The Implementation of Inquiry-based Learning in the Organization of

Students’ Research Activities on Mathematics

Kateryna V. Vlasenko

1,2 a

, Olha H. Rovenska

3 b

, Iryna V. Lovianova

4 c

Oksana M. Kondratyeva

5,6 d

, Vitaliy V. Achkan

7 e

, Yana M. Tkachenko

, and

Mariya P. Shyshkina

8,9 f

Department of Mathematics, National University of “Kyiv Mohyla Academy”, 2 Hryhoriya Skovorody Str., Kyiv, 04655,

Ukraine

Technical University “Metinvest Polytechnic” LLC, 71A Sechenov Str., Mariupol, 87524, Ukraine

Donbass State Engineering Academy, 72 Academychna Str., Kramatorsk, 84313, Ukraine

Kryvyi Rih State Pedagogical University, 54 Gagarin Ave., Kryvyi Rih, 50086, Ukraine

Bohdan Khmelnytsky National University of Cherkasy, 81 Shevchenko Blvd., Cherkasy, 18031, Ukraine

Cherkasy State Technological University, 460 Shevchenko Blvd., Cherkasy, 18006, Ukraine

Berdyansk State Pedagogical University, 4 Shmidta Str., Berdyansk, 71100, Ukraine

Institute for Digitalisation of Education of the National Academy of Educational Sciences of Ukraine, 9 M. Berlynskoho

Str., Kyiv, 04060, Ukraine

National University of Life and Environmental Sciences of Ukraine, 15 Heroyiv Oborony Str., Kyiv, 03041, Ukraine

shyshkina@iitlt.gov.ua

Keywords:

Inquiry-Based Learning, Research Activities on Mathematics, Emotional State.

Abstract:

The article looks into the issue of developing an interest of students’ research activities on Mathematics. The

study is dedicated to the feasibility of involving the inquiry-based learning to the organization of students’

scientiﬁc research during the practice on the Approximation Theory and Fourier Series. The research considers

the results of the survey among students who helped to evaluate their emotional state during the workshop. To

collect the data we used the tool of express evaluation of positive and negative emotionality the Differential

Emotion Scale by Izard. The article discusses the positive inﬂuence of the environment developed through

the inquiry-based learning on students’ emotional state and forming their interest in scientiﬁc research while

organizing practic classes. We have grounds to conclude that there is the efﬁciency of implementing workshops

based on the inquiry-based learning. The index reduction of students’ negative emotions encouraged their

activity during the practice and the improvement of interest in research activities.

1 INTRODUCTION

One of the main objectives of higher education is to

form scientiﬁc competencies among would-be spe-

cialists that are necessary for further successful pro-

fessional or academic development. Nechypurenko

and Soloviev (Nechypurenko and Soloviev, 2018),

Yarullin et al. (Yarullin et al., 2015) have called

https://orcid.org/0000-0002-8920-5680

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https://orcid.org/0000-0002-0647-5758

https://orcid.org/0000-0001-8669-6202

https://orcid.org/0000-0001-5569-2700

the organization of students’ research activities one

of the mechanisms to form their research compe-

tence. During such activities, skills that allow a grad-

uate student to create new actual methods of profes-

sional activity in the future, develop new ideas and

approaches that correspond to the changing modern

requirements, are formed. In particular, this idea is

supported in pedagogical literature dedicated to math-

ematical education where the organization of research

activities on Mathematics is considered to have a pos-

itive inﬂuence on the further graduate student’s activ-

ities in professional researches (Jahnke et al., 1983;

Turner, 2010; Vintere and Zeidma, 2016; Proulx,

2015; Koichu and Pinto, 2018). Taking it into ac-

Vlasenko, K., Rovenska, O., Lovianova, I., Kondratyeva, O., Achkan, V., Tkachenko, Y. and Shyshkina, M.

The Implementation of Inquiry-based Learning in the Organization of Students’ Research Activities on Mathematics.

DOI: 10.5220/0010929700003364

In Proceedings of the 1st Symposium on Advances in Educational Technology (AET 2020) - Volume 2, pages 169-180

ISBN: 978-989-758-558-6

169

count, the matter of organizing research activities on

Mathematics is still actual in pedagogical researches.

Traditional learning methods focused on the

teacher do not provide active students’ involve-

ment in research activities (Yore, 2001). Accord-

ing to the results of the researches conducted by

the European Association for Quality Assurance in

Higher Education, the European University Associ-

ation, and the Higher School Teachers European So-

ciety (EURASHE, 2015), the success of forming stu-

dents’ research activities depends on the selection of

learning strategy that is determined as a priority of

its methods, where methods of student-focused ed-

ucation come ﬁrst. It is connected with the vari-

ety and increasing expectations from higher educa-

tion that in its turn requires fundamental changes

in providing it and is focused on ﬂexible learning

ways of students’ involvement in research activities.

One of the methods of realizing such an approach

is inquiry-based learning that has an ofﬁcial status

in many countries of the world (National Research

Council, 2000; Rocard et al., 2007; National Research

Council, 2006). inquiry-based learning is included in

the student-focused educational paradigm where stu-

dents have to build their activities in the same way as

scientists during the process of learning and knowl-

edge grounding. In Mathematics this is emphasized

in works (Sandoval and Reiser, 2004; Jahnke et al.,

1983; Artigue and Blomhøj, 2013; Dorier and Maass,

2020), where it is stated that Inquiry is one of the most

important contexts while learning mathematics. So,

the matter of organizing research activities in Math-

ematics through the implementation of inquiry-based

learning corresponds to the requirements of the most

important issues of modern fundamental education.

Many authors have emphasized the necessity to

support active students’ research activities. Lithner

(Lithner, 2000) pointed out that international ten-

dency in Mathematics education is acquiring math-

ematical knowledge not only in terms of context but

in terms of getting skills connected with carrying out

mathematical research. Bonwell and Eison (Bonwell

and Eison, 1991), quoted in (Fallon et al., 2013),

stated that students have to do more than just listen.

They have to read, discuss, and do research on the

problems. Jones et al. (Jones et al., 2019) conﬁrm

that at every level of university students’ training it

is necessary to form their creative thinking and their

investigative skills. Scientists emphasize that the or-

ganization of students’ research activities during their

training encourages the development of research com-

petence, necessary both for solving practical prob-

lems and for being able to adapt fast to the change-

able conditions of the modern time and master their

skills constantly. We also took into account the ideas

of Dreyfus et al. (Dreyfus et al., 2018), who con-

siders research activities during Mathematics learning

as a natural part of the educational process, which is

directed at forming research competence among stu-

dents.

According to Yore (Yore, 2001), the formation

of interest in research activities is the ﬁrst stage

during the development of research competencies

while learning Mathematics. This idea is agreed

with the conclusions by Hernandez-Martinez and Vos

(Hernandez-Martinez and Vos, 2018), who have de-

scribed the critical state of the matter to form stu-

dents’ interest in research activities. Scientists em-

phasized the importance of organizing students’ ac-

tivities, the formation of their positive attitude to re-

search projects. While learning the literature, the

authors of this research were especially interested

in the work (Mathiassen, 2000) that describes a re-

search project that included a group of researchers

and practitioners who have worked for three years

to understand, support, and improve the methods of

Systems Development. The work proved a posi-

tive inﬂuence of practice on theoretically strict re-

search processes and suggested the means of devel-

oping research projects that are based on combin-

ing traditional theoretical research with experiments

and practice. However, not every practical class can

be considered a research stimulus. In the organiza-

tion of research activities, the key aspects of inquiry-

based learning are the ability of students to develop

new ideas based on previous knowledge and scientiﬁc

facts; restructure their previous ideas about the scien-

tiﬁc concept by adding new studied information; take

into account each other, monitor and evaluate their

own learning. Only due to this, it is possible to trans-

fer new knowledge into a real context.

In order to organize practice-focused research ac-

tivities scientists offer to use special courses dedicated

to special scientiﬁc researches in the priority areas of

modern Mathematics. This fact is evidenced by the

opinion of Yarullin et al. (Yarullin et al., 2015), Biza

et al. (Biza et al., 2016), Telegina et al. (Telegina

et al., 2019) about the signiﬁcant potential in the re-

searches on forming a positive attitude to students’ re-

search activities using the materials of different math-

ematical branches. In scientists’ opinion, the use of

interesting mathematical theories encourages students

to get a more meaningful education of theoretical ma-

terials, facts, and methods of solving mathematical

problems and it allows getting particular experience.

We can also meet the conﬁrmation of this opinion

in the works by Matejko and Ansari (Matejko and

Ansari, 2018), Sevinc and Lesh (Sevinc and Lesh,

AET 2020 - Symposium on Advances in Educational Technology

170

2018), who investigated the organization of research

activities related to particular branches of Mathemat-

ics.

The idea caught on, that is why guided by the con-

clusions made by the above-mentioned scientiﬁc re-

searches we decided to research the formation of stu-

dents’ interest in research activities on Mathematics

through the implementation of practice on approxi-

mation theory following inquiry-based learning. The

choice of this branch results from its extensive use in

practice. This is explained by the fact that the mod-

ern stage of science and technology development is

characterized by the use of a considerable amount

of information. As experience shows this tendency

will only enhance in the future – the development

of computer science, telecommunication, and regis-

tration equipment lead to steady growth of the data

amount. Therefore, the tools and methods of their

processing and analysis are growing. The creation of

a single methodical approach based on general math-

ematical principles is actual for several tasks such as

to get, model, register, and process data. The series

ﬁnds a mass use as a tool to represent a considerable

class of functions, carrying out analytical transforma-

tions, approximate calculations in many applied tasks.

Algorithmic and computer software that is created on

their basis is characterized by high universality and

is included in computer and hardware-computer com-

plexes of different purposes, which is conﬁrmed by

the numerous researches conducted by (Malvar, 1992;

Pankratov et al., 2009), etc.

The research is aimed at forming students’ inter-

est in research activities on mathematics through the

implementation of practice on approximation theory

following inquiry-based learning.

2 METHOD

At the ﬁrst stage of the research, we used a survey

method to assess students’ interest in Mathematics re-

search activities. We used the Differential Emotions

Scale by Izard (Izard, 1977) to survey students. The

relevance of involving this methodology to assess stu-

dents’ interest in research activities is proven by the

researches where the direct dependency between the

subject’s interest in cognitive activities and their emo-

tional state during its implementation is emphasized.

Since the feeling is a dynamic component of the emo-

tion (Panksepp, 2003) and two psychobiological pro-

cesses are connected with it – fascination and individ-

uation (Langer, 1967), motivating, managing, and in-

formative functions of feelings allow them to capture

or simplify and organize the thing that can become

(especially in difﬁcult situations) a great number of

impulses in concentrated cognitive processes. Dur-

ing 2015–2019 we surveyed master’s degree students

of Physics-Mathematics departments of Kryvyi Rih

State Pedagogical University and Berdyansk State

Pedagogical University. 49 master’s students took

part in the survey (17 male students and 32 female stu-

dents aged from 20 to 28). The use of the online sur-

vey, ﬁrst through Google form, posted on the Internet,

and then, moved to the forum of the platform “Higher

School Mathematics Teacher” (Vlasenko and Sitak,

2019) had an advantage in comparison to the survey

on paper as it encouraged the respondents’ frankness

and prevented missed questions.

According to the chosen methodology, we se-

lected the Likert scale to assess each of the basic emo-

tions where 1 – “feeling is completely absent”; 2 –

“feeling is slightly expressed”; 3 – “feeling is moder-

ately expressed”; 4 – “feeling is strongly expressed”;

5 – “feeling is fully expressed”. At the beginning of

the research, the most signiﬁcant (> 9 points) posi-

tive emotion related to the experience of Mathematics

research activities was “interest”, negative – “shame”

and “fear”. Students usually face the last two emo-

tions while learning Mathematics.

Students believe that the key problem of learning

mathematical theory is the absence of the connection

between theory and practice and the abstract character

of the subject.

At the second stage of the research, we deter-

mined the structure of practice regarding Approx-

imation theory and the main aspects of the con-

tent that ensure its correspondence to inquiry-based

learning. While selecting resources for the analy-

sis of possibilities to use inquiry-based learning we

were focused on those that represent the efﬁciency

of its use during the education. Among them, we

can name TeachThought (Lesley University Online,

2017), Lesley University (Lesley University Online,

2019), The National Academies Board on Science

Education (Bybee, 2009), Alberta Education (Alberta

Learning, 2004) (table 1).

We also found out what the purpose of using

inquiry-based learning by other scientists was. Cheng

et al. (Cheng et al., 2016) noted the efﬁciency of us-

ing the approach to increase the motivation of stu-

dents’ learning. Duran and Duran (Duran and Du-

ran, 2004) describe the use of inquiry-based learn-

ing in programs of professional development in edu-

cation. Supasorn and Promarak (Supasorn and Pro-

marak, 2015) see the use of inquiry-based learning

as an efﬁcient method of improving students’ under-

standing of natural processes.

In conclusions of scientiﬁc researches (Bybee

The Implementation of Inquiry-based Learning in the Organization of Students’ Research Activities on Mathematics

171

Table 1: The analysis of the resources that represent the efﬁciency of using inquiry-based learning.

Resources Used while learning a subject Features What are the efﬁ-

ciency grounds

Teach Though Biochemistry and Molecular Bi-

ology Education, Mathematics

Joint activities The solid knowledge

foundation through

an active part

Lesley University Mathematics, Life sciences Constructing knowledge based

on experience

Possibility for the

full cycle of educa-

tion

The National

Academies Board on

Science Education

Biological sciences Structure and sequence of edu-

cation are directed at creating a

challenging situation

Integration of learn-

ing activity with lab-

oratory experience

Alberta Education Librarianship, work with infor-

mation

Student’s involvement in

metacognition; encouragement

of critical and creative thinking

Focus on achieving

deﬁned learning out-

comes in different

subjects

et al., 2006; Abdi, 2014; Ong et al., 2018) we also ﬁnd

the conﬁrmation of the efﬁciency to use the above-

mentioned approach to improve students’ achieve-

ments in science. Considering it, we believe that

inquiry-based learning will encourage the alignment

of teaching processes with the formation of better

students’ understanding of scientiﬁc knowledge and

skills during practice.

The practice program consists of six classes.

1. The history of the development of approximation

theory and Fourier series.

2. The ways of periodic function classiﬁcation.

3. Approximation methods that are based on matrix

series summing.

4. Main tasks of approximation theory: approxima-

tion of individual function, class approximation,

precise, and asymptomatically precise ratio.

5. Examples of researches by subject.

6. Examples of using approximate aggregates in

computer complexes of broad purpose.

The practice was aimed at the formation of stu-

dents’ interest in research activities through their im-

plementation in the real process of using series in ap-

plied tasks.

The practice was held for a group of 7–8 students

twice a month for three months. Every class included

two hours of classwork and three hours of extracur-

ricular work. The classes were held by the prominent

teachers of Mathematics departments who took part

in the development of the practice and looked for the

method, the implementation of which would encour-

age the formation of students’ interest in research ac-

tivities during the practice.

During the organization of practice classes, we

developed recommendations for every practice stage

that have to encourage the increase in students’ inter-

est in mathematics research activities.

At the ﬁrst stage, the teacher has to determine

what students already know regarding the concept that

is considered and what kind of knowledge they still

need. In order to master new educational material,

it is necessary to help students to revise Mathemat-

ics sections such as Algebra, Mathematical Analysis,

Functional Analysis, and Function Theory. Moreover,

at this stage, the teacher is only a consultant who

helps students to prepare short reports encouraging

students’ interest and motivation. For this purpose,

the teacher presents the actuality of the researches

dedicated to learning approximate features of approx-

imation methods that are generated by certain trans-

formations of partial sums of Fourier series and allow

building the sequence of trigonometric polynomials

that would equally coincide for any function (table 2).

Table 2: Recommendation for the teacher on the organiza-

tion of the ﬁrst stage.

Appropriate Inappropriate

encourage students to

raise their questions

offer to compare their

ideas with others

read the lecture

give deﬁnitions to terms

explain or give tasks

The second stage is aimed at strengthening stu-

dents’ activities regarding knowledge and skills. At

this stage, students can revise the tasks that use the

methods of Approximation theory on special subjects

that they learn. As a rule, students cite examples

of tasks on periodic signal approximation in the the-

ory of control engineering, pattern recognition, non-

destructive testing, etc. Students can discuss and

write down approximation methods in every partic-

ular case. The teacher is only a consultant who offers

AET 2020 - Symposium on Advances in Educational Technology

172

students such research methods as observation, hy-

pothesis generation, forecasting. Students’ communi-

cation and work in groups without the direct teacher’s

involvement are encouraged to equally coincide for

any function (table 3).

Table 3: Recommendation for the teacher on the organiza-

tion of the second stage.

Appropriate Inappropriate

encouragement of search

for several ways to solve

the problems

comparison of ideas

self and mutual survey

use of traditional expla-

nation

implementation and in-

volvement of a great

amount of terminology

At the next stage, students can describe their point

of view regarding the search for solving extreme

problems of approximation theory. After this, the

teacher has to introduce common terminology and ac-

quaint the students with the general scheme of re-

searching integral images of trigonometric polyno-

mial variations that are generated by linear methods

of summing Fourier series, from periodic functions.

Generating students’ new ideas on methods of ap-

proximation improvement, their comparison with the

ideas of the previous stage is possible. At this stage,

the teacher also has to prevent possible mistakes

while explaining misconceptions that could arise at

the stage of engagement and exploration. During the

classes of this stage, the teacher involves interactive

methods and presentations for mathematical model-

ing of periodic processes (table 4).

After getting an explanation about the research

main scheme regarding integrated images of trigono-

metric polynomial variations during the classes of pe-

riodic functions it is important to involve students in

further research activities. Further work includes sig-

niﬁcant analytical calculations connected with exact

and approximate methods. Starting from the integral

image students can learn asymptotic behavior of exact

upper bounds of deviations of trigonometric polyno-

mials from periodic functions to inﬁnity. The stage is

aimed at helping students to develop a deeper under-

standing of general methods of mathematical analysis

and the use of approximation processes in practical

Table 4: Recommendation for the teacher on the organiza-

tion of the third stage.

Appropriate Inappropriate

teacher’s explanation

expression of the ideas using

generally accepted terms

idea review and formation of

new ones

forming a great

amount of termi-

nology

focus on indepen-

dent work

tasks. Students can carry out additional researches,

develop new approximation methods, exchange ideas,

and use acquired research experience to integrate Ap-

proximation theory in practice (table 5).

Table 5: Recommendation for the teacher on the organiza-

tion of the fourth stage.

Appropriate Inappropriate

enhancement of under-

standing through strength-

ening the ideas acquired by

experience

use of algorithms that are

close to new situations

grounds for conclusions

support of forming stu-

dent’s proper ideas

development of the

ideas that are not con-

nected with previous

experience

generating a great

number of ideas with-

out deepening in the

essence of the theory

The practice of working in small groups is impor-

tant at this stage. The lessons include planning and

preparation of students’ proper development on us-

ing the considered approximation methods from ev-

ery group of students. It is possible to create an al-

gorithmic and program-algorithmic product based on

the created methods. As the simplest and at the same

time the most natural example of a linear process of

approximation of continuous periodic functions of the

real variable can be the approximation of these func-

tions using the sequence elements of partial sums of

Fourier series, the greater majority of students have a

basic idea about the techniques of using these meth-

ods while creating an algorithmic product. But, as it is

well known, the sequences of partial sums of Fourier

series S

( f ; x) are not equally similar for the entire

class of continuous periodic functions. Thus, a con-

siderable number of students’ developments in this

area are directly dedicated to the learning of approx-

imate features of other approximation methods that

are generated by particular transformations of partial

sums of its Fourier series for this function and allow

building the sequence of trigonometric polynomials

that would be completely similar for every function

(Rovenska, 2019). Fejer sums σ

( f ; x) are arithmetic

averages for the ﬁrst n of partial Fourier sums for this

function and, as it is known, the sequence of poly-

nomials σ

( f ; x) equally coincides with its function.

Sums of de la Vallee Poussin V

n,p

( f ; x) are a synthe-

sis of sums σ

( f ; x) and have approximate features

that depend a lot on the parameter p. Trigonometric

polynomials V

n,p

( f ; x) that are generated by the re-

peated use of de la Vallee Poussin summation method

are the further synthesis of classical Fourier methods,

de la Vallee Poussin and Fejer (Novikov and Roven-

ska, 2017). Choosing particular parameters p

and

The Implementation of Inquiry-based Learning in the Organization of Students’ Research Activities on Mathematics

173

these polynomials coincide with the sums S

( f ; x),

n,p

( f ; x), σ

( f ; x). The works of practice partici-

pants should be dedicated to the learning of approx-

imate features of such approximation methods show-

ing graphically the advantages of its use (ﬁgure 1, 2).

For the visualization, students can be recommended a

system of computer mathematics Maple that includes

developed graphic means.

The demonstration of the efﬁciency of the selected

approximation methods can be done by comparing the

results of numerical experiments held simultaneously

for the operators S

( f ; x), V

n,p

( f ; x) and V

n,p

( f ; x).

Meanwhile, it is necessary to pay students’ attention

to the fact that the aggregate of all the harmonicas

that are used to build the operators S

( f ; x); V

n,p

( f ; x)

coincides with a similar aggregate for the operator

n,p

( f ; x). At the same time, the program for

the numeric implementation of the values S

( f ; x),

n,p

( f ; x) and V

n,p

( f ; x) can be developed using

Python. This tool is easy to use for students–non-

programmers and is suitable for easy calculations.

The ﬁnal stage of practice is dedicated to evalu-

ation. Evaluation is considered to be a permanent

process during which the teacher only observes the

students and supports them during report presenta-

tions, idea introduction, and question tasks. The

use of peer assessment is relevant. Such a form of

evaluation can be complemented by students’ self-

assessment of their level. During the classes of this

stage, the teacher involves interactive methods and

presentations for mathematical modeling of periodic

processes (table 6).

Table 6: Recommendation for the organization of the ﬁnal

stage.

Appropriate Inappropriate

evaluate the progress in general in

comparison to the initial level

evaluate the ability to use approx-

imate methods to solve complex

problems

give students feedback regarding

the feasibility of their ideas

encourage questions that enhance a

deeper understanding of the inﬂu-

ence of individual function features

on the approximation order

evaluate

single facts

and separate

elements of

approxima-

tion theory

offer a survey

in a test form

The use of inquiry-based learning does not oblige

the teacher to strictly follow the indicated stages. If

necessary, it is possible to repeat them several times

(Bybee and Landes, 1990). This fact proves the ﬂex-

ibility of using this approach for the implementation

of scientiﬁc practice.

3 RESULTS

During the preparation stage, we selected the target

type as a selection strategy, because the selection had

to include the students who have a high achievement

level in mathematical branches. By high level, we un-

derstand the absence of the ﬁnal mark “satisfactory”

and lower following the national 4–level scale “un-

satisfactory”, “satisfactory”, “good”, “excellent” for

each of the subjects “Algebra”, “Mathematical anal-

ysis”, “Functional analysis” and “Function theory”.

The target selected analysis provided us with a sample

size n=49 of students that represents 23% of the gen-

eral number of master’s degree students of the ﬁrst

year during 2015–2019. At the stage of organizing

data collection, we used the tool of express-evaluation

of positive and negative emotional states called the

Differential Emotion Scale (Izard, 1977), which en-

sures diagnostics of a wide range of emotional states.

Each of the ten basic emotions (x

, i = 1, 2, ..., 10)

is represented by three independent changeable 5–

character scales for factors that describe emotional

states. The points on every scale correspond to the

level of emotional feedback and can be in total from 3

to 15 points. The stage of data analysis of every pro-

ﬁle implies the selection of signiﬁcant (> 9 points)

emotions, creation of “emotion proﬁle”, determina-

tion of the dominant emotional state.

At the beginning of the research, the most signif-

icant positive emotions regarding the experience of

research activities are “interest”, negative – “shame”

and “fear” (table 7).

While processing every proﬁle we deﬁned the in-

dexes of emotional states that characterize the level of

subjective students’ emotional attitude to the present

experience of research activities. The Index of pos-

itive emotions and Index of critically negative emo-

tions could range from 9 to 45 points, the Index of

anxious–depressive emotions ranged from 12 to 60

points. We deﬁned that the positive emotional state

turned out to be dominant among 69.4% of students;

a strong level (> 36 points) of expressing a positive

emotional state was marked only among 6.1% of re-

spondents. Also, a distinct (from 29 to 36 points) level

of positive emotional state was ﬁxed among 10.2% of

students. Other students (53.1%) showed moderate

(from 20 to 28 points) and weak (< 20 points) level.

So, most students’ attitude to the research process can

be mainly characterized as positive. However, this

positive attitude is weakly expressed, unstable, and

cannot ensure the proper motivation in overcoming

difﬁculties that inevitably arise during research activ-

ities. This fact plays an important (if not the most

important) role in the failure of attempts to involve an

AET 2020 - Symposium on Advances in Educational Technology

174

Figure 1: Visualization of functions and trigonometric sums that are generated in different methods of summarizing Fourier

series in the system of computer mathematics Maple.

Table 7: Distribution of signiﬁcant emotions at the beginning of the research.

Emotion Number of students who have this

emotion as dominant (>9 points)

Comparison with the gen-

eral number of students

Interest 32 65.3%

Fear 45 91.8%

Shame 27 55.1%

unprepared student in research activities in any area,

including Mathematics.

The dominant critically negative emotional state

regarding the present experience of research activities

was ﬁxed among 12.2% of respondents, half of whom

had a strong (> 32 points) or distinct (from 25 to 32

points) level. It is important that among all the stu-

dents who had the critically negative state as dom-

inant, the factor “Dull” took no less than 4 points,

and, accordingly, made the greatest contribution to

the calculation. It testiﬁes a stereotype regarding the

complexity and absence of interest in research activi-

ties among young people. We considered this aspect

while searching for methods of practice implementa-

tion.

As mentioned above, the emotions “fear” and

“shame” were detected as signiﬁcant among 91.8%

and 55.1% of respondents. These emotions are in-

The Implementation of Inquiry-based Learning in the Organization of Students’ Research Activities on Mathematics

175

Figure 2: Visualization of deviation of Fourier series and repeated de la Vallee Poussin repeated series from the function f (x)

in the system of computer mathematics Maple.

Figure 3: Distribution of a signiﬁcant emotion.

Table 8: Distribution of signiﬁcant emotions after taking practice.

Emotion Number of students who have this

emotion as dominant (> 9 points)

Comparison with the gen-

eral number of students

Interest 44 89.7%

Surprise 18 36.7%

Fear 39 79.5%

Shame 5 10.2%

cluded in the third group of emotions that determine

the anxious–negative emotional state of the subject

regarding the experience of research activities. De-

spite this fact, the given state is dominant only among

18.4% of students. It demonstrates that these two

emotions inﬂuence the formation. 4.1% of respon-

dents have strong (> 30 points) level of emotional

state, distinct (from 21 to 30 points) – 10.2%, moder-

ate (from 12 to 20 points) and 4.1% of respondents –

weak (< 12 points). Such a noticeable selection of

two emotions in the general image of the emotional

state conﬁrms the idea that fear and shame prevent

students from implementing their interest in the re-

search process and take an active position while con-

ducting research.

The repetitive survey was carried out after ﬁnish-

ing the practice. The distribution of signiﬁcant emo-

tions after taking practice is represented (table 8).

Interest turned out to be a signiﬁcant positive emo-

tion among 44 students. We can note that the number

decrease in students who had shame as a signiﬁcant

negative emotion is well seen – 17 respondents. At

the same time, the number decrease of students who

had fear as a signiﬁcant emotion is minor – 6 students

(ﬁgure 3).

Despite this fact it is impossible to claim that this

AET 2020 - Symposium on Advances in Educational Technology

176

emotion in the context of the given research is badly

adapted. The proﬁle analysis of respondents’ emo-

tions shows the decrease of fear expression to varying

degrees among 77.5% of students. The presence of

surprise among the signiﬁcant emotions, as well as

interest, which is included in the positive group, is

predictable.

More detailed analysis of the feasibility of imple-

menting practice that was carried out using the in-

dex calculations of students’ emotional states. We

detected the increase of students with the dominant

positive emotional state up to 81.7%, where 63.2% of

respondents had a strong and distinct level. At the be-

ginning of the practice, the same indicator was 16.3%.

Thus, we managed to form a stable positive attitude to

research activities among more than half of the prac-

tice participants.

The number of students who have a critically neg-

ative emotional state as dominant remained at the

level of 12.2%, though the qualitative structure of

this subgroup changed. In our opinion, it is con-

nected with a greater amount of working practice in

small groups during classes in comparison to individ-

ual work. As teachers pointed out certain students

perceived such a format negatively.

The dominant anxious–negative subject’s attitude

to experience of research activities after taking a prac-

tice was ﬁxed among 6.1% of students. Among them

4% of respondents have moderate and 2.1% – weakly

expressed level of emotional state. The comparative

analysis of the students’ number regarding dominant

emotional states is displayed (ﬁgure 4).

The analysis of the results proved that creating the

environment based on inquiry-based learning during

the scientiﬁc practice where students did not feel neg-

ative emotions to research activities encouraged the

increase of their interest in research activities.

4 DISCUSSION

Searching for ways of forming students’ interest in

research activities on mathematics we faced the re-

searches (Sandoval and Reiser, 2004; Rocard et al.,

2007). The scientists point out that in order to form

students’ impression of the real world it is neces-

sary to show them how to organize their activities as

real scientists do during the process of learning and

knowledge grounding. Fallon et al. (Fallon et al.,

2013) offered to seek the possibilities to organize stu-

dents’ research activities through the method selec-

tion and forms of a learning organization that inﬂu-

ences active students’ involvement.

Traditional educational methods, which are fo-

cused on the teacher, don’t provide an active students’

involvement in research activities (Yore, 2001; Lin

et al., 2014; Vlasenko et al., 2019). The scientists em-

phasize the importance of searching for educational

models that encourage the strengthening of students’

learning activities. The Deductive Content Analysis

Method helped us to choose inquiry-based learning as

the foundation of developing a scientiﬁc environment

for students’ education.

The efﬁciency of inquiry-based learning to en-

courage students’ research activities is proved in (Du-

ran and Duran, 2004; Bybee and Landes, 1990; Supa-

sorn and Promarak, 2015; Cheng et al., 2016). Also,

we support the opinion by Vlasenko et al. (Vlasenko

et al., 2019), who believe that learning has to be built

so that students can research, explain, extend and es-

timate their progress, and the introduction of ideas as-

sumes students’ awareness of the reason or necessity

of their use. The indicated aims are fully agreed with

the content of inquiry-based learning.

Alshehri (Alshehri, 2016) believes that while or-

ganizing research activities it is necessary to direct

students to the main models of subject matters. One

of the key subject matters of Mathematics is Approxi-

mation theory, its broad inﬂuence on the modern state

of innovation and technology development is widely

known. The research is aimed at searching for ways

of implementing a practice on Approximation theory

to form students’ interest in Mathematics research ac-

tivities. The main research result testiﬁes that the use

of the approach inquiry-based learning inﬂuenced ef-

ﬁciently the formation of students’ positive attitude

towards research activities. Within this approach, the

involvement of the practice on Approximation the-

ory encouraged the increase of the level of expressing

students’ positive emotional state (particularly inter-

est, surprise increase) and decrease of anxiety level.

These results are agreed with the conclusions by Chin

and Lin (Chin and Lin, 2013), Abdi (Abdi, 2014),

Jung et al. (Jung et al., 2014), Ong et al. (Ong et al.,

2018), who studied the connection between interest

growth and a person’s emotional state. This justiﬁes

the use of methodology Differential Emotions Scale

by Izard (Izard, 1977) during the experiment.

5 CONCLUSION

The actuality of involving students in research activ-

ities in education arises from the fact that research

competence is considered as one of the components

of professional competence. Enhancing students’ in-

terest in research content and research activities dur-

ing the studies also requires the use of an approach

The Implementation of Inquiry-based Learning in the Organization of Students’ Research Activities on Mathematics

177

Figure 4: Distribution of dominant states.

that implies complete students’ awareness of the im-

portance of the research problem. The Deductive Ap-

proach to Content Analysis helped us determine the

possibility to involve inquiry-based learning to the or-

ganization of practical classes on Approximation the-

ory, determine its characteristics and efﬁciency pa-

rameters, predict that the approach can ensure the for-

mation of a better understanding of scientiﬁc knowl-

edge and students’ skills. According to inquiry-based

learning, we developed the content of the practice

on Approximation theory. Based on the analysis

of the current recommendations on using inquiry-

based learning while studying different subjects we

offered recommendations on the organization of prac-

tice. It should be noted that the course should be pro-

vided following the indicated recommendations that

encourage students’ activity, their interest in the re-

search activity.

Forming a positive attitude to research activities is

the ﬁrst step to the development of the research com-

petence of pre-service specialists. The analysis of the

works on the connection between the person’s inter-

est and emotional state allowed formulating the most

important positive and negative emotions that are con-

nected with the experience of the research activities.

The results of calculating the indexes of students’

emotional states proved that the creation of the en-

vironment according to inquiry-based learning where

students do not feel negative emotions to research ac-

tivities encourages emotional state and interest in re-

search activities.

The perspectives of future research involve the

creation of Math courses that use inquiry-based ap-

proaches with the purpose of further research on

forming research competence among students.

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