teaching, learning & technology in the philippines

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Teaching, learning & technology in the Philippines Barry Kissane Murdoch University

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Teaching, learning & technology in the Philippines. Barry Kissane Murdoch University. Overview. Analysis of the significance of technology in mathematics education in the Philippines Complementing the paper in the Proceedings Looking forward … I touch the future, I teach. - PowerPoint PPT Presentation

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Teaching, learning & technology in the PhilippinesBarry KissaneMurdoch UniversityOverviewAnalysis of the significance of technology in mathematics education in the PhilippinesComplementing the paper in the ProceedingsLooking forward I touch the future, I teach.Examples of suitable technologiesCalculatorsGraphics calculators Computer softwareInternet for students and teachersTechnology directions and standards

Barry Kissane MATHTED 20092Mathematics and technologyReal world applications of mathematics frequently use technology these daysSo it seems important that our curricula in schools also reflect technologyWhere this is possibleThe recent deadly storms through the Philippines provide a good, albeit tragic, exampleLets look at the present example MATHTED 20093Typhoon LupitThe Internet provided a powerful picture of the approaching stormThis satellite image was on Monday morningClick image to access website

MATHTED 20094Typhoon images and information from http://www.tropicalstormrisk.com/Forecasting typhoon behaviour A great deal of mathematics is used to predict the likely path:The increasing circles indicate increasing uncertainty of predictionsThe typhoon classification schemeThe measurement of the earthThe satellite positioning systems

a lot of technology was used to make this picture

MATHTED 20095Probabilities and errorsIn the real world, probabilities in models are rarely derived from counting finite eventsObserve also:The probability scaleUnlikely events can happenEvents with very high likelihood may not happenAll predictions of these kinds involve errorsOnly the past is certain

MATHTED 20096How to respond?Mathematics provides good information about the range of possibilities and their likelihoodsUsing statistical analysisUsing the normal distributionUsing previous experience at predictionsBut humans must interpret all that information, here shown four days ago

MATHTED 20097Mathematics, technology and typhoonsAll of this information is accessible to anyone using the Internet, not only expertsIn the next few years, it will be routinely available to many Filipino students and their familiesDoes the school mathematics curriculum provide them with the necessary skills to interpret it and to use it?Is the mathematics curriculum informed by and related to technology?

MATHTED 20098Why is technology important?As the typhoon example suggests, we inhabit a world that is awash with technologyTravelling here on a budget flight, many passengers had their own technology with themSo of course, students ought to be inducted into that world in schoolsBut technology can also make a distinctive contribution to teaching and learning mathematicsBy providing opportunities for learning and teaching that are not otherwise availableLets consider some examples MATHTED 20099Technologies for school mathsCalculatorsScientific calculatorGraphics calculatorComputer softwareGeneric software (eg Microsoft Excel)Mathematical software (eg Tinkerplots, Fathom, GeoGebra, Cabri 3D)Java and Flash appletsThe InternetFor studentsFor teachersMATHTED 200910Why calculators?They are easily portable, and so can be easily shared in a classroom or a school, used in different classes, and even used at home.They are less expensive than computers, especially when all the software needs are taken into account (as calculators contain their own software). As they are potentially more accessible on a wide scale to students than are other forms of technology, curricula can be designed on the assumption that students can access technology.MATHTED 200911 educational argumentsThey can be used in formal examinations, which are of considerable importance in many educational settings. This advantage is mostly a consequence of the preceding reasons..Most of them have been designed, and modified, for the express purpose of school mathematics education, and so are sensitive to the needs and interests of students and teachers.

MATHTED 200912Computation is facilitatedCalculators are helpful for doing computationsWhen the numbers are beyond mental arithmeticWhen many computations are neededWhen mathematical ideas are not yet firmly learnedMATHTED 200913

Computing Philippines populationAccording to the NCSB, the 1980 population of the Philippines was 48 million. The growth rate was about 2.3% per annum over the next 20 years or so.On a graphics calculator, this information can be used symbolically, numerically and graphicallyThe rule of threeNumerical solution of equations is possible

MATHTED 200914

The rule of threeBarry Kissane MATHTED 200915

Symbolic representationGraphical representationNumerical representationSolving equation to find population of 80 millionX refers to number of years after 1980, Y1 is population (millions)Exploration with calculatorsImportantly, graphics calculators provide opportunities for experimentation, not just computation, in many areas, including:GraphsEquationsStatisticsProbabilityCalculusGeometryMATHTED 200916Examples of calculator useThere are many examples of graphics calculator use discussed in papers on my website:http://wwwstaff.murdoch.edu.au/~kissane/epublications.htmThere are also examples of use of scientific calculators on the web: Go to http://edu.casio.com/dl/ and press ENTERAccept the agreementClick on Guest button (or register)Click on ES Standard Calculators Curriculum Paper Activity and then NextDownload activities of your interestThese provide many opportunities to see how exploration with calculators can affect learning.

Barry Kissane MATHTED 200917Technology and the curriculumWhen students have access to technology, the content and balance of the curriculum may be affectedHere are some examples:Negative numbers in primary schoolComplex numbers in secondary schoolExact arithmetic(Numerical) optimisationIntegration techniquesSuch changes are only reasonable when access to the technology is universalMATHTED 200918Computer softwareComputer facilities and access differ and the differences are important:Laboratory (individual)Classroom (shared)Home (individual)Software is of many kinds, including:Bundled (with the computer)Free educational softwareCommercial softwareApplets (run from a browser)

MATHTED 200919SpreadsheetsSpreadsheets have versatile uses in mathematics, although they were not designed for educational purposesThey may be important because they are available, typically as part of a software bundleHelpful for some forms of data analysis, modelling and everyday computationSome have used them powerfully; eg the Centre for Technology and Teacher Education at the University of Virginia has several downloadable examples. Here is one for simulation:

MATHTED 200920TinkerplotsTinkerplots is a commercial program that supports data analysis of various kindsEspecially important for the analysis of student-collected data, a key part of mathematical modellingSorting data is the primal act of analysisLess emphasis on sophisticated quantitative analyses and more emphasis on the story of the dataLets look briefly at an example of BackpacksData were provided with the software

21MATHTED 2009Backpacks

22MATHTED 2009Philippines population dataTinkerplots can be used to analyse data obtained from elsewhereTo illustrate, we will look at the population of the Philippines over the 20th centuryData are from the wonderful GapMinder website Data on personal wealth (GDP per capita) are also included

MATHTED 200923

Philippines population since 1900

Barry Kissane MATHTED 200924Philippines GDP per capitaThe data tell a powerful story of the 20th centuryThe effects of WWII are clearAs are the turbulent times of the 1980s Students can use technology to explore real data

Barry Kissane MATHTED 200925FathomTinkerplots is described as suitable for grades 4-8, but arguably extends beyond both extremitiesFathom (an earlier commercial statistics package from the same developer) is also designed for educational purposes, and has a slightly older focus, including regression and inferential statisticsLets look again at some population data to briefly see some differencesThe data show the Philippines population after World War IINotice how well the least squares concept is demonstratedThe data are close to linear, although clearly curvilinear

26MATHTED 2009Least squares line27MATHTED 2009

Accessing Tinkerplots and FathomFurther information about these two software packages is available on the Key Curriculum websiteEvaluation copies of the software and many examples are available.TinkerplotsFathomFrom the Philippines, these are available from Springer Hong Kong, [email protected] Resources Provider, http://www.123erp.comLearning Interactive, http://www.li.com.sg Barry Kissane MATHTED 200928Student dataData analysis is most powerful when students are addressing problems that matter to themThey can design and undertake their own data collectionThen use Tinkerplots or Fathom to store and analyse their own dataUse of the software does not require high-level ICT skillsIncidentally they will learn important lessons of data editing, dealing with missing cases, entry errors, etc. 29MATHTED 2009GeoGebraThis is an excellent free package that handles many aspects of geometry and algebra, and now (with a spreadsheet) some statistics as wellCan be downloaded or operated onlineOnline version requires Internet access and is usually a little more recentSignificant resources are being developed (eg with a Wiki)There is not time now to do more than mention it as a general purpose tool worthy of closer exploration later30MATHTED 2009Cabri 3DThree-dimensional geometry is harder to depict on a screen or in a bookConsequently has been neglected in much of school mathematics?Cabri 3D provides opportunities not previously possibleClick on the pictures

MATHTED 200931

Java and Flash appletsAnother species of computer software comprises small applets that are operated by a browserJava and Flash are popular environments for writing theseWhile these are typically available online, some can be downloaded and used locally, so that an online connection is not needed while the applets are being used.Some software (eg Geogebra and Cabri 3D) can export applets, so that programming expertise is not needed to construct themLets look at some examples

MATHTED 200932NCTMs Illuminations ProjectThis large web-based project includes a number of Java applets that can be saved for later useThe pictures show two examples (click on them)Applets can be searchedMATHTED 200933

Applets from GeoGebra wikiMany contributions to the GeoGebra wiki include downloadable applets, which have been exported from GeoGebraThese address many aspects of mathematics, not only geometryA good example concernsintegration with a RiemannsumOnly a Java-enabled browseris needed to operatethese appletClick on the image for an example

MATHTED 200934

Applets from a textbookIncreasingly, textbook publishers are providing applets with their products or as separate objects online.This is a good way to integrate technology in with other instruction.Here is an example simulating coin tosses from Baldi & Moores text, MATHTED 200935

Applets from NrichNrich is a large website in the UK, offering enrichment and extension materials of many kinds to studentsSome of the materials are interactivities, generally in the form of Flash appletsA wonderful example is TrigonClick the circle to startMATHTED 200936

Nrich teacher packagesThe (wonderful!) Nrich site in the UK offers several teacher packages, comprising a collection of related materials, including Flash applets.The Probability package contains some applets for simulation that might be well used on an interactive whiteboard.Some of these use the DIMEprobability charts, which showa succession of events.Click the pictureMATHTED 200937

Mathematics OnlineThis large Austrian web-based project includes many Java appletsConcerned mostly with senior secondary school mathematicsGood pedagogical designMaterials can be downloaded and used for learning and teachingThe Gallery contains many thoughtful examplesClick on the picture to explore the Gallery

MATHTED 200938

National Library of Virtual ManipulativesThis large collection of Java applets from Utah State University is searchable by content and levelClick on the imageApplets offer advice to students, teachers and parentsThe whole set can be purchased on CD-ROM to use when Internet access is limited

MATHTED 200939

The InternetThe Internet has changed forever the meaning and use of technology in affluent western countries like mineInternet access is rapidly rising in the Philippines, as it is elsewhereHome, community and schoolIt offers distinct advantages for both learning and teaching mathematicsDepending, of course, on access issuesLets examine what these are MATHTED 200940What Internet tasks for students?Active engagement in mathematicsReading materialBrowsing for informationCommunicatingPractisingUsing like a traditional textbookA little text and illustrationsLots of examples, questions, problems

The teachers roleLocating and storing sites (eg on Intranet)School website constructionUsing with whole classWith a data projectorIncluding IWB useReferring students to particular URLs to focus constructive student use For projects, homework, interest, Constructing or assigning webquests Categories of student useThere is now an astonishing and increasing array of free and excellent Internet materials:Interactive opportunityReading interesting materialsReferenceCommunicationProblem solvingWebquestsGood examples in each of these categories are given on my website (Internet Maths)Click on the image

What tasks for teachers?As well as helping students to learn from the Internet, there are a range of ways mathematics teachers might use the Internet:Planning lessonsAccessing official advice and helpConnecting with other professionalsGetting help from companiesDesigning and using school websitesGeneral educational referenceThese differ from student tasks, as the work of teachers differs from the work of studentsCategories of teacher useThe Internet offers significant help of other kinds to teachersA tentative list:Lesson preparationOfficial advice and supportProfessional engagementCommercial supportLocal school web sitesOther general reference Examples in these various categories are stored and described in a little detail on my website (teaching maths)Click on the image

Technology directions and standardsSome contributions to the discussion Purposes of using technologyImprove student experience Facilitate student experimentationSupport good teaching Focus on activities that cannot be done well easily without the aid of technology Issues of student access Teacher issuesProfessional development and supportIntegration into curriculumExamination practicesResearch to understand and improve practice

Barry Kissane MATHTED 200946Closing remarksNCTM Principle: Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. Technology does not teach: teachers do. Students dont learn directly from technology: rather, they might learn from what they do with the technology.

Barry Kissane MATHTED 200947Thank you!http://wwwstaff.murdoch.edu.au/~kissaneMATHTED 200948