The Use of Information and Communication Technology in Teaching Mathematics - Term Paper Example

 The Use of Information and Communication Technology in Teaching Mathematics In the UK National Curriculum, Mathematics is one of the core subjects at all key stages. This personal rationale for Mathematics in the curriculum examines what Mathematics is, its importance and what it involves, and the role of pedagogy in teaching the subject. The writer, himself a newly appointed teacher of Mathematics considers the usefulness of social constructivism in expressing his own personal stance, and the scope for using ICT. This includes a discussion of the advantages and disadvantages of using computers in Mathematics. The purpose throughout is to reflect on the subject’s meaning and significance, and to relate some research in the context of the requirements of the UK National Curriculum for Mathematics and present day problems and needs. This is then used to justify the writer’s position on an appropriate teaching methodology. Mathematics is a pure language - the language of science. It is simple but unique in that it is able "to provide precise expression for every thought or concept that can be formulated in its terms" (Adler, 1972). Yet, at the same time, it also has artistic qualities. Thus, Bertrand Russell (1959) regarded it as possessing not only truth but also a supreme beauty while comparing it to sculpture. It involves the study of numbers or quantities, shapes, space, logic, patterns, relationships, functions, proportions, analogies, quantitative models, etc. This makes it a highly significant, fundamental and creative subject. However, in regards to value or relevance, it has traditionally been underestimated, as expressed famously by the British Mathematician apologist Godfrey Harold Hardy (Ferris, 1991: 431). This is a perception owing to its abstractive nature. Actually, Mathematics per se has this perception but its usefulness is evident when it provides the basic tools for understanding other subjects and coping in various situations. This point is stressed in the description of Mathematics as a subject in the National Curriculum (QCDA, 2010): “Mathematical thinking is important for all members of a modern society as a habit of mind for its use in the workplace, business and finance; and for personal decision-making. Mathematics is fundamental to national prosperity in providing tools for understanding science, engineering, technology and economics. It is essential in public decision-making and for participation in the knowledge economy. Mathematics equips pupils with uniquely powerful ways to describe, analyse and change the world.” Today, the situation is somewhat different with the advent of computer technology to assist us. It also depends to a great extent on how Mathematics is taught. The pedagogy can make the subject as dull as it can make it fascinating for students. As a teacher writing from experience, this element of fun is useful in making the subject stimulating, but more important is making it relevant as well. As discussed further on, using ICT makes resources more visually appealing though it does not necessarily support the learning unless made to do so. In other words, the outside world should be brought into the classroom by making the subject relate to everyday reality. This is not easy in terms of mathematical concepts but mathematical ideas and skills can be related to everyday contexts (Haggarty, 2002: 77). Moreover, the essential qualities should not be lost sight of either as it develops the tools for making sense of the world and being precise. To this end, an overall prescriptive method of teaching works best but with scope for some flexibility. In terms of the learning process then, it is essential that students grasp the essence of the language of Mathematics. For a basic level of understanding, they should be able to manipulate the quantities and shapes using standard procedures in ways that make them able to relate to the world around them effectively. As a simple example, this means being able to carry out the four operations on numbers such that they are able to work out things like total cost, unit cost and change when shopping. However, this barely satisfies the more inquisitive souls in the classroom who want to appreciate the subject at a deeper level and its aesthetic beauty. The key to this is going beyond giving practice in applying logical procedures to helping students grasp the fundamental patterns and relationships. Social constructivism has some usefulness in this regard. This theory is contrasted with behaviourism is which development is seen as arising from specific forms of learning with the child as a passive learner. Constructivism in general is founded on Piaget’s theory of learning as an active process, “where new information is accommodated into previously understood meanings or mental images” (Chambers, 2008: 101). Vygotsky was a proponent of providing a social context for learning to take place in. This approach can apply equally to Mathematics as it can to other subjects. Currently, the writer is encouraging discussions (though this does not always prove to be successful unless guided), and is experimenting with providing opportunities for self-discovery. The purpose is to facilitate greater social interaction so that students can make better sense of the world around them. Incidentally, this also raises philosophical questions concerned with the epistemology of Mathematics. Mathematics as providing an objective truth or being absolute is challenged by the view of Mathematics as being “open to multiple interpretations” (Ernest, 1998: 4). However, this is not a serious dichotomy as it seems. The writer's preferred prescriptive approach is necessary to ensure that certain essentials are covered while the social dimension provides the opportunity for knowing more. Social constructivism is having a powerful effect on the "aims, content, teaching approaches, implicit values, and assessment of the mathematics curriculum, and above all else, the beliefs and practices of the mathematics teacher" (Ernest, 1992). It also facilitates the sharing of ideas among students as they work in collaboration. This aspect is discussed in detail in the ‘Mathematics Matters’ report published by the National Centre for Excellence in the Teaching of Mathematics after consulting over 150 Maths teachers from all over the UK (NCETM, 2008). For real learning to take place, ultimately it is essential that the student construct his or her own framework for understanding and applying Mathematics. Nothing is more pleasurable for a teacher of Mathematics than when seeing their students truly fascinated by the subject; when they grasp concepts and solve problems for the first time, when they discover more elegant solutions by themselves, notice underlying connections and relationships, and so on. Some of these points are also mentioned under ‘Importance of Mathematics at key stage 4’ (QCDA, 2010b). Considering the scope for using ICT in the teaching of Mathematics, we shall focus exclusively on computers. These are especially useful in two areas: (1) in performing tedious and complex calculations, and (2) in generating and visualizing complex models. They are also useful as tools for teaching Mathematics in interactive and stimulating ways. When computers are heavily involved in the instruction process, it is known as Computer Assisted Instruction (CAI) or Computer Assisted Learning (CAL). From the social constructivist perspective, computers alter the way we do mathematics (Smith, 1998). As regards generating graphics and models, computers have been used as an aid to teaching Mathematics since the beginning when computer technology had graphical capabilities. However, their use has increased as the technology has improved over time with respect to speed and graphical processing power. Computers have a distinct advantage in this case over manual drawings (as long as they are used appropriately). For example, ICT tools can generate graphics and graphical models much more quickly and accurately. They can also be manipulated in ways that are not easy to do by hand without redrawing. This is useful, for example in seeing the effects of changing some parameter values on a graph. The time savings can also allow teachers to concentrate on other aspects of the Mathematics curriculum. A study by Goodson-Epsy et al. (2007) showed that it also stimulated teachers when 3D computer graphics helped a class to gain valuable perspectives in geometry. The effectiveness of computers in terms of improving students’ learning in general has been shown in several studies. For example, a computer based instructional method successfully supported collaborative learning in primary education to help students acquire self-regulated problem solving skills in Mathematics (Lazakidou & Retalis, 2007). Actually, using computers tends to make students more motivated to learn. They are especially helpful therefore for assisting weaker and slower working students (Stone, 2007: 14). They have been proven to improve numeracy skills in such children (Rasanen et al., 2009), and students with learning disabilities after modifying certain interface design features (Seo & Woo, 2010). Computers help to make them more involved by being in an active learning environment (Janilionis & Valantinas, 2008), which supports constructive learning. Not all studies have produced completely positive results however. One study with variable results showed that a CAL program was “effective in improving [students’] comprehension of the concept of multiplication and the meaning and properties of multiplication for students who have lower prior knowledge of multiplication, but it does not significantly improve the development of multiplication-related computation skills” (Chang et al., 2008). Moreover, the use of ICT is demanding for teachers, as it requires them to be skilled in its use. Another practical downside is that it actually takes longer for some tasks, for example to write mathematical expressions as compared to writing by hand. However, once the expressions are written into computer readable form, they can be processed in a variety of ways. Technology is also costly, so it is not always easy to make computer resources available to students (NCES, 2009). However, all these factors need to be compared against the potential benefits. Nonetheless, ICT is a promising tool in the teaching of Mathematics, but as stressed earlier, only as long as it is used appropriately. Burrell’s (2009) identification of five qualities can ensure that this appropriateness is met. A successful integration of computer technology depends on (1) accuracy, (2) reasoning, (3) representation, (4) communication, and (5) connections. Thus overall, as ICT Delegates at the Asian Technology Conference in Mathematics (ATCM, 2007) concluded, Maths teachers should equip their students with tools for visualizing abstractness using good reasoning, examples and graphs. Similarly, in the U.S. the National Council of Teachers of Mathematics (NCTM, 2004) view technology as essential in Mathematics education because it influences what is taught and enhances students’ learning. In the U.K. National Curriculum, the use of ICT is an integral part of the curriculum for Mathematics in recognition of its potential, so that students can “become familiar with a range of resources” (QCDA, 2010c). Thus, the writer considers ICT to be useful but only as a complementary tool to support the overall pedagogy. This stance is supported by a review conducted by Slavin & Lake (2008) of 87 studies on effective programs in elementary mathematics. They compared CAI with mathematics curricula and instructional process programs. The effects of CAI were found to be generally moderate, and support for the effects of various textbooks had limited evidence. “The strongest positive effects were found for instructional process approaches such as forms of cooperative learning, classroom management and motivation programs, and supplemental tutoring programs.” They concluded that adopting a variety of teaching practices had greater potential than relying mainly on either curriculum or technology. The utilization of social strategies and adopting technology appropriately need to be guided in an overall instructional framework. The writer himself is personally guided by an advanced skills teacher, and another teacher as a mentor. The thrust of the teaching strategy should be (1) ensuring that essential mathematical concepts are understood and essential skills are gained, (2) providing opportunities for self-discovery and collaboration, and (3) taking advantage of computer technology in areas where it can prove useful. The first relies on a prescriptive approach, the second relies on social constructivism, and the third relies on making effective use of ICT by integrating it appropriately to support the curriculum. The latter two have already been discussed in detail. The need for ensuring standards must also be stressed especially given that there is a widespread belief of declining standards in Mathematics in the UK. For example, the ‘Making Mathematics Count’ report (Smith, 2004) noted the problem of shortages of specialist mathematics teachers, “the failure of the current curriculum … to meet the needs of many learners and to satisfy the requirements and expectations of employers and higher education institutions … [and] the lack of resources, infrastructure and a sustained continuing professional development culture to support and nurture all teachers of mathematics.” According to a British government publication (Great Britain, 2009), the Primary National Strategy has contributed to some improvements over the years at primary level, “but weaknesses persist in vital areas such as the use and application of mathematics to real-life situations and the assessment of pupil’s progress”. Ultimately, it is the student that needs to form the right concepts and acquire the right skills, but it is the pedagogy and teaching quality that they have to rely on. As Vygotsky saw it, the teacher plays a central role by providing the scaffolding for pupils to construct their learning (Chambers, 2008: 102). The aforementioned report also mentioned “pupils rating a good and enthusiastic teacher as the greatest influence in the enjoyment of mathematics”. As a teacher of Mathematics therefore, the writer endeavours to strike a good balance between teaching the essential concepts and skills to maintain high standards, permitting social interaction to foster the necessary deeper understanding and making the subject relate to the outside world, and using ICT to enhance the process of learning and make the subject fascinating to them. The aim will be to make students learn the pure aspects of the language while also appreciate its relevance and supreme beauty. References Adler, Alfred. 1972. Mathematics and creativity. The New Yorker. In Ferris, Timothy (Ed.). 1991. The world treasury of Physics, Astronomy and Mathematics. Little, Brown and Company. 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Mathematics Performance in Primary Schools: Getting the Best Results; Twenty-third Report of Session 2008-09; Report, Together with Formal Minutes, Oral and Written Evidence. The Stationery Office. Haggarty, Linda. 2002. Teaching mathematics in secondary schools: a reader. Routledge. Janilionis, Vytautas & Valantinas, Jonas. 2008. An active learning approach to teaching mathematics at Kaunas University of Technology. Proceedings of the IMA SEFI Conference 2008. http://sefi.htw-aalen.de/Seminars/Loughborough2008/mee2008/pages/proceedings.html [Accessed 21 May 2010]. Lazakidou, Georgia & Retalis, Symeon. 2007. Using computer supported collaborative learning strategies for helping students acquire self-regulated problem-solving skills in mathematics. Computers & Education, Vol. 54, Issue 1, pp. 3-13. NCES. 2009. Calculators and Computers. U.S. Departmnet of Education. Washington, D.C.: National Center for Education Statistics. http://nces.ed.gov/pubs92/web/92060.asp [Accessed 21 May, 2010]. NCETM. 2008. The NCETM publishes Mathematics Matters final report. National Centre for Excellence in the Teaching of Mathematics. https://www.ncetm.org.uk/resources/12491 [Accessed 21 May 2010]. NCTM. 2004. Overview: Principles for School Mathematics. Principles and Standards for School Mathematics. http://standards.nctm.org/document/chapter2 [Accessed 21 May, 2010]. QCDA. 2010. Mathematics key stage 4. http://curriculum.qcda.gov.uk/key-stages-3-and-4/subjects/key-stage-4/mathematics/index.aspx [Accessed 22 May 2010]. QCDA. 2010b. Importance of Mathematics key stage 4. http://curriculum.qcda.gov.uk/key-stages-3-and-4/subjects/key-stage-4/mathematics/programme-of-study/index.aspx?tab=1 [Accessed 21 May 2010]. QCDA. 2010c. 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