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Why do so many mathematics students prematurely drop out?

20. November 2017

Each year the IPN honors an excellent empirically oriented thesis related to mathematics or science education, written at Kiel University. Last year's prize was awarded to Colin Jeschke for his master's thesis in mathematics education. His thesis was about the subject-specific resilience of first semester mathematics students. Jeschke was supervised by Prof. Dr. Aiso Heinze, Head of the Mathematics Education Department at the IPN. The price committee valued the thesis as highly scientific as well as application-oriented. The commission was impressed that the work presented an independent, self-contained study. In addition, the commission praised the high methodological level of the thesis. Colin Jeschke presents his work with this article.

Measuring Academic Buoyancy of Mathematics Freshmen

Why do so many mathematics students prematurely drop out?

Colin Jeschke

As the high admissions numbers show, studying mathematics is attractive for many high school graduates. However, a majority of students drop out of mathematics during the first two semesters or change their major. Thus, the drop-out rates for the first year of study often add up to more than 40% nationally and internationally. The students indicate mostly having difficulties due to enormous demands. They experience a higher performance after the transition to higher education and must independently organize their own work processes, with self-study playing a key role. In mathematics studies, self-study at many universities is defined by the completion of math problems which, in line with the nature of  university mathematics, usually require mathematical proving skills  (see figure below). However, most undergraduate students lack the required  skills to solve these proof tasks, which is why this part of self-study is perceived as particularly time-consuming and burdensome. This indicates that a student’s academic buoyancy could influence both the duration and success of the studies in mathematics in terms of good module performance.

In the scholastic context, the ability to handle academic requirements, the so-called academic buoyancy, has already been investigated several times. Highly resilient students can cope with school-related stressors such as: handling demanding homework, time pressure or poor school grades. This construct was adapted in the present study to the learning context of mathematics studies and differentiated according to the subject-specific requirements facing first year math students. For a questionnaire instrument designed for this purpose we examined to what extent a reliable and valid measurement of subject-specific resilience is possible.

 In order to assess academic buoyancy in a sample of mathematics freshmen, an eleven-item-questionnaire was designed (see figure above) focusing on requirements that result from the weekly practice-related mathematical exercises. Each item has a 7-step scale for the given statement declaring to what extent this applies (1 = "does not apply at all"; 7 = "completely applies"). The questionnaire was administered to a sample of N = 147 mathematics freshmen of Kiel University at the beginning of the 2014/2015 winter semester. In addition to this newly developed instrument, established questionnaires assessing general resilience (RS-13) and personality traits (BFI-SOEP) have been administered in this sample. After the first semester, the participants were revisited and their continuance of mathematics studies recorded. In addition, it was ascertained to what extent the exercises in the questionnaire in the first semester were subjectively perceived as stressful.

As part of the data analysis, two items were excluded from the questionnaire on the basis of a confirmatory factor analysis and content considerations. The remaining nine items show a good unidimensionality (CFI = .966, RMSEA = .065), indicating the measurement of one latent attribute. Correlations to personality traits and general resilience were investigated to further characterize and delineate this unidimensionality. We found significant correlations to conscientiousness (r = .41, p <.001) and a weak correlation to general resilience (r = .20, p <.05). The weak connection of our newly developed instrument to general resilience can be explained by the theoretically assumed variability of academic buoyancy depending on the situational requirements. It is thus conceivable that a person can be resilient to situations requiring mathematics, but not to more general life situations. As expected, other personality traits in the five-factor model (openness, compatibility, extraversion and neuroticism) did not show significant correlations. Academic buoyancy was also identified as a significant predictor of length of stay in mathematics studies (Figure right). Therefore, students with high subject-specific resilience are more likely to reach the second semester (logistic regression: exp (B) = 1.62, p <.05, biserial correlation: r = .29, p <.05).

Overall, these results are interpreted as indications of construct validity, content validity and prognostic validity. Indications of the reliability of the questionnaire are given by a good internal consistency of the nine items (Cronbach’s α = .87). In summary, the results provide concrete indications that the questionnaire developed enables a reliable and valid assessment of an individual’s academic buoyancy in relation to mastering mathematical study requirements. However, the significance of this promising trial is limited by the small sample size. In order to review the results in a larger and more representative sample, studies are currently being conducted on subject-specific resilience with first-semester students from Kiel, Munich and Stockholm. In the future, the concept of academic buoyancy could serve to improve existing theoretical models for predicting dropouts in mathematics as well as improving teaching first year mathematics students. For example, it is still unclear whether academic buoyancy is a learnable skill. The development of targeted support before or during initial studies could hence contribute not only to reducing the stress of mathematics studies but also to promoting freshmen’s academic buoyancy.