=Paper=
{{Paper
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|title=On the Results of a Study of the Willingness and the Readiness to Use
Dynamic Mathematics Software by Future Math Teachers
|pdfUrl=https://ceur-ws.org/Vol-1356/paper_9.pdf
|volume=Vol-1356
|dblpUrl=https://dblp.org/rec/conf/icteri/SemenikhinaD15
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==On the Results of a Study of the Willingness and the Readiness to Use
Dynamic Mathematics Software by Future Math Teachers==
https://ceur-ws.org/Vol-1356/paper_9.pdf
On the Results of a Study of the Willingness and the
Readiness to Use Dynamic Mathematics Software by
Future Math Teachers
Olena Semenikhina1, Marina Drushlyak1
1
Sumy Makarenko State Pedagogical University, Romenska St. 87, Sumy, Ukraine
e.semenikhina@fizmatsspu.sumy.ua, marydru@mail.ru
Abstract. The article presents the results of pedagogical research on the will-
ingness and the psychological readiness to use dynamic mathematics software
by future math teachers. We used nonparametric method for dependent samples
– the McNemar’s test. The hypothesis, that the study of Special course on the
use of dynamic mathematics software for future teachers has a positive impact
on the willingness and the psychological readiness to use such software in their
own professional activities, is confirmed at the significance level of 0.05.
Additionally, the results of the experiment on the willingness and the readiness
to support the teaching of some subjects (algebra, planimetry, solid geometry
and analysis) with dynamic mathematics software and the willingness and the
readiness to use some dynamic mathematics software (Gran (Gran1, Gran2d,
Gran3d), GeoGebra, Сabri, MathKit, DG, GS) by Ukrainian math teachers is
given.
Keywords. The study of mathematics, computer applications in the study of
mathematics, special course, dynamic mathematics software, the McNemar’s
test.
Key Terms. InformationCommunicationTechnology, TeachingProcess,
TeachingMethodology.
1 Introduction
Ukrainian education has always tried to involve leading technologies and tools that
have spread in the world and improve the level of education of ordinary Ukrainians.
That is why since the end of the last century information technology has started to be
actively implemented in the learning process (also in mathematics). Specialized
software appeared and the main purpose of them was computational and visual
support of solving of math problems. Later the software, that allows to model
processes and to observe the changes in constructions, appeared. But the use of such
software was limited in schools because of a number of reasons, among which the
insufficient technical equipment of schools, the lack of targeted preparation of
teachers to use specialized software, the lack of software with a clear (Ukrainian,
Russian) interface, a small number of teacher’s guides, etc.
Now there is a great amount of software which can be used in teaching
mathematics. We previously conducted an analisis of the current tendencies of math-
ematics software use in education in [1]. But the workload of school teachers does not
let them to monitor the appearance of such software, to learn the tools and to use them
at their lessons. The main part of Ukrainian math teachers are 40 and more years old.
This means that they were not acquainted with mathematics software during their
preparation, and they used information technologies on the level of Internet users and
Word, Excel, РowerPoint. They do not use software consciously, because they believe
that chalk-and-Board style is better at studing mathematics.
These and other reasons have led us not only to enter the Special course of the study
of mathematics software in the curricula of preparation of modern teachers, but to
study the impact of this course on the willingness and the readiness to use mathemat-
ics software in the professional activity of math teachers.
2 Research of the Willingness and the Psychological Readiness of
Future Math Teachers to Use Dynamic Mathematics Software
During 2010-2014, we have investigated the problem of the willingness and the
psychological readiness to use mathematics software by future math teachers [2].
We allocate dynamic mathematics software (DMS), that can model and modify
mathematical objects interactively. We consider Gran, DG (Ukraine), GeoGebra
(GG, Austria), MathKit, Live Mathematics (LM) (Russia), Cabri (France), The
geometer's Sketchpad (GS, USA), etc. We allocate these software for the following
reasons: 1) software Gran and DG are recommended by the Ministry of Education
and Science of Ukraine; 2) software MathKit and Live Mathematics are actively used
by Russian teachers, as evidenced by a great number of methodological works of
math teachers; 3) software Cabri, The geometer's Sketchpad and GeoGebra are the
most popular in the world, as evidenced by the numerous translations of monographs
and multi-lingual interfaces of these software.The work with them intuitive and
identical – basic objects are built, then they can be dynamically changed and user can
observe certain quality properties and quantitative characteristics. The study of
features of these software and recommendations for their use are generalized by us in
[3-10].
The base of the reaserch was Sumy Makarenko State Pedagogical University.
Preparation of math teachers is in accordance with the curricula. The introduction of
these software was during the study of methodology of mathematics and during the
study of a special course "Computer Applications in the Study of Mathematics" (fur-
ther Special course). The program of the Special course was described in [11-13] and
was improved during the years 2008-2014. The experience of the involvement of
dynamic mathematics software in support of teaching mathematics in the school was
during teaching practice (see Table 1).
Table 1. The extract from the curriculum of the speciality “Mathematics*”
Course Feachers Note
Semester 6;7;8
Methodology The course contains the module “Computer
of Credits 2,5;2;2 support for learning mathematics” – 7-th
mathematics semester, 12 hours.
Class hours 46;46;44
At the beginning of the third quarter, within 2
Semester 8
Teaching months, on the basis of city schools
practice It is supposed to teach 10 math lessons at 5-9
Credits 6
classes
Semester 8 It is supposed to study different dynamic math-
Special
Credits 3,5 ematics software during solving algebra, geome-
course
Class hours 50 try, analysis problems
At the beginning of the teaching practice students learn how to solve mathematical
problem with the use of dynamic mathematics software (DMS) at the lessons of Spe-
cial courses. During the teaching practice they have the opportunity to see (or not to
see) and analyze lessons of those teachers who use DMS in their own professional
activity.
We believe that during this period the basis for the motivation of the learning and
further use of DMS in professional activities is formed. Therefore, the Special course,
which is studied immediately after the teaching practice, becomes the factor of impact
on the student, which gives the opportunity to talk about the willingness and the read-
iness to use DMS in the future professional activity.
Because these personal characteristics can be formed within the teaching of the
Special course, it was natural to involve such statistical methods, that give the oppor-
tunity to talk about the dynamics of change based on data about the initial and final
state of the object. So we fixed the internal state of the willingness and the psycholog-
ical readiness of the student to use DMS with the help of questionnaires at the begin-
ning and at the end of the study of the Special course (see Table 2).
Table 2. The questionnaire
№ Questionnaire Answers
1. Do You need to use DMS at the lessons of algebra (planimetry, Yes
solid geometry, mathematical analysis)? Why? Yes, not at all
No
№ Questionnaire Answers
2. Do You want to use DMS at the lessons of:
a) algebra; Yes/No
b) planimetry; Yes/No
c) solid geometry; Yes/No
g) mathematical analysis? Yes/No
Why?
3. Do You feel readiness to use DMS at the lessons of:
a) algebra; Yes/No
b) planimetry; Yes/No
c) solid geometry; Yes/No
g) mathematical analysis? Yes/No
Why?
4. Specify a priority of DMS that You like. Gran
DG
GG
Specify a priority of DMS, which is better to use at math lessons MathKit
on Your opinion. GS
Cabri
It was applied the McNemar’s test [14], because the scale of results in questions 1-
3 has two items ("Yes" or "No"). This method is nonparametric and used to compare
distributions of objects in two sets according to some property on the scale with two
categories (e.g., "like - dislike ", "ready - not ready," "willing - unwilling" and others).
For a McNemar’s test the following conditions are required: 1) random sample; 2)
dependent sample; 3) pairs (хі, yi) are mutually independent (the members of the
sample have no effect on each other); 4) the scale has only two categories.
The research was conducted from 2010 to 2014. Each year we have accumulated the
results of the sample with volume 37, 35, 38, 37, 31, respectively. The total number of
respondents amounted to 178 people. We selected results from them at random.
2.1 The Use of Dynamic Mathematics Software in the Study of Mathematics
in Secondary Schools
The beginning of our research was associated with the study of the status of the use of
DMS in the study of mathematics in secondary schools. Through conversations with
teachers, graduates, teachers-methodists of our region it was found that the “poor” use
of DMS in the learning process is not only due to the limited number of computers in
schools, but due to lack of the willingness of teachers to involve such software to the
solution of mathematical problems. Although they did not deny the feasibility of this
approach, but noted, among other things, about the inability to use DMS (68%), the
need for additional time to study them (87%), the small number of methodological
literature on the use of DMS (90%) and the lack of collections of tasks, which can be
solved by using DMS (36%).
2.2 The research of the Willingness of Future Math Teachers to Use Dynamic
Mathematics Software in Their Professional Activities
Searching for ways to solve the problem, we have suggested that a focused study of
the Special course will have a positive impact on the willingness of future math
teachers to use DMS in their profession.
The test of the assumption was carried out according the McNemar’s test on taken
results in the amount of 30 pieces from 178 at random.
Hypothesis Н0: the Special course does not impact on the willingness of students to
use DMS in the future math teacher’s profession. Hypothesis На: the Special course
has a positive impact on the willingness of future math teachers to use DMS.
We had two series of observations: Х={x1, x2, …, xN} and Y={y1, y2, …, yN}, where
(хі, yi) are the results of measuring of the willingness to use DMS in the future
professional activity of the same object (the willingness of the student before and after
the Special course). In our notation, xі or yі takes the value 0 if the object of study
does not wish to use DMS at any of the classes (algebra, planimetry, analysis, solid
geometry) and 1 otherwise. The results of the dual survey recorded in the Table 3.
Table 3. The survey on the willingness to use DMS
The second surve
The first surve yi=0 yi=1
xi=0 а=6 b=10 a+b=16
xi=1 c=2 d=12 c+d=14
a+c=8 b+d=22 N=30
In the conditions of the experiment parameter а determined the number of students
who both times said “No”; the parameter b was the number of students who the first
time said "No" and the second time said "Yes"; the parameter c was the number of
students who the first time said "Yes" and the second time said "No"; the parameter d
was the number of students who both times said "Yes".
To apply the McNemar’s test we will find Тexper= min(b,c), if n = b + c < 21. For
our data Тexper= 2, since n = 10 + 2 = 12 ˂ 20. Statistics of the criterion for
significance level α = 0,05 is р = 0,019. According to the rule of decision [14] we
have 0,019 < 0.025. We have to reject hypothesis Н0 and accept the alternative one,
and since b ˃ c, then we consider that the impact of the study of the Special course on
the willingness to use DMS is not only statistically correct, but also positive.
2.3 The research of the Readiness of Future Math Teachers to Use Dynamic
Mathematics Software in Their Professional Activities
In parallel with the research of the willingness to use DMS we explore the personal
readiness of future math teachers to use DMS in their professional activities (question
3 of the questionnaire).
The hypothesis H0: the Special course does not impact on the psychological readi-
ness of students to use DMS in their professional activities.
Then the hypothesis На: the Special course impacts on the psychological readiness
of future math teachers to use DMS.
The test of the assumption was carried out according the McNemar’s test on taken
results in 40 pieces from 178 questionnaires at random (see Table 4).
Table 4. The survey of psychological readiness to use DMS
The second surve
The first surve yi=0 yi=1
xi=0 а=7 b=16 a+b=23
xi=1 c=6 d=11 c+d=17
a+c=13 b+d=27 N=40
Since n = b + c = 22 ˃ 20, the statistics of criterion is calculated according the
formula Тexper= (b – c)^2 / (b + c) = 4,54. The assumption of the fairness of the null
hypothesis is approximated like the χ2 distribution with one degree of freedom (υ=1).
For significance level α=0,05 the critical value of the test is Тcritic=3,84. The obtained
value of Тexper=4,54 ˃ Тcritic=3,84, therefore, the hypothesis Н0 is rejected and the
alternative hypothesis, indicating that the impact of the Special course on the readi-
ness to use DMS in future professional activity is significant and cannot be explained
by random variation, is accepted.
2.4 The research of the Willingness of Future Math Teachers to Use Different
Dynamic Mathematics Software in Their Professional Activities in Teaching of
Some Subjects
Because the questionnaire was on the research of the willingness to use DMS at
the lessons of algebra, planimetry, solid geometry and analysis, and on the research of
the use of different DMS (Gran (Gran1, Gran2d, Gran3d), GeoGebra, Сabri,
MathKit, DG, GS), we were able to fix and process results about the willingness to
use DMS in teaching of some subjects – algebra, planimetry, solid geometry, analysis
(see Table 5) and about the willingness to use different DMS – Gran, DG, GeoGebra,
MathKit, GS, Сabri (see Table 6).
For each position of the table 5 we have the rejection of the null hypothesis H0 and
the acceptance of alternative hypothesis, i.e., at the significance level α=0,05 we can
say about the positive impact of the studing of the Special course on the willingness
of future math teachers to use DMS at the lessons of algebra, planimetry, analysis and
solid geometry.
Table 5. The survey of the willingness to use DMS in teaching of different subjects
Indices of the McNemar’s test
Quantitative indices
Question. Do You wish to use (α=0,05)
DMS at the lessons of: b+с Тек Р Н
a b c d N Но
а
algebra 6 11 2 11 30 13 2 0,011 0 1
planimetry 2 15 5 8 30 20 5 0,021 0 1
analysis 5 12 3 10 30 15 3 0,018 0 1
solid geometry 6 14 4 6 30 18 4 0,015 0 1
Table 6. The survey of the willingness to use some DMS
Indices of the McNemar’s test
Question. Do You Quantitative indices
(α=0,05)
wish to use:
a b c d N b+с Тек Р Но На
Gran 8 11 2 9 30 13 2 0,011 0 1
DG 5 12 3 10 30 15 3 0,018 0 1
GG 2 12 2 14 30 14 2 0,006 0 1
MathKit 6 14 4 6 30 18 4 0,015 0 1
GS 12 10 6 2 30 16 6 0,227 1 0
Cabri 20 6 3 1 30 9 3 0,254 1 0
For indeces of the table 6 we have the acceptance of hypothesis H0 for the last
two rows. This means that at the significance level 0.05, future math teachers wish to
use software Gran, DG, GG, MathKit, but we have no reason to say about the will-
ingness to use GS and Cabri. We can explain this because of "poor" interface of GS
and the absence of Ukrainian (or Russian) interface of Cabri.
Visualization of the obtained results during the experiment years is given in
Fig. 1-2.
Fig. 1. The percent of people willing to use DMS at different math lessons
Fig. 2. Increase in the number of people willing to use DMS (%)
Also we give some information about the "attractiveness" of software according to
the survey of future and working math teachers, which was conducted at scientific-
methodical seminars (on the basis of physics and mathematics faculty) (see Table 7,
Fig. 3-10).
Table 7. The attractiveness of software (%)
Gran DG GG
Year T S T S T S
2010 0,93 0,59 0,74 0,68 0,28 0,68
2011 0,75 0,71 0,51 0,80 0,32 0,91
2012 0,86 0,71 0,83 0,66 0,45 0,79
2013 0,68 0,43 0,54 0,54 0,68 0,78
2014 0,40 0,32 0,13 0,48 0,66 0,97
MathKit GS Cabri
Year T S T S T S
2010 0,11 0,32 0,00 0,24 0,00 0,00
2011 0,11 0,57 0,02 0,43 0,00 0,00
2012 0,17 0,66 0,08 0,32 0,00 0,11
2013 0,19 0,86 0,03 0,35 0,05 0,08
2014 0,13 0,94 0,00 0,19 0,07 0,13
Fig. 3. The attractiveness of DMS for teachers
Fig. 4. The attractiveness of DMS for students
Fig. 5. The attractiveness of GRAN Fig. 6. The attractiveness of DG
Fig.7. The attractiveness of GG Fig.8. The attractiveness of GS
Fig. 9. The attractiveness of MathKit Fig. 10. The attractiveness of Cabri
2.5 The research of the Readiness of Future Math Teachers to Use Different
Dynamic Mathematics Software in Their Professional Activities in Teaching of
Some Subjects
Because the questionnaire was on the research of the psychological readiness to use
DMS at the lessons of algebra, planimetry, solid geometry and analysis, as well as the
readiness to use different DMS (Gran (Gran1, Gran2d, Gran3d), GeoGebra, Сabri,
MathKit, DG, GS), then we could fix the results of the readiness to use DMS in teach-
ing of different subjects (algebra, planimetry, solid geometry, analysis) (see Table 8).
Table 8. The survey of the readiness to use DMS in teaching of different subjects
Indices of the McNemar’s
Do You feel the readiness to use Quantitative indices
test (α=0,05)
DMS at the lessons of:
a b c d N n=в+с T_2 Н0 На
algebra 6 17 7 10 40 24 4,17 0 1
planimetry 2 21 9 8 40 30 4,80 0 1
analysis 5 18 7 10 40 25 4,84 0 1
solid geometry 4 17 15 4 40 32 0,13 1 0
For all items, except the last, we have the rejection of the null hypothesis H0 and
the acceptance of the alternative hypothesis, i.e., at the significance level α=0,05, we
can say about the positive impact of studing of the Special course on the
psychological readiness of future math teachers to use DMS at the lessons of algebra,
planimetry, analysis. However, experimental results do not give grounds to say about
the positive impact on the readiness to use DMS at the lessons of solid geometry.
Increase in the number of students who feel the readiness to use DMS at the math
lessons is presented in Fig. 11.
Fig. 11. Increase in the number of people psychologically ready to use DMS
3 Conclusion
Thus, this research allows to state the following.
1. Future math teachers understand the need to use DMS and welcome the studing
of the Special course, since the research of the willingness and the readiness to use
DMS demonstrates a positive dynamics. The assumption about the positive impact of
the studing of the Special course on the psychological state of students is confirmed at
the significance level of 0.05 according to the McNemar’s test. In other words, after
the studying of the Special course "Computer Applications in Teaching Mathematics"
the number of students, who have the willingness and feel the readiness to use DMS
in future professional activity, increases.
2. Most students focused on using DMS at the lessons of algebra, planimetry and
analysis. We explain this because of not only a sufficient number of DMS and good
tools in such software, but enough number of teacher’s guide for their application and
free access to DMS with Ukrainian or Russian interface.
The percentage of students, who are willing to use DMS at the lessons of solid ge-
ometry, is too small. We explain this not only because of small number of software
and “poor” tools in such software, but of lack of Russian or Ukrainian interface in
them. Also there is the lack of methodical material of solving solid geometry
problems with the use of specialized software.
3. Teachers, who work at the school, have the willingness and the inner readiness to
use DMS, but face with the limited access to computer classes. The involvement of
DMS, as they say, is possible only during extracurricular activities.
4. GRAN and GeoGebra are the most popular in Ukraine. In recent years there has
been a decline in the use of the first and great attachment to the second. We explain
that because of free access and frequent updating of GeoGebra, the steady growth of
its tools (in particular, the version GeoGebra 5.0 with 3d-tools was tested in 2013,
and is distributed now).
5. Russian software МathKit finds his supporters (the latest version is license, but
the early versions can be found in Internet). It is attractive because of ”rich” tools and
automated control, which is not provided in other DMS.
6. Students and teachers prefer Gran and DG. We explain that because of the free
distribution, the Ukrainian interface, a sufficient number of researches in periodicals,
the recommendations of the Ministry of Education and Science of Ukraine (also at the
lessons of computer science).
Note that students prefer GS, MathKit and Сabri more then teachers. We explain
that becourse of the lack of Ukrainian interface, the license and the unwillingness of
teachers to work with unfamiliar DMS.
7. According to the research we note the increasing demand for GeoGebra (it was
pointed out by the future and working math teachers). We believe that it is necessary
to pay attention just at it, because GG is continuously updated, freely distributed, has
interface on 30 languages, that confirms its popularity.
8. Future research should be conducted towards the creation of methodical support
of school math courses based on GG. During the preparation of future math teachers
we need to focus not only on traditional for the Ukrainian school software Gran, DG,
but also on the other DMS, which are widely distributed in Internet and used by
teachers.
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