The article presents the results of two focus groups and a questionnaire implemented with
engineering students from the University of Minho, in order to assess opinions and perspectives concerning the main learning difficulties in mathematics-based disciplines. The results obtained show that students generally see the relevance of mathematics to engineering courses. Mathematics is considered as an essential discipline in course selection and a vital part of their
career as engineers. The importance of the instructor is recognized when learning mathematical concepts. Students would like their courses to address mathematical concepts that are more in line with their future professions. The 73 undergraduate students who completed the
questionnaire manifested a high self-efficacy and a high perception that the learning of
mathematical concepts and the development of mathematical skills are essential for
progression in their future career.Fundação para a Ciência e a Tecnologia (FCT

Alves, M.

Coutinho, Clara Pereira

Rocha, Ana Maria A. C.

Rodrigues, Cristina S.

Universidade do Minho: RepositoriUM

ENGINEERING STUDENTS AND THE APPLICATION OF MATHEMATICAL KNOWLEDGE: HOW TO EXPLAIN THE DIFFICULTIES EXPERIENCED?   Manuela Alves1, Cristina Rodrigues1, Ana Maria A.C. Rocha1 and Clara Coutinho2 1Algoritmi R&D Centre, Engineering School, University of Minho, Portugal 2Institute of Education, University of Minho, Portugal    Abstract  The article presents the results of two focus groups and a questionnaire implemented with engineering students from the University of Minho, in order to assess opinions and perspectives concerning the main learning difficulties in mathematics-based disciplines. The results obtained show that students generally see the relevance of mathematics to engineering courses. Mathematics is considered as an essential discipline in course selection and a vital part of their career as engineers. The importance of the instructor is recognized when learning mathematical concepts. Students would like their courses to address mathematical concepts that are more in line with their future professions. The 73 undergraduate students who completed the questionnaire manifested a high self-efficacy and a high perception that the learning of mathematical concepts and the development of mathematical skills are essential for progression in their future career.    Keywords: Learning factors, Mathematical concepts, Engineering students, University of Minho, Portugal.     1. Introduction   Engineering plays a significant role in the modern world since it is always present in day to day activities concerning construction, computers, technology, energy, electronic devices, and manufacturing process. Regardless of the area of study, the mathematical concepts are essential in the training of engineers, both for understanding the different concepts as well as the specific knowledge of their applicability. Nevertheless, and despite Mathematics constitute an essential discipline on admission to engineering courses, engineering students reveal difficulties in Mathematics based disciplines. Students’ grades reveal difficulties and motivational issues that go far beyond the required mathematical knowledge. The study involved collecting data from two complementary data sources: two focus groups and a questionnaire.  The purpose of this study is to measure and analyze tree factors identified in the literature as influencing the learning of mathematical concepts: engineering self-efficacy; perceived importance of mathematics and the anxiety towards mathematics. The remainder of this paper is as follows: in Section 2 a literature review is presented, summarizing some of the factors that could influence the learning of mathematics. Section 3 presents the methodology and afterwards we present the results of a focus group and a questionnaire. Section 5, summarizes the most relevant conclusions.  2. Mathematics learning factors  The literature review identified several studies that suggest that learning of mathematical concepts may be constrained by several factors ranked as ISBN: 978-989-97866-5-3 © 201322psychographic or demographic factors. The most reported psychographic factors include concepts such as the personality of student attitudes, socio-cognitive aspects, motivation and anxiety about mathematics. The demographic factors focus more specifically on gender differences (see for instances Bakar et al., 2010; Homayouni, 2011; Kargar et al., 2010; Sirmaci, 2010). Most Portuguese studies on the learning of mathematics focuses only on demographic factors or on the level of elementary education or high school. The literature does not identify Portuguese studies that include psychographic factors. Even so, the concerns about school failure have played a leading role in research in education in Portugal (Buesco, 2012). The PISA 2006 showed that the performance of Portuguese students in science, although improving, is still lower than most OECD countries. In 2000, Portuguese students occupied one of the last places, but in 2009 it was the first time they achieved scores that fall in the average performances of the OECD (Conboy, 2011). In this context, it is opportune to explore the learning of mathematical concepts in Portugal, particularly in the specific context of university education and of engineering education, an area with strong math component and recognized impact on the application of mathematical developments.  3. Objectives and methodology   This study was conducted in three stages. In a first stage, two focus groups were carried out with undergraduate students of Master in Industrial Engineering and Management (MIEGI) and Master in Mechanical Engineering (MIEMAC) of University of Minho. The first focus group was involved students from 3rd, 4th and 5th years of the MIEGI course with a total of 10 students, 5 female and 5 male, aged between 21 and 24 years old who participated in the study. Due to the specificity of the MIEGI course, (with a strong management component), it was of the utmost interest to reproduce the focus group and broadening the investigation to engineering courses with a stronger technical foundations and stronger needs concerning the application of mathematical concepts. We therefore conducted a second focus group with undergraduate students in the 2nd year of MIEMAC with a total of 28 students, 24 male and 4 female, aged between 19 and 32 years old participated in the study. The objective of the focus groups was to know the opinions of the students about mathematics in general and ascertain the factors that they identified as influencing their performance in UC’s with mathematics background. The focus groups, with 30 minutes each, were carried out in two stages: a discussion oriented by six questions script; 2) a comment to three sentences presented to the students.  In a second phase, we examined the literature related to the factors that influence the learning of mathematical concepts and engineering education.   In order to complement our studies, we developed a questionnaire using existing scales that included items related to engineering self-efficacy (Korea et al, 2009), items evaluating students perceptions of the relevance of mathematics in engineering (Flegg, Mallet & Lupton, 2011) and anxiety towards mathematics (Bai, Wang, Pan, & Frey,2009).   The final questionnaire consists of 8 initial questions with the purpose to characterize the sample followed by 3 sections, in the format of a five point Likert scale, with 25 items whose purpose is to measure and analyze the perspectives of engineering students about learning mathematical concepts, as well as difficulties perceived related to the importance of mathematics in their future career. The first section, with 8 items aims to assess the perceived importance of mathematics; the second section with 5 itens aims to assess anxiety towards mathematics and finally in third section, with 12 items, we intended to assess self-efficacy.  In order to validate the questionnaire a pretest was driven with a pilot group. The aim was to verify the suitability of each item to the interpretation of subjects with characteristics similar to the sample to be surveyed (Coutinho, 2011).  International Conference on Education and New Developments 2013234. Results  4.1. Focus group  From the students’ answers we were able to group their opinions in 5 categories: perceived importance of mathematics; the influence of parents/society/piers; study method/gender influence, teaching methodology/teacher. In table 1 we present the main results. Table 1. Results from focus group  4.2. Questionnaire  A total of 25 items of the instrument was analyzed. The items were presented on the format of a five-point Likert scale (1 - strongly agree, 2 - agree, 3 - not agree nor disagree, 4 - disagree or 5 - strongly disagree). The items which sound negative in their meaning were coded reversely in SPSS. All items were positively coded before proceeding with the analysis. All factors demonstrated good internal reliability, as shown in Table 2.  Table 2. Reliability Scale Nº items Cronbach’s Alpha Perceived importance of mathematics 7 (one item was removed) .741 Anxiety towards mathematics 5 .794 Self-efficacy 11 (one item was removed) .813  The characterization of the sample is presented in Table 3. From a total of 72 respondents 42.5% were female and 57.5% of them were male. The majority were MIEGI students (43.8%) followed by MIEMAT students (24.7%), MIEBIOL students (21.9%) and MIEPOL students (9.6%). Table 3. Profile of Respondents     Respondents’ Profile  Number of respondents Percentage of respondents Gender Male Female 42 31 57.5 42.5 Course MIEBIOL MIEGI MIEPOL MIEMAT 16 32 7 18 21.9 43.8 9.6 24.7   Students’ level of perceived importance of Mathematics, anxiety towards Mathematics and self-efficacy. Table 4 indicates descriptive measures of students’ level of perceived importance of Mathematics, anxiety towards Mathematics and self-efficacy. The mean of all respondents’ perceived importance of Mathematics is 3.90, the mean of their anxiety towards Mathematics is 2.15 and the mean of students’ self-efficacy is 3.69.  Category Main Results Perceived importance of mathematics - The mathematic was essential in their choice of courses; - Mathematics is considered as an essential discipline in course selection and a vital part of their  career as engineers Influences of parents/society/piers - Society is partly responsible for the negative views about mathematics  - The parents’ opinion is an important factor that influences the student’s view of mathematics.  Study method/gender - Female students are more methodical and devoted to their studies than their male counterparts, therefore there are able to obetian better results.  Teaching methodology/teacher. - The lectures, in their exhibition molds, require greater care at a motivation level and at making the students better perceive their importance. - Students would like their courses to address mathematical concepts  that are more in line with their future professions - The importance of the instructor is recognized when learning mathematical concepts. ISBN: 978-989-97866-5-3 © 201324Table 4. Students’ level of perceived importance of Mathematics, anxiety towards Mathematics and self-efficacy  N Minimum Maximum Mean Std. Deviation Perceived importance of Mathematics 72 2.57 5 3.90 0.51 Anxiety towards Mathematics 71 1 3.80 2.15 0.75 Self-efficacy 71 2.18 4.55 3.69 0.45 Valid N 72       Gender differences on students’ level of perceived importance of Mathematics, anxiety towards Mathematics and self-efficacy. Table 5 shows that the mean of perceived importance of Mathematics of female is 3.80 and the mean of perceived importance of Mathematics of male is 3.97. There isn’t significant difference between male and female groups on their perceived importance of Mathematics (t = 0.159, p>0.05). This table also shows the mean of anxiety towards Mathematics of male is 2.19 and the mean of anxiety towards Mathematics of female is 2.09. There isn’t also significant difference between male and female groups on anxiety towards Mathematics (t = 0.60, p>0.05). The mean of self-efficacy of male is 3.68 and the mean of self-efficacy of female is 3.70 which indicates there isn’t significant difference between male and female groups on self-efficacy (t = 0.88, p>0.05). Table 5. Students’ level of perceived importance of Mathematics, anxiety towards Mathematics and self-efficacy by gender.    N Minimum Maximum Mean Perceived importance of Mathematics Male Female 41 31 2.71 2.57 5 4.71 3.97 3.80 Anxiety towards Mathematics Male Female 41 30 1 1 3.80 3.80 2.19 2.09 Self-efficacy Male Female 41 30 2.18 3 4.55 4.55 3.68 3.70 Table 6. T-test analyzes based on gender   F Sig. t df Sig. (2-tailed) Mean Difference Perceived importance of Mathematics Equal Variances Assumed 0.983 0.325 1.422 70 0.159 0.12098 Anxiety towards Mathematics Equal Variances Assumed 0.030 0.863 0.532 69 0.596 0.09691 Self-efficacy Equal Variances Assumed 0.002 0.965 -0.168 69 0.867 0.01818   Students’ level of perceived importance of Mathematics, anxiety towards Mathematics and self-efficacy by course. Results presented in Table 7 indicate that the mean of perceived importance of Mathematics, anxiety towards Mathematics and self-efficacy of the four courses are similar. Hence further analyses indicated that there is no significant difference between groups on perceived importance of Mathematics (sig=0.274, p>0.05). There isn’t also significant difference between courses on anxiety towards Mathematics mean (sig=0.52, p>0.05)) and self-efficacy mean (sig=0.940, p>0.05) (Table 8) Table 7. Students’ profile based on course.   N Minimum Maximum Mean Perceived importance of Mathematics MIEBIOL MIEGI MIEPOL MIEMAT 16 32 7 17 3.14 2.57 3.29 2.57 5 4.71 4.43 4.71 4.11 3.83 3.76 3.87 Anxiety towards Mathematics MIEBIOL MIEGI MIEPOL MIEMAT 15 32 7 17 1.20 1 1.20 1 3.60 3 3.60 3.80 2.12 1.99 2.86 2.18 Self-efficacy MIEBIOL MIEGI MIEPOL MIEMAT 15 32 7 17 3.18 2.18 3 3.18 4.55 4.55 4.45 4.27 3.75 3.67 3.73 3.66 International Conference on Education and New Developments 201325Table 8. Analyzes based on course (Anova)   Sum of Squares df Mean Square F Sig. Perceived importance of Mathematics Between Groups Within Groups Total 1.027 17.581 18.609 3 68 71 0.342 0.259 1.325 0.274 Anxiety towards Mathematics Between Groups Within Groups Total 4.307 35.510 39.817 3 67 70 1.436 0.530 2.709 0.52 Self-efficacy Between Groups Within Groups Total 0.083 13.975 14.058 3 67 70 0.028 0.209 0.133 0.940  5. Conclusions   Results show that students have a high self-efficacy and a high perception that the learning of mathematical concepts and the development of mathematical skills is essential for progression in their future career. It is evident from this study that students generally see the relevance of mathematics to engineering courses. Mathematics is considered as an essential discipline in course selection and a vital part of their career as engineers. The importance of the instructor is recognized when learning mathematical concepts. Students would like their courses to address mathematical concepts that are more in line with their future professions. We consider these results as preliminary results, which require future evidence with a bigger sample and a comparison with other engineering students.  References  Bai, H., Wang, L., Pan, W., & Frey, M. (2009). Measuring mathematics anxiety: Psychometric analysis of a bidimensional affective scale. Journal of Instructional Psychology, 36 (3), 185-193. Bakar, K.A., Tarmazia, R.A., Mahyuddina, R., Eliasa, H., Luana, W.L., & Ayub, A.F.M. (2010). Relationships between university students’ achievement motivation, attitude and academic performance in Malaysia. Procedia - Social and Behavioral Sciences. 2(2), 4906-4910.  Buescu, J. (2012). Matemática em Portugal: Uma questão de Educação. Lisboa: Fundação Francisco Manuel dos Santos. Coutinho, C. P. (2011). Metodologia de Investigação em Ciências Sociais e Humanas: Teoria e Prática. Coimbra: Almedina. Conboy, J. (2011). Retention and science performance in Portugal as evidenced by PISA, Procedia Social and Behavioral Sciences, 12, 311–321 Flegg, J.; Mallet , D., Lupton , M. (2012). Students' perceptions of the relevance of mathematics in engineering. International Journal of Mathematical Education in Science and Technology, 43(6), 717-732. Homayouni, A. (2011). Personality Traits And Emotional Intelligence As Predictors Of Learning English And Math. Procedia - Social and Behavioral Sciences, 30, 839-843.  Kargar, M. Tarmizi, & R.A. Bayat, S. (2010). Relationship between Mathematical Thinking, Mathematics Anxiety and Mathematics Attitudes among University Students. Procedia - Social and Behavioral Sciences. 8, 537-542.  Korea, S.; Kore, J.; Korea, Y. (2009). Development and validation of a scale to measure the engineering self efficacy for engineering students. http://www.ineer.org/Events/ICEEiCEER2009/full_papers/full_paper_158.pdf Meelissen, M., & Luyten, H. (2008). The Dutch gender gap in mathematics: Small for achievement, substantial for beliefs and attitudes. Studies in Educational Evaluation, 34(2), 82-93 Sirmaci, N. (2010). The relationship between the attitudes towards mathematics and learning styles. Procedia - Social and Behavioral Sciences, 9, 644-648. ISBN: 978-989-97866-5-3 © 201326

Engineering students and the application of mathematical knowledge : how to explain the difficulties experienced?

http://repositorium.sdum.uminho.pt/bitstream/1822/25202/1/AMR_MA_CR_CC_END2013.pdf

Engineering students and the application of mathematical knowledge : how to explain the difficulties experienced?

Abstract

Similar works

Full text

Available Versions

Universidade do Minho: RepositoriUM