Seven hundred twenty-three Finnish 13-year-olds from 17 different metropolitan public schools were each given, at the beginning of the school year, two self-report questionnaires designed to measure "students' beliefs about school mathematics, about themselves as mathematics learners, their affective responses towards mathematics and their behavioural patterns in math classes."
|1. Self-efficacy||2. Low self-esteem||3. Enjoyment of maths|
|4. Liking of maths||5. Fear of mathematics||6. Test anxiety|
|7. Integration||8. Persistence||9. Preference for challenge|
In addition, students were given a 26-problem math test "about numbers and different calculations, various spatial and word problems, and examination of patterns." This math test provided a tenth scale (a "performance" scale) on which students were measured. The results below show intercorrelations among the nine affective scales and the performance scale. (Researchers used a benchmark of 0.15 for significance.)
Few Strong Correlations for Affect and Initial Learning
The first row of the table shows that students' self-efficacy correlated positively with their self-reported enjoyment of math (Column 3, 0.41) and with their test scores (Column 10, 0.28). In contrast, and as expected, self-efficacy correlated negatively with subjects' fear of mathematics (Column 5, -0.45) and their test anxiety (Column 6, -0.26). Once you get your head around the table, you'll find that there's nothing really surprising there. Nearly all of the "positive" measures are correlated negatively with the "negative" measures, and vice versa.
But take a look at the correlation data for what is called "integration." These are the values in Column 7 and the values in Row 7. The authors describe integration as the "tendency to integrate new math knowledge with previous knowledge and experience." Out of the nine data points for integration, five show no significant correlation, using the researchers' own metric for statistical signficance (0.15). And the correlation between integration and self-efficacy is just barely significant (0.16). The only other "insignificant" correlation shown is between test anxiety and persistence (-0.08).
So integration contains five sixths of the insignificant results in the study. Indeed, if one were to use the absolute values of the correlations in the table to find a mean correlation for each scale, integration would be at the very bottom (0.174), while fear of mathematics would be at the top (0.478 . . .). And integration was the only scale which did not interact in a statistically significant way with test scores.
Given that these data are correlational (and the raw data were taken only from self reports), it is impossible to draw reliable conclusions about causality. And generalizing from 13-year-old Finnish students to all learners would be irresponsible. Yet, it is interesting to note that the only factor that correlated moderately with integration in the study was persistence (0.51). Thus, if one could say anything, one might say that these results may provide yet another indication that integrating "new math knowledge with previous knowledge and experience" (some call this "learning") is not as interwoven with students' intrinsic personal/emotional qualities as we like to think—that it doesn't matter that they have low or high self-esteem or that they fear or do not fear mathematics or that they have or do not have test anxiety or that they like to challenge themselves or not.
What seems to matter more is that they show up and keep trying. Luckily, of all the affective traits mentioned in the study, persistence is the one that we might be able to design learning environments for without the need to pretend that we have degrees in counseling psychology.
Malmivuori, M. (2006). Affect and Self-Regulation Educational Studies in Mathematics, 63 (2), 149-164 DOI: 10.1007/s10649-006-9022-8