Innovative approaches in mathematical teaching (based on the implementation of international systems PISA and TIMSS)

Introduction. Trends in International Mathematics and Science Study (TIMSS) and the Programme for International Student Assessment (PISA) designed to assess pupil achievement across a number of countries. PISA was developed in 1997 and was first implemented in 2000. With the help of the program, changes in the education system of different countries are identified, compared, and evaluated. The number of students participating in each state is about 2 percent of the total number of 15-year-olds in the country. The PISA program is organized by the Organization for Economic Cooperation and Development with the participation of leading international organizations and national centers in the consortium.

TIMSS is an international monitoring of the quality of teaching mathematics and science in schools and is organized by the International Association for Educational Achievement Assessment (IEA). This study will help to compare the level and quality of knowledge gained by 4th and 8th grade students in mathematics and science in different countries and to identify differences in national educational systems. In addition, the content of the education provided in schools in mathematics and the natural sciences, the learning process, the possibilities of the educational institution, the potential of teachers, and the factors related to the families of students. The survey is held every four years with the participation of many research centers and organizations around the world, including the US Educational Testing Services (ETS Educational Testing Services), the Statistical Center of Canada (IEA) and the Secretariat of the International Association for Educational Achievement Assessment (IEA). Advisory committees of various state experts are also established.

Materials and Methods. TIMSS and PISA test different things, TIMSS is being more curriculum based whilst PISA assesses the application of skills to real life problems. TIMSS focuses on assessing pupils’ knowledge and skills in mathematics and science, focusing very much on what they have been taught in school. Comparisons of PISA and TIMSS mathematics frameworks can be found in a number of publications (American Institutes for Research, 2005; Hutchison & Schagen, 2007; National Center for Education Statistics, 2008; Neidorf et al., 2006). These comparisons tend to produce a descriptive list of similarities and differences between the two published frameworks, such as the classifications of the content domains and the cognitive domains. However, few published comparisons critically examined the differences. For example, would one framework lead to a test that is completely different from a test based on the other framework? Is one framework a subset of the other? If so, what is missing in that framework? Are the two frameworks essentially the same? The key differences between PISA and TIMSS are at the level of the tests and items, not just at the level of broad aims and orientations, as reflected in the frameworks. At a first glance, most would conclude that both PISA and TIMSS mathematics frameworks are comprehensive. However, the PISA mathematics framework suggests its more inclusive approach, with the following line at the beginning of the framework document: Rather than being limited to the curriculum content students have learned, the assessments focus on determining if students can use what they have learned in the situations they are likely to encounter in their daily lives (Organisation for Economic Co-operation and Development [OECD], 2003, p. 24).

The word “limited” suggests that PISA is attempting to be more inclusive in terms of coverage of the mathematics domain. It also suggests that the school curriculum, whether intended, implemented, or attained, does not focus on whether students can use what they have learned. Does this mean that TIMSS, being more curriculum-based, does not assess whether students can use what they have learned? The TIMSS mathematics framework states the following: While the assessment of abilities such as solving nonroutine problems and reasoning with mathematics will be of special interest, the factual, procedural, and conceptual knowledge that form the initial base for the development and implementation of these skills will also be assessed. Problem solving and communications are key outcomes of mathematics education that are associated with many of the topics in the content domains. They are regarded as valid behaviors to be elicited by test items in most topic areas (International Association for the Evaluation of Educational Achievement, 2003, p. 11). It would appear that TIMSS does not preclude problem solving in the framework, but there may be less emphasis on this than in PISA, where the mathematics framework is almost entirely built on the application of mathematics competencies that may reasonably be expected of students. In short, one may expect a different balance in the two tests in terms of problem solving items and fact/procedural items, but one might not necessarily expect a complete absence of one type of item.

Each assessment is developed from a framework specifying the content and skills to be measured. The mathematics frameworks of TIMSS reveal considerable agreement on the general boundaries and basic organization of mathematics content. For example, TIMSS assessments include five main content areas related to the major mathematical curricular areas of number, measurement, geometry, data, and algebra. And the framework also includes dimensions that define a range of cognitive skills and processes. PISA also specifies a range of content expectations, but the framework is organized around overarching ideas (e.g., space and shape) versus curricular-based areas like geometry or algebra and with emphasis on the contexts in which mathematics is applied (e.g., in school, in society).

Conclusion. To conclude briefly, the international assessments PISA and TIMSS provide a method for comparing the mathematics and science performance in our country to the performance of students in other countries. TIMSS and PISA provide an important international perspective and allows us to reflect both on how well our students know what we believe they should know and on where we stand among other countries.

Source used:

• 1.    Hutchison, G., & Schagen, I. (2007). Comparisons between PISA and TIMSS – Are We the Man with Two Watches? In Loveless, T. (Ed.), Lessons Learned – What International Assessments Tell Us about Math Achievement. Washington, DC: The Brookings Institution.

• 2.    Organisation for Economic Co-operation and Development. (2003). The PISA 2003 Assessment Framework – Mathematics, Reading, Science and Problem Solving Knowledge and Skills. Paris: Organisation for Economic Co-operation and Development

• 3.    International Association for the Evaluation of Educational Achievement. (2003). TIMSS Assessment Frameworks and Specifications, 2003. Chestnut Hill, MA: TIMSS International Study Centre.

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