In today's world, technology has been developing very rapidly and affecting life in all areas. As a result of this, business world needs creative individuals who are capable of thinking analytically and successful at problem solving. Therefore, mathematics education becomes crucial about raising students who give value to mathematics, who can think mathematically and solve problems by reasoning. At this point, a product of developing technology, "graphing calculators" (GC), are thought to be a mean that can provide these goals of mathematics education.
Since 1986, graphing calculators have been used in mathematics education and the National Council of Teachers of Mathematics (NCTM) recommended in the Curriculum and Evaluation Standards for School Mathematics (1989) that graphing calculators must be available to all high school students at all levels and they should be integrated into the teaching and the assessment of mathematics. However, in 2011 there is still not a consensus between mathematics teachers about using calculators and in Turkey; they are used in only some private schools. Also, even in these schools, teachers have not reached a consensus on integrating it into lessons.
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The purpose of this study is to investigate how attitudes of mathematics teachers affect using graphing calculators (GC) in teaching and testing students' learning. New inexperienced mathematics teachers and student-teachers, who will work in private schools in Turkey or work abroad, will benefit from this research by seeing discussions about some research in other countries and in Turkey. This project includes all grades of high school mathematics teaching and in the given one semester time limit, it can be feasible to investigate and understand teachers' general attitudes.
This project will address the problem that "how do teachers' attitudes affect integrating graphing calculator into mathematics lessons?" There are multiple perspectives of teachers, parents, administrators and students on the usage of calculator in classes.Â In Turkey, although it has been changing in private schools, most parents and administratorsÂ have usually beenÂ against using calculators, while students are unable to understand this situation. Parents and administrators more likely tend to traditional methods in teaching because they can see usage of GCs as time consuming and as not following the curriculum. On the other hand, students may see GCs as helpful devices enhancing their learning and motivations. This difference of perspectives surely has an effect on the perspectives of the teachers about this problem.
This problem relates to improving teaching practice in maths because using graphing calculators provides a wide range of activities including group/individualÂ working and discovery learning. It may alsoÂ be used forÂ visualization of mathematical knowledge while teaching. Therefore, again teachers' perceptions are important on deciding whether to develop mathematics curriculum and classroom dynamics by the way of using calculator or not.
Therefore, to answer the overall problem, "how do teachers' attitudes affect integrating graphing calculator into mathematics lessons?", these specific research questions will be addressed:
What are teachers' attitudes regarding advantages and disadvantages of using GC?
How teachers' beliefs about classroom dynamics affect GC usage?
What do teachers think about howÂ the use of GC interacts with curriculum?
Most research was done about how training on graphic calculators affects teachers' attitudes on integrating them into lessons. One of these studies was done by Baki and Çelik in 2005, in Trabzon, a city of Turkey, with 14 mathematics teachers, who had not been aware of graphing calculators before, about using TI-92 graphing calculators in geometry classes. After attending a course of developing activities using graphing calculators, they were interviewed for revealing if any changes occurred in their views about graphing calculators or not. Baki&Çelik (2005) stated that all of the teachers had believed that it can be harmful for students' procedural abilities and only four teachers' views had not been changed after the course. However, others thought that it can be beneficial for taking students interests and providing effective and deeply learning by encouraging investigation (p.146). Similar to this conclusion, another detailed research done by Chang (2000) on the mathematics teachers of 243 high schools in New Zealand, indicated that:
The trained and not-trained respondents showed opposite attitude to the role of graphics calculators in secondary mathematics education: the trained ones have always had a higher percent of positive agreement to every descriptive statement about the role of this technology in secondary mathematics education. This seems to suggest that enough training for every mathematics teacher is essential for integrating this technology into secondary mathematics education. (p.92)
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Also, Yoder indicated that teachers who had attended at least one workshop about how to use GC believed that they can be used for discovery activities while the others believed that their students become dependent on calculators and their basic computational skills are damaged (2000, p.29).
Besides geometry classes, there are also other studies investigating its integration into algebra or calculus classes. For example, results of a survey done on 48 algebra teachers in Ohio about graphing calculators use and views of learning algebra showed that teachers were currently using calculators at least several times a week for in-class activities, homeworks, quizzes and exams in algebra classes (Yoder, 2000, p.i).
Another point that research done on graphing calculators mostly dealt with is that what kind of beliefs of teachers affect integration of calculators into lessons. Elaine Simmt discussed a research study done by observing six mathematics teachers in Canada during lessons on teaching of a specific topic, quadratic functions using graphing calculators (1997) and by interviewing them. The interviews were focused on teachers' reasons for using graphing calculators, teachers' philosophies of mathematics education and in what ways the availability and use of graphing calculators affect teachers' beliefs on mathematics. According to results, the variety of teachers' philosophies was evidenced, not so much in choosing activities with graphing calculators, but in how the teachers use questioning or lecture notes while following up the activities. Also, it shows that although all of the teachers had the same technology and the same curricular constraints, each of them developed the mathematics curriculum within the context of his or her personal philosophy of mathematics and mathematics education (Simmt, 1997, p.269).
Similar to Simmt's conclusion, Yoder indicated that, according to Reys, research has shown that teachers are reluctant or enthusiastic about using calculators due to "their beliefs about what mathematics is and what their role as a mathematics teacher includes" (2000, p.2). For example, results of Chang's research revealed that 'rule-based' and 'non-rule-based' teachers responded differently to this technology. He defined 'rule-based' teachers as teachers who believe that learning mathematics is mostly memorizing and knowing of rules and defined 'non-rule-based' teachers as teachers who "believe that the core of mathematics learning is exploring problems to discover patterns and make generalizations" (2000, p.50). Results of this research showed that teachers who hold a more rule-based view of mathematics are more likely to hold the view that the graphing calculators do not enhance instruction and may even hinder it (Chang, 2000, p.86-87).
However, Yoder (2000) refused Chang's views according to his research done in Ohio such that the teachers' views of learning algebra were not found to be a significant factor in using graphing calculators because both teachers who had "rule-based" and "non-rule-base" view of learning algebra integrated graphing calculators in their lessons (p.27) by depending on participants', who do not use calculators, scores on the view of learning algebra composite were not any higher than participants' who use calculators. Therefore, he assumed that the reason cannot be related to teachers' views of learning algebra.
In addition to these, Baki and Çelik stated that before the workshop, most of the teachers joined to the workshop in Trabzon had believed that graphing calculators lead students to ready-made knowledge and memorization since most of the teachers thought teaching mathematics as improving students' computational skills. And, the mathematics curriculum and university entrance exam support teachers' this kind of views. After the course, most teachers, except four of them, agreed that it can be useful for making some difficult and abstract topics visual and dynamic. Moreover, at the end of the workshop, whether they are favor of integrating graphing calculator into lessons or not, all of the teachers admire the graphical and symbolical potential of the technology of graphing calculators (2005, p.158).
After reviewing some related questionnaires such as Fleener's (1995, p.484-485) Attitude Instrument for Mathematics and Applied Technology (AIM-AT) Survey questionnaire and after examining Questionnaires (Cohen, Manion, & Morrison, 2007, p.317-324); a questionnaire was developed (Appendix A). It consists of 28 items; 27 of them are with a four point scale such that 1= strongly disagree, 2= disagree, 3= agree, 4= strongly agree. These are focused on the attitudes and experience of teachers about using graphing calculators and effects of GCs on students and classroom dynamics. An introductory item providing background information to find out how many courses they have taught with GC was also inserted to the questionnaire. There are 4 types of questions and the categories are:
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Category 1: Beliefs about appropriate use of GCs
Items: 5-10, 15-17, 27
Category 2: Experience with use of GCs
Items: Introductory item, 19-22
Category 3: Beliefs about effects of using GC in classrooms
Items: 3, 4, 11-14, 18, 23-26
Category 4: Teaching philosophy
Items: 1, 2
In this research project, in order to guide the research questions, the survey was conducted on 8 mathematics student-teachers who had experience by doing internship in some of the Turkey's most important colleges during their two-year teacher education program at Bilkent University. All of the teachers had the same level of knowledge about TI graphing calculators as a result of one-term course of technology in the first year of the program. In addition to the curriculum and the educational philosophy of the schools that internships done, teachers' personal attitudes toward graphing calculators, classroom dynamics and curriculum affected their integration into the classes that they taught and by this research methodology it is aimed to reach the perspectives of mathematics teachers with varied career experiences in classrooms toward using graphing calculator.
Data was collected immediately after the teachers completed their internships by sending them the links of the questionnaires (http://www.surveymonkey.com/s/PQXTG6S, http://www.surveymonkey.com/s/RH2CXMF,http://www.surveymonkey.com/s/RHCXQQH)prepared on the internet site, Survey Monkey via e-mail and the responses were collected again on Survey Monkey.
While the fact that they were approximately at the same level of knowledge about graphing calculator had a positive effect on the survey, the number of the participants was the most important limitation of the study. Since it was conducted on only 8 teachers, it was impossible to generalize it to all country. The other limitation was the fact that the participants had been motivated to integrate technology in mathematics lessons during their education and this might influence the objectivity of the responses.
Results and discussions are organized by the categories of the items below and the consensus items were defined by over 70% agreement or disagreement responses on the survey item.
Category 1: Beliefs about appropriate use of GCs
There was consensus on several items of this cognitive category. There was 100% agreement that if graphing calculator is used, more interesting problems can be dealt with during lessons (item 16) and 87.5% agreement that
maths is easier if a GC is used to solve a problem (item 5)
GCs can be used in teaching calculus (item 8)
Students should be allowed to use calculators after they have mastered the concept or procedure (item 17)
Also, there were consensus agreements that
GCs can be used in algebra topics (item 7)
GCs are useful for teaching geometry (item 9)
On the other hand, there were 100% disagreements that GCs should be used on homework (item 15) and when students work with calculators, they don't need to show their work on paper (item 27).
Category 2: Experience with use of GCs
The teachers agreed that they have used graphing calculators in their classrooms before (item 20). Beside this, 62.5% of the teachers responded that they have taught 1-10 lessons, 25% of them taught 11-30 lessons and only one of them stated that she did not teach any lessons with graphing calculators.
Also, there were a consensus agreement that they know ways of how they can integrate GCs into lessons effectively (item 22). However, 62.5% of them indicated that they were not proficient at using GCs (item 21). In addition to that, there was a consensus disagreement that they felt confused while using GCs (item 19).
Category 3: Beliefs about effects of using GC in classrooms
In this category, there were consensuses on almost all of the items. There were 100% agreements on four items:
GCs make mathematics fun (item 3).
GCs increase motivations of students (item 4).
It is helpful for visual learners (item 23).
It allows students to discover the experimental nature of mathematics (item 25).
The other consensus agreements were that:
GCs help students visualize the knowledge (item 11).
It allows much student-centered lesson plans (item 14).
I can gain time by using GC (item 18).
The consensus disagreements were that using GC makes teacher less effective (item 12) and it does not have an effect on developing logical-mathematical intelligence. Also, there was not a consensus on the items about how it affects students' basic computational (item 13) and estimation skills (item 26).
Category 4: Teaching philosophy
In this category, all of the teachers agreed that teaching mathematics means allowing students to explore problems to discover patterns and make generalizations (item 2) while there was a consensus agreement on teaching mathematics is mostly showing the way of memorizing a set of facts and rules (item 1).
The data showed that most of the respondents were non-rule-based and similar to Chang's results (2000, p.87), it showed that most rule-based teachers agreed that teaching mathematics also means allowing students to explore problems to discover patterns and make generalizations, however non-rule-based teachers strongly disagreed that it is showing the way of memorizing a set of facts and rules. This result is apparently seen in the graph below:
On the other hand, it was seen that philosophy of teaching mathematics had not affect the use of GCs such that 87.5% of the respondents used it in their lessons. However, it is also seen that it can affect the ways of its integration to lessons, i.e. classroom dynamics, and in which topics of mathematics curriculum such as graphing, calculus, algebra or geometry. Moreover, the type of curriculum (National Curriculum, IGCSE, IB or AP) of the schools where the respondents taught their lessons was a possible effect on whether to use it since only 25% of them worked with National Curriculum. The results showed that graphing calculators were integrated with curriculum as extension tools for topics because all of the respondents agreed that students should be allowed to use calculators after they have mastered the concept or procedure Also, it is notable that all respondents, both rule-based and non-rule-based teachers thought that GCs make mathematics fun, increase students' motivations and lead more student-centered lessons.
Lastly, it can be said that self-confidence about proficiency at using GC is also another important effect on integrating GCs into lessons and the graph shows self-confidence of the respondents about using GC below.
Significance of the research
Teachers are the most effective factor on developing such curriculum or classroom dynamics that integrate technology into lessons and by this way, they are the most important means of guiding students for creativity, critical thinking and continuously developing technology in Turkey. At this point, integrating graphing calculators into mathematics lessons is an important issue for connecting these two and teachers' perspectives about advantages and disadvantages of GCs, their experiences with it, their beliefs about its effects on classroom dynamics are some points to be discussed in order to provide effective use of graphing calculators.
A further research with a wider sample of teachers that includes different range of experienced teachers from different schools in order to make some more reliable and valid generalizations according to the results.
In addition to that, some findings need to be justified. Especially, observations lessons of teachers with GCs about some specific topics can be useful for discussing how teachers' philosophies of teaching mathematics affect the ways of integrating calculators.
Also, a further research should be done on students and school administrators to investigate their perspectives about graphing calculators.