Available online at www.sciencedirect.com
Procedia Social and Behavioral Sciences 2 (2010) 2277–2281
WCES-2010
Analysis of mathematical tasks in Turkish elementary school
mathematics textbooks
Meriç Özgeldia *, Yasemin Esenb
a
b
Mersin Üniversitesi, E÷itim Fakültesi Yeniúehir Yerleúkesi 33169 Mersin, Turkey
Kocaeli Üniversitesi, E÷itim Fakültesi, Umuttepe Yerleúkesi 41380 Kocaeli, Turkey
Received October 19, 2009; revised December 28, 2009; accepted January 11, 2010
Abstract
This paper gives a perspective on the nature of the mathematical tasks in the new Turkish Elementary School Mathematics
Textbooks (grades 6, 7, and 8). The aim of the study is to explore the level of the cognitive demands of the mathematical tasks
via employing the framework developed by Smith and Stein (1998). The findings of the study indicate that the levels and types of
mathematical tasks in textbooks are predominantly at the level of procedures without connections and do not like to appreciate
the aim of the Turkish Elementary School Mathematics Curriculum.
© 2010 Elsevier Ltd. All rights reserved.
Keywords: Cognitive demands; mathematical tasks; textbook analysis; elementary school mathematics curriculum; mathematics teacher.
1. Introduction
Through the curriculum reform that started in 2004 in Turkey, the curriculum and curricular material including
the mathematics textbooks have changed and facilitated to implement the curricular intentions. Increased importance
has been placed on the curriculum material which reflects the information about the reform, curriculum objectives,
and suggestions. Likewise, the Turkish Elementary Mathematics Curriculum was prepared taking into consideration
the curriculum implementations and the previous experiences about the mathematics education. The documents
published by Talim ve Terbiye Kurulu (TTKB) [Board of Education] (2008) emphasize the students’ mathematics
skills that are related to exploring mathematical ideas, solving problems, making connections among mathematical
ideas, and applying them in the real life situations. These intentions are mainly based on the students’ development
of higher level of mathematical thinking and reasoning.
Among the curriculum material, textbooks potentially have a significant effect on the implementations of
mathematics curricular intentions (Schmidt, McKnight, Valverde, Houang, & Wiley, 1997); and textbooks make
possible a connection between the curriculum intentions and classroom activities (Schmidt, McKnight, & Raizen,
2002). Particularly, textbooks are among the most widely used and trusted written resources for school based
* Meriç Özgeldi. Tel.: +90-312-210-75-08; fax: +90-312-210-79-84
E-mail address: [email protected]
1877-0428 © 2010 Published by Elsevier Ltd.
doi:10.1016/j.sbspro.2010.03.322
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learning in all parts of the world by students and teachers (Beaton, Mullis, Martin, Gonzalez, Kelly, & Smith, 1996).
The teachers use the textbooks as a source of mathematics context and the way of teaching mathematics, and the
students use for classroom exercise and homework assignment (Fan, Chen, Zhu, Qiu, & Hu, 2004). They have an
important role as a material in classroom context, because they are the major resource for mathematical content and
pedagogical approaches (Haggarty & Pepin, 2002). Therefore, textbooks may be considered as a resource for
classroom activities which are shaped by activities and tasks.
From this point of view, mathematical tasks give students the opportunity to think conceptually, and encourage
them to make connections (Stein & Smith, 1998); and provide them to focus on a specific mathematical idea
including deeper understanding about the nature of mathematical concepts, processes, and relationships (Stein,
Grover, & Henningsen, 1996; Stein, Smith, Henningsen, & Silver, 2000). The mathematical tasks provide context
for students to “think about, develop, use, and make sense of mathematics” (Stein et al., 1996, p.459). Thus, the
examination of the tasks in the mathematics textbooks may identify the nature of the mathematical tasks and give a
perspective about the curriculum implementations.
At this point, Mathematical Tasks Framework (Smith & Stein, 1998) is not the only framework to analyze the
nature of mathematical tasks; but other frameworks, such as the Third International Mathematics and Science Study
(TIMSS) (Mullis, Martin, Ruddock, O’Sullivan, Arora, & Erberber, 2005) also are helpful to evaluate the nature of
tasks in textbooks. In fact, Mathematical Tasks Framework (Smith & Stein, 1998) was a powerful tool developed
through QUASAR [Quantitative Understanding: Amplifying Student Achievement and Reasoning] in order to
analyze the tasks appeared in curriculum materials. The framework categorizes mathematical tasks according to the
level of cognitive demands from low level- memorization, and procedures without connections- to high levelprocedures with connections, and doing mathematics-.
This paper gives a perspective on the nature of the mathematical tasks in the new Turkish Elementary School
Mathematics Textbooks (grades 6, 7, and 8). In particular, the focus of the present study is to explore the level of the
cognitive demands of the mathematical tasks via employing the framework developed by Smith and Stein (1998).
We believe that the examination of the level of the cognitive demands in textbooks provides possible suggestions to
improve the implementation of the curriculum development and a connection between the curriculum intentions and
classroom activities.
2. Method
2.1. Materials
The data source consists of the tasks in the 6th, 7th, and 8th grades mathematics textbooks in Turkey. They were
the official textbooks published and approved by the Turkish Ministry of Education, distributed free of charge to
students and teachers by the ministry itself. The underlying rationale for focusing on the textbooks was that they
would reflect the curriculum intentions and would give a good picture of the nature of tasks set up by teachers and
implemented by students.
2.2. Procedures/Data analysis
Forty-two prospective teachers performed two-hour lectures and two-hour workshops every week for 14 weeks in
the spring of 2009. In the first 6 weeks, they were assigned tasks in order to provide them to understand the role of
textbooks in the teaching and learning of mathematics and the ways of the evaluation of mathematics textbooks
including the framework stated in Smith and Stein (1998). During the following four weeks, the groups, which
consisted of 2 or 3 people, discussed the content of the items in the framework and characteristics of each level of
cognitive demand in order to be in consensus on the evaluation of mathematical tasks with respect to Smith and
Stein’s framework (1998). After those discussions, they were asked to analyze the equally distributed number of
tasks totally covering all the tasks in the 6th, 7th, and 8th mathematics textbooks.
All tasks in the textbooks appeared under the headings of “Activities”, “Examples”, “Application Questions”,
“Subject/Topic Evaluation” and, “Unit Evaluation”. The researchers decided to categorize and define tasks in the
activities, application questions, and the examples as “the explanation tasks”, since those tasks aimed to give
information about the mathematical concepts, to make relations between mathematical ideas, and to clarify the
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mathematical procedures. On the other hand, the tasks in subject evaluation and in the unit evaluation were
considered and defined as “the assessment tasks”; since they were aimed to evaluate the mathematical ideas,
concepts, and procedures. Totally, the data source consisted of 1692 of the explanation tasks and 1093 of the
assessment tasks. Particularly, the tasks that built on one another were considered as a single task. Since the purpose
of this study was to explore the level of the cognitive demands of the mathematical tasks, the analysis was motivated
by the following two research questions;
1. What are the levels of the cognitive demands of the mathematical tasks categorized as the explanation and
assessment tasks in textbooks? Are there any differences or similarities between the explanation and
assessment tasks?
2. Are there any differences across the grade levels with respect to the cognitive demands? And if so, how?
In order to provide the reliability of data analysis, researchers randomly selected 25% of total data analysis and
compared codes in terms of the level of the cognitive demands stated in the framework. They separately analyzed
and independently coded almost 25% of the data and compared their coding results to explore the percentage of
agreement, which is suggested as “inter-coder reliability process” by Neuendorf (2002). The separate findings
showed that the percent of agreement between the coders was about 90% which might be considered as a pretty high
level of inter-coder agreement (Lombard, Snyder-Duch, & Bracken, 2002).
3. Findings and Results
The results of the study are presented in three main sections. Firstly, a descriptive summary of the basic attributes
of the mathematical tasks used in mathematics textbooks is provided. The next two sections address each of the
research questions. The descriptive statistics of mathematical tasks in terms of explanation and assessment tasks is
shown in Table 1.
Table1. Number of mathematical tasks in each grade level
Grades
6
7
8
TOTAL
Explanation tasks
564
600
528
1692
# of Mathematical Tasks
Assessment task
334
417
342
1093
TOTAL
898
1017
870
2785
2785 mathematical tasks were classified along various dimensions; from low level cognitive demands
(memorization and procedures without connection) to higher level cognitive demands (procedures with connections
and doing mathematics). As seen in Table 1, there were 1692 the explanation tasks and 1093 the assessment tasks in
the 6th, 7th, and 8th grade mathematics textbooks. Furthermore, Table 2 and Table 3 display the distribution of level
of the cognitive demands required by the mathematical tasks in grades 6, 7, and 8. The vast majority of the tasks
required low levels of cognitive demands both within each grade levels and across the grade levels. The findings
revealed that 55, 3% of the explanation tasks and 64, 6% of the assessment tasks required lower-levels of cognitive
demand. The explanation and assessment tasks were predominantly at the level of procedures without connections.
Table 2. Percentage of tasks coded at the each level of the cognitive demand
Grades
6
7
8
Low-M (%)
10,3
10,3
10,6
Explanation Tasks
Low-P(%)
High-P(%)
43,6
38,1
39,8
38,5
52,1
31,8
High-DM(%)
8,0
11,3
5,5
Moreover, there was an increase in higher-levels of cognitive demand for the explanation and assessment tasks
across the grades 6 and 7 but there was a decrease in higher-levels of cognitive demand at the 8th grade. With
respect to the curricular intentions, it is expected that new textbooks include the mathematical tasks that require
higher-level of cognitive demands.
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Table 3. Percentage of tasks coded at the each level of the cognitive demand
Grades
6
7
8
Low-M (%)
11,1
11,8
10,2
Explanation Tasks
Low-P(%)
High-P(%)
48,5
29,9
50,4
31,7
56,7
26,9
High-DM(%)
4,2
6,2
6,1
4. Discussion and Conclusion
This study examined the cognitive demands of the 6th to 8th grades’ mathematical tasks in the mathematics
textbooks. The new elementary mathematics curriculum indicated the development of higher level of cognitive
demands such as mathematical thinking and reasoning (TTKB, 2008). At this point, it is important that the tasks
should require higher level of cognitive demand in order to support the students’ opportunities with understanding
and reasoning (Jones & Tarr, 2007; Stein & Lane, 1996). The findings of the study indicate that the levels and types
of mathematical tasks in textbooks do not appreciate the aim of the elementary mathematics curriculum. As
aforementioned, the tasks in the textbooks required lower-levels of cognitive demand and a great majority of the
remaining tasks were at the level of procedures without connections. Significantly, the low levels of cognitive
demand as written should not stay the same when implemented by teachers in classrooms (Stein, Grover &
Henningsen, 1996). Teachers can modify and use these tasks with respect to their students. Therefore, the
distribution of the level of the cognitive demands in textbooks does not refer to the quality of the textbooks; rather it
addresses the learning opportunities for students to develop their mathematical understanding and reasoning.
Through the mathematics textbooks, teachers and textbook writers can have access to the tasks with different
levels of cognitive demands which may give them vital information about the curriculum implementation. The
findings of this study may help teachers in selecting and implementing tasks, and curriculum developers about
issues regarding the improvement of quality of the tasks that eventually improve the implementation of the
curriculum development process. We believe that this study also makes two contributions to the mathematics
education literature on professional development. The first one is related with the professional development of
teachers. Any opportunity which canalizes teachers’ thinking more deeply about their practice supports both a
growth in pedagogical content knowledge (ways of thinking about mathematical tasks) and a change in practice
(choosing mathematical tasks). For further studies, the focus will be on specific mathematical tasks, such as
algebraic and geometrical tasks in textbooks.
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