Mathematics study outcomes as an indicator of the quality of the university education

The main aim of this contribution is to analyze the study outcomes in mathematics, which are an important indicator in assessing the quality of university education. We focused on students' knowledge in solving the tasks of mathematical analysis and linear algebra. Method of statistical testing of hypothesis was used to evaluate and analyze the results of students in selected tasks. The obtained number of points in math tasks became the object of hypotheses which were verified by methods of Ftest and t-test. Knowledge and skills acquired from mathematics will be useful basis for the study of another exact methods and procedures from mathematics and statistics. It is assumed that students will apply these methods in the analysis of empirical data in the bachelor and diploma theses.


Introduction
In the conditions of information society the content of education is still changing and very quickly updating.University study programs reflect the requirements of the labor market that requires creative, flexible and quick minded people.
At the Faculty of Biotechnology and Food Sciences (FBFS), the Slovak University of Agriculture (SUA) in Nitra, opportunities for employment of graduates are primarily focused to the area of biotechnology and food processing.
Universities are searching possibilities how to attract students, how to offer high quality education and how to bring value added and differentiation to the university education.Competitive environment around us generates need of high quality, unconventional and innovative solutions in the sphere of higher education everywhere in the world.Bologna process is one of those approaches enabling harmonization and mutual cooperation of universities around the world (Horská, Ubrežiová and Palková, 2015).
Professional public accreditation of educational programs shall be the recognition that the quality and level of training of graduates who have studied such an educational program at a particular educational organization meet the requirements of professional standards and labor market set for workers and employees of the relevant specialization (Petropavlovskiy, Smelik and Nefedova, 2015).
Most of the agro-food complex enterprises see opportunities especially in the internationalization, globalization and regionalization in the agri-food sector, in pursuance of http://dx.doi.org/10.15414/isd2016.s8.11 this, they are gradually smouldering innovative activities and trying to work on their competitive advantages (Ubrežiová, Kapsdorferová and Sedliaková, 2012).

Data and Methods
The first aim of this paper is to identify important and interesting questions associated with the quality of mathematical education of future engineers for the area of food science.At the SUA in Nitra the scope of their mathematical course is only one semester with the range: 1 hour of lecture per week and 3 hours of practical seminar per week.
We obtained data about students' skills and knowledge from the teaching of obligatory subject Mathematics (taught in the 1 st study year of bachelor degree).We focused on two basic topics of the mathematics course: -function of one real variable, -linear algebra.
We summed up results from students' partial tests during semester and final exam tests.Given test tasks are in accordance with the study literature (Országhová, Matušek, Pechočiak, Baraníková and Drábeková, 2013), (Országhová, Hornyák Gregáňová, Pechočiak, Farkašová, Drábeková and Kecskés, 2014).Appropriate methodology for analysis of obtained data followed from the aim; we used these statistical methods: -F-test, -parametric two sample t-test.
The detailed description of these statistical methods can be found in Markechová, Tirpáková and Stehlíková (2011).The existence of dependences and statistical significance among obtained data were examined by mentioned statistical testing methods.Firstly we analyzed the responses via statistical F-test whether observed random samples have the same variance.We test the null hypothesis Then we applied two-sample t-test with equal variance.We test the null hypothesis about the samples means 2 1 0 :

H
. The statistical significance was verified through the p-value, which is the probability of an error that occurs when the tested hypothesis is disapproved.If the calculated p-value is sufficiently small (p < 0.05, resp.p < 0.01), then the test suggests that the observed data are inconsistent with the null hypothesis, so the null hypothesis have to be refused (at the chosen significance level 0.05, resp.0.01).
The second aim of this paper is to present results of realized survey about the employment of graduates of the Faculty of Biotechnology and Food Science.This survey was realized during the period from November 2015 to December 2015.We used the method of an exploratory questionnaire to identify graduates opinions about their education and career opportunities after students' graduation from the university.

Results and Discussion
Mathematical knowledge and their level are being studied in this contribution and we are focusing on the students of FBFS.After graduation of engineers trained for the area of food production and food science, they often use mathematics apparatus and methods in various specialized fields.
The assessment of learning outputs is one of the crucial components of the instruction.The teachers have different ideas regarding the implementation of assessment strategies.Assessment should be objective; it should correspond to the level of knowledge achieved by students in education.Authors trying to figure out whether the final grade for the exam in the fall semester is right for the level of students' knowledge acquired in the second summer term follow-up on the results of the partial test (Švecová, Drábeková and Hajdúk, 2014).

The analysis of study results via statistical testing of hypothesis
The first research objective is to evaluate the level of students' knowledge of mathematical compulsory subject Mathematics taught in the summer semester.In the Table 1 numbers of students with examination grades are summed up from subject Mathematics within the period 2010 − 2015.Based on the average classification (last column in the Table 1) we can conclude that learning outputs in mathematics within the period 2010 -2015 are balanced and without major fluctuations.This is also confirmed by the numbers of students with exams grades A(1) -E(3) in separate years.In the contemporary educational system students are not motivated to achieve better study results and do not understand the importance of the use of mathematics.For teachers it is difficult to teach mathematics applications without basic knowledge from mathematics.
In this section we will continue in analysis of the study outputs within the period of two academic years: The formulation of the first null hypothesis 01 H : Students achieve equal level of knowledge in the topics matrices and systems of linear equations.
 Since the calculated value of the t-test criterion is greater than 0.05 the null hypothesis  Students achieve the same level of knowledge in the topics matrices and systems of linear equations.Finally, we can state that students achieve the same level of knowledge in the topics function property and derivative of a function.

  
H cannot be refused.The differences in compared values are statistically significant.Students achieve different level of knowledge in the topics function property and derivative of a function.From average number of points follows that in solving the task "derivative of a function" students gained more points.
The usefulness and applicability of mathematical knowledge are found in many publications.
As an example, we can mention the use of mathematical tools and methods for the calculations in molecular biology and biotechnology in the book "Calculations for molecular biology and biotechnology: a guide to mathematics in the laboratory" (Stephenson, 2010).
Applications of functions, derivatives and differential equations in microbiology are presented in the paper (Drábeková and Kecskés, 2010); authors focused on the model of the bactericidal effect of ultraviolet radiation.In terms of increasing the efficiency of the learning process in mathematics is needed, and might even be necessary, to present and teach applications of special mathematical methods in engineers practice and research.

The survey about the employment of graduates of FBFS in the labor market
Food science and biotechnology are important part in the issues of the sufficiency of food and nutrition for people.Interest in transgenic foods has grown rapidly in recent decades.Hudson, Caplanova and Novak (2015) used Eurobarometer 73.1 survey data on biotechnology, science and technology, with 15,650 respondents.They found that attitudes to the risks and gains are determined by socio-economic variables and also by the individual's knowledge, scientific background, their parent's education in science and their religion.
The current labor market trends are associated with high requirements for professional abilities of university graduates.At the Faculty of Biotechnology and Food Sciences, the Slovak University of Agriculture in Nitra, opportunities for employment of graduates are primarily focused to the area of biotechnology and food processing.In this context, we decided to find out in cooperation with teachers from the faculty FBFS the current situation of job placement of graduates.The sample consisted of graduates from of FBFS in academic year 2014/2015.During the period of months November -December, 2015, was conducted a survey at the Faculty of Biotechnology and Food Science (FBFS).The main interest was to find out the rate of employed and unemployed graduates in the labor market.Via the questionnaire it was interviewed 289 graduates; 107 respondents (graduates) sent back the questionnaire replies.Based on data, it was found that after graduation form SUA in Nitra in years 2014 and 2015 only 2.8 % of respondents are unemployed.Figure 1 shows the classification of the faculty graduates in engineering study programs according to their economic activity at the end of December, 2015.
Based on the results of actual survey about the employment of graduates from the faculty FBFS we can state that graduates found jobs in areas they had studied.Adding another result, from the group of 107 respondents of the survey 15 persons reported that they are working in the area of "professional, scientific and technical activities".We could assume that better knowledge in mathematics and statistics can help students to find a job in various professional and research areas after graduation.
Ongoing internationalization and world globalization processes significantly shape the market for agri-food products.Businesses face requirements to meet ever more stringent public food safety standards and maintain customer confidence at a time when global supply chains are becoming more complex.Various kinds of analysis of agri-food products are based on interdisciplinary research and knowledge.Authors (Mura, Buleca, Zeleňáková, Qineti & Kozelová, 2012) have dealt with the analysis of selected indicators of Slovak dairies international business activities within the EU.The research has shown that contacts management has been important in the penetration of Slovak dairies into target foreign markets.
Applied mathematics combines mathematics, statistics, computer science, physics, engineering, economics, and social sciences to solve real-world business problems.High school graduates still have interest in university education and some of them will have to solve current research problems using interdisciplinary methods of applied mathematics.

Conclusion
The main aim of this contribution was statistical analysis of mathematics study outcomes as an indicator of the quality of mathematics education at a university.We analyzed students' knowledge in the solving tasks from mathematics in the summer semester of the 1 st study year at the bachelor degree.Tasks were focused on four topics: matrices, systems of linear equations, function with one real variable and derivative of a function.Analyzed data were obtained as number of points from solving math tasks by students of FBFS.Points of selected tasks became the object of formulated hypotheses which were verified by statistical methods of F-test and ttest.In the contemporary society the education is gaining new attributes and for university graduates the level of knowledge and abilities is very important factor for employment on labor market.In the contribution we presented outputs to the second main aim of the paper: results of conducted survey among graduates of the Faculty of Biotechnology and Food Science of SUA in Nitra.
 Based on the obtained results of statistical analysis, we can conclude that some students have abilities to use and handle mathematical apparatus on very good level.Via the cross-curricular relations the quality of university education can be improved and help students to understand and combine knowledge of different areas.
 The level of students' knowledge from topics functions and linear algebra is adequate and fairly balanced.According to research results we can state that there are no significant differences in students' knowledge in topics matrices and systems of linear equations.Next, we found that there exist significant differences in students' knowledge in topics function property and function derivative.
 From the questionnaire and gathered views of graduates we can claim that students of the Faculty of Biotechnology and Food Science, the Slovak University of Agriculture in Nitra, consider the study of food science and biotechnology branches as a good foundation for their success in the labor market after graduation from the university.
The education of future experts and scientists in the field of biotechnology is important from many aspects.University study programs relating to food products, food science and food industry will always have the important position in the university educational system.

H
cannot be refused.The differences in compared values are statistically insignificant, caused only by random factors.

Figure 1 :
Figure 1: The employment of graduates of FBFS in the labour market (December, 2015)

Table 1 : Numbers of students with given exam grades in Mathematics at FBFS (2010 -2015) Number of students with grade Number of students
Source: authors' calculations 2013/2014 and 2014/2015.The first statistical sample consisted of 86 respondents (students) of the Faculty of Biotechnology and Food Sciences (FBFS) in academic year 2013/2014; second one consisted of 61 respondents (students of FBFS) in academic year 2014/2015.Topics from the theory of functions and linear algebra belong to the basic parts of taught course Mathematics.Math tasks from written tests were about functions, derivatives, matrices and systems of linear equations.Analyzed data were obtained as the number of points in solving these math tasks by students in partial test and exam test.For the right answer the student could obtain maximum of 10 points in each task.We realized the selection of students by single survey, non-anonymously.Then the list has been changed into anonymous; each student has appeared in the table with the serial number and with obtained points.Data processing of the statistical sample was realized by mentioned statistical methods of F-test and two samples ttest with the usage of MS Excel 2010.We tested two hypotheses.http://dx.doi.org/10.15414/isd2016.s8.11

Table 2 : Data testing and observed statistical characteristics (academic year 2013/2014)
We realized calculations via tools of MS Excel 2010 and our obtained results are in the Table2.Based on carried out statistical tests we can conclude that:  In F-test we got inequality F-test > 0.05; it means that the difference between the variances is statistically insignificant.The null hypothesis

Table 3 : Data testing and observed statistical characteristics (academic year 2014/2015) Topic Matrices Systems of linear equations Function property
We realized calculations via tools of MS Excel 2010 and our obtained results are in the Table3.Based on results of statistical analysis outputs in 2014/2015 we can conclude that: In the first case (topics -matrices and systems of linear equations): Since the calculated value of the t-test criterion is greater than 0.05 the null hypothesis The differences in compared values are statistically insignificant.Students achieve the same level of knowledge in the topics matrices and systems of linear equations.
 In F-test we got inequality F-test > 0.05; it means that the difference between the variances is statistically insignificant.The null hypothesis cannot be refused.