A Framework Supporting Literacy in Mathematics and Software

Programming

Addressing Some Challenges in STEM Education

Georg Peters

1,2

, Tom Rueckert

and Jan Seruga

Department of Computer Science and Mathematics, Munich University of Applied Sciences,

Lothstr. 34, 8033 Munich, Germany

Faculty of Education and Arts, Australian Catholic University, 25A Barker Rd, Strathfield NSW 2135, Australia

Keywords: e-Learning, STEM Subjects, Mathematics Education, Software Programming, R-Project Software

Environment.

Abstract: The second half of the last century was characterised by a shift from manufacturing to services, particularly

in mature economies. This transformation has accelerated in the past decade, due to rapid progress in

information technology. Excellence in the so-called STEM subjects (science, technology, engineering and

mathematics) is crucial if countries are to remain competitive. Mathematics as a universally applicable method

is of special significance, as is IT, which impacts on virtually all industries and can dramatically change

economies. Literacy in mathematics and computers, therefore, is more important than ever for individuals,

companies and countries. We propose a framework based on R to support the training of students in these

crucial areas. We discuss its features, including platform neutrality, costs and specialization flexibility in our

paper.

1 INTRODUCTION

We are experiencing a rapid change towards a data

driven economy. Companies like the big social media

firms or the large global online retailers that collect

data on their customers enjoy strategic advantages

over so-called old economy firms that lack such direct

access to customer data. Buzz words like big data,

business analytics, business intelligence and data

science are used to describe this trend. Recently,

artificial intelligence has been rediscovered; it finally

seems to have reached a stage of development where

it can have a significant impact on real life.

Mathematics and computer skills are of crucial

importance when it comes to analyzing this data.

Knowledge in these fields is relevant not only to

professionals working in the area but also to ordinary

people who should understand, to a certain degree,

one of the major driving forces that may impact their

lives. From an economic point of view, and from

sociological and demographic perspectives,

mathematics and computer skills are essential to

maintain a functioning society.

Embedded into STEM subjects (science,

technology, engineering and mathematics), skills in

mathematics and software programming are already

fostered in schools and universities, while

corresponding apps for smartphones have gained

attention. The use of information technology to

support mathematics education has already been

successful in various studies (Ruthven & Hennessy,

2005; Niess, 2005).

What is needed now is a tool that seamlessly

covers basic as well as advanced mathematics and

also addresses statistical analysis and data mining

techniques. Furthermore, it would be desirable that

the tool provides access through a well-designed web-

based interface for beginners with an option for

programming in a more technically-oriented console

for advanced users.

The objective of our paper is to present a

framework which is intended to support literacy in

mathematics and software programming, addressing

some vital needs in education today. In the further

course of the paper, we give the framework the

working title M*TH-F

RAMEWORK.

The remainder of the paper is organized as

follows. In the next section, we briefly review the

Peters, G., Rueckert, T. and Seruga, J.

A Framework Supporting Literacy in Mathematics and Software Programming.

DOI: 10.5220/0006629304970506

In Proceedings of the 20th International Conference on Enterprise Information Systems (ICEIS 2018), pages 497-506

ISBN: 978-989-758-298-1

497

need for mathematics literacy and programming skills

and the respective performances of students in

selected countries. In Section 3, we analyze the major

requirements for the framework, followed by the

selection of an appropriate technological platform for

our framework. We briefly review important features

of the selected platform in Section 4 and, in Section

5, we introduce our framework to support literacy in

mathematics and programming and discuss its

properties. The paper concludes with a summary in

Section 6.

2 STUDENTS’ PERFORMANCE

IN MATHEMATICS IN

SELECTED COUNTRIES

In this section, we concentrate on mathematics,

stressing the need to remain competitive in a

globalized economy. We summarize the performance

of school students in mathematics according to the

international PISA study of the OECD and also

briefly address the need for programming skills.

2.1 Need for Mathematics and

Software Programming

The vital importance of mathematics has been

recognized by governments and industry around the

world.

Leading German engineering companies are

aware of the crucial importance of mathematics and

actively promote it. The former chairman of Siemens,

Peter Löscher, expressed it thus (cited at Neunzert &

Prätzel-Wolters, 2015): “Mathematics – this is the

language of science and technology. This makes it a

driving force behind all high technologies and, thus,

a key discipline for industrial nations. Without

mathematics, there is no progress and technical

innovation.” Dieter Zetscher, current chairman of the

automotive company Daimler, said (cited at Neunzert

& Prätzel-Wolters, 2015): “As does no other science,

mathematics helps us in our branch to solve the most

varied sorts of problems – and it is exactly this

universal applicability that makes it the royal

discipline.”

Moreover, related fields like data mining and

artificial intelligence that are based on mathematics

are becoming increasingly important. A good

understanding of these fields is not only of crucial

importance for professionals working in IT-related

jobs like computer science and information systems

but for an economy as a whole to remain competitive

in a globalized world.

Regarding the importance of teaching software

programming in schools, for example, the German

chancellor Angela Merkel remarked recently

(translated from Merkel (2017): "I am convinced [..].

that the ability to program, the easy ways of

programming, that children should learn to do this.

Because they will then have a basic understanding of

how a robot works, how certain things work, how an

app is created."

2.2 Performance in Mathematics and

Software Programming

Nevertheless, despite excellent job prospects, it is still

a challenge to motivate a sufficient number of

students to step into these fields and secure a sound

education in mathematics, computer science and

information systems at schools and universities.

Figure 1: PISA - Performance in Mathematics in Selected

Countries in 2015 (OECD, 2016b).

Germany, for instance, is poor in natural resources

but has a large engineering sector, so a strong

performance in mathematics at school and university

is important to its economy. However, according to a

recent PISA study, German school students are not

amongst the top performers in mathematics. They

perform only slightly above average (OECD, 2016a).

Meanwhile, in the U.S.A., interest in STEM

subjects improved, but not in mathematics, according

to a recent study (Neuhauser & Cook, 2016): “The

2016 U.S. News/Raytheon STEM Index recorded a

slight rise in hiring, education and general interest in

technology and engineering over last year, while

math education and general interest in science

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declined.”

Performance in mathematics of the countries

covered by the PISA is depicted in Figure 1. The

study shows that eastern Asian countries like China,

South Korea and Singapore are top performers with

respect to education in mathematics. The countries on

the American continents, except Canada, are

performing under average while most countries in

Europe are ranked above average.

We are not aware of any similar study that

evaluates and compares programming skills of school

students in an international context. A possible reason

is that computer science software programming is not

a widely established subject in schools in many

countries. Due to its importance this makes the need

to support it even more pressing.

3 REQUIREMENTS FOR AND

SELECTION OF A PLATFORM

3.1 Requirements for the Framework

In this section, we present the results of our

requirements analysis for the platform that we use for

the framework to support literacy in mathematics and

programming.

In our analysis, we identified the following

criteria as essential to a framework’s success:

 Cost efficiency

 Platform independence

 Size of the platform network

 Comprehensiveness of the mathematical

implementations

 Support for possible levels of user experience.

We address these criteria in more detail in the

following paragraphs.

Cost Efficiency. Most educational sectors around

the world suffer from budget constraints even though

education is regarded as possibly the most crucial

factor to address significant issues such as

overcoming inequality and poverty, and

strengthening the competiveness of firms and

economies in a globalized world. Financing a

framework, therefore, might be a considerable

challenge for many educational institutions. Hence, a

cost efficient, ideally free, approach is of crucial

importance for the success of the framework.

Platform independence. With respect to platform

independence we distinguish two factors, namely (1)

independency from hardware platforms and (2)

independency from software. The first is related to the

possible use of the framework on smartphones,

tablets and personal computers. The second

corresponds to the independence from any particular

operating system. Note that these two factors are

beginning to overlap, for example, see the first

attempts to use the Android operating system on

personal laptops and computers (and, of course, the

initially failed strategy of Microsoft to launch a

virtually identical Windows system for all platforms,

including smartphones, tablets and personal

computers).

Size of the platform network. The underlying

platform should be well accepted, i.e., the network of

users of the platform should be large. This criterion is

motivated by classic arguments well known from the

theory of network externalities (Katz & Shapiro,

1985). For example, a large network has positive

effects on learning since support is generally

available, ranging from (online) textbooks to

discussion group and forums. A large network also

makes it more likely that the platform will be

available for the foreseeable future. This would

secure the developers’ and users’ investment in the

framework.

Comprehensiveness of the mathematical

implementations. The platform should already

provide a large range of mathematical concepts and

predefined solutions that can be used immediately.

This avoids the cost and time of starting from scratch.

Possible Levels of User Experience. Here we refer

to the different needs of a diverse range of users,

including absolute beginners and experts. The

advantages of a diverse range of users are twofold.

First, the different groups can learn from each other:

the beginners learn from the advice of the experts and

the experts benefit from explaining and answering

questions from the beginners. Second, when a

beginner improves her/his knowledge she/he can

continue to use the same platform by gradually

increasing her/his level of expertise within the

framework.

3.2 Selection of a Platform for the

Framework

In our analysis, we distinguish between three

categories of possible platforms for the framework:

 General purpose programming languages

 Mathematics solution apps, webpages and

software

 Numerical computing environments.

Note that in general some applications do not fit

into one single category but offer functionalities

across these categories.

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499

General purpose programming languages.

General purpose programming languages like C/C++

or Java provide excellent frameworks for virtually

any kind of task. In particular, due to its efficiency,

C/C++ has been a leading platform for the

implementation of mathematical/numerical problems

in industry and academia over the past decades. Take-

up by a wide range of respected libraries is an

impressive indicator of its success.

However, we wish to establish a framework that

suits beginners as well as advanced learners.

Programming languages like C/C++ are already too

“sophisticated” for beginners and will possibly lead

to frustration. On the other hand, implementing a

framework including the mathematical algorithms

from scratch would possibly exceed our resources,

even considering the advanced apps and websites

tools that are available.

Thus, general purpose programming languages do

not satisfactorily address the levels of user experience

that will be covered and also violate our cost

efficiency criteria.

Mathematics solution apps, software or

webpages. Examples of mathematics solution apps

are Mathway (mathway.com), MATH 42 (math-

42.com), MalMath (malmath.com) and Wolfram

Alpha (wolframalpha.com). All run on Android, and

Mathway, MATH 42 and Wolfram Alpha are also

available for further operating systems. Mathway and

Wolfram Alpha offer websites for mathematical

problem solving. Wolfram Alpha’s website even goes

beyond mathematics towards a structured general

purpose search engine.

While the apps and webpages are excellent for

addressing mathematical problems, they lack a

programming environment for advanced learners

who are wanting individually designed software that

perfectly fits their needs. Therefore, as with general

purpose programming languages, mathematics

solution apps, software or webpages do not

satisfactorily address our criterion about levels of user

experience.

Numerical computing environments. Leading

numerical computing environments include

Mathematica (wolfram.com/mathematica) and

MATLAB (mathworks.com/products/matlab.html).

While MATLAB has had a leading role in

engineering with many corresponding libraries,

Mathematica has a strong position in the education

sector and is also frequently used as a problem

solving tool in industry. Its particular strength is that

it integrates mathematical symbolic computation

functionality; it can, for example, symbolically

integrate or differentiate (note the same applies to the

related website Wolfram Alpha).

While Mathematica and MATLAB are

commercial products there are free alternatives

available, in particular to MATLAB. For example,

the numerical computing environment GNU Octave

(gnu.org/software/octave) claims to be compatible

with MATLAB; another popular environment, Scilab

(scilab.org/), is similar/partly compatible with

MATLAB.

R-Project (r-project.org) has gained increasing

popularity in the past decade. R started as a free

alternative to S as an environment for statistical

computing. Since then, its range of applications has

gone beyond statistics and now covers wide parts of

numerical analysis, data mining and mathematics.

According to the TIOBE Index (tiobe.com/tiobe-

index/), which ranks the popularity of programming

languages, it is leading the field of special purpose

languages for numerical computing, slightly ahead of

MATLAB: in August 2017, R is ranked #15 and

MATLAB #17 among all programming languages.

The core features of these numerical computing

environments include integrated development

environments (IDEs), purpose-built programming

languages, graphing utilities and respective

substantial libraries. Numerical computing

environments, therefore, generally address our

criterion about possible levels of user experience. All

these environments are excellent bases for the

framework.

Mathematica, with its mathematical symbolic

computation power, is an outstanding product and

leads the field in the educational sector. However, one

of our essential criteria in the framework selection

process was that the framework can be accessed for

free (cost efficiency criterion). Firstly, schools and

universities are under budget restraints that may make

it difficult or even impossible to obtain commercial

software and, secondly, students should be able to get

the framework for free and independent of their

enrolment status (for example whether they are a

current or former student). The cost efficiency

criterion also leads to the exclusion of MATLAB.

All remaining free numerical computing

environments run on all major operating systems for

personal computers. So, in terms of our platform

independence criterion they are equally suitable for

our framework. We would also consider the criterion

about comprehensiveness of the mathematical

implementations as fulfilled. However, a detailed

comparison is practically impossible: virtually

everyone can upload improved and new packages to

the R repository anytime. This has led to a puzzlingly

high number of packages, which is one of the biggest

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advantages - and disadvantages - of R.

Our final decision between GNU Octave, R and

Scilab, therefore, is based on network aspects (size of

the network of the platform criterion) and the

possibility of integrating different levels of user

experience (possible levels of user experience

criterion).

In relation to the size of the network, we have the

impression that R has a strong momentum which puts

it significantly ahead of GNU Octave and Scilab. R

and MATLAB family (in particular GNU Octave,

Scilab and MATLAB itself) are similarly popular

according to the TIOBE Index (see above). With

respect to the possibility of integrating different levels

of user experience, we found that R provides

excellent packages, particularly Shiny

(https://shiny.rstudio.com, see further down for

examples), that support the development of

interactive webpages to suit the needs of beginners.

The evaluation is summarised in Table 1. Note

that platforms with a minus (–) are excluded

(essential criteria) and the remaining criteria are not

further investigated. Therefore, general purpose

programming languages and mathematics solution

apps, software or webpages are excluded from any

further evaluation. The same applies to the

commercial numerical computing environments

Mathematica and MATLAB. Among the rest, we

consider R stronger with respect to its network size

and the possible levels of user experience that can be

addressed in comparison to GNU Octave and Scilab.

Hence R was selected as the platform for the M*TH-

RAMEWORK as it addresses most of the criteria well.

Its only considerable weakness is that it does not offer

symbolic computation functionalities like

Mathematica.

4 THE R-PROJECT

ENVIRONMENT

In this section, we briefly review the major features

of R-Project. Firstly, we describe its origin; then we

give a very brief impression about its power to deal

with mathematics and statistics. Lastly, we discuss

the package Shiny which supports the generation of

dynamic websites.

Table 1: Summary of the Evaluation of the Platforms.

Cost Efficiency Platform

Independency

Size of Network Comprehensivene

ss of Math.

Implementation

Possible Levels of

User Experience

General purpose programming language

C/C++,

Java etc.

–

not suitable for

beginners

Mathematics solution apps, software or webpages

MATH 42,

MalMath

etc.

–

limited flexibility

for experts

Numerical computing environments

Mathe-

matica

–

commercial tool

MATLAB

–

commercial tool

GNU

Octave

runs on all major

platforms

good

sufficient, no

symbolic comp.

R-Project +

runs on all major

platforms

excellent

sufficient, no

symbolic comp.

console+packages

for webpages

Scilab +

runs on all major

platforms

good

sufficient, no

symbolic comp.

Legend: + fine, = acceptable, – essential criterion, leads to exclusion.

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4.1 Fundamentals about R-Project

R-Project (r-project.org) was founded as an

alternative to S at the University of Auckland, New

Zealand, in 1993 (Ihaka, 1993). Initially its focus was

on statistical computing, but it has since become a

universal platform for mathematics, with a particular

strength in data analysis. In the past decade, it has

rapidly gained attention and is now used by both

academics and company professionals.

A core team organizes and maintains R-Project. In

addition to its core functions the user can write

packages and upload them to R repository. This

means there is a large community contributing

packages to virtually any area of mathematical

analysis.

4.2 R’s Programming Environment

The R software is console-based and can be accessed

by R’s standard console or by third party IDEs, with

RStudio (rstudio.org) probably the most popular (see

Figure 2 for a simple mathematics example using

RStudio IDE). R’s programming language is

optimized for statistical analysis and therefore

provides convenient commands to manipulate data

structures like vectors and matrices as well as more

complex structures like R’s data frames.

For example, the command for addressing the 5th

column of matrix a is:

a[,5]

or the multiplication of matrixes a and b is just one

command:

a %*% b

R not only provides virtually all standard

statistical functions, for example mean() or standard

deviation sd(), but also provides advanced

statistical methods in corresponding packages.

Besides statistics, several other areas of mathematics

are covered by R packages, for example operations

research with classic algorithms for linear

programming, or linear algebra, with linear equation

systems packages. Moreover, R has sophisticated

graphics and plotting functionalities (Murrell, 2011)

such as 2D and 3D plots, pie chart, histograms and

contour lines. R provides the possibility of writing

one’s own programs in R. The inclusion of code

writing in, e.g., C/C++ is also possible.

Figure 2: Mathematics Example in RStudio IDE (rstudio.com).

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Global companies also integrate R in their

products. Microsoft, for example, recently took over

Revolution Analytics, a company which specialises in

R. It maintains Microsoft R Open, an enhanced R

distribution (https://mran.microsoft.com/), and also

supports R in its cloud computing service Azure

(Olavsrud, 2015). Another example of the

commitment of major companies to R is Oracle,

which provides Oracle R Enterprise to support R

(Oracle, 2017). Hence, R is not only used in academia

but is also employed in and supported by companies

throughout the world as a professional statistical and

numerical computing environment (Heller, 2017;

Vance, 2009).

This popularity has generated comprehensive

literature about R. There are several text books on R,

for example Matloff (2011) and Teetor (2011), many

online resources, the most notable being

“Introduction to R” (Venables, Smith, R Core Team,

2017) by some of the main drivers of R, and a range

of discussion groups and blogs.

In our context so far, R is an excellent platform

for advanced learners in mathematics and data

analysis who can develop their mathematical skills as

well as their programming experience. However, this

console-driven programming environment would

probably overwhelm most beginners in mathematics.

For this user group app- or web-based interfaces

like MATH 42, MalMath and others would provide a

better starting point. However, as we discuss in the

next section, R has also excellent packages that

support the development of user-friendly interactive

interfaces.

4.3 Interfaces of R

Besides the console, R has strong export facilities

including several packages that help the user report

the results of an analysis. These include Sweave

(Leisch, 2016) that generates LaTeX documents from

R code.

Another package that supports the reporting is

Markdown (rmarkdown.rstudio.com/). It can

generate Word, HMTL or LaTeX/PDF files. The

basic workflow of the generation of such documents

is shown in Figure 3.

For the M*TH-F

RAMEWORK, we use R’s Shiny

package which is a web application framework

(Chang, 2017) that generates interactive and dynamic

webpages from R. Due to limited space we refrain

from a detailed technical discussion of the Shiny web

application framework and refer the reader to the

respective webpages and documents for further

information. The homepage of the Shiny framework

at https://shiny.rstudio.com/ is an especially rich

resource, providing impressive examples for websites

generated by Shiny and detailed documentations on

the framework.

An example for a webpage generated by the

framework is depicted in Figure 4. In the next section,

we discuss the concept and the layout of these

webpages.

5 A COMPUTER-BASED

FRAMEWORK FOR

MATHEMATICAL EDUCATION

In this section, we present a computer-based

framework for mathematical education based on the

R-Project.

5.1 Layout of the Web-based Interface

As already mentioned, an example for the M*TH-

RAMEWORK is depicted in Figure 4. In this case, the

screenshot was taken from the framework running in

web browser on a personal computer. However, on

smartphones and tablets the layouts are virtually

identical, allowing the user to switch seamlessly

between her/his devices. Therefore, it is sufficient to

discuss the layout as shown in Figure 4.

Figure 3: Workflow of R Markdown to Generate Reports (RStudio, 2014).

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503

Figure 4: Mathematics Example for a Webpage of the Framework.

On the left side of the browser a navigation bar

shows the tasks that are available. On the right side

the selected task is presented. In the example, the task

is to determine the intersection point of two linear

functions. The frame of the task has an orange bar at

the top. To the right there is another frame, with a blue

bar at the top. In this frame settings can be chosen,

such as the range of the parameters of the two linear

functions. Within this range the parameters are set

randomly to provide new tasks every time.

Furthermore, the command buttons are located in this

frame. The standard ones are “Apply”, “Show

Solution” and “Show Explanation”. While the latter

two are self-explanatory, “Apply” means that a new

task is generated based on the range of the parameters

as defined in the frame. In a future release of the

framework, we are considering implementing a fourth

standard button (“Show Code”) that bridges the gap

between the interface and the underlying R code.

In Figure 4, the solution is shown in a separate

frame with a green bar at the top. Besides the

numerical values of the intersection, a graph is also

shown to illustrate the solution. The mathematical

background of the solution can be found when the

user scrolls further down in the window; it is not

presented here due to space restrictions.

The presentation of the M*TH-F

RAMEWORK on a

smartphone is virtually the same since it is a website-

based framework with no separate app for mobiles.

This has the advantage that the framework runs on

personal computers/laptops and smartphones

independently of an operating system. This means

that the development and maintenance costs are

minimal in comparison to a solution where the

software needs to be adapted to PC and smartphone

operating systems. In particular, for smartphones

there is no need to develop and maintain different

apps for different mobile environments.

Finally, besides the core application involving

mathematics tasks, it is intended that the framework

will also support functions that let students interact

with each other and communicate with their

instructors (see Figure 5a). It should have a memo

board (see Figure 5b) where messages are displayed,

for example new students joining a course or the

proportion of exercises completed. It will also

provide basic tools to manage and monitor the

progress of a student from both the student and the

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Figure 5: Dashboard and Messaging Functionality of the Framework.

tutor’s perspective (see Figure 5c).

A feasibility study confirmed that these

functionalities can be implemented in R. They have

not been implemented yet as our current focus is on

extending and completing the portfolio of

mathematics tasks and developing tasks in the area of

data mining. They are scheduled for future versions

of the framework.

5.2 Discussion

The project so far has confirmed that R is an excellent

platform for the development of the framework.

Its specialized programming language makes it a

perfect environment to develop respective code very

quickly. Furthermore, CRAN (Comprehensive R

Archive Network at https://cran.r-project.org/), with

its large number of packages, is a rich repository for

“off the shelf” applications. These packages not only

support solutions for mathematical algorithms but

also support exporting functions and frameworks for

interactive dynamic websites.

R’s large network, which embraces both academia

and major international companies, has led to an

active community that provides support, including

IDE and special purpose packages. Many blogs and

tutorials can be found free of charge on the web.

Therefore, the framework is not only a tutorial in

mathematics but it also introduces beginners to R, one

of the leading platforms for statistical analysis and

data mining. In this context, it is a very suitable

environment to gain and enhance programming

experience. Furthermore, as many applications in

academia and industry show, it can be used to address

real life problems. Last but not least, there are

practically no entry barriers as it runs on virtually any

operating system and is free.

6 CONCLUSIONS

In this paper, we presented a framework for

mathematics education using R-Project. The

framework also supports the acquisition of

knowledge in computer science and information

systems, in particular in programming.

Crucial advantages of R are that it is free and runs

on virtually any platform, so it can be used regardless

of budget constraints or a given computer

infrastructure. Another important advantage is that it

A Framework Supporting Literacy in Mathematics and Software Programming

505

provides facilities that support beginners (for

example, through its interactive Shiny web

framework) as well as experts (by its programming

facilities in the console).

Finally, R already offers a portfolio of sound

mathematical functions. Many packages, often

written by senior experts in their field or even by the

people who proposed the algorithms, offer a wide

range of mathematical tools. Although R’s main

strength is in the field of statistics and data mining,

several other fields of mathematics are also covered.

Therefore, R is an ideal platform for the

framework to support mathematics and computer

literacy. Presently, we are extending the portfolio of

mathematical tasks within the Shiny web framework

and working on pathways to bridge the gap between

web- and console-based access to mathematics.

Dashboards, messaging and monitoring tools are

planned for a future version.

We are also intending to form a group of

educators who use and contribute to the framework to

further advance its coverage of important fields of

mathematics.

In the long run, a portfolio of applications in data

mining would be desirable to address one of the

hottest areas in computer science and information

systems today.

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TRADEMARKS

RStudio and Shiny are trademarks of RStudio Inc.

Mathematica is a trademark of Wolfram Research, Inc.,

MATLAB is a trademark of MathWorks, Inc. Microsoft

and Windows are trademarks of Microsoft Inc. and Oracle

is a trademark of Oracle Inc. All other trademarks are

property of their respective owners.

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