Key Issues in Mathematics Education - Essay Example

Why do some pupils achieve more than others in Mathematics” “Mathematics is not just a collection of skills; it is a way of thinking. It lies at the core of scientific understanding, and of rational and logical argument” Dr. Colin Sparrow. These days abhorrence for mathematics or ‘mathophobia’ is considered just the same as we complain about harsh weather conditions. A conceptual subject with complex collection of skills has a high credence in terms of gaining a status in society and a better paid career. Mathematics becomes a favourite subject of most students between the ages of five and eleven but after that a two way road begins. Some bear to take maths as a challenge with full determination while others have to accept an on going road to failure (Gates, 2001, p. 7). Students who remain backwards in the field of mathematics are faced by certain issues. Key Issues in Mathematics Education: An issue means something significant that needs to be finalised, an argument that is not settled. ‘Taking an issue’ means disagreement and ‘to issue onwards’ means to illustrate. Among the contemporary issues, Peter Bailey‘s statement is of value to everyone. He proposed that “teachers of mathematics can play a crucial role in making the world a fairer place” (Gates, 2001, p. 10). Individual differences: Different pupils think differently to a same mathematical problem. This creates trouble for teachers in devising the most appropriate method in the best interest of all. Some students do achieve more because of the individual differences in terms of abilities, motivation levels, preferences etc. (Orton, 2004, p. 136). Convergent and divergent thinking: Mostly mathematical calculations are thought to be convergent - having a limit however there are also divergent questions whose answers could be manifold. Hudson (1966) tested the convergent and divergent thinking ability of sixth form students in a research study of individual differences and concluded that students weak at the IQ tests were much better in subjective questions. Most of the students that perform better in mathematics are convergent thinkers, who likes logic, definite solutions etc. They are bound to have mathematics as their favourite subject while divergent thinkers have difficulties (Orton, 2004, p.139). Mathematical Ability: The basis of mathematical ability lies in the inborn inclinations as studied by Krutetskii in 1976: “Mathemetical abilities are not innate but are properties acquired in life that are formed on the basis of certain inclinations… some persons have inborn characteristics in the structure and functional features of their brains which were extremely favourable to the development of mathematical abilities…anyone can become an ordinary mathematician; one must be born an outstandingly talented one” (Orton, 2004, p.142). He further suggested that there are varieties of mathematical minds categorised as analytical, geometric etc. but harmonic minds show true mathematical aptitude (Orton, 2004, p.142). Preferences and attitudes: Generally Maths is considered a subject you cannot humanize. Russel (1938) proposed that most students have the common perception of considering mathematics class as a place of competition. It acts as a motivator for some but for others it could have a negative set back. Some pupils are satisfied by practising mathematical problems while others prefer discussions and often disregard maths as it does not allow their personalities expressed to their fullest. Russell also concluded that at higher stage, opting for mathematics is not a matter of personal liking. Most students study maths because of its usefulness in the professional world (Orton, 2004, p. 142). Developing fears: Holt (1964) provided subjective proof of the strategies students adopt in order to cope with the questions and answer session in maths class. Most students fear being ridiculed in front of their classmates, therefore they get over anxious while answering questions in class. Sometimes teachers unintentionally give such remarks that students feel embarrassing and develop a negative inclination towards the subject (Orton, 2004). Language issues: Sometimes language issues seem to create problems in learning. Anthony Orton has mentioned this phenomenon with the help of an example of his childhood years. When asked in a Maths test: “What is the difference between 47 and 23?” He considered it a difficult and odd one and innocently replied that one of the numbers is bigger than the other. In the next test the same question was inquired and he replied a new answer with confidence that one has a 4 and 7 while other don’t. It is later that he realised ‘difference’ means ‘subtraction’ in mathematical terms (Orton, 2004, p. 156). Students who are under achievers in Maths might have difficulty in memorising mathematical terms correctly. Ethnicity issues: Sometimes students’ ethnicity seats them at a disadvantage. Their cultural background affects their attainment aptitude thus they perform poorly in maths without paying heed to it (Gates, 2001). “In Britain the relative achievements of students from different ethnic groups has been the subject of The Committee of Inquiry into the Education of Children from Ethnic Minority Groups" (Askew & Brown, 2001, pp. 6). A decade later “Gillborn and Gipps (1996) discovered improving levels of attainment among ethnic groups in many areas of the country between the highest and lowest achieving ethnic groups in many Local Education Auhorities, even when differences in qualifications, social class and gender are taken into account, ethnic groups do not enjoy equal chances of success in their applications to enter university"(Askew & Brown, 2001, pp. 6). A report of Ofsted published in 1999 verified that achievements of ethnic groups in minority are improving, but few of them still continue to underachieve. (Askew & Brown, 2001, pp. 6) Ability grouping of students: Another highly debated issue is the ability grouping of students. Setting a target group of learners, teachers often play a biased role by letting others feel dejected (Gates, 2001). Dealing with misconceptions: Curriculum decisions are only possible under the national guidelines provided however there are issues underlying teaching methods that needed to be considered. An individual teacher can have a firm opinion about a principle of teaching mathematics which would be totally different from one of her colleagues e.g. If young children are allowed to use calculators would they ever learn multiplication tables? Similarly some teachers assume mathematics to be a silent activity while others prefer discussions in class. (Orton, 2004) Such misconceptions on part of the educator could yield unfavourable impact on students who are already having difficulty in the subject. The identification of student’s misconceptions and the ability of teacher to cope with them is a major concern for children in junior classes, but they are also equally important in higher standards. In order to deal with these issues Britain developed a variety of curriculums over the years to implement the best one for teaching Mathematics. Researches on development of Numeracy concepts: In United Kingdom, various researches were carried out on Numeracy concept development in children especially in 70s and 80s. Among the most successful works were the “CSMS (Concepts in Secondary Mathematics and science) and APU Assessment of Performance Unit” (Askew & Brown, 2001, pp. 10). Piaget’s findings regarding children concepts of numbers, probabilities and geometry defined two categories of mathematics which were later pronounced ‘procedural’ and ‘conceptual’ knowledge. The late 1970s researchers contributed that procedural knowledge is more prevalent in schools. Most of the mathematics learnt in classrooms is not helpful in the real world. They identified children’s misconceptions about numeracy and helped develop assessments for the guidance of teachers in this regard. But with the passage of time there was scarity in conceptual development researches (Askew & Brown, 2001, pp. 10). Numeracy standards of school leavers in England have always been a mark of criticism as compared to those of developed countries. Individuals were unable to cope with it until Government started to intervene setting a numeracy curriculum with much relativity in the real life context by the recommendations of Cockcroft Inquiry Report published in 1982. This was followed up by “Primary Initiatives in Mathematics Education (PRIME)” which introduced a “Calculator Aware Number curriculum” at primary level, thus substituting using standard written mathematic problem solving methods with a calculator. However due to the clash in strategies of numeracy and education, two revised editions of the national curriculum came immediately afterwards (Askew & Brown, 2001, pp.6). This strategy laid stress on mental calculations and technically combined the prescribed content and teaching schedule. It also helped to construct lesson structures. Although the policy received greater acclaim, restraints of time have often led to roughly planned implementations whose consequences include demoralisation of teachers. Launching new initiatives impatiently, before giving full time to the already existing ones to ripen, have become tiresome for the teachers and educators alike. National Numeracy Strategy (NNS): In recent years, the most prominent developmental change in mathemetics curriculum is the establishment of National Numeracy Strategy (NNS) that constitutes underlying principles and practices in numeracy teaching. Mike Askew examined the basis of current academic essentials and found some of them in international comparative studies of mathematical attainment. In a research study he mentioned that teachers become more apt at teaching numeracy when they are able to guide students in constructing rich interconnecting network of mathematical ideas. Teaching policies involving widespread use of mathematics is more beneficial than its disintegration (Askew & Brown, 2001, pp.53). In September, 1999 the execution of the National Numeracy Strategy started in all primary schools of England. The rationale of the policy is to perk up standards in mathematics. 300 primary schools were chosen as the representative sample of the nation by the Office for Standards in Education (OFSTED). The next year, sample size was further reduced to 200 schools. “Qualifications and Curriculum Authority (QCA)” (HMI 333, 2001, pp.5) constituted an annual testing Programme to offer data on students’ achievement and progress in mathematics in third, fourth and fifth year respectively in all sample schools. It gives an overview of the implemented strategy in England’s primary classes (HMI 333, 2001, pp.5). Earlier ‘numeracy’ was interpreted as the skill to utilize number proficiency and concepts in the present world. With the advent of National Numeracy Strategy, its meaning has further elaborated. “Not only it has laid stress on proficiency at abstract number skills and relations, but have also broaden its horizon to include measurement and data handling so that at least at primary level, there is no clear distinction between numeracy and mathematics” (Askew & Brown, 2001, pp. 10). The National Curriculum for England: It is devised for schools to opt for the best systematized curriculum for mathematics. Generally the programme concerned with math constitutes what students should learn at fundamental stages 1, 2, 3 and 4 and presents the foundation for scheduling ‘schemes of work.’ For devising a curriculum, schools should regard the broad-spectrum teaching practices for insertion, proper use of technology, language and communication applicable throughout the curriculum. The knowledge highlights the salient features of mathematics in which pupils show improvement (Primary curriculum, 2010, para 4). “At key stage 1, teaching should ensure that appropriate connections are made between the sections on number, and shape, space and measures. At key stage 2, teaching should ensure that appropriate connections are made between the sections on number; shape, space and measures; and handling data. At key stages 3 and 4, teaching should ensure that appropriate connections are made between the sections on number and algebra; shape, space and measures; and handling data” (Primary curriculum, 2010, para 6). Role of Computers in teaching Mathematics: “An increasing number of teachers have completed their training in the use of information and communication technology (ICT) and schools have invested substantially in computers, software and accommodation. However, the use of ICT in the daily mathematics lesson is still infrequent. Many schools recognize that the increased use of ICT needs to be one of their priorities for development” (HMI 333, pp.2). Thus by critically evaluating performance of high and low achievers in Mathematics, assessing their achievements in a continuum and elucidating the key issues obscuring the path towards progress, this controversial issue can be eradicated to some extent. Implementing highly advanced curriculum and teacher training programmes will, in turn, lend under-achievers and slow learners a confidence that even they can excel in Mathematics and be the valuable contributors to the society at large. Bibliography: Gates P, -Ed (2001) Issues in Mathematics Teaching, p. 7-10, Routledge  Orton A, (2004) Learning Mathematics 3rd Edtn. Issues, Theory and classroom practice. Pub Continuum  Askew M & Brown M, (2001) Teaching and Learning Primary Numeracy: Policy, Practice and Effectiveness A Review of research Pub. BERA, Retrieved from http://www.bera.ac.uk/files/reviews/numeracyreview.pdf The National Numeracy Strategy: The second year. An evaluation by HMI (HMI 333) Retrieved from:  www.ofsted.gov.uk/Pub. The National Curriculum for England Retrieved from: http://www.nc.uk.net/nc_resources/html/download/bMa.pdf Read More