Curriculum Theories In Relation To The Research Education Essay Example

child (intrapsychological). This applies to voluntary attention, logical memory, and the formation of concepts.

All the higher maps originate as existent relationships between persons.
More Knowing Other ( MKO ) The MKO refers to anyone who has a better apprehension or a individual who possesses a higher ability degree than the scholar with regard to a peculiar undertaking. The instructor is the usual MKO in a schoolroom context.
Zone of Proximal Development ( ZPD ) The Zone of Proximal Development or ZPD is defined as the distance between a pupil 's ability to execute a undertaking under grownup counsel and / or with peer coaction and the pupil 's ability to work out the job independently i.e. the scope of accomplishment that can be developed with big counsel or peer coaction exceeds what can be attained entirely.

According to Vygotsky, learning takes place within the zone of proximal development (ZPD), and the complete development of this zone relies on extensive social interaction. Vygotsky posited that humans utilize tools that emerge from their culture, such as language and writing, to mediate their social environments. Initially, children acquire these tools primarily as means of fulfilling social functions and communicating their needs. Vygotsky believed that the internalization of these tools results in heightened cognitive abilities.

Vygotsky's Social Development Theory offers numerous advantages when implemented. One major benefit is its ability to enhance learning environments where students are actively engaged in the learning process. By incorporating ICT based activities, classroom instruction is focused on student-centered learning. The teacher's role in this context is to collaborate with students to facilitate learning. The teacher's presence is primarily to provide assistance when needed. As a result,

learning becomes a collaborative experience for both students and teacher.

Dewey 's Learning By Making

According to John Dewey, students learn through "directed life" by engaging in workshop-style projects that combine learning with hands-on activities and practical relevance. Dewey rejected the traditional method of rote learning that was prevalent during his time. His ideas form the basis of the constructivist curriculum, which emphasizes meaningful and relevant activities that enable students to apply the concepts they are learning.

The key to creating effective learning experiences is through hands-on activities. The theory of experiential learning, developed by David A. Kolb, builds upon the previous work of John Dewey and Kurt Levin. According to Kolb, learning is the process of transforming experience into knowledge. His theory outlines four stages of learning that are based on a four-stage learning cycle.

Kolb's theory provides significant benefits for researchers, as it offers an understanding of individuals' diverse learning styles and a description of the experiential learning cycle that applies universally. The four-stage learning cycle and learning styles can be summarized in a two-by-two matrix, as demonstrated below.

Absorbing

The four categories explaining learning styles can be summarized as follows.

Diverging (Feeling and Watching)

This indicates that diverging learners thrive by observing and gathering a wide range of information from various perspectives. These learners prefer to watch rather than actively participate. They also prefer collaborative group work.

Assimilating (Thinking and Watching) – Learners in this category benefit from receiving logical theories visually rather than engaging in practical activities.

Converging (Thinking and Doing) – Those who belong to this group learn best when they are presented with practical applications of concepts and theories. They prefer tasks that allow

them to apply their knowledge to find solutions.

Accommodating (Feeling and Doing) – Obligers, or individuals in this learning style, learn better through hands-on experiences. This style is particularly useful in roles that involve actions and initiatives.

Students in this learning style prefer to work in teams to complete tasks.

Students' Background Knowledge

Students who want to pursue Advanced Level Mathematics usually need to have obtained at least a Credit 6 in Mathematics Syllabus 'D', regardless of whether they have taken Additional Mathematics or not in their Ordinary Level Cambridge Examinations. In my opinion, this minimum requirement only gives students the impression that Advanced Level Mathematics is easy, which is not true at all. The fundamental Trigonometry knowledge that students should have learned during their Form 5 level mainly involves the Trigonometric Rules for a right-angled triangle, i.e.

SOH CAH TOA.Evidence of Low Achievement on TrigonometryHaving taught Advanced Level Mathematics since 2004, I have been able to identify and observe students' learning difficulties in subjects such as Functions, Trigonometry, Series Expansion, Vectors, etc. In Chapter 1, I discuss the problems encountered by students in learning Trigonometry. The Advanced Level Examination Reports by Cambridge (2007 - present) have provided evidence and indications that students have struggled to answer questions correctly in Trigonometry.

The Cambridge testers provided general feedback on the performance of students in Trigonometry. The feedback focused mainly on three areas: solving trigonometric equations, graph sketching, and identifying trigonometric identities. Regarding the task of solving trigonometric equations, I chose a question that most students struggled with, for example: Solve the equationfor.

Report:

While the majority of candidates correctly substituted equatedwith, many weaker candidates mistakenly substituted it withor

with. A surprising number mistakenly addedto instead of subtracting it, and a significant minority of all candidates only considered angles in the first quarter-circle. In terms of graph sketching, most students were unable to accurately plot the given equations or answer sub-questions like: Sketch, on the same diagram, the graphs ofandfor.

Report:
Despite numerous curves being excessively consecutive or being parabolic, most campaigners received some Marks for this section and most obtained the correct end-points for both curves. Many campaigners unnecessarily drew accurate graphs and wasted a significant amount of time. Regarding proving trigonometric identities, I have chosen a question that the majority of students have difficulties with. Prove the identity.

Report: Despite efforts, many campaigners encountered difficulty in finding a common denominator or numerator for the fractions on the left side of the identity. It is important for campaigners to realize that simply expressing the solution without showing intermediate steps is insufficient.

Why Use ICT? Drawing from my experience teaching Advanced Level Mathematics, I have utilized traditional teaching methods such as writing on a chalkboard and lecturing. Although my students consistently achieved above-average results over time, they failed to meet my expectations. Students frequently express comprehension during lessons but encounter challenges when attempting to apply their understanding onto paper.

Using readily available educational packages and the easy access to online resources, educators have created activities to improve students' understanding of mathematical concepts. These activities involve the use of graphing software, allowing students to visualize and comprehend concepts through graphical representations. Incorporating technology resources can provide teachers with additional support in the form of sequencing and scaffolding (John and Catherine, 2009). According to John and Catherine, scaffolding refers to

providing temporary support to students by supplying them with learning materials that enable them to achieve a desired performance.

Scaffolding will gradually decrease and students will be able to work independently once a sequenced pattern is implemented. Additionally, the use of ICT will increase the teachers' readiness to provide assistance when students can complete assignments independently. Studies have shown the benefits of using ICT in learning. One study found success in using multimedia approaches such as charting software or PowerPoint presentations to enhance students' understanding (Ferrer, 2002). Selinger (2004) stated that the quality of instruction can be improved with the use of multimedia, as it helps illustrate and explain difficult concepts that traditional teaching methods cannot achieve.

According to Arellano (2002), she discovered in her survey that Information Communications Technology (ICT) is frequently utilized for literacy. It is crucial for educators to move beyond solely using ICT for education to guarantee that all students possess equal ICT abilities. Moreover, instructors should strive towards cultivating a learning culture that empowers students. Arellano also highlighted the fact that employing ICT for investigations and explorations can transition students from passive recipients of knowledge into active processors of knowledge. This approach will also assist students in developing reflective thinking skills, such as critical and creative thinking, when comprehending their lessons.

By implementing ICT into education, students can gain a sense of ownership over their own knowledge. However, despite the numerous advantages of using ICT, Leong (2008) warns of the potential danger of teachers transitioning from traditional teaching methods to interactive drill-and-practice, which could become monotonous and unproductive. Research on Bruneian teachers' perceptions of using ICT to teach also supports this statement. The

lack of confidence in using ICT seemed to be a major barrier to its implementation in the classroom (Chong ; Wong, 2004). Sallimah (2005) discovered that 27% of the variation in willingness to implement ICT into classroom instruction was primarily influenced by the teachers' attitudes, such as preferences and enjoyment.

In her research, she also mentioned that the implementation of ICT was directly influenced by factors such as perceived behavioral control, including the ability to use ICT, success, and effectiveness. According to Susilawati and Kyeleve (2005), who interviewed Mathematics instructors in Brunei, most schools have two or three ICT research labs with LCD units and interactive whiteboards. However, many instructors reported a lack of specific software for teaching Mathematics, logistical issues with using the ICT labs, and a shortage of preparation time and knowledge.

ICT and Mathematics Education

Information Communications Technology (ICT) tools also provide learning opportunities for students to develop the conceptual foundation needed to better understand Trigonometry. In a study conducted by researchers in Pakistan (Safdar, Yousuf, Parveen, and Behlol, 2011) titled "Effectiveness of Information and Communication Technology (ICT) in Teaching Mathematics at Secondary Level," the researchers aimed to determine the effectiveness of ICT compared to traditional teaching methods on students' academic achievements in Mathematics at the secondary level in Pakistan.

The researchers aimed to analyze the effectiveness of ICT compared to traditional methods on the academic achievements of students in Mathematics at the secondary level in both public and private sectors. A sample of 120 students in class IX studying mathematics was taken from two selected schools, one from the public sector and one from the private sector. Both schools had the same mathematics curriculum and

computer lab facilities. The researchers concluded that students from private schools performed better than students from public schools when ICT was used as a teaching strategy due to the availability of technological facilities and greater dedication during the lessons. The researchers have found the answers to their research questions regarding the effectiveness of ICT on students' academic achievements compared to traditional teaching methods. The results showed the effectiveness of ICT in teaching Mathematics in general, but it depended on variables such as the availability of technologies at school and home, as well as the dedication of students during the lessons.

There have not been any studies conducted in Brunei on the use of ICT in learning Sine and Cosine Graphs at the Advanced Level or in Trigonometry as a whole. However, a similar survey was conducted by Y. T. Leong in Sarawak, Malaysia.

The research conducted by Leong focused on the "Effective and Affectional Teaching of Trigonometric Graphs Using ICT and Acting." The research aimed to evaluate various effective solutions for addressing problems in teaching trigonometric graphs through the use of acting and different ICT programs. It also aimed to investigate the effectiveness of these solutions in improving students' competence and interest in sketching trigonometric graphs in Additional Mathematics. The research included Form 5 Additional Mathematics students as the sample, and data was collected through pre-tests, post-tests, and questionnaires given to the students. The research employed software such as Microsoft Excel, Microsoft Power-Point, Geometer Sketchpad, and Hot-potatoes. Through analyzing the questionnaire given to the students, the researcher highlighted the benefits of integrating ICT into education, including making teaching and learning more effective and

student-centered, as well as making learning fun. Ultimately, the researcher concluded that implementing ICT in the classroom/computer room would enhance the delivery process for both students and teachers.

In her survey titled "Associating Geometry and Algebra: A Multiple-case Study of Upper Secondary Mathematics Teachers' Concepts and Practices of Geogebra in England and Taiwan," Lu (2008) examined the perspectives and practices of Geogebra among mathematics teachers in England and Taiwan. Geogebra is a dynamic geometry package. Lu interviewed two instructors from both countries and found that they considered Geogebra to be a versatile educational tool. They used Geogebra for various purposes, including preparing learning materials, conducting assessments, delivering presentations, exploring geographic concepts, and more.

• Teachers from Taiwan primarily viewed Geogebra as an entertaining tool for presentations. They also saw it as a means to engage students in their learning.
• Lu's data classified the instructors into three types:

Unskilled Teachers

These instructors were not familiar with technology and only used Geogebra to create lesson plans and presentations.

Technology-skilled Teachers - These instructors are proficient in using technology and are willing to share their knowledge on the Geogebra software.

Geogebra Advanced-skilled Teachers - These teachers are considered experts who have created interactive lessons that encourage students to explore and experiment with the provided activities. However, some teachers mentioned that Geogebra may not be suitable for all subjects, particularly those that require 3D visualization. Other preferred software options included Archimedes 3D, Sketchup, or Autograph.

Summary - The majority of students struggle with Trigonometry at an advanced level. They are expected to understand the concepts and apply them in various

aspects such as graphing, solving trigonometric equations, and proving identities.

Using mathematical packages and online resources that are easily accessible can enhance the quality of teaching and learning in classrooms, ultimately improving students' achievements.