Using software for teaching mathematics

I. Introduction

Mathematics helps develop positive attitudes in children; allowing them to perform calculations and mathematical operations confidently, quickly and accurately. This subject is also useful in applying mathematical knowledge and skills to familiar and new problems: collecting, organizing, analyzing, synthesizing, evaluating and making generalizations in solving problems. solve mathematical problems [15]. Mathematics to some extent can be considered the queen of all subjects when considering its usefulness to other subjects and fields of study such as: Arts, Social Sciences, Religion. Mysticism, Commerce, etc. It is an indispensable tool in natural science research as well as humanities related to logical reasoning and quantitative calculations.

The importance of mathematics is also demonstrated in the presentation of Solarin (2012), who sees this subject as a description of life because one cannot talk about life without mathematics. Salman (2017) found that Mathematics is useful in carpentry, construction, graphics, industry, astronomy, surveying, trading, thus, pointing out its usefulness in almost all fields. field of research and human activity. It also provides simple knowledge and skills needed by an individual in solving problems of daily life.

Mathematics Education

Education is the sum of ideas, methods, institutions, facilities and personnel designed and developed by society to teach its members how to go through life by realizing set goals. out [5, p. 92-106]. It is the process of facilitating learning or the acquisition of knowledge, skills, values, beliefs, and habits [11, p. 24-29]. Education normally takes place under the guidance of educators, but in some specific cases learners can also educate themselves. Education can take place in formal or informal settings, and any experience that has a formative impact on how a person thinks, feels, or acts can be considered educational.

Inheriting the above, within its scope mathematics education is a field of research related to tools, methods and approaches to facilitate the practice of teaching and learning mathematics. Mathematics education prepares students for quantitative and symbolic reasoning as well as advanced mathematics skills through general education, major and minor courses, and graduate programs [9, p. 122-129]. Mathematics education can also be described as the process of bringing about the desired mathematical knowledge, skills, values, beliefs and habits in an individual. The people responsible for this are mathematics educators who are trained and certified to teach mathematics.

Mathematics educators have used many different methods of teaching mathematics in the past. However, with the current technological developments in society, the question that needs to be raised is that there are challenges in using technology to support the teaching and learning of mathematics. A brief and relevant review of technologies for teaching mathematics will be given in this article.

Technology

Technology is the use of tools, machines, techniques, crafts, systems and organizational methods to solve a problem, improve an existing solution to a problem, achieve a goal or perform a specific function. It can also be called digital tools used for teaching and these tools include computers, computer software and the internet [19]. It is also a collection of tools, machines, modifiers, arrangements and processes. Research shows that computer technology can help support learning and that it is especially useful in developing higher-order skills in critical thinking, analysis and scientific inquiry.

According to Aparna (2016), the use of technology has a long history in mathematics education. Starting from magic board, books, magic lantern, Blackboard, OHP, radio, slide rule video tape, Television, Calculator, computer, Interactive board and Apple Ipad all come under technology. Banknotes and coins, beans, bears, buttons and other small objects are useful for counting and calculation skills. Straws grouped into dozens are great for teaching Math. Inclinometers are very useful for teaching and learning Trigonometry. The abacus allows children to conceptualize mathematical formulas by working with tangible objects [2].

Information communication technology (ICT)

There is no clear definition of IT. This is because its meaning is considered contextual and varies across fields such as education, healthcare, military, etc. However, it is generally accepted that ICT is a converging technology for information and communication. It is also said to mean all the devices, network components, applications, and systems that, when combined together, enable people and organizations to interact in the digital world [21]. IT is technology that supports information-related activities. Such activities include data collection, processing, storage and presentation. These activities increasingly involve collaboration and communication. From now on, Information Technology (IT) has become IT. It includes any product that will store, retrieve, manipulate, transmit or receive electronic information in digital form. Examples include personal computers, digital television, email and robotics [13]. IT is a technology that provides access to information through telecommunications. It is similar to IT but focuses mainly on communication technology. This includes the internet, wireless networks, mobile phones and other means of communication [14].

Suh (2010) asserts that IT is an umbrella term for all communication technologies that provide access to information. Such IT tools are Internet, wireless networks, mobile phones, satellite communications, digital television computers, network hardware and software. As well as devices and services related to these technologies, such as video conferencing, e-mail, blogging, etc.

According to Aparna (2016), there are many types of technology currently being used in the classroom. Among the software used to teach and learn mathematics are Graphics Calculator, Dynamic Graphing Tool, Dynamic Geometry Tool, Microsoft Excel/spreadsheet, Microsoft Math, Geo Gebra, Autograph, and Mat lab.

According to Ly-Huong, Tejal, Laurie, and Wael (2022), ICT includes six effective technologies. Including:

• Data: These are facts, images or raw statistics. They are unprocessed information used as input for IT.
• Hardware: These are the physical components of the computer or peripherals.
• Software: This is the name of computer programs.
• Information: This is the result obtained from converting data from raw facts into meaningful and useful information.
• Procedures: These are actions carried out in a certain sequence to ensure the system operates smoothly.
• Humans: they are responsible for entering data by various means into the computer, e.g. keyboard, voice recognition, mouse, etc.

The human part of this component is the most important component. This is because without human resources, the most sophisticated IT equipment will remain useless [12]. The role of IT in education over the past 20 years cannot be overemphasized. The main activity in the teaching and learning process is communication. IT is also mainly related to communication. This is perhaps the reason why IT has earned itself an important role in education.

Technology tools in teaching and learning Mathematics

There are many Information Communication Technology (ICT) tools available that can be applied to the teaching and learning of mathematics in schools and colleges. IT tools include hardware tools like OverHead Projectors, LCD Projectors, Handheld Devices, advanced computers, PDAs, etc. There are many software tools for effective mathematics teaching and learning, some of which are graphing tools, dynamic geometry software, computer algebra systems, spreadsheets, and online tools. online for learning.

According to Inayat and Hamid (2016), the most common tools and media used for effective mathematics teaching and learning are as follows.

Dynamic graphing tool

Dynamic graphing tools are effective tools for visualizing and representing relationships between entities in readable, scalable, and efficient diagrams.

There are many dynamic graphing tools available to effectively display relationships between entities. According to Gadanidis and Geiger (2010), there are several popular dynamic graphing tools available for building dynamic graphs:

Google Charts: Google Charts is a free, powerful, and easy-to-use interactive tool for creating data visualizations for browsers and mobile devices. Google Charts is the perfect tool for visualizing data on websites. The Google Charts chart library provides a number of sample chart types including simple line charts to complex hierarchical tree maps.

D3.js: This is an efficient JavaScript library for displaying and manipulating data-based documents. It allows to tag arbitrary data into the Document Object Model (DOM) and then apply data-driven transformations to the document. For example, D3 can be used to create an HTML table from a series of numbers or an interactive SVG bar chart with smooth transitions and interactions.

iii. am Charts: am Chart is an advanced library for data visualization. It includes several chart options from simple line, bar, column, area, step, and stepless to more advanced charts.

Chart Stream: this is a Java library for creating, importing, exporting, and displaying dynamic charts. Graph Flow provides several graph classes that allow modeling directed and undirected graphs, 1-graphs or p-graphs. It also allows storing any data attribute on chart elements, i.e. numbers, strings or any objects. It can be customized using CSS stylesheets for chart visualization.

Computer Algebra System (CAS)

A computer algebra system is a software package used to manipulate mathematical expressions to automate algebraic manipulation tasks that are tedious and sometimes difficult to solve manually. The fundamental difference between Computer Algebra Systems and traditional computers is the ability to handle CAS rather than numerically. The specific capabilities and uses of these systems vary widely from system to system, however the purpose remains the same, that is, the manipulation of computer algebra systems can be divided into two types: specialized CAS applications and general purpose CAS. Specialized CAS is designed to deal with group theory, number theory or teach basic mathematics. General-purpose CAS is useful for users who need to manipulate mathematical expressions in any scientific field.

Table 1

Summary of Dynamic Algebra Systems - Source: Inayat and Hamid (2016)

Examples 1. Using Maple software we could solve the following problems (but not only the those problems): Check if a number M is prime or not? Indicate the nth prime number? The smallest prime number greater than or equal to the given number A; Decompose number N into prime factors? Decompose the number N into prime factors and write it as a list?!

Using the following commands:

+ isprime(M);

+ ithprime(n);

+ prevprime(A);

+ ifactor(N);

+ ifactors(N).

Examples 2. Please check whether the two following statements are tautology or false? Explain?

E = (p Ù q) ® (p Ú (˥q) Ú r) and F = (p ® q) ® [(p ®q) ®(p ®(˥ r))]

By using Maple software we have the answer instead of the lengthy transformations, that can cause confusion.

Fig. 1.

So that E is Tautology and F is neither a Tautology nor a False.

Examples 3. A student buys 2 hats from a store that has 3 types of hats A, B, C. List all the student's purchasing possibilities.

Using Maple software we have the answer as follow:

Fig. 2.

Dynamic Geometry Software (DGS)

According to Inayat and Hamid (2016), Dynamic Geometry Software is an effective mathematical tool for representing and interactively manipulating geometric objects. One of the features of such programs is the construction of geometric models of objects, such as points, lines, circles, etc., with interdependencies between these objects [5]. Dynamic geometry technology can be used to maximize students' geometry learning and allow them to visualize the geometric concepts being studied. Below is a summary of some of the popular dynamic geometry packages available worldwide.

Table 2

Summary of Dynamic Geometry Software - Source: Inayat and Hamid (2016)

Data analysis and statistics tools

Data analysis tools are computer programs used to design, analyze and implement algorithms to find numerical solutions (including exact or approximate solutions) for problems containing continuous variables. Statistical tools are used to analyze large volumes of data and derive some meaning from it for further analysis and decision making.

Table 3

Summary of Numerical Analysis and Statistical Tools - Source: Inayat and Hamid (2016)

In addition to the tools mentioned above, we also need to mention WME (Web-based Mathematics Education) – a modern online distribution system for mathematics education. The WME system provides an extended set of facilities for effective online teaching and learning. Web-based learning can help in extending the reach of education and also expand its impact and influence [20, p. 621-629]. Also we should remained spreadsheets - It were invented in the 1970s and since then used as a tool for mathematical, scientific, financial, and statistical calculations. Aparna (2016) stated that spreadsheets in mathematics education have several benefits it including:

1. Calculation of complex mathematics expressions with ease.
2. Provision of automatic updates by just changing the variables in the previously defined formulas.
3. Visualized data can be presented by creating graph charts from the range of data.

Besides trends like Applet - applet is an application independent of the platform that is designed to perform a specific task and run within another application such as a web browser [3]. An applet interacts and provides a means to capture user input that results in changes to the graphical, numerical, and algebraic content displayed on it. The last trend worth mentioning is: Calculator - calculator is a device used in solving mathematical problems. Kissane, McConney, and Ho (2015) asserted that the calculator can be much more than a device for calculation. It can be used effectively to develop concepts.

III. Advantages of Technological Tools for Mathematics Teaching

The usefulness of ICT in mathematics education is endless. The following includes a few such:

A. Development of Student's Mathematical Skills

Technologies increase learners' access to information, ideas, and interactions that can support and enhance sense-making, which is central to the process of taking ownership of knowledge.

B. Ease of Lesson Planning for the Teachers

The ease and speed of obtaining information on the internet help teacher users empower themselves.

C. Accessibility to the Latest Evaluation Tools.

Technology provides different assessment tools such as Checklists, rating scales, and rubrics to assess 21st-century skills such as creativity, problem-solving, decision making, and leadership skills which are criteria for project-based learning.

D. Provision of New Ways of Learning

Technology can reduce the effort devoted to tedious computations and increase learners' focus on more important mathematics.

E. Assignment of New Roles for the Teacher

In the present time, the teacher's role in teaching mathematics is the facilitator.

Conclusion: This paper mainly focuses on the reviewing about the technological tools available for effective teaching and learning of mathematics. It also considered the role of technologies in the teaching and learning of mathematics and the benefits of integrating technology in teaching and learning mathematics as evident from various research.