Identifying the Factor of Mathematical Reasoning That Affects the Ability to Programming Algorithm

This paper examines the limited proficiency to engage in programming algorithms among university students in information technology and information system in several universities across Surabaya, Indonesia. The purpose of this research is to find the most influential factor in learning programming algorithm using a quantitative approach. The research subjects were second-semester information technology students in several private universities in Surabaya, Indonesia. The research instruments were mathematical reasoning and basic algorithm programming test. Mathematical reasoning tests incorporated linear algebraic, basic calculus, and mathematical logic. The data analysis used was variant-based Structural Equation Modelling, also known as Partial Least Squares Structural Equation Modelling based on Smart-PLS 3. With α = 5%, the research results conclude that mathematical reasoning positively influences algorithm programming ability with an R score of 0.999, and that the most influential variable among mathematical reasoning abilities was algebra with an R score of 0.732.


Introduce the Problem
This study was motivated by the findings of Hartati (2014). A review of the literature shows that the algorithm programming is a course that is not easy for the students majoring in Information System and Informatics in several private universities in Indonesia (Marisa, 2008;Sarah-Bibi, 2015;Arifin, 2017). These results indicate that since 2008, the algorithm programming has been a challenge for the lecturers in several private universities in Indonesia. The learning objectives of programming algorithms include making computational algorithms, which is a skill that must be taught in schools (Weintrop et al., 2016). Mohaghegh (2016) recommends computational thinking as a core topic in basic and secondary education. Meanwhile, according to Hsu, Chang, & Hung, (2018), computational thinking has been an interesting discussion in various countries, including in Australia and North Korea, since 2006. Computational thinking is the everyday living skills needed by everyone, not just programming skills used commonly by computer scientists (Wing, 2006(Wing, , 2008. According to (Haseski, Ilic, & Tugtekin, 2018), computational thinking is an important part of learning in the 21 st century. (Weintrop et al., 2016) assigned 10 initial skills in computational thinking that must be taught in school. One of them is making an algorithm. Based on these considerations, the difficulty in understanding algorithms for students in several private universities in Indonesia is an interesting problem that requires a solution. To this end, we seek to identify the factors of mathematical logic that affect the ability to programming algorithms (Pendidikan, Kebudayaan, & Indonesia, 2018). However, the fact is that the mathematical reasoning ability of Indonesian students is still far behind that of other countries. In 2018 Indonesia ranked 72 out of 78 countries with a score of 379 (OECD Better Policies For Better Lives, 2019). While the average value of PISA participants from 78 countries is 489 (OECD Better Policies For Better Lives, 2019). Based on the results of the national examination evaluation conducted by the Indonesian Ministry of Education and Culture, the national exam scores for high school mathematics subjects decreased, in 2017, 2018, and 2019 namely 37.61, 33.86, and 34.94, respectively. This value is far below the standard set by the Indonesian Ministry of Education and Culture, which is 70-85 (Utomo & Narulita, 2018). This is a challenge for private university lecturers organizing Informatics Engineering Study Programs to continue to provide greater opportunities for high school graduates to study computer science. Hartati (2014) mentioned that the characteristics of the knowledge learned in programming algorithms are conceptual and metacognitive. Therefore, prospective new students must have above-average mathematical thinking skills. This explains why the study programming algorithm is included in the category of natural sciences in the national education system in Indonesia. However, these requirements are not a major concern in several private universities in Indonesia. With the consideration that the college should give the opportunity to every citizen to continue to higher education in accordance with his choice. As mandated by the Constitution Article 31, every citizen is entitled to education (Mohammad, 2010). Consequently, the lecturer or educator of algorithm programming must think hard to solve the challenge. The general purpose of learning to programme algorithm is to provide a computational rationale, specifically in the stages of turning certain inputs into specific outputs (Kachroo, Krishen, & Agarwal, 2017;Eglen, 2009;Ou, 2005) using computers. Computational thinking is presented in the form of a flowchart and/or pseudo code. Hartati (2017) concluded that making programming algorithms requires creative mathematical logic to compile a set of reasoning by deduction, which is a systematic collection of several propositions. According to Johar, Yusniarti, and Saminan (2018), Indonesian children are not accustomed to the training of logical thinking, particularly proportional reasoning. Tourniaire and Pulos in 1985 argued that proportional reasoning is reasoning about the equality of two ratios (Johar, Yusniarti, & Saminan, 2018). However, according to Septia, Prahmana, Pebrianto, and Wahyu (2018), logical ability can be enhanced with continuous training. Based on these facts, mathematical reasoning training is needed for Informatics Engineering study students whose majority of students has low mathematical abilities. For this reason, mathematical reasoning factor analysis is needed that can improve the ability to make basic level computational algorithms.

Describe Relevant Scholarship
This paper aims to identify the most influential mathematical logic that increases capabilities to programming algorithms. This discussion is important, as part of an effort to improve the ability of the programming algorithm because it cannot stand alone. Especially for subject participants who have mathematical abilities below 70. It includes the logical ability to solve problems in linear algebra, calculus, and mathematical logic. There are two thoughts underlying the selection of those three abilities. First, the three materials are the basic mathematics material taught in the first semester, as well as in programming algorithms. Second, based on Plato's opinion contained in Attridge (Attridge & Inglis, 2013), people who have the competency to calculate in general understand other knowledge faster. If they are trained in arithmetic, then the ability to understand knowledge is expedited. Calculation competencies are studied in basic calculus and algebra. In basic calculus, there are calculations on number theory. In algebra, there is a discussion on matrix operations.
Several studies relating to the problem of improving the ability of programming algorithms are still being discussed today in Indonesia and elsewhere. Maulana (2017) believes that logic and algorithms are abstract material, making it difficult for students to learn. He overcame this problem by creating learning media called EL-algorithm, such as modules, Edmodo, and the like. However, it does not address the fundamental difficulty of students which is increasing the ability of abstraction. In addition, there is no information concerning the research that was conducted and the research subject. Likewise, Nuraini (2015) argues that making the matrix multiplication operation algorithm is considered difficult for some people to understand. The difficulties include arranging the steps, the logic sequence, the decision making, and the arithmetic process. She accomplished this by making a flowchart and pseudocode for matrix multiplication. The solution from the perspective of learning theory does not solve the problem. Whereas Combéfis et al. (2017) argue that computer scientists must have the skills to design efficient algorithms. This means that according to them, computer scientists are not only able to make algorithms, but also must produce efficient algorithms. The efficiency is measured using the analysis called big O, or running time (McConnell, 2001;Kozen, 1991) in the form of the mathematical functions found by the algorithm generator. Thus, high-level mathematics logic capability is necessary for programming algorithms.
Hwang, Kuo, Yin, and Chuang (2010) developed a learning system that can detect the behaviour of the students in the context of learning in the real world with the help of technology (sensors) supported by Heuristic Algorithms. The students are guided to operate the objects of the real world through the digital world so that a learning pathway model is found according to the students' needs. However, what was developed was elementary ecological learning and was carried out outside Indonesia. Thus, there are no factors that affect the ability to increase the ies.ccsenet.org International Education Studies Vol. 13, No. 5; capacity to programming algorithms. Inglis and Attridge (2016) argue that studying advanced mathematics will develop conditional logic, although not for all students who are forced to study advanced mathematics. Thus, to improve the ability of basic level programming algorithms for students with mathematical abilities below 70 years requires the analysis of basic reasoning mathematical factors that affect the ability to compile a basic level programming algorithm. This is important because it is very difficult to find publications that discuss the topic.
Some studies use SEM (Stands for Structural Equation Modelling) to perform factor analysis. According to Khosrow-Pour (Schmalbach & Maza-Avila, 2018), the aim of this technique is to explain the relationship between latent variables and observed variables. SEM is a standard for analyzing cause-effect relationships between latent constructs (Hair, Ringle, & Sarstedt, 2011). According to Gefen, Straub, and Boudreau (Achjari, 2004), the use of SEM assumes that the relationship between items and their constructs and relationships between constructs is linear. While for Sarstedt, Hair, Cheah, Becker, & Ringle (2019), SEM is a high-level construction, which facilitates modelling of the construction at a more abstract high-level dimension and a more concrete low-level subdimension. There are two methods, namely covariant-based called CB-SEM and variant-based called VB-SEM, which were introduced by Wold in 1966 (Hamdollah & Baghaei, 2016), with the name PLS-SEM (Partial Least Square -SEM). One of the differences between the two is that the CB-SEM requires a large sample size, a minimum of 200 (Schmalbach & Maza-Avila, 2018), while PLS-SEM can be used for small samples. PLS-SEM is widely used in research in the fields of business, management, accounting studies, computer science, social science, engineering, and social science. As for education, such as mathematics has not been as much as mentioned above. Hamdollah and Baghaei (2016) use PLS-SEM to investigate factors that contribute to the apathy dimension in adulthood. These factors include cognitive, emotional, and behaviour. They found that various apathetic factors related to cognition to varying degrees. Shahijan, Rezaei, and Amin (2016) investigated the impact of perceived brand orientation, intercultural friendship, and university reputation in international classes on the satisfaction and intentions of continuing student studies in higher education in Malaysia. Their findings indicate that brand orientation and university reputation positively influence satisfaction and intentions to continue studies, intercultural friendships affect intentions to continue studies but not with satisfaction. Hamdollah and Baghaei (2016) studied the factors that contribute to the psychological and sociocultural adaptation and welfare of students in the international class of the host country (Malaysia). Their model shows that the length of stay in the host (Malaysia) negatively affects the attachment to the host. Furthermore, positive attitude adjustment influences psychological and sociocultural adaptations. Hauser, Paul, & Bradley (2012) studied the relationship between changes in computer self-efficacy and computer anxiety and their effects on performance on online computer-related and face-to-face education tasks. They concluded that, in face-to-face education, ongoing dialogue is needed with students to enhance learning, logical organizing is essential in online media. Al-Azawei and Lundqvist (2015) investigated factors related to student satisfaction in online Arabic courses. Their findings indicate that learning styles and gender do not have a significant effect on perceived usefulness, perceived ease of use, and of course satisfaction.
Given the small sample in this study, PLS-SEM was chosen, whereas for data processing, Smart-PLS was chosen. According to Garson (2016) and Monecke and Leisch (2012), Smart-PLS is free software commonly used for path models. The software was developed by Hair et al. (2011), Monecke and Leisch (2012), Wong (2013), Al-Azawei and Lundqvist (2015), Hamdollah and Baghaei (2016), Garson (2016) and Sarstedt et al. (2019) on the Java Eclipse platform. In other words, Smart-PLS is the leading software application for PLS-SEM.

State Hypotheses and Their Correspondence to Research Design
Based on the explanation above, this paper seeks to determine the level of influence of mathematical reasoning abilities on the ability to make programming algorithms. It analyses the most influential mathematical logic on the ability to create a programming algorithm. In this research, mathematical logic refers to algebra, calculus and the logic of mathematics. The hypothesis tests the extent mathematical logic influences the ability to create a computing algorithm, and the results show that it has a very significant effect on the ability to create a computational algorithm.
This results showed: (1) there is a correlation between algebraic and programming algorithm ability with a correlation score of 0.935, (2) there is a correlation between mathematical logic and programming algorithm ability with a correlation score of 0.796, (3) there is a correlation between basic calculus and programming algorithm ability with a correlation score of 0.664, (4) there is a correlation between mathematical reasoning and algebraic ability with a correlation score of 0.624, (5) there is no correlation between mathematical reasoning and basic calculus ability, where the correlation score is only 0.125, (6) there is a correlation between basic calculus and algebraic ability with a correlation score of 0.659.

Procedures in the Study
Flow in Figure 1 is a research process that begins with the selection of research samples. Then, proceed with tests of mathematical logic abilities, algebra, basic calculus, and programming algorithms. The ability test results are then processed and analyzed using smart-pls software. The results of testing are obtained (i)the Average Capability of Mathematical Logic, Algebra, Basic Calculus, and Programming Algorithms, (ii) the value of R Square for the ability to Programming Algorithms, algebra, and calculus, (iii)correlations between the variables programming algorithm, algebra, calculus, and logic of mathematics, and (iv)the Path Coefficient of model.

The Conceptual Model of Research
There are six hypotheses that are tested: (1) H 1 : Proficiency in algebra influences algorithm programming proficiency, (2) H 2 : Proficiency in the logic of mathematics influences algorithm programming proficiency, (3) H 3 : Basic arithmetic capabilities influence algorithm programming proficiency, (4) H 4 : Proficiency in the logic of mathematics influences algebra proficiency, (5) H 5 : Proficiency in the logic of mathematics influences basic arithmetic proficiency, (6) H 6 : Proficiency in basic arithmetic capabilities influences algebra proficiency. The conceptual model of this hypothesis is presented in Figure 2.

General Description of Data
The sample comprises of 54 students studying linear algebra and programming algorithms. At the beginning of semester 2, they were given a test of basic calculus and logic of mathematics, which is a semester 1 course. At the end of semester 2, they were given an algebra test and a programming algorithm. The test results are presented in the form of a graph of the average ability of algebra, logic of mathematics, calculus, and programming algorithms shown in Figure 3. The result of the processed data showed that the average score for mathematical reasoning was below 55. The highest average score was in algebraic ability, and the average score is 54.93, with a standard deviation of 10.9. It is followed by a programming algorithm which scored an average score of 50.37 with a standard deviation of 10.13. The third is basic calculus with an average score of 50.7 and standard deviation of 9.54. The lowest average score is in mathematical logic ability, where the average score is 46.5, with a standard deviation of 16.36.
The algebra test material includes addition, subtraction, and matrix multiplication operations. Matrix operations provide the basic ability to understand operations on variable arrays, both one-dimensional (1-D) and two-dimensional (2-D). The test results show that students cannot perform arithmetic operations for array variables. The error occurred because students did not understand the terms of the multiplication operation on two matrices.
The calculus test questions consisted of basic arithmetic operation, equality, and inequality. The equation is divided into two parts, explicit and implicit. Most of the mistakes in basic arithmetic operations were in the operations with a rational number less than one. It resulted in an incorrect equality solution. For inequality problems, most of the students were unable to give a set of solutions. Understanding equality and inequality theory are basics for differentiating "command" or "instruction" and "condition" to programming algorithms. Students were inexperienced to change implicit equality into explicit equality. Creating "command" and "instruction" in the program's algorithm is related to the ability to explicitly make algebraic equations. Meanwhile "condition" is related to the ability to determine the implication and relation of two or more prepositions.
The logic of mathematics tests consisted of true proposition value problems. In relation to calculus, it leads to the creation of value example that includes solution to inequality. In relation to programming algorithm, it is understanding of condition concept. The algorithm programming test seeks is to determine the students' ability to understand the basics of algorithms that were presented in flowcharts and pseudocode.

Correlation Analysis
Based on the results of the data processing by utilizing Smart-PLS, the R Square model is obtained and presented in Table 1. R Square model's function is to elaborate on the independent variable's contribution to dependent variables (Hamdollah & Baghaei, 2016). In this research, the dependent variable is the programming algorithm. Independent variables are algebra, calculus, and logic of mathematics. The results of the calculation are shown in Table 1.  Table 1 showed that, altogether, algebraic proficiency, mathematical reasoning proficiency, and basic calculus proficiency contributed to programming algorithm proficiency by 99.9%. Mathematical logic and basic calculus collectively contributed to algebraic proficiency by 73.2%. Whereas mathematical logic has a very low contribution to calculus proficiency at only 1.6%. Correlations between the variables (capability) programming algorithm, algebra, calculus, and mathematical logic are presented in Table 2. According to (Sarwono, 2006), the criteria to explore the correlation of two variables are as follows: (1) if the value of correlation coefficient is = 0, it means there is no correlation between the two variables, (2) if the value of correlation coefficient is 0 < ≤ 0.25, it means they have very weak correlation, (3) if the value of correlation coefficient is 0.25 < ≤ 0.5, it means they have sufficient correlation, (4) if the value of correlation coefficient is 0.5 < ≤ 0.75, it means they have strong correlation, (5) if the value of correlation coefficient is 0.75 < ≤ 0.99, it means there is very strong correlation, (6) if the value of correlation coefficient is = 1, it means they have the perfect correlation.  Table 2 showed that there is a correlation between the ability of algebra with the capability to programming algorithm by 93.5%. There is a correlation between the ability of the calculus with the capability to programme algorithms by 66.4%. A correlation between the ability of the logic of mathematics with the capability to programme algorithms by 66.4%. There is a correlation between the ability of algebra with the capability of calculus by 65.9%. There is a correlation between the ability of algebra with the capability of mathematical logic by 62.4%. Whereas the correlation between the ability of logic of mathematics and calculus is very small with 12.5% (which is a very weak correlation). This is in accordance with the value of R Square, in which the contribution of the variables that affect the ability of calculus is very small at 1.6%. It means that the correlation between the ability of mathematical logic and the ability of calculus is very weak. According to Nugroho (2014), Table 3 can be arranged into a mathematical equation as follows equation (1), (2), and (3).

Discussion
With α of 5%, if P values are less than 5%, it can be concluded that a variable may affect other variables. Based on Table 3, the result is that the ability of the algebra, the ability of calculus, and the ability of logic of mathematics have a positive effect on the ability to programming algorithm, which means that every improvement on the proficiency of algebra, calculus, and logic of mathematics will improve the ability to programme algorithms. The ability of calculus and logic of mathematics also has a positive effect on the ability of algebra, which means that any increase in calculus proficiency and logic of mathematics will improve algebra proficiency. Whereas mathematical logic proficiency does not affect calculus proficiency. The graph of coefficient path distribution is supported by Figure 4. shows the highest frequency of coefficient path distribution of algebra proficiency and its influence on programming algorithms is around 0.4, meaning that the ability of algebra affects the ability to programming algorithm. The graph of the coefficient path distribution of the basic arithmetic ability and its influence on programming algorithms in Figure 4.b. shows the highest frequency is around 0.35, meaning that calculus proficiency affects the ability to programming algorithms. The graph of coefficient path distribution of the ability of logic of mathematics compared to the ability of programming algorithm in Figure 4.c. shows the highest frequency is around 0.5, meaning that the logic of mathematics proficiency affects the ability to programming algorithms. The graph of coefficient path distribution of the ability of the logic of mathematics to the ability to algebra in Figure 4.d. shows the highest frequency is around 0.55, meaning that programming logic proficiency affects algebra proficiency.
The graph of coefficient path distribution of the logic of mathematics proficiency and its influence on basic calculus capabilities in Figure 5 shows the highest frequency is located around the 0.12, meaning that the logic of mathematics proficiency does not affect basic calculus proficiency. ies.ccsenet.

Figure 5
The indire variable th     Vol. 13, No. 5; Figure 9. Correlations between the ability to programming algorithm, algebra, calculus, and logic of mathematics

Conclusion
Proficiency in algebra, calculus, and logic of mathematics has a positive effect on the ability of programming algorithms. The mathematical logic with the highest influence over the ability to programme algorithms in algebra, with a percentage of 93.5%. It is followed by the logic of mathematics by 79.6% and calculus by 66.64%. Calculus proficiency and the logic of mathematics proficiency have a positive effect on algebra proficiency. It means an increase in calculus and logic of mathematics proficiency will improve algebra proficiency. The influence of calculus proficiency on algebra proficiency is 65.9%, and the influence of the logic of mathematics proficiency on algebra proficiency is 62.4%.
Proficiency in the logic of mathematics does not affect calculus proficiency. As a result: (1) Calculus proficiency as a mediating variable is not able to increase the influence of the logic of mathematics proficiency on algebra proficiency.
(2) Calculus proficiency as a mediating variable is unable to increase the influence of the logic of mathematics proficiency on the ability to programming algorithms. Calculus proficiency (through algebra) does not affect proficiency in the logic of mathematics indirectly. It means algebra proficiency as a moderating variable is unable to improve the influence of calculus proficiency on proficiency in the logic of mathematics.
Algebra proficiency as a mediating variable increases the effect of the logic of mathematics proficiency on the ability to programming algorithms. Therefore, it is necessary to increase algebra proficiency after mathematical logic in order to improve the ability to programme algorithms.
Based on the findings, it is recommended that the programming algorithm lecturers collaborate with algebra, basic calculus, and mathematical logic to improve learning material and methods. The findings may become a stepping stone for future research such as media development for programming algorithm study that prioritizes improvement in algebra, basic calculus, and mathematical logic.