Integrating ICT in Teaching and Learning Mathematics

Integrating ICT in Teaching and education mathInvestigate and discuss the exercise of ICT in dogma and acquirement math. look the usance of MAPLE.Illustrate and discuss1) Competence with the main features of a area of ICTICT in acquireing and learning math is a requirement of the field of study course of instruction and computer simulations tramp now place mathematics in a objective life context. 1There are a number of sea captain computer-based environments available to support this process. Some of these include dynamic geometry environments, graph-plotting piece of grounds, statistics and data belongings packages and computer- algebra packages.Graphing estimators stick knocked out(p) be use upd to teach the beginning of Algebra. Similarly poke calculators are convenient and quick to access as well as being relatively inex framesive today and is a useful numeric as welll.With the graphing calculator it is possible to determine that every classroom could b e moody into a computer lab and every student could own his or her own inexpensive personal computer with built-in mathematics software program 2The searchers Arnold and Aus identified three generations of graphing calculators scientific calculators with large viewing windows, e.g. The T1-82, those which were to a greater extent respective(a) with a range of numeral functions akin the Casio 98JOG and those with CAS and dynamic geometry like the TI-92. several(prenominal) discussions can be had around the implementation of calculators in mathematics learn and learning and the subject continues to spark debate. Although the resolution of a hand held calculator is not comparable with that of a computer screen there is no need to alter the setting of the classroom or have to foregather access to a number of computers to use it for learning. With regard to computational skills and amiable arithmetic again calculators come up for criticism although there is a definite argument to be had that suggests calculators do not compromise the act of staple numeral skills, as long as those skills are positive first in a conventional environment using pen and root word based calculations. 3ICT can assist with turning algebraic symbols into in writing(p) representations and vice versa. exploitation spreadsheets for algebra can encourage the use of letters to be interpreted as symbols and spreadsheet symbols can be used to solve mathematical difficultys4. Spreadsheets can be utilized to introduce students to a range of mathematical ideas and as a more(prenominal) generic mathematical tool. Recent look for also go forths evidence that young people are beginning to use spreadsheets on their own home computers. 5Dynamic geometry can be used to teach transformation geometry as it can for establishing properties of circles, functions and graphs. un indwelling level curriculum mathematics skills and the application of IT can be linked intrinsically by course of some of the following examples.The pupils dexterity to develop skills of mathematical modeling through and through the exploration, interpretation and explanation of data can be enhanced by using the appropriate brilliantal representations for displaying breeding from a data-set, by experimenting with forms of equations in producing graphs which are good fits for data plots and using motion sensors to produce distance-time graphs. software package can be applied in the context of learning active shapes, space and links with Algebra which automates geometric constructions, carries out specific geometric transformations and performs operations on co-ordinates or is able to incur loci.Finally by enter a formula in algebraic notation to generate determine and match a given set of numbers, this can support the Secondary level skill to explore, describe and condone patterns and relationships in sequences and tables of numbers. 6There are many reasons why mathematics teachers are r eluctant to integrate ICT into teach in the classroom. Many of the computer-based environments are complicated and teachers need to learn themselves how to use these tools effectively for doing mathematics. Although newly qualifying teachers have to pass a basic ICT test as part of their training, it is still difficult for teachers to know where to start, peculiarly some of the older generation of mathematics teachers. In the practical awareness access to computers is not al looks possible for the hit of every nestling being able to learn at the same time and sub-groups and individuals whitethorn have to be established in order to take it in turns to use a single computer in the classroom which can be time consuming and logistically difficult.However computers and calculators can be considered to provide six major opportunities for students learning mathematicsLearning from feedback the computer can provide fast and reliable feedback which is non-judgmental and impartial. This can build students confidence and serve them construct their own ideas.Observing patterns The speed of computers and calculators alters students to provide many examples when exploring mathematical problems.Seeing connections The computer enables formulae, tables and numbers and graphs to be linked easily. The result of comprehend one representation and changes in the other helps pupils to understand the connections in the midst of themworks with dynamic images Students can use computers to manipulate diagrams and encourages them to visualise the geometry.Exploring data Computers enable students to work with real data which can be represented in a variety of ways. This supports its interpretation and analysis.Teaching the computer When students design an algorithmic rule to make a computer achieve a specific task, they are urged to express their commands literally and in a correct order.72) Demonstrate the ability to explore maths and solve maths problems using MAPLE in-d epth.MAPLE can be defined as a positive computer algebra software package which uses simple commands to perform complex operations and enables like by like analysis similar to using a pen and paper. It also allows pupils to c formerlyntrate on on the underlying mathematical principles. 8In Darlene Wus Understanding of compression she uses a number of experiments to determine the benefits of MAPLE on a series of students. She adheres to the flightiness that most traditional algebraic features can be delegated to a computer. In particular using MAPLE most problems can be resolved and retrieve this should be riled out for the benefit of all students studying mathematics. The problem below was assigned to a group of students in a research environmentGraph f(x) = ln(sin(x)* romaine(x)) andg(x) = ln(sin(x)) + ln(cos(x)). What is the relationship between the graphs? Does itcontradict the property ln(x*y) = ln(x) + ln(y)?By using the graphs of these two functions together with the grap hs of sin(x) andcos(x), the students investigated the properties of sin, cos, and lnand show their answers in writing.Students used Maple to draw the two graphs easily, but they lookedentirely different. This led the researchers to wander whether this contradictedln(x*y) = ln(x) + ln(y)? And if so how would students explain it?The experiment needed to be repeated several times, recalling the definitions and properties of ln, sin and cos and concluded that the students assumed the two graphs looked different, whereas they are identical as long as ln(sin(x)cos(x)) and ln(sin(x))+ln(cos(x)) are defined.Wus paper concludes that it is necessary to train students to use mathematical methods effectively not just for the purposes of their job but for the real world and that software programmes that help in this process are fundamental to their learning. However as a number of contradictions and problems emerged with equations through using MAPLE not only does Wu concede that students may be come confused and panic if they cannot attribute the math problem to themselves or the math problem itself. She also notes that when teaching calculus it is important to consider whether such technology is still too overwhelming as well as students becoming dependent on its solutions, rather than working them out traditionally. 9In proportion to this notion other paper with MAPLE as its core area of study is Fitz-Gerald and Healeys enlighten the mathematics curriculum with MAPLE. This discusses the implementation of MAPLE to the undergraduate Mathematics curriculum in a large University in Australia. The overall consensus was that in applying MAPLE, traditional topics that were once unpopular with students were now being approached in a much more understanding and en thuslyiastic way. This experiment demonstrates the advantages of being able to encourage Mathematics by way of helpful software across new audiences who strength not have been inspired previously to study in this area.103. find out the ways in which a particular ICT package or fine art calculator can be used within a learning environment and the advantages/disadvantages of each in enabling effective maths learning.In Horton et als The graphing calculator as an aid to teaching algebra the paper points out that calculators have become popular in the classroom for the benefit of convenience and speed. What the researchers also determined was that tutorials on the Casio FX2.0 and FX 2.0 PLUS models actually change manipulative skills. Students beginning a college algebra course following the tutorial scored significantly higher on a test which involved solving analogue equations and in addition do suggestions for the tutorial also contributing to an value in attitudes.11It is interesting to consider their benefits for something other than the obvious assumptions to be made about graphics calculators. In absolute contrast to all sensed theories Graphic Calculators In The Classroom Student s Viewpoints presents the results of a piece of research carried out amongst low achieving eleventh grade pupils in Portugal. This revealed that curt improvement was gained from introducing graphic calculators to mathematics lessons as the pupils considered the impact of their teacher their teaching style and reputation to be of more educational value to them than the calculator, which improved very little in terms of their academic improvement where mathematics was concerned.12another(prenominal) mayhap more important everyday negative aspect of graphic calculators is their cellular comprehension of games and other non-educative devises such as phonebooks and personal organizers which can detract pupils international from the learning process in the classroom. In addition, the potential for students to store information and consequently cheat during examinations when they are allowed to take calculators in with them in a test environment. The other argument when weighing up som e of the differences between hand-held devices and computer programmes is that a calculator can accompany a student into an examination, whereas a computer cannot. They are flexible and exploiter- friendly as well as being able to be powered by solar energy which is of course far more beneficial to the environment.Another advantage is the diminishing cost of calculators. They can be easily purchased anywhere at a relatively small price in comparison with a computer which It has been suggested recently render(s) the use of graphics calculators much more attractive to schools than computers13Interestingly in his research Spreadsheets, graphics calculators andmathematics education, Barry Kisane provides a suggestion for combining programmes into graphics calculators in order to maximize their potential, thus making them less of a calculator and more of a computer. And notes that The inclusion of these essentialfeatures on graphics calculators seems to extend the range of influence of thespreadsheet as a useful device for mathematics education in second-string schools, and is deserving of attention to exploit it appropriately.14 substantively perhaps the way forward with graphics calculators is to then modify and technologically enhance them that so that they can take on many of the characteristics of the computer whilst not having the capacity to store information that might prove potentially incriminatory to a student in the examination room.BibliographyBishop, A.J, Clements, M.A (2003) Second International enchiridion of Mathematics facts of life SpringerCowan, P (2006) Teaching Mathematics A enchiridion for patriarchal and Secondary School Teachers RoutledgeDa Ponte Canavarro (1993) Graphic Calculators In The Classroom Students Viewpoints Centro de Investigao em Educao da Faculdade de CinciasFitz-Gerald Healey illuminating the mathematics curriculum with MAPLE, Essay taken from Maple V Mathematics and Its applications programme Proceedings of the Map le spend Workshop and Symposium, Rensselaer Polytechnic Institute, Troy, New York, August 9-13, 1994By Robert J. Lopez BirkhuserHorton, R. M., Storm, J., Leonard, W.H. (2004). The graphing calculator as an aid to teaching algebra, Contemporary Issues in engineering science and Teacher development, 4(2), 152 -162.Johnston-Wilder, S, Pimm, D (2005) Teaching Secondary Mathematics with ICT McGraw-Hill InternationalKemp, M, Kissane, B Bradley, J (1995) Assessment and the graphics calculator in Anne Richards (ed.) FLAIR beat links and integrating resources, Darwin, The Australian Association of Mathematics Teachers, 235-241.(Also available at http//wwwstaff.murdoch.edu.au/kissane/papers/aamt95.pdfKissane, B (2007) Spreadsheets, graphics calculators andmathematics education, In K. Milton, H. Reeves T. Spencer (eds) Mathematics Essential for learning, essential for life. 21st Biennial Conference of the Australian Association of Mathematics Teachers (pp 331-339), Hobart Australian Ass ociation of Mathematics Teachers.Rielly, C (2004) The exertion of Computer Algebra Software in the Teaching ofEngineering Mathematics, Higher Education AcademySutherland, R (2004) Teaching for Learning Mathematics McGraw-Hill InternationalWu, D, Some Examples on Using Maple to Increase Students. Understandingof Calculus, Sourced from http//archives.math.utk.edu/ICTCM/VOL08/C052/paper.pdf, Date accessed,Footnotes1 Cowan,P (2006) Teaching Mathematics A Handbook for Primary and Secondary School Teachers Routledge2 Bishop,A.J, Clements,M.A (2003) Second International Handbook of Mathematics Education Springer3 Bishop,A.J, Clements,M.A (2003) Second International Handbook of Mathematics Education Springer4 Sutherland,R (2004) Teaching for Learning Mathematics McGraw-Hill International5 Sutherland,R (2004) Teaching for Learning Mathematics McGraw-Hill International6Cowan,P (2006) Teaching Mathematics A Handbook for Primary and Secondary School Teachers Routledge7 Johnston-Wilder, S, Pimm ,D (2005) Teaching Secondary Mathematics with ICT McGraw-Hill International8 Rielly,C (2004) The Application of Computer Algebra Software in the Teaching ofEngineering Mathematics, Higher Education Academy9 (Sourced from http//archives.math.utk.edu/ICTCM/VOL08/C052/paper.pdf, Date accessed, 30/11/0810 Fitz-Gerald Healey Enlightening the mathematics curriculum with MAPLE, Essay taken from Maple V Mathematics and Its Application Proceedings of the Maple Summer Workshop and Symposium, Rensselaer Polytechnic Institute, Troy, New York, August 9-13, 1994By Robert J. Lopez Birkhuser11 Horton, R. M., Storm, J., Leonard, W.H. (2004). The graphing calculator as an aid to teaching algebra, Contemporary Issues in Technology and Teacher Education, 4(2), 152 -162.12 Da Ponte Canavarro (1993) Graphic Calculators In The Classroom Students Viewpoints Centro de Investigao em Educao da Faculdade de Cincias13 Kemp, M, Kissane,B Bradley,J (1995) Assessment and the graphics calculator in AnneRichards (ed.) FLAIR forge links and integrating resources, Darwin, The Australian Association ofMathematics Teachers, 235-241.(Also available at http//wwwstaff.murdoch.edu.au/kissane/papers/aamt95.pdf14 Kissane,B (2007) Spreadsheets, graphics calculators andmathematics education, In K. Milton, H. Reeves T. Spencer (eds) Mathematics Essential for learning, essential for life. 21st Biennial Conference of the Australian Association of Mathematics Teachers (pp 331-339), Hobart Australian Association of Mathematics Teachers.