3 Examples,The Greek Financial Crisis, The Greek financial crisis was the main topic of an extended mathematical modelling and. problem solving task given to Year 12 students In the first part of the assignment the students. were asked to consider the implications of imposing higher taxes and austerity measures on the. Greek population If these measures were to be taken how could this be done fairly Should some. pay more than others To investigate this further the students were asked to calculate the Gini. Coefficient for Greece from given data the Gini Coefficient being a measure of the inequality in. the distribution of income in a country which is calculated from the Lorenz Curve Students were. given the MATLAB code for a program which approximates the area under a curve using the. trapezoidal method Figure1 below shows a screenshot of the graph produced by this MATLAB. Figure 1 Screenshot of the execution of the supplied program. Student A adapted the given code and used it to calculate the Gini coefficient She then. produced a graph displaying the Lorenz curve The result of this is shown in Figure 2 below. Figure 2 Calculating the Gini coefficient and displaying the Lorenz Curve. In the second part of the assignment each individual student was given the Gini Coefficient for a. different country In this part the students had to construct a Lorenz Curve for the country from the. Gini Coefficient They then had to add more code to the MATLAB program so that it would. display the Lorenz Curve for Greece along with the Lorenz Curve for the country they were given. Figure 3 below shows how Student B displayed the Lorenz Curves for Greece along with the. country they were allocated and then demonstrated understanding of the context by making. interpretive comments on the differences between the curves. Figure 3 Displaying two countries Lorenz Curves,Rip currents. In this example the students investigated the effect of rip currents on the safety of swimmers in. the sea Swimming in the sea may seem similar to swimming in a pool but there are hidden. dangers In particular rip currents can put the lives of swimmers at risk What may appear to be a. calm inviting area between the breaking waves may in reality be very dangerous The students were. each given data on the performance of a strong swimmer over a five second time period when the. swimmer was already in full flow An example set of data is shown below in Figure 4. Figure 4 Data showing performance of strong swimmer. The students were also given code see Figure 5 below to assist them in producing a smoothed. curve illustrating the change in speed of the swimmer The way that this code worked was. explained to the students in a video tutorial The students then had to perform calculations to. determine the variations in the speed of the swimmer over the time period They were then required. to adapt the given code to suit these measurements and add commands so as to produce a fully. labelled animated graph showing the changing speed of the swimmer They were then able to judge. how the swimmer would be affected by a powerful rip current How would this particular swimmer. cope if faced by a rip current traveling at 2 m s, x 0 217 0 45 0 751 0 984 1 201 1 435 1 702 1 952 2 219. 2 569 2 686 2 953 3 253 3 437 3 687 3 937 4 204 4 471 4 688. y 1 567 1 33 1 395 1 545 1 521 1 368 1 723 1 4 1 236 1 543 1 368 1 348 1 7. 1 413 1 2 1 64 1 461 1 273 1 613 1 314,xx linspace 0 217 5 1000. plot xx csapi x y xx x y Linewidth 3,for i 1 numel x. plot x i y i r Linewidth 4, Figure 5 Code for illustrating changing speed of swimmer. Figure 6 below contains an explanation by Student C of how she adapted the given code. Figure 6 Student C explains how she adapted the given code. Bringing the astronaut home, In another assignment students were challenged to rescue an astronaut who had become. stranded on Mars In the part that involved the use of MATLAB the students had to assist the. astronaut in making a tricky manoeuvre to reach his rocket Student D explains his method in. Figure 7 below,Figure 7 Finding a safe path for the astronaut. 4 Discussion, The examples above provide excerpts from the students responses to the assessment tasks. These excerpts relate to the parts of the tasks where coding with MATLAB was involved They. give some insight into the nature of the tasks The tasks may be viewed in full from the academia. section of the MathWorks website 5 Full details of all the tasks are available from this location. along with the associated MATLAB scripts helpful video tutorials and indicative responses A. description of the journey taken by Ormiston College in introducing MATLAB into mathematics. assessment is also available from the company section of the MathWorks website 6. Providing students with tasks that require the use of mathematical modelling for real world. problem solving is consistent with the aims of curricula across the world The OECD mathematics. framework 8 for example states that, an individual s capacity to identify and understand the role that mathematics plays in the. world to make well founded judgments and to use and engage with mathematics in ways that. meet the needs of that individual s life as a constructive concerned and reflective citizen. In the United States the Common Core State Standards Initiative USA 2 states that. Mathematically proficient students can apply the mathematics they know to solve. problems arising in everyday life society and the workplace p 1. In Australia the Australian Curriculum Assessment and Reporting Authority 1 make the. assertion that, mathematics aims to ensure that students are confident creative users and communicators. of mathematics able to investigate represent and interpret situations in their personal and. work lives and as active citizens p 1, The tasks not only connect with priorities associated with mathematical modelling and problem. solving they also relate to the meaningful use of technology in mathematics education Moreover. the combination of mathematical modelling and technology brings opportunities to integrate with. other disciplines Of great significance in this regard is that mathematical modelling aided by the. use of technology can be viewed as a bridge to STEM education 4. Finally the interaction between real world problem solving and the use of technology brings. together generic skills that are beneficial for students of the 21st century In the 21st Century. Learning Design framework 3 teachers are encouraged to set extended tasks that promote Real. World Problem Solving and Innovation A student centered use of technology is also encouraged in. this framework whereby the students are actively engaged in the use of technology rather than. being passive recipients The excerpts from the students responses illustrate the students. engagement with the problem solving and their active use of technology. This paper has described how the use of MATLAB was introduced into high school. mathematics assessment tasks A collection of assessment tasks was produced as a result of a. productive partnership between Ormiston College in Queensland Australia and the manufacturers. of MATLAB The tasks were designed to develop students skills in mathematical modelling for. real world problem solving and at the same time give them experience in using technology that. they are likely to use in STEM related courses after school Actual excerpts from students. responses were reproduced which illustrated how the students dealt with incorporating the use of. this technology into the mathematical modelling and problem solving tasks Giving students. experience with both mathematical modelling for real world problem solving and the use of. technology was shown to be consistent with current international perspectives in education. References, 1 ACARA 2016 Australian Curriculum Mathematics Aims Retrieved 4 July 2016 from. http www australiancurriculum edu au mathematics aims. 2 CCSSI 2012 Mathematics Standards for Mathematical Practice Model with. Mathematics Retrieved 4 July 2016 from,http www corestandards org Math Practice MP4. 3 ITL research 2012 21st Century Learning Design Retrieved 4 July 2016 from. http www itlresearch com itl leap21, 4 Kertil M Gurel C 2016 Mathematical modeling A bridge to STEM education. International Journal of Education in Mathematics Science and Technology 4 1 44 55. DOI 10 18404 ijemst 95761, Retrieved 4 July 2016 from http ijemst com issues 4 1 5 Kertil Gurel pdf. 5 MathWorks 2016 MathWorks Academia,Retrieved 4 July 2016 from. http au mathworks com academia, 6 MathWorks 2016 Ormiston College Secondary School Students Learn Math and. Programming with MATLAB,Retrieved 15 August 2016 from. https au mathworks com company user stories ormiston college secondary school. students learn math and programming with matlab html by product. 7 MATLAB Matrix Laboratory software available from. http au mathworks com products matlab, 8 OECD 2009 Mathematics framework In OECD PISA 2009 assessment framework Key. competencies in reading mathematics and science pp 83 123 Paris OECD Publishing.

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