LEARNING STYLES FOR K-12 MATHEMATICS E-LEARNING

Atakan Aral and Zehra Cataltepe

Department of Computer Engineering, Istanbul Technical University, Maslak, Istanbul, Turkey

Keywords:

e-Learning, Learning Styles, Adaptive Learning, K-12 Mathematics.

Abstract:

This review paper analyzes signiﬁcant studies in learning style and e-Learning ﬁelds in order to synthesize

an answer to the question “Does considering learning styles improve e-Learning performance especially for

K-12 mathematics education?”. Included studies can be categorized into the following topics: learning style

models, learning style detection methods, considering learning styles in traditional education and e-Learning,

considering learning styles in K-12 mathematics education. The review shows that applying different teaching

methods for different learning styles could actually help a K-12 student understand a mathematics subject

better.

1 INTRODUCTION

Computer supported education environments offer a

signiﬁcant alternative to traditional learning methods.

Among other beneﬁts, they also allow specializing or

adapting according to learners’ needs. Herein, de-

signing an e-Learning application that is capable of

detecting user’s learning style and teaching a subject

by accommodating itself to that style is an interesting

research area. However, it is necessary to investigate

the impact of learning styles on e-Learning environ-

ments before launching out such a research.

This paper aims to review the existing literature

for teaching mathematics to K-12 students in an e-

Learning environment according to students’ learning

styles. Reviewed papers were selected according to

their signiﬁcance and relevance. Signiﬁcance is mea-

sured by the quantity and quality of citations while

relevance is decided according to the the applicabil-

ity of the study to K-12 mathematics e-Learning. Al-

though we tried to cover as many papers as possible,

we are aware that we may have left out some signiﬁ-

cant and relevant papers.

The paper is organized as follows: section 2 pro-

vides a summary of notable learning style models,

while in section 3 methods for detecting them are ex-

plained. To justify the positive effect of considering

learning styles, studies considering e-Learning and

face-to-face learning in general are given in section

4. Then, in section 5 other studies focussing on K-12

and mathematics education are considered. Finally,

section 6 summarizes the ﬁndings and comments.

2 LEARNING STYLE MODELS

Learning style or cognitive style is the preferences

or methods of a learner in his/her learning activi-

ties (Felder and Silverman, 1988). Different people

have different methods to understand a subject better.

Some individuals may prefer visual learning while

others may ﬁnd auditory or verbal approaches more

useful. Yet, some may succeed by only studying the

theory while experimenting may be essential for oth-

ers. Learning style models aim to specify and des-

ignate general preference categories similar to these

examples. They also classify learners according to

their approaches in learning and understanding sub-

jects by means of various measures (Felder and Sil-

verman, 1988).

Learning styles have aroused interest of re-

searchers from various ﬁelds through the years. As

a result, many different models have been proposed

by theoreticians and made use of by educational spe-

cialists. According to a relatively recent and exten-

sive report (Cofﬁeld et al., 2004), at least 71 learning

style models are present and 13 of them are consid-

ered major or more inﬂuential than the others. They

mainly differ from each other according to the extent

that they may change over time for an individual.

In his Mind Styles Model (MSM) (Gregorc, 1985)

Gregorc considered learning styles as unchangeable

and inborn. He stated that each individual can be

strong in one or two of the four styles deﬁned by two

dual dimensions: Abstract-Concrete and Sequential-

Random. Similarly, there are two dual dimensions in

317

Aral A. and Cataltepe Z..

LEARNING STYLES FOR K-12 MATHEMATICS E-LEARNING.

DOI: 10.5220/0003916603170322

In Proceedings of the 4th International Conference on Computer Supported Education (CSEDU-2012), pages 317-322

ISBN: 978-989-8565-06-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

Ridings Cognitive Styles Analysis (CSA) (Riding

and Rayner, 1998): Holist-Analytic and Verbaliser-

Imager. Unlike the former, learning strategies are re-

garded changeable in this model, however learning

styles are still ﬁxed.

Some models such as Kolb’s Learning Style In-

ventory (LSI) (Kolb and Kolb, 2005) and Felder-

Silverman learning style model (LSM) (Felder and

Silverman, 1988) did not consider learning styles

constand. According to them, learning preferences

may change slightly depending on time and situation.

Kolb proposed two dimensions (Abstract-Concrete

and Active-Reﬂective) and four styles (Converging,

Diverging, Assimilating and Accommodating) while

the Felder and Silverman intruduced four dimensions

(Active-Reﬂective, Sensing-Intuitive, Visual-Verbal

and Sequential-Global).

Different from the approaches above, Dunn and

Dunn (Dunn and Griggs, 2003) included other pref-

erence factors such as environmental factors (sound,

temperature, light), emotional factors (motivation, re-

sponsibility), physical factors (learning preferences,

intake and time of the day) and sociological factors

(such as learning groups, parental motivation). Vi-

sual, Auditory, Kinaesthetic and Tactile learning are

proposed as physical learning preferences.

3 LEARNING STYLE

DETECTION

Before trying to teach a subject using a method that

matches the learning style, challenge of determin-

ing the learning style stands. There are both tradi-

tional and computerized approaches trying to solve

that challenge.

3.1 Questionnaires

Custom designed questionnaires are the most com-

mon method of learning style determination. Nearly

all of the models mentioned above have their own

questionnaires, surveys or inventories. Some ques-

tionnaires contain less than 15 items such as Gregorc

Mind Style Delineator (MSD) or Kolb’s LSI while

some of them contain more than 100 items such as

LSI for the Dunn and Dunn model or Vermunt’s In-

ventory of Learning Styles (ILS) (Vermunt, 1998).

Questionnaires also differ by the type of their

items. In Gregorc MSD and Kolb’s LSI, respondents

should rank 4 alternative responses for each item ac-

cording to how much it ﬁts them. An example item

of that type can be “I learn best from...” while the re-

sponses to be ranked are: “rational theories”, “per-

sonal relationships”, “a chance to try out and prac-

tice” and “observation”. Each of these responses con-

tributes to a different learning style for the respondent

(Cofﬁeld et al., 2004).

Another quite common type of question is the 3

or 5 point Likert scale in which the respondents are

asked in what level they agree to the given statement.

This scale is used in Felder and Soloman’s Index of

Learning Styles (IXLS) (Soloman and Felder, 2001),

LSI for the Dunn and Dunn model, and Vermunt’s

ILS. An example item is “I dislike things uncertain

and unpredictable” where the possible responses are

“true”, “uncertain” and “false” (Cofﬁeld et al., 2004).

Distinct from the ones above, Riding did not em-

ploy a self-report measure in his CSA for his model

of cognitive style. Instead, he developed a “com-

puterised assessment method” where the respondents

are presented with “matching tasks” and “embedded

ﬁgures tasks” on a computer where their response

times are saved and used to determine learning style

(Cofﬁeld et al., 2004). Although Riding’s method is

not a questionnaire and the respondent is not aware

of how his/her preferences are measured, it cannot be

considered as an automatic detection method either,

because; user is still tested on a custom-engineered

setting instead of natural learning environment.

Questionnaires designed for some models provide

valid and reliable classiﬁcations in ideal situations;

however, there are problems with the questionnaire

approach, because; it is not realistic to assume that

learners are aware of their learning style and mo-

tivated to answer the questionnaire properly (Graf,

2007). This awareness and motivation problem is es-

pecially evident in the case of younger children in K-

12 level and it puts the validity and reliability of the

questionnaires in question.

3.2 Automatic Detection

Learning indicators (Papanikolaou and Grigoriadou,

2004) are the observable and quantiﬁable behavior of

the learners and they can be grouped into three cate-

gories: (i) navigational indicators; (ii) temporal indi-

cators; (iii) performance indicators. As an alternative

to traditional questionnaires, learning indicators are

proposed in a web based learning environment (Bous-

bia et al., 2009). This method proposes a track based

system called “Indicators for Detection of Learning

Style” which logs learner behavior. Then the system

analyzes the logs mainly focusing on navigational and

temporal indicators and suggests learning styles.

Another approach (Graf and Kinshuk, 2006)

based on Felder-Silverman LSM, presents a generic

tool to detect learning style by extracting it from the

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learning management system database. They use

the same approach as the IXLS questionnaire devel-

oped for Felder-Silverman LSM. Similarly, yet an-

other approach (Graf, 2007) aims to automatically

assign Felder-Silverman learning styles by applying

Bayesian Networks on indicators such as percentage

of time spent on certain pages, percentage of per-

formed self-assessment questions, percentage of cor-

rectly answered questions about certain subjects, time

spent in the forum or percentage of times a learning

object is skipped via the navigation menu.

Although automatically detecting learning style

according to user behavior offers a more natural and

unnoticeable solution to the detection problem, there

is not as much research as questionnaires demonstrat-

ing its validity and reliability. Moreover, logging de-

tailed user behavior and deducing a meaningful model

from the data to guess a learning style is not an easy

task. There are enormously many user actions and

it is required to decide which action contributes to

which learning style and in what level. Automatic

detection functionality is also hard to implement af-

terwards, unless the e-learning system is natively de-

veloped with logging capabilities.

There are also detection methods making use of

wearables and video/audio sensors which are not ex-

amined here as we focus mainly on methods that

do not require any additional hardware other than a

personal computer on the user side. Nevertheless,

it is worth mentioning the affective tutoring system

for mathematics called “Easy with Eve” (Sarrafzadeh

et al., 2008) which successfully evaluates primary

school students’ emotional states.

4 LEARNING STYLES AND

PERFORMANCE

When developing an application that considers learn-

ing styles, it is important to understand whether

designing different learning processes for different

learning styles actually affect learning performance

positively. Intensive research has been devoted on the

impact of learning style models for both traditional

learning and e-Learning environments.

4.1 Traditional Learning Performance

Learning style models and effects of educating stu-

dents in methods matching their learning styles have

been thoroughly researched for traditional learning

environments. For example, in a research (Riding and

Grimley, 1999), eighty 11-year-old students were as-

sessed for their learning style applying 3 different ed-

ucation methods. It was observed that students of cer-

tain learning styles perform better learning achieve-

ment using certain education methods.

On the other hand, surveys were conducted in

(Ballone and Czerniak, 2001) on K-12 teachers. They

were inquired about applying different instructional

strategies to match students of different learning

styles. Results demonstrate that science teachers be-

lieve doing so will “increase student success, motivate

students, meet all student needs, make science a good

learning experience for all students, encourage partic-

ipation, and create interest in science”.

Another interesting analysis (Cafferty, 1980) de-

termined the learning styles of both students and their

teachers. Then, the students were grouped into four

categories with gradual amount of match of elements

on their proﬁle with that of their teachers. Per-

formance evaluation showed that, greater degree of

match between the teacher’s and students’ learning

styles will result in higher Grade Point Average for

that group of students.

4.2 e-Learning Performance

Studies that examine the effect of learning styles in

e-Learning environments can be grouped roughly in

two categories: (i) studies that do not consider adap-

tive systems and experiment how e-Learning suits on

certain learning styles; (ii) studies that experiment the

effects of adapting the e-Learning system for different

learning styles. Studies in the ﬁrst category provide

the same content using the same methods to all learn-

ers and measure the effect of e-Learning on different

learning styles. While in the second category, a spe-

ciﬁc method is applied for each learning style and the

performance improvement with respect to the same

method for all case is measured.

A study (Manochehr, 2006) from the ﬁrst cate-

gory used Kolb’s LSI to measure learning styles and

compared performance of learning style groups for

traditional and e-Learning methods. Their research

indicated that undergraduate students from certain

learning styles (namely, assimilator and converger)

achieved better results with the e-Learning.

Another research (Shrestha et al., 2007) con-

ducted face-to-face interviews to 43 Undergraduate

students to detect both their learning styles and their

usage preferences on a Virtual Learning Environment

(VLE). Results revealed the inﬂuence of learning

style preferences on VLE performance and demon-

strated that VLE is particularly supportive for certain

types (namely, activist and reﬂective).

As an example to the second category of studies,

(Ford and Chen, 2001) explored the relation between

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319

matching and mismatching teaching styles with stu-

dents learning style by asking them to create web-

pages after giving instructions either matching or mis-

matching their learning style. Performance of the stu-

dents in matching group was superior in the multiple

choice test that is applied afterwards.

On the other hand, (Moallem, 2007) de-

signed multiple instructional materials using Felder-

Silverman LSM for an online course. Their results

suggest that although learning performance does not

show major difference, developing speciﬁc materials

for people of different styles results in higher motiva-

tion and more interaction with the course content.

Another study (Papanikolaou et al., 2003) pre-

sented an Adaptive Hypermedia prototype called IN-

SPIRE that focuses on learning style differences.

It dynamically generates “learner-tailored lessons”

through “curriculum sequencing, adaptive navigation

support, adaptive presentation, and supports system’s

adaptable behavior”. Their results supported the hy-

pothesis that learners of different styles discover and

prefer resources of INSPIRE that are beneﬁcial for

their learning style.

4.3 Overview of Studies

We draw two conclusions from the studies on both

traditional teaching methods and on e-Learning: (i)

When the same teaching method is applied to all

learners, there is a correlation between learning per-

formance and learning style. Learners of certain

styles perform better while some others fail to im-

prove. Although, this outcome is suggested as a draw-

back of e-Learning in some studies such as (Ross and

Schulz, 1999), it can be considered primarily as a

drawback of just the methods where the same con-

tent and methods are applied to all learners regardless

of their learning styles. (ii) When a learning method

which is compatible with the learner’s learning style

is used, learning achievement signiﬁcantly increases.

Both conclusions support the claim that: in an ideal

learning environment each learner should be treated

differently depending on his/her learning style.

5 LEARNING STYLES IN K-12

MATHEMATICS TEACHING

In this section, we cover the details on the learning

performance effects of learning styles and adapting

teaching style according to learning styles. We focus

only on mathematics teaching for K-12 students and

examine the effects in two cases: traditional (face-to-

face) learning and e-Learning, respectively.

5.1 Traditional Mathematics Teaching

Literature on the relationship of learning style and

K-12 mathematics education is not broad. One of

the few studies in the area (Riding and Agrell, 1997)

investigated the relationship between learning style,

intelligence and school achievement of 205 age 14-

16 students in 5 core subjects including mathematics.

Riding’s CSA was chosen as the learning style model

while mathematics performance was measured by the

end of year marks. Results of the study demonstrate

that in mathematics, students with wholist-verbaliser

style perform best among the high intelligence group,

while analytic-verbalisers are most successful among

the low intelligence group. They also ﬁnd no correla-

tion between learning style and intelligence.

Another approach (Kopsovich, 2001) tried to un-

derstand whether “a positive correlation between stu-

dents’ learning styles and their achievement test

scores in mathematics” exists for ﬁfth grade students.

500 students were tested for their learning style us-

ing LSI for the Dunn and Dunn model. Mathematics

achievement was measured using Texas Assessment

of Academic Skills Test (TAAS) that is an account-

ability system for all public schools in Texas, United

States. Results revealed that signiﬁcant differences

exist in the mathematics test scores of ﬁfth grade stu-

dents with different learning styles.

We were not able to ﬁnd a study on K-12 math-

ematics teaching where adaptive methods were ap-

plied to children of different learning styles. Even so,

a study on 108 college students (Chamberlin, 2011)

that analyzes the impact of differentiated instruction

on mathematics teaching, is worth mentioning at this

point since those students were prospective teachers

of K-12, and a purpose of the study was to “assist

them with implementing differentiated instruction in

their future mathematics teaching”. Instructors at-

tending the experiment were taught differentiated and

traditional courses of 5 sections each. Mean scores

of the experimental group were signiﬁcantly higher

showing that to meet diverse learning style needs of

the students is a factor for mathematics performance.

5.2 Mathematics Teaching through

e-Learning

In the evaluation of adaptive e-Learning performance

in K-12 mathematics teaching, little research that we

are awareof has been carried out. One of the few stud-

ies to mention is the A-MathS Multimedia Course-

ware (Zin, 2009) which is an adaptive system for

teaching mathematics, based on learning styles. The

system detects learning styles (in global/analytical

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320

and visual/verbal scales) in the diagnostic module and

provides one of the four instructional modules accord-

ingly. They applied pre- and post-tests in order to

evaluate the performance of courseware on 35 sec-

ondary school students. Their ﬁndings indicate that

adaptability resulted in signiﬁcant post-test score in-

crease. Experimental group with matching learning

styles achieved 10.5 points mean gain of score while

the control group with mismatching learning styles

only achieved 1.8 points. Moreover, in the question-

naire presented to students to rate the usability of the

courseware, control group rated the interface design

much lower than the experimental group showing that

they had difﬁculty in using and navigating in an envi-

ronment incompatible with their learning style.

Carnegie Learnings Cognitive Tutor is a differen-

tiated mathematics instruction software for learners

including middle school students that features multi-

ple representations of problems for different abilities

and learning styles. Some evaluations for Cognitive

Tutor are summarized in (Ritter et al., 2007). In one

example, performances of two classes using Cogni-

tive Tutor and a textbook they had been previously

using are compared. Results show that, students using

Cognitive Tutor get higher grades as well as reporting

greater conﬁdence in their mathematical abilities and

usefulness of these abilities in real life. Another eval-

uation demonstrate that among more than 6000 high

school students, ones who use Cognitive Tutor out-

performed others signiﬁcantly in a state exam. Per-

formance improvementis especially obvious for some

groups of students such as receiving Exceptional Stu-

dent Education or having limited English proﬁciency.

We also would like to mention adaptive, web-

based learning environment called ActiveMath which

generates interactive mathematics courses adapted to

the student’s preferences (Melis et al., 2001). Al-

though we were not able to ﬁnd any published pa-

per on its performance, it is asserted that summative

evaluations continue in 10 German schools as well as

universities of Edinburgh, UK and Malaga, Spain.

5.3 Overview of Studies

In the case of K-12 mathematics education there is

not an adequate number of studies on either tradi-

tional learning or e-Learning to enable reliable de-

ductions. However, the small number of studies con-

sidered above create an impression that similar posi-

tive outcomes in other age groups and other subjects

can also be obtained for K-12 mathematics. More

research should be devoted especially on adaptive

teaching methods based on learning style to under-

stand its impact on K-12 mathematics performance.

6 CONCLUSIONS AND FUTURE

WORK

Our literature review shows that the research in learn-

ing style models and their application to e-learning

environments is quite adequate both theoretically and

empirically. There is a potent and detailed back-

ground for learning style models despite of some mi-

nor differences among them. Moreover, there are

many publications suggesting that, considering learn-

ing styles appropriately enhances the learning expe-

rience. On the other hand, amount of studies on the

effects of learning styles in younger learners (K-12 in

our case) and in speciﬁc school subjects (Mathematics

in our case) are not proportionally intensive, although

a few available studies are encouraging.

Besides, almost all of the learning style detec-

tion/determination methods are either questionnaires

or automated systems that track user behavior in an

e-Learning environment. Those are not quite suit-

able for K-12 students due to lack of learner self-

awareness and motivation in the case of question-

naires and due to highly sophisticated infrastructure

and decision algorithm requirements and lack of reli-

ability/validity experiments in the latter case.

Our aim is to develop an educational game which

detects learning style of a K-12 student (especially 3

to 5 graders), then tries to teach a simple mathematics

subject in accordance with his/her learning style and

ﬁnally measures the level of cognition. We would like

to give an example for how learning style differences

could be used for easier multiplication table learning.

This subject is chosen due to the difﬁculty that stu-

dents have in learning it as well as its applicability

to multiple teaching styles on a computer. For in-

stance, multiplication table can be taught through a

game with numbers, spoken explanations and apply-

ing speech recognition to learner responses for verbal

learners or using symbols, animations or images of

real-life objects such as fruits for visual learners. User

interaction can be emphasized by allowing dragging

and dropping symbols or numbers to the multiplica-

tion equations in order to support kinesthetic learners

who prefer to learn by getting involved and carrying

out a physical activity.

Learning style can be detected via a separate game

presented beforehand or concluded from learner’s

performance in abovementioned games. Alterna-

tively, these two approachescan be combined in a sys-

tem where initially detected learner and game proﬁles

change over time based on how students perform on

various games.

We expect to observe that, games which are natu-

ral ways of learning for students of these ages, can

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321

accurately detect learning style and increase learn-

ing performance when suitable teaching methods for

learning style are employed. Results of that study will

hopefully contribute to the quest of ﬁlling in the gap

of reliable empirical analysis in the area.

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