What International Studies Say about the Importance and Limitations of Using Computers to Teach Mathematics in Secondary Schools Jaime Carvalho e Silva Departamento de Matemática/CMUC Universidade de Coimbra 1
Tragedy!!! 2
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2014 July 7, 2014 6
“Público” 24-4-2013 7
12-4-2013 laudatur calculator matriculation examinations: a symbolic cas calculator can be used to get top marks without much mathematical knowledge Finland 8
Claude Allègre (MinEd, France,1997-2000) “Les maths sont en train de se dévaluer de manière quasi inéluctable. Désormais, il y a des machines pour faire les calculs. Idem pour la construction des courbes. ” (Interview à France-soir, 29-11-99.) 9
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What can/should we do? Which are the principles to follow? What do we want to do with ICT? Sell? How do we know what is the best option? Simple calculators? ...? Advanced CAS software? How to convince decision makers? 11
person with artifact some culture instrument classroom/home 12
“PISA 2009 Results: Students On Line: Digital Technologies and Performance”, OECD 2011 13
“PISA 2009 Results: Students On Line: Digital Technologies and Performance”, OECD 2011 Korea is the top-performing country in digital reading by a significant margin. Korea is followed by New Zealand and Australia. In most countries, student performance in digital and print reading is closely related. in Korea, Australia, New Zealand, Ireland, Sweden, Iceland and Macao-China, students perform significantly better in digital than in print reading. 14
“PISA 2009 Results: Students On Line: Digital Technologies and Performance”, OECD 2011 Proficient digital readers tend to know how to navigate effectively and efficiently. PISA results show that even when guidance on navigation is explicit, significant numbers of students still cannot locate crucial pages. The digital reading assessment offers powerful evidence that today’ s 15- year-olds, the “digital natives”, do not automatically know how to operate effectively in the digital environment. 15
“PISA 2009 Results: Students On Line: Digital Technologies and Performance”, OECD 2011 Using a computer at home is related to digital reading performance in all 17 participating countries and economies, but that is not always true for computer use at school. moderate users attain higher scores in digital reading than both rare and intensive users 16
“PISA 2009 Results: Students On Line: Digital Technologies and Performance”, OECD 2011 the relationship between students’ computer use at school and performance in digital reading tends to be negative with a slight curve, which means that more intensive use is associated with lower scores. the frequency of computer use at home, particularly computer use for leisure, is positively associated with navigation skills and digital reading performance, while the frequency of computer use at school is not 17
“PISA 2009 Results: Students On Line: Digital Technologies and Performance”, OECD 2011 18
“Are the new millennium learners making the grade?” (OECD 2010) 19
“Are the new millennium learners making the grade?” (OECD 2010) There is a stronger correlation between educational performance and frequency of computer use at home than at school. ln a large majority of countries, the benefits of greater computer use tend to be larger at home than at school. ln every country, students reporting "rare" or "no use" of computers at home score lower than their counterparts who report frequent use. Clearly, in the case of school use, more computer use does not mean better results in subject-based standardised tests such as PISA 2006. 20
“Are the new millennium learners making the grade?” (OECD 2010) With the right skills and background, more frequent computer use can lead to better performance. The analysis of PISA data shows that for educational performance, computer use amplifies a student's academic skills and competences. These competences are closely related to the student's background, and particularly to his/her economic, cultural and social capital. Given the lack of such capital, the benefits from more computer use would be limited. 21
“Are the new millennium learners making the grade?” (OECD 2010) In a number of respects, those responsible for teaching the new millennium learners have to be able to guide them in their educational journey through digital media. Teacher training, both initial and in- service, is crucial for disseminating this key message and for equipping teachers with the required competences. 22
“Are the new millennium learners making the grade?” (OECD 2010) Promote greater computer use at school and experimental research on its effects. 23
“Are the new millennium learners making the grade?” (OECD 2010) An alternative explanation for the lack of correlation between computer use at school and educational performance is that frequency of use is currently irrelevant. There are positive gains from computer use at home because the frequency of use has reached a critical level. (...) such a level is far from the marginal one a student currently experiences at school. Governments need to create the necessary incentives to engage teachers in the exploration of the benefits of ICT in education. 24
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PISA 2012 For the first time, PISA 2012 includes an optional computer-based assessment of mathematics. Specially designed PISA questions are presented on a computer, and students respond on the computer, although they can also use pencil and paper as they think through the test questions. 26
PISA 2012 The design of the computer-based assessment ensures that mathematical reasoning and processes take precedence over mastery of using the computer as a tool. 27
PISA 2012 Each computer-based item involves three aspects: the mathematical demand (as for paper-based items); the general knowledge and skills related to information and communication technologies (ICT) that are required; These are intentionally kept to a minimum; competencies related to the interaction of mathematics and ICT, such as making a pie chart from data using a simple “wizard”, or planning and implementing a sorting strategy to locate and collect desired data in a spreadsheet. 28
PISA 2012 (...) computer-based items can be more interactive, authentic and engaging than paper-based items. They can be presented in new formats (e.g. drag-and-drop), include real-world data (such as a large, sortable dataset), and use colour, graphics and movement to aid comprehension. 29
PISA 2012 Students may be presented with a moving stimulus or representations of three-dimensional objects that can be rotated, or have more flexible access to relevant information. New item formats can expand response types beyond verbal and written, giving a more rounded picture of mathematical literacy. (...) computers have become essential tools for representing, visualising, exploring, and experimenting with all kinds of mathematical objects, phenomena and processes, not to mention for realising all types of computations at home, at school, and at work. 30
PISA 2012 "there is a high degree of consistency in student performance on items delivered on paper and by computer” In the field of mathematics, one participant (Shanghai-China) saw a large diffrence, of around 50 score points, in favour of the paper based format. 31
PISA 2012 there are also countries for which computer delivery of the assessment appears to have been advantageous. The largest difference, of about 30 score points, was seen in Brazil. 32
Singapore “Emphasis is also given to reasoning, applications, and use of technology. Advances in technology have changed the way we teach and learn mathematics. The computer and hand-held calculator, for example, offer great potential to enhance the teaching and learning of mathematics. ” 33
Singapore (1) Achieve a better balance between the emphasis on computational skills and problem solving skills in teaching and learning and in assessment (2) Widen the repertoire of teaching and learning approaches to include investigations and problems in authentic situations (3) Help students, particularly those with difficulty learning mathematics, develop greater confidence in doing mathematics 34
http://www.corestandards.org/ 35
CCSS for Mathematics Standards(for(Mathema/cal(Prac/ce( Carry%across%all%grade%levels% ! Describe%habits%of%mind%of%a%mathema6cally%expert%student% ! Standards(for(Mathema/cal(Content( K;8%standards%presented%by%grade%level% ! Organized%into%domains%that%progress%over%several%grades% ! Grade%introduc6ons%give%2–4%focal%points%at%each%grade%level% ! High%school%standards%presented%by%conceptual%theme% ! (Number%&%Quan6ty,%Algebra,%Func6ons,%Modeling,% Geometry,%Sta6s6cs%&%Probability)% 36
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South Korea 2007 38
South Korea 2007 39
South Korea 2007 40
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