Introduction
Studying mathematics can seem daunting and boring to many students because of the need to learn and apply theoretical concepts, theorems, and formulas. Nevertheless, most students in the 11th year of study are preparing to take GCSE exams, and the study of mathematics is compulsory for them. For this reason, I have developed a SMART plan that provides additional time and outside classroom support for students to increase their confidence and knowledge, which helps them to pass the exams. This paper will review and critically evaluate the innovative methods and technologies used for the SMART plan’s extra-curricular activities to determine the most relevant ones.
Innovative Teaching Methods for Mathematics
Modern technology and understanding of student needs allow teachers to explore and use various innovative teaching methods. As noted by Thomas, Hong and Oates (2017, p. 110), digital technology has a universally positive effect on the study of mathematics in schools. The first method that should be applied is blending learning that involves the use of traditional teaching resources, such as textbooks, and technologies such as video materials (Rajkumar and Hema, 2016, p. 72; Bhatti et al., 2016). This approach can be used in additional classes, especially in virtual teaching, without difficulty. Another method is flipped classrooms, which can be combined with blending learning. This approach assumes that students study the lesson’s topic at home, for example, by watching video lectures and use the time in class to complete assignments (Rajkumar and Hema, 2016, p. 71). This method allows teachers to cover more complex math problems that students cannot solve on their own at home.
Moreover, since individualised learning is more effective in teaching any knowledge, this method should also be applied to the math club. However, since an individual approach to each student is problematic in groups with limited 1.5 hours classes, the teacher should use computer programs’ assistance. For example, Parikh (2020) notes that using such a program as “Zearn” in math classes provides more personalised learning for students in groups. After explaining or discussing the topic with all students, the teacher can divide the students into groups to explain the concepts in more detail using visualisation to one group, while the rest of the students independently studies the topic and performs tasks selected according to their level. Thus, the teacher can see the progress and needs of each student and provide the necessary assignments to master the topic.
Specific approaches for use in the classroom should be problem and laboratory methods and oral presentation of the topic studied. The first method assumes that children are faced with a problem close to real life and are looking for options for solving it using mathematical methods (Vijayabarathi, Pramila and Sengamalaselvi, 2013, p. 304 ). This approach also refers to authentic learning because the proximity of the problem to real life makes it easier to visualise and helps to understand abstract concepts (Algani, 2019, p. 503).
The laboratory method is also a similar approach but differs in that students can in practice measure and apply mathematics to solve a problem; for example, this approach is most appropriate in geometry (Rajitha, Rathika and Abisha, 2019, p. 346). At the same time, modern technologies have made this method more accessible, for example, using 3D modelling. Another way is to present the topic orally to classmates. This method is most suitable for those students who have strengths in the humanitarian sciences because studying the issue in detail, such as the history of creating the theorem, helps them understand it better (Khongji and Nongbsap, 2013, p.1346). Thus, these methods and approaches can be used at levels to prepare students for exams.
Innovative Technologies
As mentioned in the section above, many of the methods today are technology-related. Online classes save time and protect student health; however, the lecture formats online in many cases prove to be ineffective but appropriate software have positive effects on performance (Ariyanti and Santoso, 2020, p. 18-19). For this reason, technologies such as computer programs, augmented reality and virtual reality can be used in the classroom.
First, modern technology provides many available options for computer programs for the study of mathematics. The simplest are video materials, programs with explanations or tasks with a high level of visualisation. More complex programs can include simple programs for modelling geometric objects, statistics and probability theory (Kopp, 2017). Therefore, since most of today’s students have laptops, tablets and smartphones, they have free access to use them at home or in schools.
A newer but also available technology is augmented reality, which also has significant potential for teaching mathematics. Cai et al. (2019) note that augmented reality technology has already shown itself to be successful in visualising abstract concepts, teaching algebra, geometry and statistics. In addition, these technologies have increased students’ self-efficacy, which has impacted their confidence. Therefore, this technology is suitable for the purposes of the SMART plan.
Virtual reality technologies are also effective in learning mathematics. These technologies allow students to study 3D models, explore their properties and mathematical formulas applicable to them, and visualise abstract concepts (Lei et al., 2018). In addition, students are placed in an environment that reflects the real, which expands the possibilities of the laboratory approach to the study of mathematics dozens of times. Consequently, these technologies can also be applied to implement a SMART plan.
Critical Assessment
Some of the approaches, methods and techniques described above may not be suitable for teaching mathematics to students preparing for exams due to different factors. The main reasons for unsuitability are unavailability, high cost, low efficiency, as well as the inadequacy of training levels that some technologies and digital applications can provide. Consequently, all methods and technologies will be evaluated to select the most appropriate and effective.
The blending teaching method is the most necessary for implementing the plan as technology brings significant benefits to the learning process. Fazal and Brayant (2019, p.60) note that blending learning of mathematics increases assimilation of educational materials and students’ confidence, especially those who are behind academically. At the same time, since for most students technology is an integral part of their life and available for use at home and in the classroom, their application will not be challenging. Flipped learning as a form of blending teaching also shows significant effectiveness. For example, Wei et al. (2020) and Ramakrishnan and Priya (2016) conducted researches in China and the United States, respectively, and in both cases, flipped learning was highly effective. In addition, this approach only requires the teacher to prepare video or text materials for students and reduces the burden of homework, which makes it accessible and convenient.
The strategy of individualised learning with the help of computer programs has several aspects that call into question the need for its application. Firstly, it is the cost and availability of programs developed for the course. Secondly, it is the size of the group of students who will be attending additional classes. If the group is small, then purchasing the program is unnecessary, since the teacher can pay attention to each student. However, if the lessons will be attended by 12 or more students and the program’s cost is low, it is necessary to promote individualised learning.
The development of the modern computer technology market demonstrates that various training programs are also appropriate and practical. Many educational applications can be found for free and at a low cost while creating and watching videos is affordable for everyone. In addition, augmented reality apps are also widely available and inexpensive, since students only need a smartphone to use them. However, it is necessary to examine the availability and cost of suitable mathematical or simulation programs to select the most useful. For example, GeoGebra 3D Calculator allows users to place geometric shapes in any environment and see them from different sides and also offers formulas and explanations (“GeoGebra,” n.d.). Thus, these technologies are suitable for lessons because of their availability and usefulness.
Although VR technologies are most useful in the study of mathematics, they have such a disadvantage as their relatively high cost. VR technology enhances the learning process as it expands the laboratory’s ability to learn abstract concepts and theorems by placing students in a visualised environment. However, the cost of the sets can be high for some students to purchase for individual use. Therefore, this technology is not suitable for the format of additional training offered by the SMART plan.
Conclusion
Therefore, this review demonstrates that most modern technologies are appropriate and necessary for teaching mathematics. The combination of technology and traditional teaching methods and approximation of mathematical concepts to real life can be used to implement a SMART plan, since they are easy to use. At the same time, technologies such as digital applications and augmented reality will help to apply these approaches more efficiently and at a low cost. However, although virtual reality technology is effective, it cannot be used within the framework of the project because of its price.
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