Dispute between the use of concrete and abstract in Mathematics has been going around for quite a long time. One group favors the old curriculum which focuses on computational and symbolic manipulation skill, others say that the old curriculum does not work and children have to learn Mathematics which is centered on real-world problems. It is obvious the majority of education society tends to favor the latter, with the development of mathematics learning approaches like RME, as well as terms like ‘constructivism’ and ‘contextual teaching learning’ being used widely and extensively. However it does not imply that no one wants to defend the use of abstract learning materials. Kaminski, Sloutsky, and Heckler’s (2008) publication, for instance, caused a major stir by stating that students may gain more from learning Mathematics through abstract, symbolic representation than from concrete examples.
Unaware of all the elitist arguments, research and publications done by people of influence though, Mathematics classrooms in most developing countries (which is basically most countries) for various reasons are inclined to believe the former standpoint rather than the latter. It is mainly because using concrete and contextual learning material tend to use up a lot of time and money, which is simply too problematic to carry out in an economically unaccommodating condition. Interestingly enough, this is claimed to be the reason behind these countries’ low rank in PISA. Indonesia, for example, only ranks as the 57th in 2009 and the 64th in 2012. Zulkardi et. al. (2013) claimed that it is due to students’ unfamiliarity with solving contextual problem. This leads to a suggestion that some countries are put on clear advantage due to their economic capability to fund Mathematics contextual teaching and learning. Is PISA assessment unfair? Does the type of the problems need to be changed to fit the participants’ background better?
The answer to this question lies in the nature of PISA itself. First, PISA is designed to find out whether or not students can use what they have learnt in school and apply that knowledge to real life situations and problems (OECD, 2009). Of course, the use of contextual problems comes as a no brainer. Second, PISA is often seen as the world cup of international education, but testing and ranking the students to see which one is better is not the main emphasis here. PISA uses the test results to compare the effectiveness of each country’s education system, determine the main characteristic of the higher ranking countries and use it as a foundation for future policy making (OECD, 2009). Therefore the use of contextual problem should not be a problem; not using it may kill the purpose of the test.
The reason PISA is biased, if at all, might lies at other things. The context itself is one of them, along with the statistical method. Questions used in PISA have been culturally or linguistically biased toward certain countries, but when OECD tried to tackle this problem by ruling out questions suspected of bias, it can “smooth out” the key difference between countries (Stewart, 2013). The data is also problematic. Shanghai, for instance, scored number one in all three domains during the 2009 test, leading to China being crowned the country with best education system in the world. Shanghai province, whose population is 1.7% of the entire China’s and historically known to comprise the elite and the wealthy, in no way can be seen as representative of China. Some problem with sampling also occurs in countries like UK and Denmark (Stewart, 2003), which led to a conclusion that PISA “tend to say too much for what it can do and tends not to publicize the negative or the weaker aspect” (Stewart, 2003).
Kaminski, J. A., Sloutsky, V.M, and Heckler, A.F. (2008). The advantage of abstract examples in learning math. Science, 320, 454-455.
OECD. (2009). PISA 2009 Assessment Framework Key Competencies in Reading, Mathematics and Science. OECD.
Stewart, W. (2013, July, 26). Is PISA fundamentally flawed?. TES. Retrieved from http://www.tes.co.uk/article.aspx?storycode=6344672
Lutfianto, et. al. (2013). Unfinished Student Answer in PISA Mathematics Contextual Problem. IndoMS-JME, Volume 4, No. 2, July 2013, pp. 188 – 193.