Academic journal article Higher Education Studies

Using Potential Performance Theory to Assess Differences in Math Abilities between Citizens from India and the United States

Academic journal article Higher Education Studies

Using Potential Performance Theory to Assess Differences in Math Abilities between Citizens from India and the United States

Article excerpt

Abstract

For years, researchers and academics have known that American students perform more poorly on average compared to students from some other countries, including India. The usual explanation is that some systematic factor (e.g. knowledge, skill set, test-taking ability, etc.) is responsible for the differences. The current study examines the issue from a different perspective; we assess the consistency in which participants performed in an Algebra test, and used this consistency to determine their potential performance. Participants were randomly selected from India and the United States and were given a 50-question algebra test, followed by a break, and then followed by the same test again. The data revealed that while the Indian participants scored about 8% higher on the test, the majority of their performance increase was due to being more consistent than their American counterparts.

Keywords: PPT, potential, performance, theory, mathematics, India, United States

1. Introduction

It is well known that an emphasis on mathematics education, and taking more mathematics classes, is associated with better performance on problems in mathematics. In countries where there is more focus on education in mathematics, students tend to have superior mathematics performance compared to students in countries with less of a focus on mathematics education (e.g. Phelps, 2001). Although the association of mathematics experience with performance in mathematics is indisputable, the underlying reason for this association is not completely clear. Our goal is to attempt a first investigation of this general issue, using algebra as the subject of interest. However, to understand the rationale for our investigation, it is important to distinguish between consistency and potential performance as possible explanations.

1.1 Potential Performance Theory (PPT)

The distinction between consistency and potential performance comes out of potential performance theory (hereafter, PPT; Trafimow & Rice, 2008), and has been supported by numerous empirical studies as well as simulations (Hunt, Rice, Trafimow & Sandry, in press; Rice, Geels, Hackett, Trafimow, McCarley, Schwark, & Hunt, 2012; Rice, Geels, Trafimow & Hackett, 2011; Rice & Trafimow, in press; Rice, Trafimow & Hunt, 2010; Rice, Trafimow, Keller, Hunt & Geels, 2011; Trafimow, Hunt, Rice & Geels, 2011; Trafimow, MacDonald & Rice, in press; Trafimow & Rice, 2008; 2009; 2011). The idea is that there are two general classes of impediments to performance on any task, including algebra problems. One class of impediments constitutes systematic factors (e.g., simply not knowing the material) and another class constitutes factors leading to a lack of consistency (e.g., a door slams in another room that provides a distraction while choosing the answer to a problem). Appendix A provides an abstract overview of how to conduct a PPT study, but we wish to further explain it here with the specific example of taking an algebra test.

Let us consider consistency first, as it is the most important PPT concept to understand. In the usual PPT paradigm, the researcher has participants complete two blocks of trials rather than one block, and every problem on the first block is repeated on the second block. Given that every participant completes two blocks of trials, it is possible to compute a correlation coefficient across the two blocks of trials, for each and every participant. This correlation coefficient measures each participant's consistency across the two blocks of trials and it also can be called a "consistency coefficient." We emphasize that consistency does not refer to doing the same thing on every trial (e.g., choosing "true" on a true-false test), but rather two making similar responses on similar trials across both blocks of trials.

As has been known since at least Spearman's (1904) seminal work, it is a fact of statistical regression that inconsistency pushes observed scores towards the chance level. …

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