We now present the discussion according to the two-levels structure of the paper:
we start with some consideration about the “content”, then we continue with the method.
what are we learning from classification trees?
The first branching in each classification tree concerns cognitive variables, then the affective factors emerge. They emerge both for students who are likely to take the degree and for students who are likely to dropout, but in different manners.
In fact, for the first group, we observed that a high T2, a not too high sense of responsibility (prc), and a low availability of effective models (smt2) predicts
“success”. The same variable smt2 intervenes also when T2 is low, but here it predicts “failure” when it is low. This is a phenomenon which would never be
observed in traditional correlation or multiple regression analysis. Whether this ambivalent (predictive) role of a single factor corresponds to a causal role or not, it is unclear by now. Yet, such phenomena are not manifestly absurd: an excessive sense of responsibility and self-comparison with effective models could actually be negative factors for academic achievement (figure 1); in turn, high adaptability is expected to be a positive factor for academic achievement, but could also lead students experiencing difficulties to decide more easily to change to a different curriculum (adp1 and adp4 in figure 2). Our study, along with Maggiani (2011), confirms that the transition from high school to university is a personal process where –beyond learning skills and motivation– self-beliefs, locus of control and adaptability interact in complex and “nonlinear” patterns, which cannot be explored by traditional correlation analysis.
This should not be assumed to describe the actual process which determines the academic achievement: it rather indicates that, for instance, students getting a good score in T2 and nevertheless failing to reach 21 ECTS could be singled out (with reasonable accuracy) by considering a specific combination of sense of responsibility, previous availability of effective models as a source of mathematical self-efficacy, and adaptability. To relate this predictive evidence with a causal process, further investigation is required: in particular, one should compare patterns emerging from this exploratory analysis with models proposed by current research on affective factors. For the time being, in fact, we are able to describe the sample of interest rather than to show its predictive power. We stress that, given both the novelty of the methodology and the specificity of the sample, there are few results in literature that can help us better understanding the phenomenon. However, we hope to have given a contribution in the understanding of students’ difficulties.
the classification tree methodology
The first aspect we bring to light is that in our study we used the results from previous years (since 2001/02) to infer on the present (and the future) students enrolled in the mathematics under graduate course. This implies an overarching assumption: the situation of ten-years-ago students is the same of today’s one.
The term ‘situation’ has to be meant in a wide way, in order to take into account socio-economical, psychological, and cognitive aspects. Although we are aware of the changes our formative system –as well as our country and our society– had gone through in the last ten years, we claim that some facts are still worthy to be considered. In fact, if we look at the classification tree which contains information about the enrolling to the second year, we can see a confirmation of this.
The methodology of the classification tree can be seen not only as a way to disentangle a complicated (and sometimes contradictory) picture, but also as a generator of research questions –a way to bring into light issues that need further elaboration. It provides the researcher an articulated frame, and the researcher has to make sense of it, without relying on constraining assumptions such as linearity correlations of variables.
We would like to point out that we do not believe that the future of undergraduate students may be completely predicted by means of tests (neither cognitive-based, nor affective-based), or other tools. Our research may serve as a source of information for professors and administrative operators who mind about the students’ career, for any reason, to be aware of what is likely to happen in certain circumstances.
General considerations on the research
We conclude this paper with some general considerations. The first one concerns the role of the items used to collect data: the picture that emerges from the analysis depends on the data that had been collected. Items are not “neutral”
to the research, as well as the assumptions that lay on the background of the methodology used.
Among the items, the affective-based ones have a significant role. As expected, the first split is determined by cognitive factors, but the affective aspects contribute to delineate a varied and multifaceted landscape. Without them, the trees would have stopped after very few steps. In other words, this research contributes to prove that affect-related issues are of crucial importance in the learning processes, considered in a wide perspective.
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