TPACK: Technological, Pedagogical and Content Model Necessary to Improve the Educational Process on Mathematics through a Web Application?

This quantitative research aims to analyze the design and implementation of the Web Application on the educational process of the Linear Function (WALF) considering the TPACK (Technological Pedagogical and Content Knowledge) model and data science. The sample consists of 45 students who studied the Basic Math course at a Mexican university during the 2015 school year. The TPACK model allows the planning and organization of WALF through technological knowledge (HTML and PHP languages), content knowledge (formulas on the linear function and slope) and pedagogical knowledge (data simulation). The results of machine learning (linear regression) with 50%, 60% and 70% of training indicate that the contents of WALF influence the assimilation of knowledge about the identification and evaluation of the linear function. Data science identifies 2 predictive models on the use of WALF in the field of mathematics by means of the decision tree technique. Finally, the TPACK model facilitates the implementation of technological tools and construction of educational virtual spaces through technological, content and pedagogical knowledge.

Teachers need to develop the technological and pedagogical competences to achieve a successful incorporation of digital tools in the teaching-learning process (Cejas-León, Navío-Gámez, & Barroso-Osuna, 2016). For example, the TPACK model facilitates the integration of digital tools and media in the teaching-learning process considering the pedagogical, content and technological aspects (Chen & Jang, 2014;Chua & Jamil, 2014;Vaerenewyck, Shinas, & Steckel, 2017).
In particular, this quantitative research uses the TPACK model to organize and implement WALF in the field of mathematics through technological knowledge (HTML and PHP languages), content knowledge (formulas on the linear function and slope) and pedagogical knowledge (data simulation).
The research questions are: • What is the impact of WALF on the assimilation of knowledge about the identification and evaluation of the linear function?
• What are the predictive models of the use of WALF in the field of mathematics education?

TPACK MODEL
TPACK is a model that proposes the use of technological, pedagogical and content knowledge to achieve an adequate integration of ICT in the teaching-learning process (Cejas-León, Navío-Gámez, & Barroso-Osuna, 2016;Chen & Jang, 2014;Gómez, 2015). Nowadays, this pedagogical and technological model is transforming school activities inside and outside the classroom (Bueno-Alastuey, Villarreal, & García-Esteban, 2018;Turgut, 2017). For example, the TPACK model facilitated the updating of activities for the educational process of mathematics through the use of Raptor software, YouTube videos and Facebook (Salas-Rueda, 2018).
The origins of the TPACK model come from the ideas about the use of pedagogical and content knowledge in the educational field proposed by Shulman (Leiva-Núñez, Ugalde-Meza, & Llorente-Cejudo, 2018). Subsequently, Mishra and Koehler created the TPACK model by integrating technological knowledge with content and pedagogical knowledge (Chua & Jamil, 2014). The TPACK model has been implemented in the courses on history (Vaerenewyck, Shinas, & Steckel, 2017), languages (Sancar-Tokmak & Yanpar-Yelken, 2015) and mathematics (Kartal & Cinar, 2018). Kartal and Cinar (2018) used the TPACK model to analyze the impact of digital tools and technological applications (e.g., GeoGebra and Mathematica) in the teaching-learning process on mathematics. Even this pedagogical and technological model has improved academic performance through the creation of digital stories in language courses (Sancar-Tokmak & Yanpar-Yelken, 2015).
Finally, the TPACK model allows evaluating the use of digital tools and technological applications in the teaching-learning process and identifying the impact of ICT in school activities (Cabero-Almenara, Roig-Vila, & Mengual-Andrés, 2017;Cheng & Xie, 2018;Phillips, 2016).

METHOD
This quantitative research aims to analyze the design and implementation of WALF considering the TPACK model and data science.

Procedure
The procedure of this quantitative research began with the use of the TPACK model in the educational process on the linear function (See Table 1). Table 2 describes the functions of WALF by means of the Use Cases Scenario.
WALF requests the information of the coordinates to start the simulation of data on the linear function (See Figure 1). This web application is available at the following web address: http://sistemasusables.com/mat/ap1/inicio.html The web application presents the procedure to identify and evaluate the linear function.
Step 1: Find the slope (m) Step 2: Find the ordinate at the origin (b) Step 3  The research hypotheses about the use of WALF in the learning process are: • Hypothesis 1 (H1): The contents of WALF positively influence the assimilation of knowledge on the identification of the linear function • Hypothesis 2 (H2): The contents of WALF positively influence the assimilation of knowledge on the evaluation of the linear function The predictive models on the use of WALF in the teaching-learning process of mathematics are: • Predictive model 1: Contents of WALF and assimilation of knowledge on the identification of the linear function • Predictive model 2: Contents of WALF and assimilation of knowledge on the evaluation of the linear function

Data Analysis
This quantitative research uses the Rapidminer tool to evaluate the hypotheses about the use of WALF in the educational field by means of machine learning (linear regression) with 50%, 60% and 70% of training (See Figure 2).
In addition, the Rapidminer tool allows the construction of predictive models on WALF and assimilation of knowledge through the decision tree technique (See Figure 3).

Data Collection
Data collection was done in a Mexican university at the end of the Functions unit during the 2015 school year. Table 3 shows the measurement instrument (questionnaire).

RESULTS
Below are the results on the web interface and impact of WALF in the teaching-learning process on mathematics.

Web Interface
WALF is composed of 4 web pages: • Web page 1: Request for information WALF requests the information on coordinates to start the data simulation on the linear function (See Figure 4).   Figure 5).
WALF presents the formula and calculation of the ordinate at the origin (See Figure 6). Finally, WALF presents and evaluates the linear function (See Figure 7). Table 2 shows that the contents of WALF facilitate too much (n = 31, 68.89%), some (n = 13, 28.89%) and little (n = 1, 2.22%) the process of learning about mathematics. The use of technology in school activities facilitates too much (n = 30, 66.67%), some (n = 12, 26.67%) and little (n = 3, 6.67%) the assimilation of knowledge on the identification of the linear function. In the same way, the use of technology in school  The results of machine learning with 50%, 60% and 70% of training indicate that the contents of WALF positively influence the assimilation of knowledge on the identification and evaluation of the linear function (See Table 4).

Identification of the Linear Function
The results of machine learning with 50% (0.705), 60% (0.749) and 70% (0.661) of training indicate that hypothesis 1 is accepted (See Table 4). Therefore, the contents of WALF positively influence the assimilation of knowledge on the identification of the linear function. Figure 8 shows the predictive model 1 on the use of WALF. For example, if the student thinks that the contents of WALF facilitate too much the process of learning about mathematics, attends the career of Marketing and is Man then the use of technology in school activities facilitates some the assimilation of knowledge on the identification of the linear function. Table 5 shows the 12 conditions of the predictive model 1 (accuracy of 80.00%). For example, if the student thinks that the contents of WALF facilitate some the process of learning about mathematics, attends the career   Little ---Little 9 / 13 of Accounting and has an age > 18.5 years then the use of technology in school activities facilitates some the assimilation of knowledge on the identification of the linear function. Table 5 presents 6 conditions where the use of technology in school activities facilitates too much the assimilation of knowledge on the identification of the linear function. For example, if the student thinks that the contents of WALF facilitate too much the process of learning about mathematics, attends the career of Marketing and is Woman then the use of technology in school activities facilitates too much the assimilation of knowledge on the identification of the linear function.
Likewise, the predictive model 1 has 5 conditions where the use of technology in school activities facilitates some the assimilation of knowledge on the identification of the linear function (See Table 5). For example, if the student thinks that the contents of WALF facilitate some the process of learning about mathematics and attends the career of Administration then the use of technology in school activities facilitates some the assimilation of knowledge on the identification of the linear function.
Finally, Table 5 indicates 1 condition where the use of technology in school activities facilitates little the assimilation of knowledge on the identification of the linear function. For example, if the student thinks that the contents of WALF facilitate little the process of learning about mathematics then the use of technology in school activities facilitates little the assimilation of knowledge on the identification of the linear function.

Evaluation of Linear Function
The results of machine learning with 50% (0.656), 60% (0.657) and 70% (0.578) of training indicate that hypothesis 2 is accepted (See Table 4). Therefore, the contents of WALF positively influence the assimilation of knowledge on the evaluation of the linear function. Figure 9 shows the predictive model 2 on the use of WALF. For example, if the student thinks that the contents of WALF facilitate too much the process of learning about mathematics, attends the career of Administration and is Man then the use of technology in school activities facilitates too much the assimilation of knowledge on the evaluation of linear function. Table 6 shows 12 conditions of the predictive model 2 (accuracy of 75.56%). For example, if the student thinks that the contents of WALF facilitate some the process of learning about mathematics, attends the career of Commerce and is Woman then the use of technology in school activities facilitates too much the assimilation of knowledge on the evaluation of linear function.  Table 6 presents 5 conditions where the use of technology in school activities facilitates too much the assimilation of knowledge on the evaluation of linear function. For example, if the student thinks that the contents of WALF facilitate too much the process of learning about mathematics, attends the career of Administration and is Man then the use of technology in school activities facilitates too much the assimilation of knowledge on the evaluation of linear function.
Likewise, the predictive model 2 has 6 conditions where the use of technology in school activities facilitates some the assimilation of knowledge on the evaluation of linear function (See Table 6). For example, if the student thinks that the contents of WALF facilitate some the process of learning about mathematics and attends the career of Marketing then the use of technology in school activities facilitates some the assimilation of knowledge on the evaluation of linear function.
Finally, Table 6 shows 1 condition where the use of technology in school activities facilitates little the assimilation of knowledge on the evaluation of linear function. For example, if the student thinks that the contents of WALF facilitate little the process of learning about mathematics then the use of technology in school activities facilitates little the assimilation of knowledge on the evaluation of linear function.

DISCUSSION
ICTs are causing teachers to design and carry out new school activities inside and outside the classroom (Cardellino, Araneda, & García, 2017;Earle & Fraser, 2017;Magen & Steinberger, 2017). In particular, this quantitative research analyzes the design and implementation of WALF considering the TPACK model and data science.
The TPACK model facilitated the construction of WALF through technological knowledge (HTML and PHP languages), content knowledge (formulas on the linear function and slope) and pedagogical knowledge (data simulation). The results of machine learning with 50%, 60% and 70% of training indicate that the contents of WALF positively influence the assimilation of knowledge about the identification and evaluation of the linear function.
This quantitative research shares the ideas of various authors (e.g., Martin, Ritzhaupt, Kumar, & Budhrani, 2019) about the use of technological tools in the educational field to develop competences in students.
Also, the decision tree technique (data science) identifies 2 predictive models on the use of WALF in the educational field and assimilation of knowledge with the accuracy greater than 75.50%. In the predictive model 1, if the student thinks that the contents of WALF facilitate too much the process of learning about mathematics, attends the career of Marketing and is Man then the use of technology in school activities facilitates some the assimilation of knowledge on the identification of the linear function. In the predictive model 2, if the student thinks that the contents of WALF facilitate too much the process of learning about mathematics, attends the career of Administration and is Man then the use of technology in school activities facilitates too much the assimilation of knowledge on the evaluation of linear function.

CONCLUSION
The TPACK model allows modifying the teaching-learning process through the incorporation of ICT in school activities. In particular, this research proposes the use of technological knowledge (HTML and PHP languages), content knowledge (formulas on the linear function and slope) and pedagogical knowledge (data simulation) for the construction of WALF.
The results of machine learning indicate that the contents of WALF positively influence the assimilation of knowledge about the identification and evaluation of the linear function. Also, data science identifies 2 predictive models on the use of WALF in the field of mathematics. WALF presents the procedure and calculation of the slope and the ordinate at the origin to facilitate the assimilation of knowledge on the identification and evaluation of the linear function.
The limitations of this quantitative research are related to the construction of WALF to present the simulation of the linear function and use of the Spanish language in the contents. Therefore, future investigations can create web applications for the educational process on the quadratic, exponential, rational and logarithmic functions by means of the TPACK model. Also, the contents can be designed considering the English language.
The implications of this research drive the use of the TPACK model in the educational field in order to improve teaching-learning conditions. Likewise, the design and construction of web applications allow innovating and updating school activities.