ECER, Bolzano, Italy, 4 - 07 September 2018, pp.1-3
Exploring
Cognitive Demands of Mathematics and Geometry Questions
in Turkish
National University Entrance Exams
from 2006 to 2017
(except 2014 and 2015)
Behiye UBUZ and
Aysenur ALP
Middle East Technical University
Introduction
In Turkey, as in many other countries (e.g. China, Greece,
Iran, Japan, Russia, and Spain) university entrance exam is the sole criterion
for student selection to higher education. The importance of the university
entrance exam is increasing as millions of students sit in this exam and their
results determine entry into universities or alternatives. In each year, high
school graduates in Turkey take a stringent, centralized university entrance
exam, seeking a place in one of the public or private universities. The
competition is fierce and the exam content rigorous. In recent years, although
the number of public and private universities increased, the seats at
universities are still limited. In addition, willing to enter high prestige
universities to gain employment and a higher status in society upon graduation
still forces the competition.
University entrance exam determines the future of
millions of young people and is the potent forces that influence
the implemented curriculum in schools, particularly in high schools. Thus, the exam mathematics questions’ cognitive
demands were examined by various researchers (e.g., Keleş & Karadeniz, 2015;), particularly using Bloom’s
taxonomy. It is claimed that although the analyses of questions’
cognitive levels using Bloom’s taxonomy give an idea about their cognitive
level, yet it is criticized by researchers (Tekkumru-Kisa, Stein, & Schunn,
2015) that “cognitive actions” as such application and evaluation do not
constitute the cognitive demand and therefore could be low or high depending
upon the nature of the situation. As pointed out by Tekkumru-Kisa, Stein, and
Schunn, (2015), a task analysis guide (TAG) developed by Smith and Stein (1998)
has proven to be useful both in research and practice setting. In the
framework, there are four cognitive demand levels: 1) memorization, 2)
procedures without connections, 3) procedures with connections, and 4) doing
mathematics. While the levels, memorization
and procedures without connections
are categorized as “lower-level cognitive demands”, the other two levels, procedures with connections and doing mathematics are categorized as
“higher-level cognitive demands”. The distinction made between the categories procedures with connections and procedures
without connections is particularly useful. Procedures without connections refer broadly to “tasks that require
students to perform a memorised procedure in a routine manner” (Stein et al.,
2009, p. 1). Procedures with connections
refer broadly to “tasks that demand engagement with concepts and that stimulate
students to make powerful connections to meaning or relevant mathematical
ideas” (ibid.). Although the framework
was originally developed for instructional and curricular materials in
mathematics and used in several studies in mathematics (e.g., Aysel, O’Shea, & Breen, 2011; Ubuz, Erbaş, Çetinkaya, & Özgeldi, 2010; Ubuz
& Sarpkaya, 2014), in this study, it was adapted to be used in the analysis
of mathematics and geometry questions in the university entrance examination. Cognitive
demand is defined as “the kind and level of thinking required from students in
order to successfully engage with and solve the task” (Stein, et al., 2000,
p.11).
The main purpose of this study was to
investigate the cognitive demand of mathematics and geometry questions in the
Turkish university entrance examinations held between 2006 to 2017 (except 2014
and 2015). The
findings of this study can be used for comparative studies of different
countries assessment systems, and can provide insights into the improvement of
mathematics education from an international perspective. The cognitive demands of the questions can shed new
light on the TAG framework.
Methods
Mathematics
and geometry questions of university
entrance exams held between 2006 to 2017 (except 2014 and
2015) in Turkey were examined in this present study. The questions were developed and implemented by the Öğrenci
Seçme ve Yerleştirme Merkezi (ÖSYM) (Measurement, Selection and Placement
Center), and accessed from the web page of ÖSYM (ÖSYM, 2017a). ÖSYM was
established by the Üniversitelerarası Kurul Başkanlığı (ÜAK) (Council of Intercollegiate) in 1974 (ÖSYM, 2017b). ÖSYM
also develops and implements several nation-wide exams in addition to the
university entrance exams.
Between 2006 and 2009, students took one-stage exam,
called Öğrenci Seçme Sınavı (ÖSS) (Student
Selection Examination). The test was divided into two main parts: first part
covered mostly 9^{th} and 10^{th} grade subjects (e.g., numbers,
word problems) and rarely 11^{th} grade subjects (mostly geometry
subjects: circle, analytic geometry) and the second part included 11^{th}
and 12^{th} grade subjects (e.g., complex numbers, functions) with some
questions on 10^{th} grade subjects (e.g. trigonometry). Even these
questions were given in one stage, in the present study the first part
questions were called as ÖSS-1 and the second part questions as ÖSS-2. Starting
from 2010-2011 academic years, the exam was implemented in two-stage with
different names, around two months between them: Yüksek Öğrenime Geçiş Sınavı
(YGS) (Higher Education Exam) and Lisans Yerleştirme Sınavı (LYS) (Undergraduate
Placement Exam). Students need
to receive a score of 180 points in YGS (36% of the total points = 500) to be
eligible to take the LYS. Generally
speaking, the contents in ÖSS-1 and YGS, and ÖSS-2 and LYS are similar. For
that reason, ÖSS-1 and YGS questions, and ÖSS-2 and LYS questions were
considered together. Given
that there are different names for exams, in this paper we prefer to use exam
names as first and second stage university entrance exams.
Multiple-choice
questions with five options constituted the exams. Totally 360 mathematics and
geometry questions (278 mathematics and 82 geometry questions) from the first
stage exam (ÖSS1 and YGS) and 600 mathematics and geometry questions (386
mathematics and 214 geometry questions) from the second stage exam (ÖSS2 and
LYS) were constituted the data sources of this study. Each question
will be categorized based on the TAG framework by the researchers. Following
this, the frequency of each demand across years and different subjects will be
provided.
Conclusion
The
cognitive demand levels of mathematics and geometry questions in national
university exams in Turkey between 2006 and 2017 (except 2014 and 2015) will be
categorized across the large range of years as well as across different
mathematics and geometry subjects. This categorization is not only beneficial
for Turkish University Entrance
Examination System, but also international ones since many
other countries have also their own standardized university entrance exams
(e.g. Spain and Japan). Additionally, this study aims to improve Stein and
Smith’s (1998) cognitive demand framework, by providing detailed descriptions
of each cognitive demand. Although Stein
and Smith (1998) provided several key characteristics for each category in
order to categorize mathematical tasks (see Stein et al., 2000), we
believe that by specifying definitions of each demand in the current framework,
we can identify the related cognitive demand levels of different kind of tasks
much easier by using action verbs (e.g. execute, formulate, investigate,
create). Moreover, in this way, we will contribute to related literature in specifying
different cognitive demand levels by using concrete examples.
References
Aysel A., O'Shea, A., & Breen,
S. (2011). A classification of questions from Irish and Turkish high-stakes
examinations. In Proceedings of the
British Society for Research into Learning Mathematics. BSRLM, London, pp.
13-18.
Keleş, T., & Karadeniz, M. H. (2015). An analysis of mathematics
and geometry questions in OSS, YGS and LYS according to the revised bloom
taxonomy between 2006-2012 years. Turkish Journal of Computer and
Mathematics Education (TURCOMAT), 6(3), 532-552.
ÖSYM (Ölçme, Seçme ve Yerleştirme Merkezi) (2017a). ÖSYS: Öğrenci Seçme
ve Yerleştirme Sistemi Sınav Soru ve Cevapları. Retrieved from http://www.osym.gov.tr/TR,12910/2017.html.
ÖSYM (Ölçme, Seçme ve Yerleştirme Merkezi) (2017b). ÖSYM Tarihçe.
Retrieved from http://www.osym.gov.tr/TR,8789/hakkinda.html.
Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a
framework for reflection: From research to practice. Mathematics Teaching in
the Middle School, 3(4), 268-275.
Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E. (2000). Exploring
cognitively challenging mathematical tasks: A casebook for teacher development.
New York: Teachers College Press.
Stein, M. K., Smith,
M. S., Henningsen, M. A., & Silver, E. A. (2009). Implementing standards based mathematics
instruction, A casebook for professional development (2nd ed.). Reston, VA:
National Council of Teachers of Mathematics.
Tekkumru-Kisa, M., Stein, M. K., & Schunn, C. (2015). A framework
for analyzing cognitive demand and content‐practices integration: Task analysis
guide in science. Journal of Research in Science Teaching, 52(5),
659-685.
Ubuz, B., Erbaş, A. K., Çetinkaya, B., & Özgeldi, M. (2010).
Exploring the quality of the mathematical tasks in the new Turkish elementary
school mathematics curriculum guidebook: The case of algebra. ZDM, 42(5),
483-491.
Ubuz, B., & Sarpkaya, G. (2014). The investigation of algebraic
tasks in sixth grades in terms of cognitive demands: Mathematics textbook and
classroom implementations. Elementary Education Online, 13(2), 594-606.