What International Studies Say about the Importance and Limitations - - PowerPoint PPT Presentation

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

Long history

3

Long history

3

Long history

3

Long history

3

Long history

3

Long history

3

Long history

3

2013

4

2013

5

July 7, 2014 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

10

10

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

artifact person with 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

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

“PISA 2009 Results: Students On Line: Digital Technologies and Performance”, OECD 2011

16

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

“PISA 2009 Results: Students On Line: Digital Technologies and Performance”, OECD 2011

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

25

PISA 2012

For the first time, PISA 2012 includes an

• ptional 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

• ver 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

“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,

• ffer great potential to enhance the teaching and

learning of mathematics. ”

Singapore

33

(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

Singapore

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

37

South Korea 2007

38

South Korea 2007

39

South Korea 2007

40

41

41

42

ICMI the International Commission on Mathematical Instruction 1908

43

ICMI Study 17 (2010)

44

ICMI Study 17 (2010)

Making technology legitimate and mathematically useful requires modes of integration (...) requires tasks and situations that are not simple adaptation of paper and pencil tasks, often tasks without equivalent in the paper and pencil environment, thus tasks not so easy to design when you enter in the technological world with your paper and pencil culture.

45

ICMI Study 17 (2010)

the slow progress in the integration of digital technologies for mathematics learning in school classrooms is due to an invariance of values and norms in mathematics education, an underestimation of both the complex process of transforming mathematics with technology in the classroom and the mathematical demands placed on learners, and a dissonance between technical and conceptual aspects of mathematical activity

46

ICMI Study 17 (2010)

Mathematics, a human construction and practice with a variety of purposes, is in constant change and dialectically entwined with technology. While we may imagine the possibilities that rapidly emerging digital and communication technologies affords for mathematics, its application and for learning, there will always be a lag between the development of “new mathematics” and its implementation in education systems.

47

ICMI Study 17 (2010)

Implementation of mathematics afforded by digital technologies is more likely to occur when and where there is a shared vision among political leaders, education authorities, mathematicians and mathematics teachers.

48

effective student learning of mathematics is facilitated through: (a) long-term engagement in collaborative projects for which they take individual and collective responsibility, and “tools [that] approach students from an angle that seems interesting and relevant to them”; (b) integration of sustained emphasis on content knowledge, deep engagement of student interests, and support for student experience and progress; and (c) commitment to learning through interactive microworlds that foster modeling and collaboration.

49

Challenges - graphing

d(x)=149.6*(1-0.0167 *cos x)

50

Challenges - limits

f(x) = ln x + 10 sin x

51

Luc Trouche

CAS “learning of the use of instruments is made most of the time alone or between friends"

52

Luc Trouche

53

Final Questions

How much and when teach Numerical Methods? Elementary School? When should we introduce CAS? When teach programming/coding?

54

John Conway (1997)

We have to embrace technology, I don’ t mean just tolerate it; embrace it and celebrate it. The professional mathematics community must adapt and learn how to best incorporate technology into instruction. With the existence of powerful, inexpensive computers I see mathematics departments rethinking their entire curriculum. Otherwise, we are out of business.

55

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

56