Background

Methodology

Results

Discussion and conclusion

References

Abstract

Many studies have found a strong relationship between the mathematics students study in school and their performance on an academic or school mathematics assessment but not on an assessment of mathematics literacy (ML). With many countries, like the USA, placing emphasis on finishing secondary education being mathematically literate and prepared for college or career, this raises the question about the relationship between the mathematics studied in school and any ML students may have. The Programme for International Student Assessment (PISA) ML assessment is embedded in real-world contexts that provide an important window on how ready students are to tackle the situations and problems that await them whether they intend to pursue further education beyond high school or intend to go directly into the labour force. In this paper, we draw upon the PISA 2012 data to investigate the extent to which the cumulative exposure to rigorous mathematics content, such as that embedded in college- and career-ready standards, is associated with ML as assessed in PISA. Results reveal that both exposure to rigorous school mathematics and experiencing the instruction of this mathematics through real-world applications are significantly related to all the real-world contextualized PISA ML scores.

Background

The common sense notion that the exposure students experience related to a topic is related to what they learn about that topic has played an important role in education research for over a century. This psychological perspective on OTL is an idea that was evident in the writings of psychologists Edward Thorndike and William James as far back as around the turn of the last century (Cogan & Schmidt, in press; James, 1983; Thorndike, 1913). OTL describes a focal aspect of schooling—the coverage of content in the classroom that is directly related to what a student learns. Learning theories have a long and rich heritage in the psychological and education literatures but Carroll’s (1963) model was among the first to specifically address classroom learning. It defines classroom learning as an interaction between the instruction provided and what is needed by the student in order to learn, e.g. aptitude, ability and perseverance. Bloom and his colleagues made use of Carroll’s theory in the OTL measures developed and used in the First International Mathematics Study which became, in turn, the example for relating OTL to learning for much education research over the past 50 years especially in the international comparative literature (Cogan & Schmidt, 2015). Typically teachers are the ones providing the information on OTL; however, obtaining such information from students has the benefit of reflecting the student’s perception which is likely affected by the student factors included in Carroll’s model. Nonetheless, the focus of most of the research that has investigated the relationship of OTL to what students know has been conducted with measures of students’ learning of the formal/ academic mathematics taught in school. The emphasis of this paper on literacy and the application of mathematics knowledge to real-world, everyday situations raises the question as to what specifically occurs in schools that might support the development of ML (de Lange, 2003)? This uncertainty about what type of OTL in schooling may be related to the development of literacy is related to at least two issues. One has to do with the nature of learning and the other has to do with the nature of instruction.