investigating which mathematical competencies are acquired by the engineering students at the end of their study. For this research, it was important to understand the engineering students’ possession of mathematical competencies from their own perspective. A survey with a set of open-ended questions was distributed to the students. They responded to the

questions of what mathematical competencies they acquired from their mathematics courses. A summary of the two phases of study is provided in Table 1.

TABLE I: SUMMARY OF TWO PHASES OF STUDY

The Study Participants’

Level of Experience

Participants’ Discipline(s)

Number of Participants

Duration

Workplace Study:

Open-ended

Questionnaire

Interviews with

Engineers

5 - 20 years Engineering

Job Experience

Civil, Mechanical, Industrial, Electrical

22

10

10-20 minutes

15-25 minutes

University Study:

Open-ended

Questionnaire Answered by

Students

Engineering Undergraduates

(Seniors)

Civil, Mechanical,

Electrical

41

10-20

minutes

C. Required MCs − Workplace Study Findings

In the workplace study, different statements were extracted from interviews with engineers to describe their required MCs in their job engagement. This extraction gave rich findings from the workplace study. A list of these required MCs forms is arranged in Table 2. The first column presents the clusters of mathematical competencies that are described in previous paper by the authors (refer to [10]) as the required MCs; the second column presents all the statements which emerged from interviews and open ended questionnaires answered by the engineers; a checkmark in the last column indicates that the particular form of MCs was one of the mathematical competencies mentioned by at least one of the 10 study participants. Many of the statements that were evident in interviews also appear in the answers to the open-ended questions.

As shown in Table 2, in their descriptions about their work, engineers acknowledged all eight mathematical competencies concepts albeit in different words. For instance, regarding the competency of using aids and tools they refer to mathematics as a tool to solve their engineering problems. As mentioned in interviews, they do simulation with some software or may use mathematics programs to solve some problems they may face in their engineering engagements. Regarding the competency of thinking mathematically, they claim specializing, generalizing and understanding of mathematical concepts are required in their work. According to them, they do reasoning mathematically when they refer to the well-known mathematics concepts or formulas or proving arguments in their working system. On problem solving, they use some strategies to solve their engineering problems or they

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apply their knowledge of mathematics they learned before to solve their problems or in formulating the problem. Referring to the mathematical modelling competency, they claim they design models, set up a model or may check the process of a system and so on. Engineers also mentioned they do require representing their work mathematically such as with statistics or mathematics measurements or some other related forms of representation. In terms of using symbols and formalism language, they noted they may check a system by computing results using math symbols. Regarding the competency of communicating mathematically they mentioned they may use simple mathematics to describe their work procedures or they may refer to mathematics textbooks or asking their friends when they have faced an issue.

TABLE II: REQUIRED MATHEMATICAL COMPETENCIES FROM QUALITATIVE STUDY ON ENGINEERS DATA

Mathematical Competency

Forms of Mathematical Competencies

Engineers

Symbols and Formalism

Mathematical Manipulating √

Using Aids and Tools

Computer Usage (Programming, Simulation, Internet, Mathematics Software, Excel)

√

Using aids (Forum, Spreadsheets, Calculator)

√

Problem Handling Problem Solving Strategies/ Appling Mathematics/ Formulating/ Calculating/ Computing

√

Modeling Mathematically

Modelling a processes/ Designing/ Testing Ideas/ Validating a Model/ Simulating

√

Representation Multiple Representation/ Statistics Application/ Measurement

√

Reasoning Mathematically

Proving/ Referring √

Thinking Mathematically

Specializing/ Generalizing/ Understanding Mathematical Concepts/ Visualizing/ Decision Making/ Problem Posing/ Analyzing

√

Communicating Mathematically

Working with others in a group and understand them/ Asking from Others/ Using Informal Mathematics Language

√

D. Acquired MCs− University Study findings

The data obtained from students study was analyzed qualitatively in the same manner as those of the engineers study. Students who were in the final year of study were asked to list the mathematical competencies they acquired from mathematics classes. The mathematical competencies that emerged from their responses appear different; however on close scrutiny the responses could be organized and classified according to the eight mathematical competencies identified earlier. Table 3 showed the students’ perceptions of the acquired MCs in their mathematics learning at the university.

TABLE III: ACQUIRED MATHEMATICAL COMPETENCIES FROM STUDY ON ENGINEERING STUDENTS DATA

Forms of

Mathematical Competencies Related Mathematical

Competency Students

Validating a model Modeling Mathematically

√

Justifying Results Reasoning mathematically

√

Decision Making/ Problem Posing/ Understanding the Concepts/ Visualizing

Thinking Mathematically

√

Using Graphs Representing Mathematically

√

Formulating/ Problem Solving/ Calculating

Problem Handling √

Communicating with Others Statements/ Determining

Communicating Mathematically

√

Translating to Mathematics Language Using Symbols and Formalism

√

Using Mathematical Software/ Using Calculator

Using Aids and Tools √

III. DISCUSSION AND CONCLUSION

This paper provides an overview of two studies investigating engineers’ and engineering students’ mathematical competencies and a synthesis of the findings. Table 4 gives a summary of the findings from both studies. The checkmarks indicated the competencies as perceived by the group of engineers and engineering students who participated in the study. The results showed that the engineers and engineering students used more than just knowing the mathematical concepts and skills that they learned from the mathematics courses. At the workplace, engineers are expected to be able to use problem solving competency, able to think mathematically, to reason and to model phenomena mathematically, communicate with their peers using mathematics especially when dealing with engineering problem to find an effective solution and in trying to better understand real life functions. They were expected to be able to represent their empirical work mathematically and in doing so may need to use mathematical tools such as calculators, mathematics software.

Nevertheless, the findings indicated the MCs acquired by the final year engineering students at university are lacking in some forms compare to the engineers’ requirements. For instance, in terms of mathematical modeling, problem handling, and in using aids and tools, need to be enhanced in students learning. Similarly for mathematical thinking such as specializing and generalizing do require improvement. Therefore students need fostering in some forms of MCs at university. On the other hand, there are other forms of MCs that students acquired but are not at the center of concern at the workplace. These forms of acquired MCs include for example justifying results in reasoning, the use of graphs in representing mathematically and translating in symbolism and formalism language.

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TABLE IV: COMPARISON BETWEEN ENGINEERS AND STUDENTS PERCEPTION ON MATHEMATICAL COMPETENCIES

Mathematical Competency

Form of Mathematical Competency

Engineers Study

Engineering Students

Study

Thinking

Mathematically

Specializing √ Generalizing √ Problem Posing √ √ Decision Making √ √ Visualizing √ √ Understanding the Concept √ √

Analyzing √

Reasoning Mathematically

Doing Reasoning √ √ Proving √ Referring √ Justifying Results √

Problem Handling

Using Formulas √ Applying Mathematics √

Calculating/ Computing √ √

Using Problem Solving Strategies √ √

Formulating √ √

Modelling Mathematically

Modeling a Processes √ Validating a Model √ √ Designing √ Testing Ideas √ Simulating

Representing Mathematically

Using Multiple Representation √ √

Measuring √ Using Statistics √ Using Graphs √

Communicating Mathematically

Working with Others in a group √

Determining √ Communicating with Others Math Statements

√

Asking from Others √ Using Informal Mathematics Language

√

Symbolism and Formalism

Mathematical Manipulating √

Translating √

Using Aids and

Tools

Using Mathematical Software √ √

Using Forum √ Using Spreadsheet √ Programming √ Using Calculator √ √

In summary the results showed that there is discrepancy between the MCs required in the workplace and those acquired by the students. Therefore, it is suggested that the focus of mathematics teaching to prospective engineers should take into account mathematical competencies and these competencies need to be included as vital learning outcomes besides the development of mathematical concepts, aptitude and skills as required.

ACKNOWLEDGMENT The authors acknowledged Exploratory Research Grant

Scheme (ERGS), Ministry of Higher Education of Malaysia and Universiti Teknologi Malaysia (UTM) for the financial support given in making this study possible.

REFERENCES [1] B. Alpers, “The mathematical expertise of mechanical engineers,” in

Proc. SEFI MWG Seminar, 2006. [2] SEFI, “A Framework for Mathemati cs Curricula in Engineering

Education,” 2011: pp. 1-71. [3] SEFI, “A Framework for Mathematics Curricula in Engineering

Education,” 2013. [4] B. Alpers, “The SEFI Mathematics Working Group’s new Curriculum

Framework Document,” 41th SEFI Conf., Leuven, Belgium, 16-20 September, 2013.

[5] M. Niss, “Mathematical competencies and the learning of mathematics: The Danish KOM project,” in the 3rd Mediterranean Conference on Mathematical Education. Athens: Hellenic Mathematical Society proc., 2003.

[6] OECD, PISA, “The PISA 2003 Assessment Framework: Mathematics, reading, science and problem solving knowledge and skills,” 2003, OECD Publishing.

[7] OECD, “PISA 2009 Assessment Framework: Key Competencies in Reading, Mathematics and Science,” 2010, OECD Publishing.

[8] K. Stacey, “The international assessment of mathematical literacy: PISA 2012 framework and items,” 2012.

[9] S. Firouzian, et al., “Mathematical Learning of Engineering Undergraduate,” Procedia-Social and Behavioral Sciences, 2012. 56: pp. 537–545.

[10] S. Firouzian, et al. “A Conceptual Framework for emphasizing Mathematical Competencies in the Mathematics Curriculum of Undergratuate Engineers” in 2013 Research in Engineering Education Symp. Proc., 2013© Pusat Pengajaran Dan Pembelajaran Universiti Teknologi Malaysia, pp. 287–294.

[11] M. Y. Yudariah, et al. “Mathematical and Engineering Thinking Skills: What Do Engineers and Lecturers Percieve?,” in Research in Engineering Education Symp. Proc., 2013© Pusat Pengajaran Dan Pembelajaran Universiti Teknologi Malaysia, pp. 82–89.

[12] J. Creswell, Qualitative inquiry and research design: Choosing among five approaches. SAGE Publications, Incorporated, 2012, ch. 8 , pp. 236– 265.

[13] M. Cardella, AC 2007-2853: “Engineering Students’mathematical Thinking: in the Wild and With a Lab-Based Task,” 2007.

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