Blended Learning in Multi-disciplinary Classrooms

Experiments in a Lecture about Numerical Analysis

Marcelo Barros

, Antão Moura

, Laurent Borgmann

and Uwe Terton

Systems and Computing Department, Federal University of Campina Grande (UFCG), Campina Grande, Brazil

University of Applied Sciences Koblenz, RheinAhrCampus, Koblenz, Germany

University of the Sunshine Coast, Sippy Downs, Australia

Keywords: Blended Learning, Gamification, Real-life Experiments, Multicultural Classes, Numerical Analysis,

Evaluation.

Abstract: Numerical analysis (NA) is a core, compulsory discipline in most scientific, particularly engineering

undergraduate programs. Teaching numerical analysis to students with diversified backgrounds and

different abilities of learning (visual, aural, read/write kinesthetic learners) is challenging because of its

interdisciplinary nature and modelling requirements. Such a challenge in turn, can lead to low success

indicators (related to but not limited to student performance) at both whole-class and per-student levels.

Negatively affected indicators include subjective (e.g. satisfaction with the subject) and objective ones (e.g.

lower overall grade average and absenteeism from class). This paper reports on efforts made at the Federal

University of Campina Grande (UFCG) in Brazil to favorably change such indicators. The efforts involve

applying blended learning (BL) together with gamification procedures to motivate students to engage more

deeply in the learning of numerical analysis. As a consequence, it is expected that the other performance

indicators will also be positively impacted. Data for a set of success indicators have been collected since

2007 at UFCG. A total of 25 classes encompassing close to 1,500 students and other professionals using the

approach in different application domains – including chemical, electrical and civil engineering,

environmental studies, security services, health services – have been observed. Collected evidence indicates

the BL/gamified procedures improve results over conventional face-to-face only classes. This positive

evidence suggests that “soft skills”, typical of social sciences (as opposed to the “hard skills” of numerical

calculus) as well as interdisciplinary subjects – particularly those that is crossovers of computer science and

design or culture or music – may also benefit from such an approach, particularly in multicultural

classrooms.

1 INTRODUCTION

The co-existence of diverse interests, assumptions,

patterns of thinking, backgrounds, knowledge levels,

skills, and tools students in a class bring forth and

use while attempting to conceive, develop and apply

a solution to a problem. This solution may require

building a model, i.e., a simplified abstraction of

relevant aspects of reality – and selecting and/or

adjusting methods for solving the model. Of

particular interest here are mathematical problems

that cannot be solved exactly due to computational

complexity or lack of closed-up formulae. Solving

such problems approximately is the subject of

numerical analysis (Burden and Faires, 2010).

Numerical analysis (NA) is a mandatory subject

in almost all science and engineering courses at

university level. NA classrooms are usually made up

of students from subject areas as different as Health

Care and Civil Engineering and could thus be

termed “multi-disciplinary” because the students are

used to very different approaches to problem-

solving. A NA multi-disciplinary classroom has

interests in diverse problems originating from real-

world situations in several scientific and engineering

application domains. The disciplinary of

participants' backgrounds and the diversity of the

subject matter can turn teaching NA into a

challenging task with sometimes undesirable yet

frequent psychological effects such as lack of

motivation, decline of engagement in group work

and failing performance among students.

196

Barros M., Moura A., Borgman L. and Terton U..

Blended Learning in Multi-disciplinary Classrooms - Experiments in a Lecture about Numerical Analysis.

DOI: 10.5220/0005409001960204

In Proceedings of the 7th International Conference on Computer Supported Education (CSEDU-2015), pages 196-204

ISBN: 978-989-758-108-3

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

Conventional, face-to-face NA didactics tend to

emphasize the application of numerical methods to

generic mathematical problems with no explicit

linkage to real-world, professional scenarios of

interest to the students. This tendency, also observed

in other calculus subjects (Thome et al., 2014), only

compounds shortfalls in NA learning outcomes.

NA´s applicability (usefulness in real-world

situations) and scope (most if not all science and

engineering fields use it) make its teaching and

learning important and worthy of attention.

We suggest that blended learning/gamification

combined with modelling of real-life phenomena,

activities on the Web and face-to-face sessions may

improve NA didactics and student engagement and

performance. We use “gamification” here with the

same meaning as that provided in (Werbach &

Hunter, 2012; Deterding et al., 2013), that is, the

ancillary use of game mechanics and game design

techniques in non-game contexts (e.g., in an NA

lecture).

Blended learning (BL), in its simplest and initial

form, refers to the integration of online and face-to-

face-instruction (Bersin, 2004; Graham, 2006). BL

experiments have since evolved to deal with richer

blending options and have become frequent in

particular in many university and other higher

education courses (Garrison and Kanuka, 2004;

CSEDU, 2010-2014; see also Section 2). Little

attention, however, has been devoted to NA courses.

Notable and recent exceptions include: the work

(Mrayyan, 2013)

reports on the performance of 45

students when video lecture notes are blended with

conventional classes; and, (Cepeda, 2013) blends

regular classes with online and mobile materials for

engineering students whose performance was

observed over three years. However, additional

experiments with other blended resources (e.g.,

gamification) and a more comprehensive coverage

of application domains with more students are still

needed. This paper contributes to the discussion with

such additional experiments.

Experiments did run with conventional learning

and the suggested BL, gamified approach (detailed

in Section 3) applied to NA lectures in 25 classes

encompassing almost 1,500 students and

professionals from different application domains,

including chemical, electrical and civil engineering,

environmental studies, security services, health

services, at the Federal University of Campina

Grande (UFCG), Brazil.

The general research question (RQ) of interest

with these experiments is (see also Section 4):

Can there be evidence that the suggested BL

approach for multi-disciplinary NA classrooms

addresses shortfalls of conventional face-to-face

lectures?

Here, we assume that statistically significant

evidence may consist of (1) increased motivation by

students; (2) increased student engagement; and (3)

improved test scores. (Evidential statistics collection

and analysis are carried out in Section 5.)

A positively answered RQ could signal that other

multi-disciplinary classrooms – particularly those

that deal with crossovers of computer science and

design or art or music – may also benefit from the

suggested BL approach. (Section 6 concludes the

paper by discussing whether a similar BL approach

could facilitate the acquisition of “soft skills” or

"transferable skills" – the core of art studies and

social sciences – as opposed to the “hard skills” in

the core of NA.)

2 RELATED WORK

This paper directly relates to BL and gamification

research efforts in higher education courses with

multicultural audiences. Although experimentation

with BL is on the rise in all fields of education, the

work of Drysdale et al., (2013) indicates that much

of it is carried out at the university level. The

analysed works in (Drysdale et al., (2013) – over

200 graduate dissertations and theses on BL – relate

to this paper in the sense that in one way or another

they investigate the benefit of BL-programs over

traditional face-to-face programs. Gamification was

use as a means to add the important factor called joy

which can enhance the level of engagement

(Nielsen, J. 2002).

For instance, subjective outcomes such as

learning effectiveness, cost effectiveness,

institutional commitment, student satisfaction,

faculty satisfaction, etc. were described (Moore,

2005); another study noted that students preferred

BL classes compared to traditional classes in the

following areas: “(a) accessibility and availability of

course materials; (b) use of web-based or electronic

tools for communication and collaboration; (c)

assessment and evaluation; and (d) student learning

experiences with real-life applications” (Arano-

Ocuaman, 2010). These two works parallel ours in

the choice of (some) performance indicators and BL

course design aspects (web tools and real-life

applications). The work (Caputo, 2010) considers

calculus; ours, numerical calculus.

Graham (2013) outlined opportunities for

BlendedLearninginMulti-disciplinaryClassrooms-ExperimentsinaLectureaboutNumericalAnalysis

197

research exploring the link between satisfaction data

and specific blended learning methods (besides

accessibility, opportunity costs, cost effectiveness,

and psycho-social relationships), which is also done

here for NA students and in (Miyazoe and Anderson,

2010) for English as a foreign language (EFL) in a

university in Japan. The BL EFL considered three

different online writing facilities (forums, blogs and

wikis). A mixed-method evaluation of BL EFL was

applied with survey, interview, and text analysis

used for triangulation. Section 4 ahead also uses

triangulation but with questionnaires, peer reviews

and NA exams.

The inclusion of online and offline game aspects

and simulation in our proposal of a BL approach for

NA can be said to have been influenced by the

VITAE approach (Fox, 2009). Some works in the

literature use games to provide an engaging, self-

reinforcing context in which to motivate and educate

players (serious games) (Kankaanranta and

Neittaanmki, 2008). Other works simply try to

engage users with work through fun (Castellani et

al., 2013). The bibliography on gamified education

indicates that gamification aspects facilitate learning

and working in professional and business

environments in general (cf. proceedings of CSEDU

2010-2014). Intrinsic motivators such

as achievement, responsibility and competence are

motivators that come from the actual performance of

the task or job, which can be facilitated through a

game. Those motivators trigger intrinsic interest of

the work, in our case the learning of mathematical

procedures. Extrinsic motivators on the other hand

such as scores, promotion to the next level, positive

feedback, are designed by the game desigfner to

nurture interest and to keep the lerener gamer in the

state of flow. As described by Csikszentmihalyi, M.

(2014). Aaron Delwiche (2006) argues that games

such as massively multiplayer online games

(MMOs) are living, breathing textbooks that provide

students with first-hand exposure to critical theory

and professional practice and therefore ideal to

enhance the teaching and learning experience. Not

much, however, has been published on applying

gamification to NA teaching contexts.

Our proposed BL approach also took into

consideration some of the "Harvard Consortium

Calculus principles", namely: motivate by practical

problems ("the way of Archimedes"); chose topics

which interact with other disciplines; and, favour a

completely example-driven approach and natural

language (plain Portuguese in our case) over formal

descriptions

Our analysis of face-to-face NA instruction

shortfalls correlates well with that of (Mrayyan,

2013) but we consider a much longer observation

period, larger student population and a BL

experiment encompassing more NA topics.

The Blended Learning in Numerical Analysis

(BLIN) project developed tools and modules are

oriented towards students in engineering and

informatics curricula and applied them to over 600

students (USI, 2008). Although BLIN seems

interesting and useful, we found no information on

its results. Development efforts were also reported in

(Cepeda, 2013) where the aim was to simulate /

integrate several numerical methods in order to

mathematically analyse complex engineering

problems. It might be a good experiment to blend

the resulting tools of these works with existing

resources of our proposed BL approach.

The BL approach proposed in this paper

contributes to existing BL research by illustrating,

complementing or extending most of the works

briefly reviewed here.

3 A BL COURSE FOR NA

The proposed BL, game-based approach for students

of a numerical analysis course in a university in

Brazil is detailed here in order to ascertain how the

approach will: i) motivate and prepare students,

regardless of their backgrounds, to absorb and apply

NA concepts, methods and tools to solve real-life

problems of their application domains; ii) help to

reduce their aversion to the subject; and, iii) improve

their grades in the subject compared with face-to-

face instruction.

Intended NA learning outcomes cover

proficiency with numerical methods (Burden and

Faires 2010) for: determining roots of functions;

solving systems of equations; interpolation and

curve fitting; numerical integration; and error

analysis for each method. Students´ proficiency is

checked through game achievements (accumulated

“knowledge currency”) and by conventional exams.

The proposed BL gamification approach is

simple and consists of making groups of up to six

students; identify problems of interest to persons and

institutions in the real world that can be solved

through numerical methods. For instance, if one had

a model (e.g. a multivariate function) for thefts in a

city, and if all model variables were kept fixed but

for the number of police officers, how big should the

police force be for thefts to drop by 40%? (The

solution is obtained from the police size roots of the

function.) Problem enunciation and model building

CSEDU2015-7thInternationalConferenceonComputerSupportedEducation

198

are carried out with the assistance of invited, real-

world application professionals (such as an expert on

crime and police work).

Problem and solution identification activities are

carried out by each group of students according to

missions they receive in a Role-Playing Game

(RPG) (Kim, 2014) called N-able. Activities take

place in three spaces: i) the physical space of the

classroom used for intra- and inter-group, lecturer-

mediated communications, including face-to-face

classes and exams; ii) a virtual space in the Web

(“Mathville”) that serves to synchronize and support

N-able´s activities, including mandatory Web

lessons (also available but optional to face-to-face

classes); and, iii) the real-world surroundings of the

students´ living spaces. Students move between

spaces as they are exposed to a sequence of

situations during four months according to

gamification strategies that include missions,

challenges, deterministic and random rewards (e.g.,

the right to ask the tutor whether an answer to an

exam question is correct), peer reviews of tasks,

tutorials, knowledge money (e.g., to buy extra time

for task completion) and progressive game levels.

N-able situations are created within a story

where a “MathWizard” (the NA lecturer) coaches,

rewards or penalizes other characters (played by

students in each group) as they strive to become

heroes. Missions are short, 5-step journeys during

which, students: i) always depart from the classroom

(The Council of Wise Persons - CWP) where they

are assigned missions and are motivated to pursue

them by the MathWizard; ii) go through the Village

of Reachable Knowledge (VRK) in the world of

Mathematics (a collection of five online

environments, one for each of the learning outcomes

that in turn, defines a level of the game) where they

face challenges that include reading and production

of multimedia content that help them understand and

share knowledge about NA; iii) wander in their own

(real-world) city where they identify, model and

solve problems using NA (e.g., the theft modelling

problem) and face challenges to motivate other

group members and to convince experts from other

areas (cultures) to help them; iv) return to VRK to

publish their group´s feat of heroism (problems-NA

solutions) and to evaluate other groups’ feats; and,

finally, v) return to the CWP where they present

their work to the MathWizard, to other groups and to

invited, participating experts. Although details of the

story change to reflect seasonal, cultural or class´

preferences, basic game-structuring elements, such

as those in (Campbell, 1949), and alternate reality

aspects as in (McConigal, 2011) to create alternative

social experiences around every day spaces, are

maintained. Heroism is achieved by finding a NA

solution to a problem that affects individuals, or

society as a whole – as in the above theft-reducing

modelling example. During the journey, all players

develop the ability to manage the multicultural

knowledge as advocated in (Girard, John P., and

JoAnn L. Girard, 2011).

Modelling activities are simplified by validating

functions using proportionality of influencing

factors, i.e., sensitivity analysis (Saltelli et al., 2008).

This allows students to abstract from formal

mathematical demonstrations and to concentrate on

the most relevant aspects of identifying cause-effect

relationships of real-life cases and on the application

of numerical methods to solve them.

The N-able RPG was implemented on the

Moodle learning management system (LMS) with

graphical and animation add-ons developed with

several image editing software and game engines

such as Construct2 and RPGMaker. The LMS was

integrated into an RPG development platform

because the N-able methodology needs to create a

hero experience (hero´s journey) in collaborative

learning under the supervision of the NA lecturer.

Properly supporting such an experience by just using

a conventional game engine is rather difficult if not

impossible. Moodle was chosen for its open source

code that facilitates the integration of add-ons.

Further, it offers a range of facilities and resources

for people who play MathWizards to instigate

potential heroes to explore knowledge made

available in the virtual scenarios as well as in real

life. Resources include forums, wikis, blogs,

synchronous and asynchronous communication

tools, and facilities for uploading files with real-

world-challenge-overcoming proof. In addition, such

an integrated system allows for the continuous and

automatic logging and evaluation of players’

contributions or other actions (e.g., access to games,

completion of activities), peer evaluations,

accumulation of quantitative indicators (game

money, awards, grades, badges) and even, the

elicitation of attitudes in written tasks by

differentiating between connected knowledge (CK)

and separate knowledge (SK) (Galotti et al (1999).

(While players with higher CK tend to enjoy

learning, cooperate more easily and build on others’

ideas, SK players tend to be critical and to

polemicize more frequently. They may therefore be

coached appropriately, in order to reduce intra-group

friction). These integration and combinations may

make the proposed N-able RPG an innovative tool

for multicultural professional education and

BlendedLearninginMulti-disciplinaryClassrooms-ExperimentsinaLectureaboutNumericalAnalysis

199

knowledge management.

The success factors of the resulting BL, gamified

course for NA relate to the students´ capacity to: i)

isolate a problem (question) in a real-professional or

personal-life situation and quantitative human and

natural factors which influence the problem (i.e.,

students should be able to model the real-world by

means of quantitative variables); ii) establish

proportional and inversely proportional

mathematical relations between these factors (i.e.,

build coherent, linear and non-linear equations and

models); and, iii) produce and apply numerical

methods to solve the resulting equations/models.

Players collect or lose points (“knowledge

currency”) as they achieve or fail to achieve success

in assigned activities, which increase in complexity

at higher game levels.

4 DESIGN OF EXPERIMENTS

Evaluation of the proposed BL, gamified approach

for NA as compared to that of face-to-face lectures

involved 1,478 students at UFCG, Brazil, in 25

classes from 2007 to 2014. All students were taught

the same program with the same learning objectives.

The same lecturer taught and assessed both BL

gamified & face-to-face using the same criteria. To

reduce eventuality of a bias towards BL a large

number of classes and students were considered.

Face-to-face students totaled 552 in 9 classes; the

remaining 926 BL students composed 16 classes.

Students were mainly, but not exclusively, from

engineering undergraduate programs: agricultural,

chemical, civil, electrical, environmental, food,

materials, mining, etc. Professionals who assisted

the N-able RPG groups had varied backgrounds,

such as food safety, health services, public health,

and security. Face to face students have the same

challenge situations (isolate, modeling and solve a

problem) and scheduling to home study but the

problem is proposed by the lecturer, the activities

(lectures and assessments) are performed in the class

and knowledge are mainly constructed by

interactions between lecturer and coleagues, with no

contributions of characters from the two (virtual and

real) worlds of the game.

Experiments were designed to objectively

compare the NA proficiency and engagement of BL

students against the expected, “typical behavior” of

their face-to-face counterparts. Here we assume that

this “expected, typical behavior” is provided by the

average for each of the objective indicators of the 9

face-to-face classes in the experiments.

The experiments also call for students to

subjectively evaluate their overall experience with

the adopted NA lecturing approach (either face-to-

face or BL).

4.1 Objective Indicators

The objective analysis focuses on grades as

representatives for NA proficiency and class

attendance and subject dropouts as proxies for

student engagement. Objective indicators are:

 µ - mean of students´ grades over all 9 face-to-

face classes; it is used as the expected mean of

BL students in corresponding H

testing.

 µ

- mean of students´ grades in BL class k =

1, 2, … 16; it is used as the k

observation for

this indicator in Chi-square calculations. (µ

the average of all µ

 σ – average standard deviation of students´

grades over all 9 face-to-face classes; it is used

as the expected standard deviation of BL

students´ grades in corresponding H

testing.

 σ

- standard deviation of students´ grades in

BL class k = 1, 2, … 16; it is used as the k

observation for this indicator. (σ

is the

average of all σ

A more effective BL NA course should yield µ

µ and possibly, σ

< σ – meaning in this last case

that BL students show more homogenous

proficiency with less grade scattering around the

mean.

And as an engagement indicator, we define:

 η – overall mean fraction of failing face-to-face

students per class (includes dropouts, failures

due to insufficient grades and excessive

absenteeism); it is used as the expected failing

fraction of BL students in corresponding H

 η

- fraction of failing students in BL class k

= 1, 2, … 16; it is used as the k

observation

for this indicator. (η

is the average of all η

Similarly, if the BL approach motivates more

students to follow through with the NA course, one

expects η

> η.

4.2 Subjective Indicators

Subjective evidence data collection was carried out

by structured questionnaires available to the

students. Questions attempted to determine the

average satisfaction level of the students with the

adopted NA lecturing approach. Given “satisfaction”

is highly subjective, we attempted to obtain an

indication of its level from respondents’ perception

of each NA lecturing approach´s contribution to:

CSEDU2015-7thInternationalConferenceonComputerSupportedEducation

200

a) Grades.

b) Understanding and use of concepts.

c) Engagement in course activities.

d) Help colleagues with activities.

e) Work in a multicultural environment.

f) Having fun during the course.

Respondents could offer their answers on a 5-

point Likert scale (Uebersax, 2006): 1- Very little 2-

Little 3- Neutral 4- Much 5- Very much.

φ was defined as the mean and ψ as the mean

standard deviation of the satisfaction level overall 9

face-to-face classes. One may thus write:

φ = 1/6

∑

∈,,,,

Eq. 1

ψ = 1/6

∑

∈,,,,

Eq. 2

where φ

and ψ

for ∀i ϵ {a,b,c,d,e} are the mean and

standard deviation, respectively, for the values of the

answers in Question a,b,c,d,e and f above over all 9

face-to-face classes.

One may define and write equivalent equations

to 1 and 2 for φ

and ψ

likewise for the overall 16

BL, gamified classes. (We leave this out, in the

interests of brevity.)

The basic tool for data collection from BL

students is the N-able´s game platform itself since it

offers evaluation instruments for the indicators (e.g.,

questionnaires) – some of which are implicit in the

gameplay while others are explicit in the highest

game level. Face-to-face students may answer the

questionnaire on the Web or during the written, last

formal exam.

4.3 Research Questions and H

The Research Questions (RQs) which the objective

evaluation experiments are designed to answer take

the following general form: Are there statistically

significant differences between the objective

performance “indicator x” of the BL, gamified NA

students and that of face-to-face students?

Here, “indicator x” refers to one of the indicators

in section 4.1, i.e., x ϵ { µ

, σ

, η

} and each of

these is to be compared to its face-to-face

counterpart µ, σ or η, respectively.

Thus, the corresponding underlying Null

Hypothesis (H

) for each objective “indicator x”

takes the form: There are no statistically significant

differences between the objective performance

“indicator x” of the BL, gamified NA students and

that of face-to-face students. In the experiments, H

will be tested using p-values (Nuzzo, 2014) and will

be rejected if p ≤0.05. A rejected H

implies a

positively answered RQ.

In contrast to the objective indicators, subjective

indicators are essentially, “impressions” concerning

satisfaction with a given lecturing method, i.e.,

indications are attributed depending on the

respondent´s feelings, personal preference and even,

state-of-mind. Hence, it seems appropriate to discuss

and interpret the subjective results, rather than

offering a more formal statistical analysis.

Therefore, the RQ for the case of the subjective

indicators is more loosely presented as: Is there

evidence that the BL, gamified approach offers a

more satisfying student experience than the face-to-

face alternative? Answering this RQ omits null

hypothesis testing. Rather it is done by comparing

’s to φ

’s (and ψ

’s to ψ

’s) for ∀i ϵ {a,b,c,d,e}

in order to lead to comparisons of φ to φ

(and ψ to

) and then check for gains in favor of the

proposed BL, gamified approach for NA.

5 RESULTS

Face-to-face classes varied in size from 47 to 80

students with a mean of 61.33 students/class.

Populations of BL classes varied from 26 to 83 with

a mean of 57.88. Classes were offered in the

morning, afternoon and in the evening. All face-to-

face classes but one were at night; out of the 16 BL

classes, 7 were at night. Class hours did not seem to

perceptibly affect performance results.

5.1 Objective Results

Grade intervals were from 0.0 to 100 (perfect score).

Minimal passing grade at UFCG is 50.0. Students

who are absent from a quarter of classes and other

programmed official activities fail the course. The

face-to-face classes’ “typical behavior”, as given by

the triple (µ, σ, η), was observed to be: µ = 64.3, σ =

20.3 and η = 27.43%.

Results for the BL students are plotted in Figures

1 and 2. The face-to-face corresponding indicator for

typical behavior is inserted in each figure for

comparison purposes.

Figure 1 plots and compares the average grade

(top solid line) for each of the 16 BL classes (µ

for k=1,2,…,16) against the overall mean (broken

line) of the 9 face-to-face classes (µ = 64.3) – one

can see that the BL approach offers higher grade

averages throughout; it also plots and compares the

standard deviations (underlined, solid line in the

bottom) for each of the 16 BL classes (σ

for

k=1,2,…,16) against the overall average standard

deviation (underlined broken line) of the 9 face-to-

BlendedLearninginMulti-disciplinaryClassrooms-ExperimentsinaLectureaboutNumericalAnalysis

201

face classes (σ = 20.3). Here, the BL approach

shows lower standard deviations for class grades.

From the values in Figure 1, one can calculate

that, for the case of the grade average of BL

students, p ≤ 0.05. This value for p indicates that H

is to be rejected and that there are in fact,

statistically relevant differences in favor of the BL,

gamified approach. Similarly, for the standard

deviation: the corresponding H

is also rejected since

p ≤ 0.05. For the case of NA lectures, BL

approaches not only increase the class grade average

but they also tend to homogenize attainment of

learning outcomes, as a lower spread of grades

(smaller standard deviation on the average)

indicates.

Figure 1: µ

vs. µ and σ

vs. σ, k=1,2,…,16.

Figure 2 plots and compares the fraction of

students who fail the NA courses (the solid line is

again, for BL).

Figure 2: η

vs. η, k=1,2,…,16.

Figure 2 also leads to p ≤ 0.05, indicating once

again that H

be rejected. This figure tells us that the

BL, gamified NA lectures have the added benefit of

motivating students to participate in class activities

more consistently. When the fraction of failures is

broken down into its 3 component types, the

advantage of the BL, gamified approach over face-

to-face NA lectures become clear: failures due to

failing grades, 3.05% vs. 14.07% on the average

overall; failures due to absenteeism, 3.99% vs.

9.73%; and, failures due to dropout, 3.63% vs.

3.06%. Here, BL has a slight higher dropout rate. A

possible reason for this is that BL requires more

effort to take part in activities (see also Section 5.2).

The overall BL advantage may be because it is more

fun or because it is more attractive and challenging,

because it promotes “cross pollination” with other

cultures, as the subjective results seem to suggest.

Table 1 summarizes overall comparison results.

Table 1: Face-to-face vs. BL/gamified averages.

Face-to-face BL, gamified

Mean class grade µ = 64.3 µ

B L

= 79.6

Grade Std. Dev. σ = 20.3 σ

= 14.6

Mean Fraction Fail η = 27.43% η

= 10.10%

5.2 Subjective Results

Figure 3 shows and compares the averages and

standard deviations for the answers to each question

provided by the face-to-face and BL/gamified NA

classes, i.e, the figure compares φ

’s to φ

’s and

’s to ψ

’s for ∀ i ϵ {a,b,c,d,e} (please refer to

sections 4.2 and 4.

Figure 3: φ

, φ

, ψ

and ψ

for ∀i ϵ {a,b,c,d,e}.

Figure 3 provides evidence that on average, one

can expect the proposed BL, gamified NA lecture to

have higher-valued satisfaction components

(questions a to f of Section 4.2) than its face-to-face

alternative, i.e., φ

≥ φ

, ∀i ϵ {a,b,c,d,e}. The BL

approach is clearly superior when students consider

its contribution to work to be carried out in

multicultural settings. Indeed, for question e, the

difference in means is +1.50 in favor of BL, a full

50% gain over that of the face-to-face lecture (and

over a full 50% reduction in the mean standard

deviation). Note however, that the means for

question f (having fun with NA classes) are close

(4.01 vs. 4.27) and that the mean standard deviation

of the BL approach is actually less favorable

(higher) than that for the face-to-face classes (0.13

CSEDU2015-7thInternationalConferenceonComputerSupportedEducation

202

vs.0.25). This may challenge the natural expectation

of more fun in a BL, gamified class: the actual,

additional effort of participating in a RPG and in

online studying and reporting activities is likely to

increase the time allocated to learning the subject.

(This may also explain BL’s higher proportion of

dropout students.) The evidence supporting that

however, should be the subject of more

investigation.

Overall, the mean satisfaction level for the face-

to-face NA lecture comes out as φ = 3.60 < φ

4.43, i.e., the satisfaction level of the BL, gamified

approach is 23% higher on the average. (The overall

mean standard deviation is also 34% better, i.e.,

lower.) These results provide clear evidence in favor

of a positive answer to the research question: for the

considered subjective experiments, the BL, gamified

approach proposed in this paper leads to higher

satisfaction levels of the participants, i.e., they have

a better learning experience.

6 CONCLUSION & OUTLOOK

Teaching Numerical Analysis (NA) in face-to-face

classes has typically yielded mixed results in terms

of success indicators (students’ grades and

motivation). An alternative, BL and gamification

approach was described in this paper as applied to

NA lectures at UFCG in Brazil. This paper has

presented the results of a seven-year effort that

collected data and evidence on the learning

effectiveness from close to 1,500 students and 25

classes, of which nine were face-to-face and served

as reference for “expected results”. The pilot courses

were designed with game-based blended learning

components in the hope of favorably changing

success indicators. Results of the BL, gamification

classes were significantly better,–both in objective

(better grades and lower absenteeism) and subjective

(satisfaction with the lectures) terms. As such, the

paper contributes to the existing knowledge of BL

applications, by offering data from long-running

experiments with BL (and serious games).

The results, so far, are restricted to engineering

NA students working in settings at UFCG.

Experiment was geared towards a NA course for

engineering students at UFCG which may limit

application of conclusions. But results seem to

indicate that BL and gamification may indeed help

with other science and technology courses. Also, in

this work step the aim was evaluate the integrated

impacts (grades and satisfaction) of the two

combined dimensions of the approach (BL and

gamification).

Could we attune BL and gamification

dimensions to improve the approach in order to

achieve learning objectives? Could these

encouraging findings in the subject area of "hard

skills" possibly be transferred to so-called "soft

skills" (or "people skills", or "transferable skills")

such as leadership, team work, or intercultural

awareness? Would the less specific, but also more

complex subject matter of "soft skills" perhaps allow

educators to create even more complex, captivating

and intriguing story-lines than the model building

for the "theft vs. police officers" ratio (see point 3

above)? Perhaps the officer who can quickly and

reliably calculate that in order for thefts to drop by

40%, New York City needs 11.543 new permanent

staff, can be proud of their numerical skills.

However, this "solution" may be too simple for

contemporary challenges and unlikely to be put into

practice. A colleague with better-trained "soft skills"

is likely to find a more complex solution, which

does not involve massive recruitment.

In the light of changing requirements in the work

place where in almost all sectors "soft skills" have

become more relevant than specific knowledge of

the product and market or "hard skills", it is time to

explore the full potential of blended and game-based

learning. If the same levels of objective and

subjective improvement could be demonstrated for

"soft skills", blended and gamified learning could

enter the domain of social and communicative skills.

Further studies and a truly international approach to

teaching "soft skills" with a blended and game-based

learning approach promises to generate useful and

much-needed didactic advice for the future of

education.

ACKNOWLEDGEMENTS

This work is partially supported by the ClipCult

Project of the Paraíba State R&D Foundation

(FAPESQ), the Brazilian Ministry of

Communications and UFCG. Comments and

suggestions from anonymous reviewers are also

gratefully acknowledged.

REFERENCES

Arano-Ocuaman, J., 2010., Differences in student

knowledge and perception of learning experiences

among non-traditional students in blended and face-

BlendedLearninginMulti-disciplinaryClassrooms-ExperimentsinaLectureaboutNumericalAnalysis

203

to-face classroom delivery. University of Missouri—

Saint Louis, USA.

Bersin, J., 2004., The Blended Learning Book:

BestPractices, Proven Methodologies, and Lessons

Learned. John Wiley & Sons.

Burden, R. and Faires, J., 2010., Numerical Analysis.

Cengage Learning, 9th Edition – Mathematics, p. 888.

Campbell, J., 1949., The Hero With a Thousand Faces.

Pantheon Books.

Caputo, M. G., 2010. Undergraduate mathematics

students' attitudes towards online mathematics

education and achievement in a hybrid calculus

course. Teachers College., Columbia University.

Castellani, et al., 2013., Game Mechanics in Support of

Production Environments. CHI’13, ACM Press.

Cepeda, F.J.D., 2013., A Numerical Methods Course

Based on B-Learning: Integrated Learning Design and

Follow Up. International Journal of Mobile and

Blended Learning, 5(1), pp. 39-57.

CSEDU 2011, Proceedings of International Conference

on Computer Supported Education [online]. [Accessed

15 October 2014]. Available from: http://

pubs.iids.org/index.php/publications/show/1814.

Csikszentmihalyi, M., 2014. Flow and the Foundations of

Positive Psychology. Springer Science and Business

Media Dortrecht, Germany, pp.227.Delwiche, A.,

2006. Massively multiplayer online games (MMOs) in

the new media classroom. Educational Technology &

Society, 9 (3), pp160-172.

Deterding, S., Sicart, M., Nacke, L., O'Hara, K., and

Dixon, D., 2013., Gamification: Using Game Design

Elements in Non-Gaming Contexts. CHI’13, ACM

Press.

Drysdale, J.S., Graham, C. R., Spring, K. J., and

Halverson, L.R., 2013., An analysis of research trends

in dissertations and theses studying blended learning.

Internet and Higher Education, 17., pp. 90-100.

Fox, A., 2009., Fun and Games in professional

development – Chapter 5 of “Mentoring for 21st

Century Skills – It´s All about the Learning”,

University of Salford, UK.

Galotti, K. M., Clinchy, B. M., Ainsworth, K., Lavin, B.,

and Manseld, A. F., 1999., A New Way of Assessing

Ways of Knowing: The Attitudes Towards Thinking

and Learning Survey (ATTLS). Sex Roles, 40(9/10),

pp. 745-766.

Garison, D. R., Kanuka, H., 2004. Blended learning:

Uncovering its transformative potential in higher

education. Internet and Higher Education, 7, pp. 95–

105.

Girard, John P., and Girard, JoAnn L., 2011., Social

Knowledge: Using Social Media to Know What You

Know. IGI Global, pp. 1-358.

Graham, C. R., 2006., Blended learning systems:

Definition, current trends, and future directions,

Handbook of blended learning: Global perspectives,

local designs. Pfeiffer Publishing, San Francisco, CA,

pp. 3–21.

Graham, C. R., 2013,

Emerging practice and research in

blended learning. M. G. Moore (Ed.), Handbook of

distance education (3rd ed.), Routledge, New York,

pp. 333-350.

Hughes-Hallet, D., Gleason, A. M. et al, 2000, Calculus,

Alternate Version. 2nd Ed. [online]. [Accessed 20

October 2014]. Available from: http://

www.math.harvard.edu/~knill/pedagogy/harvardcalcul

us/index.html.

Kim, J., 2014, What is a Role-Playing Game. [online]

[Accessed 26 November 2014]. Available from:

http://www.darkshire.net/jhkim/rpg/whatis/.

McConigal, J., 2011., Reality Is Broken. Why Games

Make Us Better and How They Can Change the

World. Penguin Press HC.

Mrayyan, S., 2013., The Impact of Blend Methods of

Teaching Numerical Analysis on Students

Achievement, as Study Case. Greener Journal of

Educational Research 3 (3), pp. 155-159.

Miyazoe, T. and Anderson, T. A., 2010, Learning

outcomes and students' perceptions of online writing:

Simultaneous implementation of a forum, blog, and

wiki in an EFL blended learning setting. Systems, 38,

(2), pp. 185-199.

Nielsen, J., 2002. User empowerment and the fun factor.

In: Jakob Nielsen’s Alertbox [online]. [Accessed 15

October 2014]. Available from: http://

www.nngroup.com/articles/user-empowerment-and-

the-fun-factor/.

Nuzzo, R., 2014., Scientific method: Statistical errors.

Nature 506 (7487): pp. 150.

Saltelli, A. et al., 2008., Global Sensitivity Analysis. The

Primer, John Wiley & Sons.

Thome, F. et al., 2014., How to make Calculus II seem

motivated, interesting, and useful. [online]. [Accessed

05 November 2014]. Available from:

http://matheducators.stackexchange.com/questions/24

28/how-to-make-calculus-ii-seem-motivated-

interesting-and-useful.

Uebersax, J., 2006., Likert scales: Dispelling the

Confusion. [online]. [Accessed 06 December 2014].

Available from: http://john- uebersax.com/stat/

likert.htm.

USI, 2008., Blended Learning in Numerical Analysis.

University dela Svizzera Italiana, [online]. [Accessed

20 October 2014]. Available from: http://

search.usi.ch/people/fbf972d416a9a395e2f8c88656eb

9fdd/Tardini-Stefano/projects.

Werbach, K. & Hunter, D., 2010. For the Win: How Game

Thinking Can Revolutionize Your Business. Wharton

Digital Pres.

CSEDU2015-7thInternationalConferenceonComputerSupportedEducation

204