Keywords

1 Introduction and Literature Review

In modern mathematics curricula, the teaching of statistics is carried out from the first years of elementary school. It is reported that [1] it is necessary to prepare students for a world marked by information as they should acquire the ability to understand and manage information with the available tools of statistics, in order to make logical decisions on global issues. The teaching of graphic representations “satisfies” the globalized tendency to visualize the world, with the aim of gaining the maximum possible knowledge, as they make the learning-scientific-statistical material attractive, interesting and understandable, and function as an epistemological and pedagogical tool [2, 3]. The student needs to know the techniques of Summary Statistics and data visualization and not to confuse the concepts. This is why a statistics course in a university, should emphasize statistical thinking, focus on understanding concepts, integrate real data into teaching, use technologies and scenarios that encourage discovery learning [4].

A professor should know pedagogical approaches and technologies that he/she can apply [5]. A modern teaching approach is necessary which will take into account the level of knowledge of the students, will use real data so that the results of the processing become understandable and will use appropriate technologies [6].

Modern statistical software can implement the main modern statistical techniques and data processing methods. However, this software has a complexed environment that needs learning, and the anxiety about this learning often acts as a hindrance for the student. For example, in this kind of software, in order to enter data, after learning the environment for entering data and data types supported by the software, rules must be applied concerning the data validation [7]. The situation becomes more complex when students have different levels of knowledge of basic mathematical and statistic concepts. In this case, special attention is needed and the matter should be dealt with in an appropriate way, so that differences of this kind are mitigated in the classroom. Pedagogical learning theories advocate that discovery and cooperative learning can help even weak students understand mathematical concepts through discovery and construction. Learning by observation can bring about a positive result with appropriate software and generally through modeled direct, symbolic or complex behaviors [8].

It has been observed that visualization of concepts and simulations that allow experimentation are suitable tools for the discovery of knowledge. Researchers report that the use of simulations can help in understanding statistic concepts [9,10,11]. Other research has shown that software that has the ability to visualize concepts and results enables students to make sense of data and results, draw conclusions, and understand concepts [12,13,14]. It is also reported that the use of specialized software applications can help solve problems of understanding statistic concepts and have positive effects in the teaching of Statistics as well as in environments where students have different backgrounds [15]. These applications can be built using programming tools, but also using spreadsheet software or mathematical software. The usefulness of spreadsheets in the organization, presentation, management of quantitative data and their processing results is proven, as well as that spreadsheets can be used as tools with which models can be built and models already built by third parties can be explored [16].

Also there is Mathematical software that is user-friendly and easy to grasp and has the ability to create interactive applets. This software can be used to create specialized applications that will visualize or simulate concepts and allow experimentation for their users [17, 18]. The aim of this paper is to demonstrate that the use of specialized software applications can motivate and help the students to explore statistic concepts.

2 Materials and Methods

2.1 Research Methodology

This paper studies the effect on understanding and change in performance in Statistics courses when students use specialized software applications to learn statistics concepts. For this purpose, an introductory statistics course was taught in a Business Administration department at a tertiary institution using such applications. The teaching intervention was designed and adapted without making any changes to the course outline. Specialized Software applications were used, simple to understand and use, which were adapted to suit. These applications acted as software that could simulate concepts, and allowed students to experiment with real data and answer the worksheets they were given.

The students who participated in this survey, were divided in two groups for the purpose of the research. The separation was done in such a way that the two groups have approximately the same average level of knowledge and have approximately the same composition in terms of gender and origin. One of these groups, the experimental group, in each teaching unit, used an appropriate designed application together with the corresponding worksheet. This application was used by the students for experimentation and the completion of the corresponding worksheet which contained exercises and questions of exploration and experimentation with data changes. Students usually worked in groups of two.

In other words, during the semester the experimental group used a set of specialized software applications that visualized and/or simulated basic concepts of statistics and probability theory, descriptive statistic measures, and plotted distributions of random variables and created a model for the correlation of two variables that plotted the regression line using the method of least squares. The applications used in this teaching intervention, covered almost the whole course. Students in the experimental group worked in small groups and using the appropriate application explored these concepts and gathered knowledge. Worksheets are distributed weekly for completion by groups of students working together for experimental group only.

The control group, used general statistical software only and teaching was done in the traditional way. Forty-eight (48) students participated in each of the two groups, of which at the end of the semester, 47 from the control group and 46 from the experimental group participated in the final examination of the course and were taken into account in the present study. For all students who participated in the final examination of the course, their performance and the result (pass/fail) were recorded. It was then examined whether the contribution of the use of specialized software applications actually contributed to the result of the final exam of the course.

3 Findings

After analysis and statistical processing of the data, it was found that the use of specialized software applications can positively affect the performance of students in the final exam of the course and could be an important factor for understanding statistical concepts and acquiring statistical knowledge (Table 1).

Table 1 Group statistics
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A hypothesis was tested at the 5% significance level as to whether the mean final grade on the course exam was significantly different between those who used specialized software applications and those who did not. As seen in Table 2, it must be rejected that there is no difference between the two groups since it is p-value = 0.02(<0.05) and we must accept in a one-sided test that the average final grade in the course exam is higher for the group that used wrote specialized software applications.

Table 2 Independent samples test
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Also, for the difference in the average final grades in the course exam between the two groups with the specific composition, the non-parametric Mann–Whitney test was performed, which concerns two independent samples, so as to ensure, in case it can be considered that there is no normality that again there is a statistically significant difference in the average final grade (Table 3).

Table 3 Ranks
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This test, which was done at a significance level of α = 0.05, as shown in Table 4, gave a p-value = 0.008 < 0.05, which means that even in the event that the grade in the final exam of the course does not follow the normal distribution, it can be considered that there is a statistically significant difference in the average grade of the final exam between the two groups.

Table 4 Test statisticsa
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4 Discussion and Conclusion

To teach an introductory statistics course in the University of West Attica, a set of specialized software applications were built in spreadsheet software and mathematical interactive software was used.

In the basic benefits of these applications is that they make it easy for the student to explore, discover, deepen into concepts and modify data instantly and easily for experimentation. Also, these applets have a user friendly interface that does not present difficulties in its learning and thus the student does not have additional stress for learning commands, rules and tricks of the software. With any changes in the data, recalculations are made and it is not necessary to re-execute commands most of the time, so that the user's attention is not distracted from exploring the concepts.

According to literature review the use of software that has the ability to visualize concepts and simulations can help in understanding statistic concepts [9,10,11,12,13,14]. It is also reported that the use of specialized software applications can help solve problems of understanding statistic concepts even in environments where students have different backgrounds [15].

In conclusion, it appears that the use of specialized software applications that visualize and/or simulate statistical concepts, if done in an appropriate way, can lead students to discover statistical concepts and inferences and ultimately promote statistical literacy.

How a person learns, and which didactic approaches and learning theories are appropriate so that the possibilities of acquiring knowledge by the student are great, have preoccupied researchers and are topics for which there are aspects that need to be investigated more [19]. In any case, the teacher, after first investigating and getting to know the knowledge level of the class, should apply modern teaching methods promoting active learning. Specialized software applications can help discover statistical concepts. Further research could take place to examine other potential Implications from use of specialized software applications in learning of statistic concepts for higher education.