Assignment 01: ICT/ Calculator Task Prepared by Khundakar Nilufar Sharmin S3493820 (Extension for submission was approved) Why ICT in classrooms? For last four decades Educational policymakers have been giving high emphasis on providing access to ICT in education as a part of renewal and reform for education policies. It was first put up to international level in the Millennium Development Goals Target 8.F (United Nations, 2000; 2012). Proper application of ICT can play a pivotal role by making benefits available of new technologies, broadening access, eliminating exclusions and improving quality of education (The Dakar Framework for Action, UNESCO, 2000). World Summit on the Information Society (WSIS) declared very clear commitment by the world leaders to achieve an inclusive information society in the convention held at 2005. Two of the targets to be achieved by 2015 were 1. Connecting all primary and secondary schools to ICT (pre-condition) (Target: 2) 2. Adapting all primary and secondary school curricula to meet the challenges of the information society (Target: 7) Setting up the targets actually set up the benchmark for the countries to implement applications of ICT in the classrooms. (Partnership on Measuring ICT for Development , 2011). ICT or not ICT that is the question If anyone likes it or not, it is a proven that Asians and people from some parts of Europe are very good at mathematics. Their numeracy skills are higher than average Australian. Asia contains 60% of the world population (UN Population Division, 2014), which exhibits significant economic disparity. In many developing countries in Asia, computer provision tends to be 1
Transcript
Assignment 01: ICT/ Calculator Task
Prepared byKhundakar Nilufar SharminS3493820(Extension for submission was approved)
Why ICT in classrooms?
For last four decades Educational policymakers have beengiving high emphasis on providing access to ICT ineducation as a part of renewal and reform for educationpolicies. It was first put up to international level inthe Millennium Development Goals Target 8.F (UnitedNations, 2000; 2012). Proper application of ICT can playa pivotal role by making benefits available of newtechnologies, broadening access, eliminating exclusionsand improving quality of education (The Dakar Framework forAction, UNESCO, 2000).
World Summit on the Information Society (WSIS) declaredvery clear commitment by the world leaders to achieve aninclusive information society in the convention held at2005. Two of the targets to be achieved by 2015 were
1. Connecting all primary and secondary schools to ICT(pre-condition) (Target: 2)
2. Adapting all primary and secondary school curriculato meet the challenges of the information society(Target: 7)
Setting up the targets actually set up the benchmark forthe countries to implement applications of ICT in theclassrooms. (Partnership on Measuring ICT for Development, 2011).
ICT or not ICT that is the question
If anyone likes it or not, it is a proven that Asians andpeople from some parts of Europe are very good atmathematics. Their numeracy skills are higher thanaverage Australian. Asia contains 60% of the worldpopulation (UN Population Division, 2014), which exhibitssignificant economic disparity. In many developingcountries in Asia, computer provision tends to be
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concentrated in laboratories (World Bank, 2010; ADB,2012) (Appendix A). However broader sense of ICT not onlyincludes computers, projectors CAS and scientificcalculators but also radios and televisions. Still Asiansare showing significant understanding in numeracy andliteracy skills. While planning for ICT applications inthe classrooms, policy makers and teachers should keep inmind that only ICT is not going to invite a radicalchange in the classroom environment. It only can boost uplearning if it is used properly as an aid to teaching toengage students more effectively.
I have migrated to Australia from an under developedcountry of Asia and having a challenging socio economicbackground. I was one of the four females in my time inthe university who studied Engineering and only one whoworked for power generation. I am still the only one frommy organisation who was awarded Aus-AID scholarship toUniversity of Melbourne. When I first went to thatuniversity, I felt like an alien because there were somany technologies around that I had absolutely no ideaabout. I worked 11 years as a Professional Engineer and Ihave never seen a CAS calculator before I stated studyingin this course. However, it doesn’t mean that I couldn’tcope with the technologies or couldn’t learn theapplications. I ended up my masters with 70% marks.Similarly, in my teaching placement round, I havedemonstrated to my students how to use CAS in effectiveway. So my argument is, if a person has goodunderstanding and sufficient knowledge on mathematics,she can learn ICT quicker than others and can effectivelyuse it. Otherwise it will create a “Technology asmaster” situation. However, basic understanding andproper knowledge of mathematics will lead to shift from“Technology as a servant” to “ Technology as a partner”and eventually “Technology as extension to self” bycontinuous practice and application (Goos et al. 2000, p317).
Pedagogical values- articulation and coherence
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A study on teachers’ perception on using calculators,projectors and other ICT tools in classrooms has foundsignificant improvement on students as these toolsdeveloping their mathematical skills and concepts, enablethem to give geometric interpretations to algebraicconcept and visualise them. So students develop deeperunderstanding on concepts. Students who would ordinarilybe frustrated or bored by the tedious manipulations oreven students suffering from dyscalculia can makeprogress. Students get immediate feedback fromcalculators or computer programs and learn throughexploring and discovering. This process increases theirconfidence and challenges their abilities. It is proventhat use of ICT in mathematics classrooms is encouragingstudents to be involved and engaged more with the topics.Innovative environment can enhance the learning ineffective way. However in a study in Thailand, someteachers found that the complexity of ICT usages has anegative effect on the students until they gainsufficient usage skills. Use of technologies can also bea source of frustration for students with special needsas small screen, colour, lights and sounds can causefrustration for some of them.
By using ICT applications properly, students get a chanceto think and explore a problem. That enhances peerlearning and shy students can also participate. That alsoprovides them opportunity to challenge their abilitieswithout waiting for the teachers to explain the contentsto them. With efficient combination of teachers and ICTthe barrier of introducing difficult mathematical ideasin algorithm and logic become easier that have beenbeyond the teach of traditional non- tech curricula,which provides a chance to the classrooms to work as acommunity of mathematical practice (Goos et al. 2000, p305).
Use of ICT provides more times to teachers to developdeeper conceptual understanding and problem solvingskills (Demana & Waits, 1998). Teachers can present thelesson more meaningful way to the students withappropriate application and demonstration of ICT, which
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would be more appealing to the students. Appropriateapplication of ICT empowers teachers to teach difficulttopics and free them from the role of sole provider ofinformation to facilitator of learning in discussion andcollaborative exploration ( Heid, Sheets, & Matras,1990). At the same time, ICT provides wide options forthe teachers to modify tasks and present it moreeffectively to the students with special needs. Use ofICT changes the dynamics of the classrooms leading to aless teacher centred and more investigative environment(Simonsen & Dick, 1997). By using “Technology asextension of self” teachers would be able to developtheir expertise as an integral part of mathematicalrepertoire (Goos et al. 2000, p 312). However, researchhad shown that teachers had to achieve a sensible balancein use of traditional pen-paper techniques and ICTapplications to achieve maximum benefit (Demana & Waits,1998).
Evolution of ICT didn’t lead the human kind to use it apartner from the beginning (Appendix B). It took usdecades to move hand in hand with ICT and make it as apart of our lives. Mathematics classrooms can no longerignore the ongoing demand of using ICT. To do so, at thebeginning “Technology as Master” (In some cases, forstudents with special needs) or “Technology as Servant”(For new learners or to introduce new ideas) can be agood start. Maths teachers have no option but to leadthese to “Technology as partner” relationship for thestudents to prepare them meet the ongoing need of keepingtrack with new technologies.
Impact of CAS in VCE/Advanced mathematics
CAS is a powerful tool for the students to makecalculation easier and also to have better understandingin mathematics. To get maximum benefit of CAS, studentsmust have strong numeracy knowledge. If students don’thave clear understanding of terminating decimals andrecurring decimals, and the impact of decimals incalculations, CAS will not provide actual answer. Forprobability related problems, students need to produce
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their answers in fractional form. By using CAS, they cando it. However, they need to develop the understandingwhich answers should be in fractional form and whichshould be in decimal form and why. Another hurdle forthe students is to set the calculator in the right mode(degree, radian, gradient etc.) according to thecalculation needs.
For the function, x = t2 – 5t + 4 ; to find the distancetravelled in the first two seconds, if CAS is used togenerate the graph, it’ll show the negative curve aswell. But for this particular problem, time cannot benegative; hence there cannot be any negative portion ofthe graph. But the graphical representation in CAS willprovide the students idea of actual representation of theproblem and also they’ll be able to identify the turningpoint. Another point is, in CAS, there is no option toput “t” as an input and the students need to use anotherletter instead in calculation. So there is a high chanceof mistake if students do not have clear idea about thecalculation. If a student uses x instead of t in CAS, inthis particular case, there is a high chance that she getconfused with x’s in both the sides of the equation. It’sa common mistake by the students that they forget to usethe right letter instead of “x” that they used on CASwhen they write the calculation and answer.
For VCE, if the question is worth 2 marks, I have seen mymentor in the placement school suggesting the students touse CAS and write down the answer. But if the questionweights more marks, students are marked according totheir workout. However, detailed workouts provide anoption of partial marking for the teachers, whereasdirect use of CAS leads to two options: correct orincorrect.
For problems where students need to construct equationsfrom word problems, they need to have literacy andnumeracy skill to interpret the words to translate intoequations. CAS calculators can never do these. Similarly,substituting values from one equation to another is not
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possible by CAS. Same way, without having clearunderstanding of conversion table, students will never beable to get right answer using CAS when they need unitconversions. In measurement, to use scale factor onsimilarity problems, students will never be able to getthe right answer using CAS unless the idea of scalefactor and enlarging and reducing are clearly understood.They need to understand the logic behind the idea why wemultiply by scale factor to enlarge and divide to reduce.Sometimes we need to leave the calculation in fractionform to carry it on to the next step and find the findanswer in the decimal form to get more accurate answers.
In maximum and minimum problems, CAS is never going toindicate local maximums and minimums. Another drawback ofCAS is, in graphical representation, as the screen is notsquare but a rectangle, the scale of x-axis is differentthan y-axis and that makes the graphs look different.
Example problem for CAS
I have chosen this particular problem of Yr. 12 Mathsmethods to demonstrate the skill and understandingrequired by the students to use CAS properly (AppendixC). For this problem, no calculation is possible unlessstudents use their prior understanding and knowledge ofalternate angles and find angle ABC, which is, in thiscase 60. By using geometry function of the CAScalculators, students can input 80m, 150 m and includingangle 60 to create the triangle and can get the values ofx and angle BAC. However, without clear understanding ofcorresponding and alternate angles, they would never beable to understand that the value of angle BAC is not theanswer for the bearing and to get the correct answer theyneed to add 70 with 87.80 to find the true bearing.
Calculator is an amazing supplementary learning resourcethat simplifies the problems and provides betterunderstanding. However, the use of calculators requiresknowledge and understanding of numeracy and practice.Students need to know how and when to use it properly toget maximum benefit out of it. I would like to say, we
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have to be smarter than the calculators to use themproperly and establish “Technology as a partner”relationship.
Conclusion
Human brain develops through practicing numeracy andliteracy. When we work on a mathematical problem andlearn something, a bridge is been created between partsof brain and it last forever holding that information.When we memorise times tables, bridges are made likewiseleading us remembering the numbers and the logics oftimes tables. But if a person do not learn them by heartand uses calculators to replace the times tables, hisbrain will not develop the numeracy skills required.Teachers need to be very careful to make the judgementwhere and how to use ICT and balance the application withother teaching techniques and use it as “Technology as apartner” (Goos et al. 2000, p 312)
References
1. The Dakar Framework for Action, UNESCO, 20002. Partnership on Measuring ICT for Development, 20113. UN Population Division, 20144. World Bank, 2010; ADB, 20125. Recsam, S. (2013). Mathematics Teacher’s Perception On The Use
Of Graphing Calculator, Retrieved from (http://epatcm.any2any.us/EP/EP2001/ATCMP209/fullpaper.pdf )
6. Evolution of Technology, Retrieved from ( http://www.graphs.net/wp-content/uploads/2012/07/evolution-of-technology-timeline.jpg )
7. Goos et al. 20008. Demana & Waits. (1998). Retrieved from
