ERIC EJ927391: An Investigation Related to the Modelling Levels and Values of Elementary School Prospective Mathematics Teachers

2011·0.21 MB·English

by  ERIC

Kuram ve Uygulamada Eğitim Bilimleri • Educational Sciences: Theory & Practice - 11(2) • Spring • 1065-1071
©2011 Eğitim Danışmanlığı ve Araştırmaları İletişim Hizmetleri Tic. Ltd. Şti.
An Investigation Related to the Modelling Levels and
Values of Elementary School Prospective Mathematics
Teachers
Soner DURMUŞa
Abant İzzet Baysal University
Abstract
With the discussions on the nature of mathematics, mathematics is regarded as a value laden area. That it con-
tains a wide range of values has led to consideration of new approaches in classroom practices. The model-
ling approach which also includes traditional problem solving is consistent with different values of mathema-
tics. With the recognition of mathematics that has different values with the traditional values, mathematics te-
acher training programs need to be addressed again. It has been intended to contribute the implementation of
the program by examining the profiles of prospective mathematics teachers in the current state and the views
for modelling. The profiles and modelling levels of 136 prospective mathematics teachers who study in mathe-
matics teacher training programme at Abant Izzet Baysal University in 2008-2009 and 2009-2010 academic ye-
ars have been analyzed. When the participants’ levels of having positivist values and levels of having construc-
tivist values were compared, a significant difference was determined in favor of constructivist values. When the
values were analyzed in terms of gender variable, the female participants’ levels of having constructivist and po-
sitivist values showed a significant difference in favor of constructivist values. Modelling levels were examined in
different dimensions, and it was determined significant differences between sub-dimensions. In terms of gender
variable, when sub-dimensions of each modelling levels were analyzed, there was no significant difference bet-
ween female and male prospective mathematics teachers. Also, there was a positive correlation between valu-
es and modelling levels among prospective mathematics teachers.
Key Words
Values in Mathematics, Constructivist Value, Positivist Value, Modelling, Prospective Mathematics Teachers.
Although mathematics and mathematics teaching many examples of these interactions in the history
are different study fields, the nature of mathemat- of mathematics (Davis & Hersh, 2002). This new
ics and application of mathematics to mathemat- perspective on the nature of mathematics requires
ics teaching are inseparable complements. Math- us to reconsider teaching mathematics (Ernest,
ematics just like many other fields interacts with 2007). In this context, two points are raised as the
social sciences such as psychology, sociology, and starting point of this study: Values in mathemat-
philosophy (Bishop, 2000). In addition, there are ics and modelling approach. Whereas values are
about what is attached importance to in teaching
mathematics, modelling is about how to approach
a Correspondence: PhD. Soner Durmus is cur- teaching mathematics.
rently an Associate Professor at the Department
of Primary School Teaching. His research inte-
rests include curriculum development, values,
Values in Mathematics Education
studies with teachers, prospective teachers and
students related to special topics in mathamatics While beliefs are mostly about true/false kinds of
education and use of technology. Correspondan-
views and judgments, values correspond to signifi-
ce: Assoc. Prof. Soner Durmus, Abant Izzet Bay-
cant/insignificant kinds of views and judgments
sal University, Faculty of Education, Department
of Primary School Teaching, 14280 Golkoy/Bolu/ (Chin & Lin, 2001; Jorgensen & Ryan, 2004; Seah,
Turkey. E-mail: [email protected] Phone: +90 Bishop, FitzSimons, & Clarkson, 2001). Values di-
374 254 1626.
1065
EDUCATIONAL SCIENCES: THEORY & PRACTICE
rectly affect learning (Gedik, 2010). Hence, values tures (Crouch & Haines, 2004; Doerr & Lesh, 2003;
should be taken into consideration in mathematics Kaput, 1987; Korkmaz, 2010; Lesh & Doerr, 2003a;
(Matthews, 2001). Indisputability of corollaries in Lester & Kehle, 2003; Taşova & Delice, 2010). In
mathematics is related to assumptions (axiom and the study of Kertil (2008) in which the problem
series of theorems based on it) which are made solving skills of prospective mathematics teachers
during the process. This leads to the acceptance in modelling process was analyzed, it became clear
of them in terms of values (in an unquestionable that the ability of prospective teachers’ problem
way). However, when the values such as accuracy solving skills was found to be insufficient. Another
and fallibilism are investigated in the context of result of the mentioned study was that prospective
mathematics, it can be concluded that it is similar teachers were not familiar with modelling activi-
to the results in social sciences (Bishop & Clark- ties, but if they get enough experience, modelling
son, 1998; Bishop & Seah, 2002; Ernest, 1998, activities help them enhance their problem solv-
2004; Glas, 1998). The accuracy of mathematical ing perspectives a lot. As the rich potential mod-
knowledge together with fallibilism calls forth elling in different studies shows, a lot of countries
questioning common knowledge in mathematics. have begun to include modelling in their curricula
(Australia Ministry of Education, 2008, Depart-
Thus, the research on the nature of mathematics is
ment for Education and Employment, 1999; Linge-
directed towards this subject (Baki, 2008; Bishop,
fjärd, 2002a; Milli Eğitim Bakanlığı [MEB], 2004,
2000; Brown, 1999; Chin & Lin, 2001; Dede, 2010;
2005; National Council of Teachers of Mathematics
Ernest, 1998, 2004; FitzSimons, Bishop, Seah, &
[NCTM], 2000).
Clarkson, 1999; Glas, 1998; Seah, Bishop, FitzSi-
mons, & Clarkson, 2001). As the mismatch between the structure and the
process the model represents cause changes, the tri-
For this reason, the research on both prospective
al of the match of model with the situation is an im-
mathematics teachers and mathematics teachers
portant step in modelling (Durmuş & Kocahülah,
need to be implemented to determine the val-
2006). Thus, modelling has a cyclic structure: de-
ues and their relationship on teaching learning
fining, manipulating, transforming, predicting and
process. FitzSimons, Bishop, Seah and Clarkson
confirming (Lesh & Doerr, 2003b, p. 17)
(1999), after determining the values that teachers
have, examined how teachers reflect their values The dynamic and rich content that modelling will
to classroom environment. An important result of bring to mathematics teaching has attracted the at-
this study is that teachers overtly or covertly reflect tentions of many researchers (Çoban, 2009; Doruk,
their values in their teaching. While teachers do 2010; English & Watters, 2004; English & Watters,
teaching activities according to their values, some- 2004; Eraslan, 2010; Güneş, Gülçiçek, & Bağcı,
times their activities contrast with their values (Pe- 2003; Güzel & Uğurel, 2010; Justi & Gilbert, 2002;
kince, 2010; Sosniak, Ethington, & Valeras, 1991). Kaf, 2007; Zbiek & Conner, 2006). How students
In another research on prospective teachers, values use informal and personal information was ob-
of prospective teachers and how they are imple- served, and it was found out that this information
mented into classroom are examined (McGowen would help them in modelling process and make
writing reports easier for them. There are differ-
& Gary, 2001). One of the results of this study is
ent studies done with the prospective mathematics
that it is harder to change the values of prospective
teachers, though limited (Eraslan, 2011; Lingefjärd,
teachers than to teach new mathematical formulas
2002b; Lingefjärd, & Holmquist, 2005; Verschaffel,
to the prospective teachers. Prospective teachers
De Corte, & Borghart, 1997). Prospective teach-
constantly keep referring to the values, that they
ers expressed that activities requiring modelling
are used to, and have difficulty accepting new ones.
require higher level of thinking and include differ-
ent features than problem solving in which differ-
Modelling ent perspectives lead to different results. In view of
prospective mathematics teachers who were raised
In traditional problem solving process, basically a
according to the traditional viewpoint of mathe-
linear way from the given to the goals is followed. matics, it is not easily accepted not to be able to find
The complicated structure of doing mathematics a ‘one’ definite answer in modelling activities. It is
requires the revision of the perspective towards a significant matter that prospective mathematics
problem solving (Bonotto 2007; Doerr & English, teachers should have an awareness about the typi-
2003; Thomas & Hart, 2010). In fact, activities re- cal values of mathematics and teaching approaches
quiring modelling instead of problem solving draw consistent with these values in their education in
attention due to their dynamic and multi-faced fea-
1066
DURMUŞ / An Investigation Related to the Modelling Levels and Values of Elementary School Prospective Mathematics Teachers
the process of their training. This study aims to Data Analysis
shed light on other researches constructing a pro-
The acquired data have been processed with the
file of values which prospective mathematics teach-
help of a statistics software. Appropriate statisti-
ers have, specifying the awareness level oriented to
cal techniques have been operated to answer the
different dimensions of modelling and analyzing
research questions.
the relationship between possessed values and the
modelling levels. As suitable for the purposes men-
tioned, the following questions will be investigated: Results
1. Is there a statistically significant difference be- When the average values pertaining to partici-
tween the values which prospective mathematics pants’ positivist values were examined, it was seen
teachers have? that they were on “undecided” level (x=2.83), and
2. Is there a statistically significant difference ac- the average values pertaining to their constructiv-
cording to the gender of prospective mathematics ist values were seen that they were on “I agree”
x
teachers in terms of possessed values? level ( =3.60). When the levels of participants hav-
ing positivist values and the levels of their having
3. Is there a statistically significant difference be-
constructivist values were compared, there was a
tween the levels of modelling which prospective
significant difference in favor of the constructivist
mathematics teachers have?
values. In terms of the gender variable, when the
4. Is there a statistically significant difference ac- participants having positivist values were com-
cording to the gender of prospective mathematics pared, the male prospective mathematics teach-
teachers in terms of modelling levels which pro- ers were more positivist than female prospective
spective mathematics teachers have? mathematics teachers. The result showed that there
was no significant difference among the modelling
5. Is there a statistically significant relation between
levels of the participants. In order to determine
values and modelling levels which prospective
among which groups there was significant differ-
mathematics teachers have?
ence, Scheffe’s Test was performed. According to
the results of this test, it was determined that the
Method significant differences were between seeing mod-
x
els as multi-representations ( =3.73) and models
This study is a survey research owing to the fact x
as accurate copies ( =3.20) in favor of models as
that prospective mathematics teachers’ point views
multi-representations; between seeing models as
have been tried to be analyzed without any effects
multi-representations and models as explanatory
from the outside to the conditions of the situation x
tools ( =4.00) in favor of models as explanatory
at hand (Karasar, 2000).
tools; between seeing models as accurate copies
and models as explanatory tools in favor of mod-
els as explanatory tools; between seeing models
Instruments x
as accurate copies and use of scientific models (
For the purpose of data collection, Mathematics =3.62) in favor of use of scientific models; between
and Mathematics Educational Values Scale devel- seeing models as accurate copies and change of
x
oped by Durmuş and Bıçak (2006) has been ap- structure of models ( =3.89) in favor of change
plied in the scope of this study. This scale consists of structure of models; between seeing models as
x
of 34 items designed in 5-point Likert-type for the accurate copies and model examples ( =3.60) in
purpose of revealing the prospective mathematics favor of model examples; between seeing models as
teachers’ values. Models and Modelling Question- explanatory tools and use of scientific models in fa-
naire developed by Güneş, Gülçiçek and Bağcı vor of seeing models as explanatory tools; between
(2004) has been used to reveal the point of views seeing models as explanatory tools and model ex-
of prospective mathematics teachers about models amples in favor of seeing models as explanatory
and modelling. This questionnaire has been devel- tools; between use of scientific models and change
oped to reveal the views of Science and Mathemat- of structure of models in favor of change of struc-
ics teachers about model and modelling. When the ture of models, and between change of structure of
items in the questionnaire are taken into consid- models and model examples in favor of change of
eration, it can be seen that some ideas arising in structure of models.
the literature oriented to model and modelling are
One of the results of the study indicated that there
reflected. The questionnaire consists of 30 items
was significantly positive relationship between the
designed in 5-point Likert-type scale.
1067
EDUCATIONAL SCIENCES: THEORY & PRACTICE
levels of participants having positivist values and the potential to remove the gender factor in per-
modelling sub-dimensions which were model ex- ception of mathematics.
amples and accurate copies. Besides, it was pointed
The interaction between among sub-dimensions
out that there was a significantly positive relation-
is expected situation because the process of mod-
ship between the levels of participants having con-
elling and the models are complex. There is a re-
structivist values and modelling sub-dimensions
spectively difference between the level of viewing
which were models as explanatory tools and use of
models as multi-representations and the level of
scientific models.
viewing models as accurate copies on behalf of the
latter one. When the items of questionnaires aimed
to determine the level of viewing models as multi-
Discussion
representations were observed, it was found that
When the positivist and constructivist values that there were expressions in relation with the variety
participants have were compared, it was clear of models and productiveness of models. However,
that there was a considerable variation in favor of it was aimed to determine the level of participation
constructivist values. Renewed elementary school with the expressions in the questionnaires aimed
mathematics curricula included significant changes to find out the views of the models restricted and
(Kuş, 2009; MEB, 2004, 2005). These changes were narrow scoped in viewing the models as accurate
reflected in course books, and the values included copies (Grosslight, Unger, Jay, & Smith, 1991). The
in course books were analyzed by Dede (2006). models in the study of Berber and Güzel (2009)
Some of the changes among the mentioned above with prospective teachers were seen multi-rep-
were as follows: It is important to construct knowl- resentations, not as accurate copies. Viewing the
edge by the teacher and the students together, the models as multi-representations shows us that par-
teacher needs to facilitate the process of the work ticipants have a wide view of models in this study.
as well as the result, and mathematics should be no
The reason why there is no significant difference
longer regarded as a working area which consists
between male and female prospective mathematics
of unquestionable, independent, and certain facts
teachers can be considered that constructivism has
(Boz, 2008). Accordingly, there have been some
the potential to reveal the gender factor in percep-
changes in teacher training programmes. Courses
tion of mathematics.
such as Philosophy of Mathematics and History of
Mathematics have been added to the teacher train- Because of the fact that models and modelling
ing programmes. Furthermore, each university process are complex, it is expected situation to have
aims to contribute to the process of training teach- interaction among sub-dimensions. When the
ers by increasing elective courses depending on state of models seen as multi-representations and
the number of instructors. Dede (2009) found that the state of models seen as accurate copies are com-
the level of primary school and secondary school pared, a significant difference was found in favor
prospective mathematics teachers’ rate of accepting of model seen as multi-representations. When the
constructivist values were higher than positivist scale items of models seen as multi-representations
values. There was no significant difference among were analyzed, statements were about the diversity
the teachers in terms of gender who had construc- and productiveness of the models. Unlike these
tivist values. On the other hand, it was noticed that items, when the scale items of models seen as ac-
the level of having positivist values of prospective curate copies were analyzed, it was aimed to reveal
male teachers was higher than the prospective fe- the acceptance levels of participants to models in
male teachers’ values. It can be concluded that the terms of their limited features. In the study of Ber-
reason why the level of having positivist values of ber and Güzel (2009) with the prospective teachers
prospective male teachers is higher than the pro- have also been accepted as multi-representations
spective female mathematics teachers’ values is that rather than copies. In this study, the state of mod-
there is a male dominant approach both culturally els’ being seen as multi-representations shows that
and historically towards the nature of mathematics, the participants have a broad point of view on the
and this approach is traditionally close to positivist models. When all sub-dimensions were consid-
values (Barkatsas, Forgasz, & Leder, 2001; Davis & ered, it was concluded that the participants could
Hersh, 2002; Forgasz, Leder, & Gardner, 1999). reason the models with their most general mean-
ing; they could determine model examples cor-
The reason why there is no significant difference
rectly and could make appropriate choices among
among male and female prospective mathematics
them. Hence, it can be concluded that models and
students can be considered that constructivism has
1068
DURMUŞ / An Investigation Related to the Modelling Levels and Values of Elementary School Prospective Mathematics Teachers
modelling activities offer a rich content and the Bishop, A. J. (2000). Critical challenges in researching cultural
prospective teachers have a clear idea about models ıssues in mathematics learning. Journal of Intercultural Studies,
23 (2), 119-131.
and modelling. It can be said that the participants
Bishop, A., & Clarkson, P. (1998). What values do you think
have acquired this extensive comprehension during
you are teaching when you teach mathematics? In J. Gough & J.
their undergraduate education as primary school
Mousley (Eds.), Mathematics: Exploring all angles (pp. 30-38).
mathematics teaching program aims. The fact that Melbourne: Mathematical Association of Victoria.
the education the prospective teachers have about Bishop, A. J., & Seah, W. T. (2002). Values, mathematics and
the models and modelling during their education society: Making the connections. Retrieved May 15, 2010 from
process has a positive effect on their modelling lev- http://www.education.monash.edu.au/research/groups/smte/
projects/vamp/mav2002.pdf.
els was shown to be true by Keskin’s (2008) study
with primary school prospective teachers. Blum, P., Galbraith, P. L., Henn, H., & Niss, M. (Eds.). (2007).
Modelling and applications in mathematics education: The 14th
No significant difference has been found between ICMI Study. New York: Springer.
the prospective mathematics teachers’ six different Blum, W., & Ferri, R. B. (2009). Mathematical modeling: Can
modelling states and gender variable. It has been it be taught and learnt? Journal of Mathematical Modeling and
Applications, 1 (1), 45-58.
found out that the participants perceive the models
and modelling in a similar way without gender dif- Bonotto, C. (2007). How to replace word problems with
activities of realistic mathematical modelling. In W. Blum,
ference.
P. L. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and
It can be said that the traditional approaches of the Applications in Mathematics Education. The 14th ICMI Study
(pp. 69-78). New York: Springer
participants who have positivist thoughts intended
Bonotto, C. (2010). Engaging students in mathematics
for mathematics can restrict the rich possibilities
modelling and problem posing activities. Journal of
the modelling offers. Kertil’s (2008) study which re- Mathematical Modelling and Application, 1 (3), 18-32
vealed that the traditional problem solving abilities
Boz, N. (2008), Turkish pre-service mathematics teachers’
were insufficient in modelling process confirmed beliefs about mathematics teaching. Australian Journal of
that result. Teacher Education, 33 (5), 66-80.
When all sub-dimensions of modelling are com- Brown, J. R. (1999). Philosophy of mathematics: An ıntroduction
to the world of proofs and pictures. New York: Routledge.
pared, there are positive relations that support the
Chin, C., & Lin, F. (2001). Value-loaded activities in
model and modelling as to be thought as a whole.
mathematics classroom. Psychology of Mathematics Education,
Critical approaches towards the nature of math- 2, 249-256.
ematics affect the way mathematics and its edu-
Clarkson, P., FitzSimons, G., Bishop. A., & Seah, W. T. (2000,
cation are seen. By considering that mathematics December). Methodology challenges and constraints in the
is also seen as including specific values like social values and mathematics project. Paper presented at The
sciences, models and modelling approaches have Annual Meeting of the Australian Association for Research in
Education, Sydney, Australia.
the potential of enriching teaching mathematics
Crouch, R., Haines, C., (2004). Mathematical modeling:
(Blum, Galbraith, Henn, & Niss, 2007; Bonotto,
transitions between real world and the mathematical model.
2010; Clarkson, FitzSimons, Bishop, & Seah, 2000). Instructional Journal of Mathematical Education in Science and
The possibilities of models and modelling need to Technology, 35 (2), 197-206.
be analyzed with teacher education, prospective Çoban, G. Ö. (2009). Modellemeye dayalı fen öğretiminin
teaching training and studies towards in-class ap- öğrencilerin kavramsal anlama düzeylerine, bilimsel süreç
plications for different levels and subjects. becerilerine, bilimsel bilgi ve varlık anlayışlarına etkisi: 7. sınıf
ışık ünitesi örneği. Yayınlanmamış doktora tezi, Dokuz Eylül
Üniversitesi, Eğitim Bilimleri Enstitüsü, İzmir.
Davis, P. H. & Hersh, R. (2002). Matematiğin seyir defteri (çev.
References/Kaynakça
E. Abadoğlu). İstanbul: Doruk Yayınları.
Australia Ministry of Education. (2008). Australian
Dede, Y. (2006). Mathematical values conveyed by high school
curriculum. Retrieved April 10, 2010 from http://www. mathematics textbooks. Kuram ve Uygulamada Eğitim Bilimleri,
australiancurriculum.edu.au/Mathematics/Rationale. 6, 81-132.
Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi Dede, Y. (2009). Turkish preservice mathematics teachers’
(gen. 4. bs.). Ankara: Harf Eğitim Yayıncılığı. mathematical values: Positivist and constructivist values.
Barkatsas, A. N., Forgasz, H., & Leder, G. (2001, July). The Scientific Research and Essay, 4, 1129-1235.
gender stereotyping of mathematics: Cultural dimensions. Paper Dede, Y. (2010, Ekim). Türk ve Alman matematik
presented at the 24th Annual MERGA Conference, Sydney. öğretmenlerinin matematiksel değerleri. IX. Ulusal Fen
Berber, N. C. & Güzel, H. (2009). Fen ve matematik öğretmen Bilimleri ve Matematik Kongresi’nde sunulan bildiri, İzmir.
adaylarının modellerin bilim ve fendeki rolüne ve amacına Department for Education and Employment. (1999).
ilişkin algıları. Selçuk Üniversitesi Sosyal Bilimler Enstitüsü Mathematics: The national curriculum for England. London:
Dergisi, 21, 87-97. HMSO.
1069
EDUCATIONAL SCIENCES: THEORY & PRACTICE
Doerr, H. M., & English, L. D. (2003). A modeling perspective Grosslight, L., Unger, C., Jay, E., & Smith, C. (1991).
on students’ mathematical reasoning about data. Journal for Understanding models and their use in science: Conceptions
Research in Mathematics Education, 34 (2), 110-136. of middle and high school students and experts. Journal of
Doerr, H. M., & Lesh, R. (2003). A modeling perspective Research in Science Teaching, 28 (9), 799-822.
on teacher development. In R. Lesh & H. M. Doerr (Eds.), Güneş, B., Gülçiçek, Ç., & Bağcı, N. (2003). Fen bilimlerinde
Beyond constructivism: A models & modeling perspective on
kullanılan modellerle ilgili öğretmen görüşlerinin tespit edilmesi.
mathematics problem solving, learning & teaching (pp. 125-
XII. Eğitim Bilimleri Kongresi, 15-18 Ekim, Antalya.
139). Mahwah, NJ: Lawrence Erlbaum.
Güneş, B., Gülçiçek, Ç., & Bağcı, N. (2004). Eğitim
Doruk, B. K. (2010). Matematiği günlük yaşama transfer etmede
Fakültelerindeki fen ve matematik öğretim elemanlarının
matematiksel modellemenin etkisi. Yayınlanmamış doktora tezi,
Hacettepe Üniversitesi, Sosyal Bilimler Enstitüsü, Ankara. model ve modelleme hakkındaki görüşlerinin incelenmesi.
Türk Fen Eğitimi Dergisi, 1 (1), 35-48.
Durmuş, S., & Bıçak, B. (2006, July). A scale for mathematics
and mathematical values of preservice teachers. Paper Güzel, E. B., & Uğurel, I. (2010). Matematik öğretmen
presented at The 3rd International Conference on the Teaching adaylarının akademik başarılarının matematiksel modelleme
of Mathematics, İstanbul, Türkiye. yaklaşımlarına olan etkisinin incelenmesi. Ondokuz Mayıs
Üniversitesi Eğitim Fakültesi Dergisi, 29 (1), 69-70.
Durmuş, S. & Kocakülah, S. (2006). Fen ve matematik
öğretiminde modelleme. M. Bahar (Ed.), Fen ve teknoloji Jorgensen, L., & Ryan, S. (2004). Relativism, values and
öğretimi içinde (s. 299-317). Ankara: PegemA Yayıncılık. morals in the New Zealand curriculum framework. Science &
English, L., & Watters, J. (2004). Mathematical modeling in the Education, 13, 223- 233.
early school years. Mathematics Education Research Journal, 16 Justi, S. R., & Gilbert, K. J. (2002). Modelling teachers’ views
(3), 59-80. on the nature of modelling and implications for the education
English, L. D. (2006). Mathematical modeling in the primary of modellers. International Journal of Science Education, 24 (4),
school: Children’s construction of a consumer guide. 369-387.
Educational Studies in Mathematics, 63, 303-323.
Kaf, Y. (2007). Matematikte model kullanımının 6. sınıf
Eraslan, A. (2010, Eylül). İlköğretim matematik öğretmen öğrencilerinin cebir erişilerine etkisi. Yayınlanmamış yüksek
adaylarının model oluşturma etkinlikleri (Model Eliciting lisans tezi, Hacettepe Üniversitesi, Ankara.
Activities) üzerinde düşünme süreçleri. IX. Ulusal Fen Bilimleri
ve Matematik Kongresi’nde sunulan bildiri, İzmir. Kaput, J. (1987). Representation systems and mathematics. In
C. Janvier (Ed.), Problems of representation in the teaching and
Eraslan, A. (2011). Prospective elementary mathematics
learning of mathematics (pp. 19-26). Hillsdale, NJ: Lawrence
teachers’ perceptions on model eliciting activities and their
Erlbaum Associates.
effects on mathematics learning. İlköğretim Online, 10 (1),
364-377. Karasar, N. (2000). Bilimsel araştırma yöntemi. Ankara: Nobel
Ernest, P. (1998). The constructivism as a philosophy of Yayınları.
mathematics. Albany: The State University of New York Press. Kertil, M. (2008). Matematik öğretmen adaylarının problem
Ernest, P. (2004, July). What is the philosophy of mathematics çözme becerilerinin modelleme sürecinde incelenmesi.
education? Paper presented at the 10th International Congress Yayınlanmamış yüksek lisans tezi, Marmara Üniversitesi,
of Mathematical Education, Copenhagen. Eğitim Bilimleri Enstitüsü, İstanbul.
Ernest, P. (2007). The philosophy of mathematics, values and Keskin, Ö. Ö. (2008). Ortaöğretim matematik öğretmen
keralese mathematics. The Montana Mathematics Enthusiast, 4 adaylarının matematiksel modelleme yapabilme becerilerinin
(2), 174-187. Retrieved November 10, 2010 from http://www. geliştirilmesi üzerine bir araştırma. Yayınlanmamış doktora
math.umt.edu/tmme/vol4no2/TMMEvol4no2_pp.174_187_ tezi, Gazi Üniversitesi, Ankara.
UK.pdf.
Korkmaz, E. (2010). İlköğretim matematik ve sınıf öğretmeni
FitzSimons, G. E., Bishop, A. J., Seah, W. T., & Clarkson, P.
adaylarının matematiksel modellemeye yönelik görüşleri ve
C. (1999). Conceptions of values and mathematics education
matematiksel modelleme yeterlikleri. Yayınlanmamış doktora
held by Australian primary teachers: Preliminary findings
tezi, Balıkesir Üniversitesi, Fen Bilimleri Enstitüsü, Balıkesir.
fromVAMP. Paper presented at the Australian Association
for Research in Education Annual Conference, Melbourne, Kuş, D. (2009). İlköğretim programlarının, örtük programın
Australia. Retrieved February 5, 2010 from http://www. ve okul dışı etmenlerin değerleri kazandırma etkililiğinin 8.
education.monash.edu.au/research/groups/smte/projects/ sınıf ilköğretim öğrencilerinin ve öğretmenlerinin görüşlerine
vamp/hpm2000c.pdf göre incelenmesi Yayınlanmamış doktora tezi, Yıldız Teknik
Forgasz, H. J., Leder, G. C., & Gardner, P. L. (1999). The Üniversitesi, Sosyal Bilimler Enstitüsü, İstanbul.
Fennema-Sherman ‘Mathematics as a male domain’ scale re-
Lesh, R., & Doerr, H. M. (2003a). (Eds.). Beyond constructivism:
examined. Journal for Research in Mathematics Education, 30
Models and modeling perspectives on mathematics problem
(3), 342-348.
solving, learning, and teaching. Mahwah, NJ:Lawrence Erlbaum.
Gedik, E. G. (2010). Sınıf öğretmenlerinin değer yönelimlerinin
Lesh, R., & Doerr, H. M., (2003b). Foundations of a models
ve öğrencilerine aktarmak istedikleri değerlerin incelenmesi.
Yayınlanmamış yüksek lisans tezi, Zonguldak Karaelmas and modeling perspective on mathematics teaching, leraning,
Üniversitesi, Sosyal Bilimler Enstitüsü, Zonguldak. and problem solving. In R. Lesh & H. M. Doerr (Eds.),
Beyond Constructivism: A models & modeling perspective on
Glas, E. (1998). Fallibilism and the use of history in
mathematics problem solving, learning & teaching (pp. 3-33).
mathematics education. Science & Education, 7, 361-370.
Mahwah, NJ: Lawrence Erlbaum.
1070
DURMUŞ / An Investigation Related to the Modelling Levels and Values of Elementary School Prospective Mathematics Teachers
Lester, F. K., & Kehle, P. E. (2003). From problem solving Zbiek, R. M., & Conner, A. (2006). Beyond Motivation:
to modeling: The evolution of thinking about research Exploring mathematical modeling as a context for deepening
on complex mathematical activity. In R. Lesh & H. M. students’ understandings of curricular mathematics.
Doerr (Eds.), Beyond Constructivism-Models and modeling Educational Studies in Mathematics, 69, 89-112.
perspectives on mathematics problem solving, learning, and
teaching, and teaching (pp. 501-517). Hillsdale, NJ: Lawrence
Erlbaum Associates, Inc.
Lingefjärd, T. (2002a). Teaching and assessing mathematical
modelling. Teaching Mathematics and its Applications, 21 (2),
75-83.
Lingefjärd, T. (2002b). Mathematical modeling for preservice
teachers. A problem from anesthesiology. International Journal
of Computers for Mathematical Learning, 7, 117-143.
Lingefjärd, T., & Holmquist, M. (2005). To assess students’
attitudes, skills and competencies in mathematical modeling.
Teaching Mathematics and its Applications, 24 (2-3), 123-133.
Matthews, B. (2001). The Relationship between values and
learning. International Education Journal (Educational
Research Conference 2001 Special Issue), 2 (4), 223-232.
McGowen, M. A., & Gary, E. (2001, October). What
mathematical knowledge do pre-service elementary teachers
value and remember? Paper presented at The Annual Meeting
of the North American Chapter of the International Group for
the Psychology of Mathematics Education, Snowbird, UT.
Milli Eğitim Bakanlığı [MEB]. (2004). İlköğretim matematik
dersi (1-5.Sınıflar) öğretimi programı. Ankara: Devlet Kitapları
Müdürlüğü Basımevi.
Milli Eğitim Bakanlığı [MEB]. (2005). İlköğretim matematik
dersi (6-8.Sınıflar) öğretimi programı. Ankara: Devlet Kitapları
Müdürlüğü Basımevi.
National Council of Teachers of Mathematics [NCTM]. (2000).
Principles and standards for school mathematics. Reston, VA:
Author.
Pekince, D. (2010). An analyze of Teachers’ value preferences
in classroom management on the basis of length of service
variable. International Journal of New Trends in Education and
Their Implications (special issue), 1 (4). 13-20.
Seah, W. T., Bishop, A. J., FitzSimons, G. E., & Clarkson, P.
C. (2001, December). Exploring ıssues of control over values
teaching in the mathematics classroom. Paper presented at
The 2001 Annual Conference of the Australian Association for
Research in Education, Fremantle, Australia.
Sosniak, L. A., Ethington, C. A., & Varelas, M. (1991). Teaching
mathematics without a coherent point of view: Findings from
the IEA Second International Mathematics Study. Journal of
Curriculum Studies, 23 ( 2), 119-131.
Taşova, H. İ., & Delice, A. (2010, Eylül). Matematik öğretmen
adaylarının Krutetskii Düşünme Yapıları bağlamında
modelleme etkinliklerindeki performanslarının incelenmesi.
IX. Ulusal Fen Bilimleri ve Matematik Kongresi’nde sunulan
bildiri, 23-25 Eylül, İzmir.
Thomas, K., & Hart, J. (2010). Pre-service teacher perceptions
of model eliciting activities. In R. Lesh et al. (Eds.), Modeling
students’ mathematical modeling competencies (pp. 531-539).
New York, NY: Springer Science & Business Media.
Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service
teachers’ conceptions and beliefs about the role of real-
world knowledge in mathematical modelling of school word
problems. Learning and Instruction, 7 (4), 339-359.
1071