Productive and ineffective efforts: how student effort in high school mathematics relates to college calculus success

Abstract

Relativizing the popular belief that student effort is the key to success, this article finds that effort in the most advanced mathematics course in US high schools is not consistently associated with college calculus performance. We distinguish two types of student effort: productive and ineffective efforts. Whereas the former carries the commonly expected benefits, the latter is associated with negative consequences. Time spent reading the course text in US high schools was negatively related to college calculus performance. Daily study time, however, was found to be either a productive or an ineffective effort, depending on the level of high school mathematics course and the student's performance in it.

Keywords:

• productive effort
• ineffective effort
• college calculus

Acknowledgements

An earlier version of this paper was presented at the 2011 annual meeting of the National Science Teachers Association. Any opinions, findings, and conclusions in this article are the authors’ and do not necessarily reflect the views of the National Science Foundation.

Notes

1. See also [2,Chapter 13] and [3].

2. Among middle school students, mastery goal orientations, but not self-efficacy, in sixth grade English classes have been found to predict effort in eighth grade.[24] One possible explanation for this finding is that the middle school environment may influence changes in effort because social motivations trump academic motivations, leaving only students who possess a deep desire to learn English to persist over time. In addition, among undergraduate students, both mastery and performance-approach (the latter meaning to seek to succeed merely on examinations and/or to receive high grades; the former meaning to strive towards mastering the material beyond the classroom) achievement goals have been found to be significant predictors of effort, as well as of persistence, when approached with a difficult task.[25]

3. The controversy over the origins and malleability of aptitude in general – whether it is a heritable trait and to what extent it can be boosted by learning and effort – has been long-standing among both the wider public and the research community.[30–34]

4. Interestingly, among Asian students, those with immigrant mothers have been found to earn significantly higher grades and scores than their counterparts with native-born mothers.[42]

5. In a study of 88 volunteer respondents from psychology and education courses, Plant et al. [53] found that the quantity of study time predicted cumulative GPA only when quality of study was included in the model.

6. DeLuca and Rosenbaum [51] found that time spent on homework in high school, however, did not have a long-term pay-off for low SES students when it came to educational attainment.

7. Female teachers’ anxiety has been found to influence female student mathematics achievement, but not boys’.[58]

8. Students who exert ineffective effort are different from students who possess disorganized learning goals.[25] Disorganized learning goals stem from the lack of a structured, consistent approach to effort, whereas ineffective effort is methodical and consistent. Despite the differences, poor performance is a hallmark of both approaches.

9. Programmes focused on supporting women and minorities interested in pursuing a STEM field have been found to increase the likelihood of students persisting beyond their initial calculus class, which is a good predictor of students’ majoring in STEM.[67]

10. The SAT and ACT are two standardized examinations that, until recently, most, if not all, American colleges and universities required applicants to submit, at least one set of scores, along with their application materials. Several colleges and universities in the past several years have become test-optional, however, because studies have found these examinations to be biased against students from disadvantaged groups.

11. Students may have mistakenly included the time they spent reading in their answer for the time they spent studying/doing mathematics work. If this were the case, we would expect the time spent studying/doing mathematics work to be greater than the time spent reading the text. Students who reported that they read more than they studied (11%), however, clearly distinguished between the two forms of effort. Furthermore, the question wording clarified the act of studying as ‘doing work for math,’ which implies a more problem-based type of work – something that most secondary mathematics classrooms in America emphasize [72,73, cf. 74] and likely require students to do outside of class, too – as opposed to simply reading the text.

12. Suspecting that the relationship might be non-linear because certain deviations from linearity appeared in Figures 1 and 2, we added quadratic terms of effort to our models of college calculus grade. This resulted in significant effects for both effort variables and their quadratic terms; however, once the high school preparation variables were controlled for, the quadratic terms were no longer significant. Furthermore, the two distinct bumps in Figure 1, led us to model reading the text as a cubic relationship, but the cubic term was not significant. Hence, all subsequent models conceptualized calculus grade as a linear function of reading the text and studying.

13. While SAT mathematics scores do not directly test a student's calculus knowledge, they do serve as a proxy of a student's foundational math ability.

14. Studies report that high school GPA, even more so than SAT scores, is a strong predictor of college success.[75,78] While high school GPA does not isolate the effect of high school mathematics grade on college success, it is reasonable to assume that, if high school GPA is a strong predictor of college success, then a student's high school mathematics grades may represent a student's prior mathematical ability/preparation that predicts success in college mathematics. This is confirmed in Table 4.

15. The race/ethnic group labels of white, black, and Asian/Pacific Islander are thus short for non-Hispanic white, non-Hispanic black, and non-Hispanic Asian/Pacific Islander, respectively.

16. We did estimate a model that controlled for the type of institution – two-year vs. four-year. When modelled with effort, students who attended two-year institutions earned lower college calculus grades than did students who attended four-year institutions. This variable was not significant, however, in succeeding models. Therefore, we do not report models that included type of institution.

17. Significance values based on Bonferroni correction. Sidak and Scheffe tests yielded similar results. p-values were averaged across 20 multiple data imputations.

18. Percentages by race/ethnicity were generated by categorizing students by whether they took high school calculus (yes or no) and whether they earned below a 3.10 (i.e., the point at which effort among low-performing, non-calculus students was in ‘equilibrium’). Percentages were averaged across 20 multiple data imputations.

Additional information

Funding

Funding for this research was provided by the National Science Foundation [grant number. 0813702].