Teachers attitudes affecting integration of graphing calculators Essay Example

learning and motivation. This difference among stakeholders affects instructors' attitudes towards incorporating calculators into their teaching practices in mathematics. Using calculators allows for a wide range of activities such as group or individual work and discovery-based learning, which directly relates to improving teaching practices in mathematics. In Trabzon, Turkey, Celik (2005) conducted a study involving 14 mathematics teachers with no prior knowledge of graphing calculators to examine the impact of training on these devices on teachers' attitudes towards integrating them into their lessons. After attending a training course on using TI-92 graphing calculators in geometry classes, the teachers were interviewed to determine if there were any changes in their perspectives on graphing calculators.
The significance of understanding teachers' attitudes and beliefs regarding the advantages and disadvantages of using graphing calculators, as well as their perception of how these calculators interact with the curriculum, is emphasized in this study (Literature Review). According to Celik's 2005 study, most instructors believed that using calculators could harm students' procedural abilities. However, only four instructors did not change their positions after the course. Conversely, some instructors believed that calculators could benefit student engagement and promote effective and deep learning through inquiry (p.146).

In a similar vein, Chang conducted extensive research in 2000 on mathematics instructors from 243 high schools in New Zealand. The study found that trained and untrained respondents had opposing attitudes towards using calculators in secondary mathematics instruction. Trained respondents consistently showed a higher percentage of positive agreement towards statements about technology's role in mathematics instruction. This suggests that adequate teacher training is crucial for incorporating this technology into secondary mathematics instruction (p.92).

Yoder noted in 2000 that instructors who attended

workshops on using graphical calculators (GC) believed they could utilize them for discovery activities; however, there were concerns about students relying too heavily on calculators and experiencing a decline in their basic math skills (p.29).In addition to geometry classes, other studies have explored the integration of calculators in algebra or calculus classes. A study conducted in Ohio involving 48 algebra instructors found that they regularly incorporated charting calculators into various activities such as in-class exercises, homework, quizzes, and tests (Yoder, 2000, p.i). This implies that charting calculators have become an essential part of the learning process in algebra.

Another area of research focused on examining instructors' beliefs about charting calculators and how these beliefs influenced their decision to incorporate them into their lessons. Elaine Simmt's study involved observing six mathematics instructors in Canada during lessons on quadratic functions and interviewing them about their reasons for using charting calculators, philosophies of math instruction, and the impact of using charting calculators on their beliefs about math. The results showed that instructors had varying philosophies regarding questioning techniques and lecture notes when incorporating activities with charting calculators. Despite having the same technological resources and curricular constraints, each instructor developed their own mathematics curriculum based on personal beliefs about mathematics and mathematics instruction (Simmt, 1997, p.269).Reys (2000, p.2) supports Simmt's findings by stating that instructors' beliefs about mathematics and their role as a mathematics teacher play a significant role in their willingness to use calculators. Chang conducted a study that revealed contrasting responses to technology between "rule-based" and "non-rule-based" instructors. According to his research, "rule-based" instructors perceive learning mathematics as primarily memorizing rules, while "non-rule-based" instructors believe in problem exploration

for discovering patterns and making generalizations (Chang, 2000, p.50). The results indicate that instructors with a more rule-based perspective on mathematics are more likely to hold the view that graphing calculators do not enhance instruction and may even hinder it (Chang, 2000, p.86-87). However, Yoder's research in Ohio contradicted Chang's views on the impact of teachers' perspectives on learning algebra and using graphing calculators (Yoder, 2000). It was discovered that incorporating graphing calculators into algebra lessons had no significant effect on participants' scores for the complexity of learning algebra, regardless of whether teachers believed in a "rule-based" or "non-rule-based" approach (p.27). This suggests that solely attributing the outcome to teachers' perspectives is not valid.At first, most instructors believed that graphing calculators caused students to rely on prior knowledge and memorization due to the emphasis of computational skills in math education. This belief was reinforced by the math curriculum and university entrance exams. However, after attending a workshop (excluding four individuals), the majority of instructors agreed that graphing calculators could be beneficial for visually representing complex and abstract concepts in a dynamic way. The examination of various questionnaires, such as Fleener's Attitude Instrument for Mathematics and Applied Technology (AIM-AT) Survey questionnaire (1995, p.484-485), as well as questionnaires by Cohen, Manion & Morrison (2007,p.317-324), led to the creation of a new questionnaire called Appendix A. This questionnaire consists of 28 items, with 27 using a four-point scale to measure agreement levels. These items primarily focus on instructors' attitudes and experiences when using graphing calculators (GCs) and how they impact students and classroom dynamics. Additionally, the introductory item in the questionnaire gathers information about the number of classes

taught by instructors who use GCs.The text describes a questionnaire divided into four categories: Category 1 focuses on beliefs about appropriate usage of GCs (items 5-10, 15-17, and 27), Category 2 explores experience with GC usage (introductory point and items 19-22), Category 3 examines beliefs about the effects of GC use in classrooms (items 3,4,11-14,18,and23-26), and Category 4 relates to teaching philosophy (items1and2). The study included eight participants who interned at prestigious colleges in Turkey during their two-year teacher training program at Bilkent University. All instructors had equal knowledge about TI charting reckoners from taking a one-term engineering class in their first year. The incorporation of charting reckoners in teaching was influenced by instructors' personal attitudes towards these devices and classroom dynamics and curriculum preferences. The main objective was to gain insights into mathematics instructors' perspectives on using charting reckoners in classrooms based on their career experiences. Data collection occurred through online questionnaires sent via email after instructors completed their internships. However, it is important to note that the study had a limited number of participants (only eight instructors), which restricts the generalizability of the findings.The study participants were motivated to incorporate engineering into mathematics lessons, which may affect their responses. The data analysis categorized the consequences and treatments mentioned by the participants. Consensus points were defined as having over 70% agreement or disagreement responses.

In Category 1: Beliefs about appropriate usage of GCs, there was consensus on several points. It was unanimously understood that using a graphing calculator allows for dealing with more interesting problems during lessons (point 16). Additionally, there was an 87.5% understanding that math becomes easier when a graphing calculator is used

to solve a problem (point 5).

The text discusses various opinions and agreements regarding the usage of graphing calculators (GCs) in classrooms. It was agreed that students should be allowed to use calculators once they have mastered the concept or process. There was also consensus that GCs can be used in algebra subjects and are useful for learning geometry. However, there was unanimous disagreement regarding the use of GCs for homework assignments. Furthermore, it was agreed upon that when students use calculators, they do not need to show their work on paper.

Moving on to Category 2: Experience with usage of GCs, the instructors confirmed their past use of charting calculators in their classrooms.Among the instructors, 62.5% taught 1-10 lessons with GCs, while 25% taught 11-30 lessons. Only one instructor did not use GCs at all. While there was a general understanding among the instructors about incorporating GCs into their lessons effectively, they also acknowledged that they lacked skill in using them and often felt confused when doing so. Moving on to Category 3: Beliefs about effects of utilizing GC in classrooms, there were agreements on several points. The text emphasizes unanimous agreement on the benefits of using GCs in math education, such as making mathematics fun (item 3), increasing student motivation (item 4), aiding visual learners (point 23), and facilitating exploration of the experimental nature of math (point 25). Other points that had consensus agreement included helping students visualize knowledge (item 11), allowing for student-centered lesson plans (item 14), and saving time (point 18). However, opinions varied regarding the effectiveness of GCs in teaching. Some believed it made teachers less effective and had no impact on

logical-mathematical intelligence development (item12). There was also no consensus on its effect on students' basic computational skills (item13) and assessment abilities(point26). In terms of teaching doctrine, all instructors agreed that learning mathematics involves problem exploration to discover patterns and make generalizations(point2).There was a consensus among respondents that learning mathematics involves memorizing facts and rules (point1). This aligns with Chang's findings (2000, p.87), which showed that most respondents were not rule-based. However, non-rule-based instructors disagreed strongly with the idea that mathematics only entails memorization. The graph below visually represents this disagreement. Interestingly, the teaching doctrine of mathematics did not significantly impact the use of calculators (GCs) as 87.5% of respondents used them in their lessons. However, it can affect how they are integrated into lessons, such as classroom dynamics and specific subjects like graphing, concretion, algebra, or geometry. The usage of calculators in schools may be influenced by the type of curriculum taught (National Curriculum, IGCSE, IB, or AP). Only 25% of respondents worked with the National Curriculum. Charting calculators were used as supplementary tools for subjects within the curriculum. All teachers agreed that students should be allowed to use calculators once they have mastered the concept or process. Both rule-based and non-rule-based instructors believed that calculators make math more enjoyable, increase student motivation, and promote student-centered lessonsThe integration of calculators has increased respondents' confidence in using them, as shown in the graph below. This research highlights the importance of teachers incorporating technology into lessons and developing curricula or classroom dynamics to guide students towards creativity, critical thinking, and continuous technological development in Turkey. Therefore, it is essential to have discussions on the integration of charting

calculators in math lessons. These discussions should include instructors' perspectives on the advantages and disadvantages of using them, their personal experiences with the calculators, and their beliefs about how these tools impact classroom dynamics. The main objective of such discussions is to ensure effective utilization of charting calculators. To achieve more reliable and valid generalizations, further research involving a diverse group of instructors from different schools with varying levels of experience is needed. Additionally, providing justifications for specific findings is important. It would be beneficial to observe lessons conducted by instructors who use graphing calculators for specific subjects and analyze how their teaching philosophies influence the incorporation of these tools. Furthermore, conducting additional research that explores students' and school administrators' viewpoints regarding the use of graphing calculators is recommended.