Teaching, learning & technology in the Philippines

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

2. 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. • Examples of suitable technologies • Calculators • Graphics calculators • Computer software • Internet for students and teachers • Technology directions and standards Barry Kissane MATHTED 2009

3. Mathematics and technology • Real world applications of mathematics frequently use technology these days • So it seems important that our curricula in schools also reflect technology • Where this is possible • The recent deadly storms through the Philippines provide a good, albeit tragic, example • Let’s look at the present example … MATHTED 2009

4. Typhoon Lupit The Internet provided a powerful picture of the approaching storm This satellite image was on Monday morning Click image to access website Typhoon images and information from http://www.tropicalstormrisk.com/ MATHTED 2009

5. Forecasting typhoon behaviour A great deal of mathematics is used to predict the likely path: The increasing circles indicate increasing uncertainty of predictions The typhoon classification scheme The measurement of the earth The satellite positioning systems … a lot of technology was used to make this picture MATHTED 2009

6. Probabilities and errors In the real world, probabilities in models are rarely derived from counting finite events Observe also: The probability scale Unlikely events can happen Events with very high likelihood may not happen All predictions of these kinds involve errors Only the past is certain MATHTED 2009

7. How to respond? Mathematics provides good information about the range of possibilities and their likelihoods Using statistical analysis Using the normal distribution Using previous experience at predictions But humans must interpret all that information, here shown four days ago MATHTED 2009

8. Mathematics, technology and typhoons • All of this information is accessible to anyone using the Internet, not only ‘experts’ • In the next few years, it will be routinely available to many Filipino students and their families • Does 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 2009

9. Why is technology important? • As the typhoon example suggests, we inhabit a world that is awash with technology • Travelling here on a budget flight, many passengers had their own technology with them • So of course, students ought to be inducted into that world in schools • But technology can also make a distinctive contribution to teaching and learning mathematics • By providing opportunities for learning and teaching that are not otherwise available • Let’s consider some examples … MATHTED 2009

10. Technologies for school maths • Calculators • Scientific calculator • Graphics calculator • Computer software • Generic software (eg Microsoft Excel) • Mathematical software (eg Tinkerplots, Fathom, GeoGebra, Cabri 3D) • Java and Flash applets • The Internet • For students • For teachers MATHTED 2009

11. Why 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 2009

12. … educational arguments • They 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 2009

13. Computation is facilitated • Calculators are helpful for doing computations • When the numbers are beyond mental arithmetic • When many computations are needed • When mathematical ideas are not yet firmly learned MATHTED 2009

14. Computing Philippines population • According 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 graphically • The rule of three • Numerical solution of equations is possible MATHTED 2009

15. The rule of three Symbolic representation Graphical representation X refers to number of years after 1980, Y1 is population (millions) Solving equation to find population of 80 million Numerical representation Barry Kissane MATHTED 2009

16. Exploration with calculators Importantly, graphics calculators provide opportunities for experimentation, not just computation, in many areas, including: • Graphs • Equations • Statistics • Probability • Calculus • Geometry MATHTED 2009

17. Examples of calculator use • There are many examples of graphics calculator use discussed in papers on my website: • http://wwwstaff.murdoch.edu.au/~kissane/epublications.htm • There are also examples of use of scientific calculators on the web: • Go to http://edu.casio.com/dl/ and press ENTER • Accept the agreement • Click on Guest button (or register) • Click on ES Standard Calculators Curriculum Paper Activity and then Next • Download activities of your interest • These provide many opportunities to see how exploration with calculators can affect learning. Barry Kissane MATHTED 2009

18. Technology and the curriculum • When students have access to technology, the content and balance of the curriculum may be affected • Here are some examples: • Negative numbers in primary school • Complex numbers in secondary school • Exact arithmetic • (Numerical) optimisation • Integration techniques • Such changes are only reasonable when access to the technology is universal MATHTED 2009

19. Computer software • Computer 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 software • Commercial software • Applets (run from a browser) MATHTED 2009

20. Spreadsheets • Spreadsheets have versatile uses in mathematics, although they were not designed for educational purposes • They may be important because they are available, typically as part of a software bundle • Helpful for some forms of data analysis, modelling and everyday computation • Some 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 2009

21. Tinkerplots • Tinkerplots is a commercial program that supports data analysis of various kinds • Especially important for the analysis of student-collected data, a key part of mathematical modelling • Sorting data is the primal act of analysis • Less emphasis on sophisticated quantitative analyses and more emphasis on the story of the data • Let’s look briefly at an example of Backpacks • Data were provided with the software MATHTED 2009

22. Backpacks MATHTED 2009

23. Philippines population data • Tinkerplots can be used to analyse data obtained from elsewhere • To illustrate, we will look at the population of the Philippines over the 20th century • Data are from the wonderful GapMinder website • Data on personal wealth (GDP per capita) are also included MATHTED 2009

24. Philippines population since 1900 Barry Kissane MATHTED 2009

25. Philippines GDP per capita The data tell a powerful story of the 20th century The effects of WWII are clear As are the turbulent times of the 1980s … Students can use technology to explore real data Barry Kissane MATHTED 2009

26. Fathom • Tinkerplots is described as suitable for grades 4-8, but arguably extends beyond both extremities • Fathom (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 statistics • Let’s look again at some population data to briefly see some differences • The data show the Philippines population after World War II • Notice how well the ‘least squares’ concept is demonstrated • The data are close to linear, although clearly curvilinear MATHTED 2009

27. Least squares line MATHTED 2009

28. Accessing Tinkerplots and Fathom • Further information about these two software packages is available on the Key Curriculum website • Evaluation copies of the software and many examples are available. • Tinkerplots • Fathom • From the Philippines, these are available from • Springer Hong Kong, springer@springer.com.hk • Educational Resources Provider, http://www.123erp.com • Learning Interactive, http://www.li.com.sg Barry Kissane MATHTED 2009

29. Studentdata • Data analysis is most powerful when students are addressing problems that matter to them • They can design and undertake their own data collection • Then use Tinkerplots or Fathom to store and analyse their own data • Use of the software does not require high-level ICT skills • Incidentally they will learn important lessons of data editing, dealing with missing cases, entry errors, etc. MATHTED 2009

30. GeoGebra • This is an excellent free package that handles many aspects of geometry and algebra, and now (with a spreadsheet) some statistics as well • Can be downloaded or operated online • Online version requires Internet access and is usually a little more recent • Significant 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 later MATHTED 2009

31. Cabri 3D • Three-dimensional geometry is harder to depict on a screen or in a book • Consequently has been neglected in much of school mathematics? • Cabri 3D provides opportunities not previously possible • Click on the pictures MATHTED 2009

32. Java and Flash applets • Another species of computer software comprises small applets that are operated by a browser • Java and Flash are popular environments for writing these • While 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 them • Let’s look at some examples MATHTED 2009

33. NCTM’s Illuminations Project • This large web-based project includes a number of Java applets that can be saved for later use • The pictures show two examples (click on them) • Applets can be searched MATHTED 2009

34. Applets from GeoGebra wiki • Many contributions to the GeoGebra wiki include downloadable applets, which have been exported from GeoGebra • These address many aspects of mathematics, not only geometry • A good example concernsintegration with a Riemannsum • Only a Java-enabled browseris needed to operatethese applet • Click on the image for an example MATHTED 2009

35. Applets from a textbook • Increasingly, 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 & Moore’s text, MATHTED 2009

36. Applets from Nrich • Nrich is a large website in the UK, offering enrichment and extension materials of many kinds to students • Some of the materials are interactivities, generally in the form of Flash applets • A wonderful example is Trigon • Click the circle to start MATHTED 2009

37. Nrich teacher packages • The (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 picture MATHTED 2009

38. Mathematics Online • This large Austrian web-based project includes many Java applets • Concerned mostly with senior secondary school mathematics • Good pedagogical design • Materials can be downloaded and used for learning and teaching • The Gallery contains many thoughtful examples • Click on the picture to explore the Gallery MATHTED 2009

39. National Library of Virtual Manipulatives • This large collection of Java applets from Utah State University is searchable by content and level • Click on the image • Applets offer advice to students, teachers and parents • The whole set can be purchased on CD-ROM to use when Internet access is limited MATHTED 2009

40. The Internet • The Internet has changed forever the meaning and use of technology in affluent western countries like mine • Internet access is rapidly rising in the Philippines, as it is elsewhere • Home, community and school • It offers distinct advantages for both learning and teaching mathematics • Depending, of course, on access issues • Let’s examine what these are MATHTED 2009

41. What Internet tasks for students? • Active engagement in mathematics • Reading material • Browsing for information • Communicating • Practising • Using like a traditional textbook • A little text and illustrations • Lots of examples, questions, problems

42. The teacher’s role • Locating and storing sites (eg on Intranet) • School website construction • Using with whole class • With a data projector • Including IWB use • Referring students to particular URLs to focus constructive student use • For projects, homework, interest, … • Constructing or assigning webquests

43. Categories of student use • There is now an astonishing and increasing array of free and excellent Internet materials: • Interactive opportunity • Reading interesting materials • Reference • Communication • Problem solving • Webquests • Good examples in each of these categories are given on my website (Internet Maths) • Click on the image

44. 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 lessons • Accessing official advice and help • Connecting with other professionals • Getting help from companies • Designing and using school websites • General educational reference • These differ from student tasks, as the work of teachers differs from the work of students

45. Categories of teacher use • The Internet offers significant help of other kinds to teachers • A tentative list: • Lesson preparation • Official advice and support • Professional engagement • Commercial support • Local school web sites • Other general reference • Examples in these various categories are stored and described in a little detail on my website (teaching maths) • Click on the image

46. Technology directions and standards • Some contributions to the discussion … • Purposes of using technology • Improve student experience • Facilitate student experimentation • Support good teaching • Focus on activities that cannot be done well easily without the aid of technology • Issues of student access • Teacher issues • Professional development and support • Integration into curriculum • Examination practices • Research to understand and improve practice Barry Kissane MATHTED 2009

47. Closing remarks • NCTM 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 don’t learn directly from technology: rather, they might learn from what they do with the technology. Barry Kissane MATHTED 2009

48. Thank you! http://wwwstaff.murdoch.edu.au/~kissane MATHTED 2009