1 / 24

OECD Programme for International Student Assessment (PISA) Mathematics

OECD Programme for International Student Assessment (PISA) Mathematics. Margaret Wu ACER & University of Melbourne. OECD PISA Project - led by ACER, with ETS, Westat, NIER, Cito. 15 year-old students end of compulsory education not intact class sample About 40 countries 3-year cycle:

abe
Download Presentation

OECD Programme for International Student Assessment (PISA) Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. OECD Programme for International Student Assessment (PISA) Mathematics Margaret Wu ACER & University of Melbourne

  2. OECD PISA Project - led by ACER, with ETS, Westat, NIER, Cito • 15 year-old students • end of compulsory education • not intact class sample • About 40 countries • 3-year cycle: • 2000 Reading • 2003 Mathematics • 2006 Science • Student and School questionnaires

  3. Mathematics Framework - 1 • Experts driven, not curricula driven • TIMSS based on common curricula • PISA based on “definition of Mathematics” deefined by a group of “expert” mathematics educators. • Expert Group Members • Jan de Lange, Werner Blum, Mary Lindquist, Vladmir Burjan, Sean Close, John Dossey, Zbigniew Marciniak, Mogens Niss, Kyungmee Park, Luis Rico, Yoshinori Shimizu

  4. Mathematics Framework - 2 • Definition of PISA Mathematics Literacy: • Mathematics literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgements and to engage in mathematics, in ways that meet the needs of that individual’s life as a constructive, concerned, and reflective citizen.

  5. Mathematics Framework - 3 • Organisation of content • TIMSS by topics and subtopics of mathematics • Number, Algebra, Measurement, Geometry, Data • PISA by overarching ideas (phenomenological approach) • Quantity, Space and Shape, Change and Relationships, Uncertainty • Conception of assessment items is different; making a distinction between teaching and assessment

  6. Mathematics Framework - 4 • Processes • Emphasis on Mathematisation - the processes involved from encountering a real-world problem to generating a solution • Three competency classes • Reproduction - practised routine procedures • Connection - making judgements, reasoning • Reflection - making generalisations

  7. Item Context Emphasis on authenticity - 1 • No “naked” drills items, e.g., • Solve a linear or quadratic equation • Construct an angle • Simplify a fraction • Few intra-mathematics items, e.g., • pattern observation in sum of odd numbers • properties of numbers, e.g., perfect numbers.

  8. X Item Context Emphasis on authenticity - 2 • Problem context is not just for the sake of adding context, but for real-world application. How far is the foot of a 2 m ladder from the wall when the top of the ladder is 1.92 m above the ground?  Not a good PISA item!

  9. Another example of better context • Farmer Dave keeps chickens and rabbits. Dave counted altogether 65 heads and 180 feet. How many chickens does Dave have? • Tickets to the school concert costs $4 for an adult and $2 for a child. 65 tickets were sold for a total of $180. How many children’s tickets were sold?

  10. Item Context Emphasis on authenticity - 3 • Problems with contexts that influence the solution and its interpretation are preferred for assessing mathematical literacy. • If a card has a vowel on one side, it must have an even number of the other side. Which cards should you turn over to check? • A 6 J 7 (Wason. Griggs&Cox) • You must be over 21 to drink alcoholic drink. Which people should you check? • drinking beer 22 yrs old drinking coke 16 yrs old

  11. Item Format • MC and Open-ended; about half of each kind. • Raw responses captured as much as possible • Double-digit coding to keep track of different approaches

  12. 1 6 2 5 3 4 Example Mathematics Item - 1 The picture shows a spinner used in playing games. (1) What is the probability of spinning a “3”? (2) What is the probability of spinning an even number? The picture shows a spinner used in playing games. For a game, the spinner is used to choose a person at random to start the game. Explain how you will use this spinner to choose a person at random if there are (1) three players, and (2) nine players. Fits PISA framework better

  13. Example Mathematics Item - 2 • Break-in • On the radio, an advertisement for an insurance company ran as follows: “Every 10 minutes, a car is stolen in Zedland. Every 21 minutes, a house is broken into. Take up an insurance policy today.” • Using only the information given in the advertisement, can you conclude • (1) anything about the chance a car will be stolen in Zedland? • (2) that it is more likely to have a car theft than a house break-in? • Give reasons to support your answer.

  14. Example Mathematics Item - 3 To date, no humans can react in less than 0.110 of a second.

  15. Challenges for Test Developers • Real-world mathematics are not easy to find (for 15 year-olds) • Predominantly about price, cost, discounts in everyday life (too domestic?). • PISA is somewhat “middle-class” - telephone, internet, cars, computers

  16. Hong Kong Performed Well

  17. Compare TIMSS and PISA

  18. Compare TIMSS and PISA

  19. Cluster Analysis cae òûòø nsl ò÷ùòòòø eng òûò÷ùòòòòòø sco ò÷óùòòòòòø aus òòòòòòò÷óó irl òòòòòòòòòûòòò÷ùòòòòòòòø usa òòòòòòòòò÷óó bfl òòòòòòòòòûòòòòòòòòò÷ó nld òòòòòòòòò÷ó rus òòòòòòòòòòòòòòòòòòòûòòòòòòòòòòòòòøó hkg òòòòòòòòòòòòòòòòòòò÷ùòòòòòøó kor òòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòò÷ùòòòòòòòòò÷ jpn òòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòòò÷

  20. Item Hong Kong found easier

  21. Apples M136Q02 • Number of apple trees = n2 • Number of conifer trees = 8n • where n is the number of rows of apple trees. • There is a value of n for which the number of apple trees equals the number of conifer trees. Find the value of n and show your method of calculating this.

  22. Item Hong Kong found more difficult

  23. Speed (km/h) Speed of a racing car along a 3 km track (second lap) 180 160 140 120 100 80 60 40 20 0.5 1.5 2.5 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 Distance along the track (km) Starting line Speed of Racing Car M159Q03 What can you say about the speed of the car between the 2.6 km and 2.8 km marks? • The speed of the car remains constant. • The speed of the car is increasing. • The speed of the car is decreasing. • The speed of the car cannot be determined from the graph.

  24. Conclusions • PISA mathematics relates to real-world • PISA tests something a little different from TIMSS • For Hong Kong, • Mathematics education must be made more relevant to everyday life and to real-world applications.

More Related