pisa

Estu Yen Retno Asun/1431032

The Programme for International Student Assessment (PISA) is a project of the Organisation for Economic Co-operation and Development (OECD). PISA seeks to assess how well 15-years-olds are prepared for life’s challenges. And assess students in three different domains: reading, mathematics and science.

Content, contexts, competencies and mathematical literacy are building blocks for the PISA mathematics framework. The process of “mathematisation” describe the ability of student to solve real world problems by shifting between real world and mathematical world contexts.

PISA organizes mathematical content into four overarching ideas:                    

a.       Change and Relationships

Change and relationships involves the knowledge of mathematical manifestations of change, as well as functional relationships and dependency among variables

b.      Space and Shape

Space and shape relates to the understanding of spatial and geometric phenomena and relationships

c.       Quantity

Quantity requires an understanding of numeric phenomena, quantitative relationships and patterns

d.      Uncertainly

Uncertainly involves probabilistic and statistical phenomena as well as relationships that become increasingly relevant in the information society

For certain topics and groups of countries, PISA mathematics questions are reclassified into five traditional curriculum topics: Number, Algebra, Measurement, Geometry and Data.

PISA mathematics questions are set in four different contexts:

a.       Personal

The unit SKATEBOARD contains three questions, Q1, Q2 and Q3, classified

in the personal context, day-to-day activities.

b.      Educational and occupational

The educational and occupational contexts include problem situations that students might confront while at school, including those rather artificial problems

designed specifically for teaching or practice purposes, or problems that would

be met in a work situation

c.       Public

Public contexts are those situations experienced in one’s day-to-day interactions with

the outside world

d.      Scientific (including intra-mathematical)

and scientific or explicitly mathematical problems.

PISA groups the underlying skills into three competency clusters:

a.       Reproduction

those involving familiar mathematical processes and computations

b.      Connections

those involving a degree of interpretation and linkages

c.       Reflection

those involving deeper insights and reflection

PISA mathematics questions cover a wide range of difficulties in a wide range of formats. The difficulty of PISA mathematics questions is determined using three different approaches: with simple percentages, logistic models, and the statistically calculated PISA mathematics scale. Student performance is measured on a scale with an average score of 500. Students are grouped in six levels of proficiency, plus a group below Level 1.

Differences in curricula and traditions, and in grade level partly explain performance patterns across countries. The chapter concludes with examination of item difficulty by competency clusters and context areas by country and overall. Previous research identifies four groups of countries with similar performance:

a.       English-Speaking Group:  Australia, Canada, England, Ireland, New Zealand, Scotland and the United States.

b.      Post-Communist Group:  Bulgaria, Czech Republic, Hungary, Latvia and Lithuania, The Russian Federation, Romania, Slovak Republic and Sloveni

c.       Nordic Group:  Denmark, Iceland, Norway and Sweden.

d.      Eastern Asian Group:  Hong Kong-China, Japan, Korea, and Singapore.

Performance patterns in PISA questions can provide useful insights for curriculum design, PISA questions can be classified by traditional mathematic domains, Algebra and Measurement are relatively more difficult, while Data, Geometry and Number are easier. Across domains, one can identify different country groups.

Students from higher grades perform better. An analysis of the performance differences across grades shows that student performance is closely related with instruction. Across competency clusters, Reproduction was the easiest and Reflection the most difficult. Both competency clusters and traditional domains are related to the difficulty of PISA questions. PISA questions presented in a personal context were easier than those in other contexts. Conclusion : Performance in PISA is related to curriculum and instruction, Patterns of performance emerge across countries, grades, competency clusters, and contexts.

PISA can also be used to analyse student strategies and misconceptions. Mathematisation refers to the problem-solving process students use to answer questions. The mathematisation cycle, and the three phases of mathematisation:

a.       Phase 1.  Understanding the question (e.g. dealing with extraneous data), which is also called horizontal mathematisation.

b.      Phase 2.  Sophistication of problem-solving approaches, which is also referred to as vertical mathematisation.

c.       Phase 3.  Interpretation of mathematical results (linking mathematical answers to the context

The coding of PISA questions provides clues to the student’s understanding, Double coding can help disentangle student’s problemsolving strategies and understanding. Conclusion : The PISA Framework of mathematical literacy (OECD, 2003) described the problemsolving process in terms of the process of “mathematisation”. This chapter presented two examples of PISA items that make the problem-solving cycle visible. In these examples the problem-solving cycle comes alive in almost all aspects of the questions. Each problem solving strategy was not a routine procedure. Unfortunately the authors cannot shed light on the actual specific strategy students used. The PISA scoring format does not provide specific information on the thinking and argumentation processes students actually used in solving problems.At the level of daily practices of instruction in schools, however, it is possible to ask additional questions and, particularly, let students give arguments for their solutions. Teachers and other researchers might try using PISA items with their students and compare their results with those observed in this chapter.