Julia Dietrich

The influence of math anxiety on symbolic and non-symbolic magnitude processing

Deficits in basic numerical abilities have been investigated repeatedly as potential risk factors of math anxiety. Previous research suggested that also a deficient approximate number system (ANS), which is discussed as being the foundation for later math abilities, underlies math anxiety. However, these studies examined this hypothesis by investigating ANS acuity using a symbolic number comparison task. Recent evidence questions the view that ANS acuity can be assessed using a symbolic number comparison task. To investigate whether there is an association between math anxiety and ANS acuity, we employed both a symbolic number comparison task and a non-symbolic dot comparison task, which is currently the standard task to assess ANS acuity. We replicated previous findings regarding the association between math anxiety and the symbolic distance effect for response times. High math anxious individuals showed a larger distance effect than less math anxious individuals. However, our results revealed no association between math anxiety and ANS acuity assessed using a non-symbolic dot comparison task. Thus, our results did not provide evidence for the hypothesis that a deficient ANS underlies math anxiety. Therefore, we propose that a deficient ANS does not constitute a risk factor for the development of math anxiety. Moreover, our results suggest that previous interpretations regarding the interaction of math anxiety and the symbolic distance effect have to be updated. We suggest that impaired number comparison processes in high math anxious individuals might account for the results rather than deficient ANS representations. Finally, impaired number comparison processes might constitute a risk factor for the development of math anxiety. Implications for current models regarding the origins of math anxiety are discussed.

A Systematic Investigation of Accuracy and Response Time Based Measures Used to Index ANS Acuity.

The approximate number system (ANS) was proposed to be a building block for later mathematical abilities. Several measures have been used interchangeably to assess ANS acuity. Some of these measures were based on accuracy data, whereas others relied on response time (RT) data or combined accuracy and RT data. Previous studies challenged the view that all these measures can be used interchangeably, because low correlations between some of the measures had been observed. These low correlations might be due to poor reliability of some of the measures, since the majority of these measures are mathematically related. Here we systematically investigated the relationship between common ANS measures while avoiding the potential confound of poor reliability. Our first experiment revealed high correlations between all accuracy based measures supporting the assumption that all of them can be used interchangeably. In contrast, not all RT based measures were highly correlated. Additionally, our results revealed a speed-accuracy trade-off. Thus, accuracy and RT based measures provided conflicting conclusions regarding ANS acuity. Therefore, we investigated in two further experiments which type of measure (accuracy or RT) is more informative about the underlying ANS acuity, depending on participants’ preferences for accuracy or speed. To this end, we manipulated participants’ preferences for accuracy or speed both explicitly using different task instructions and implicitly varying presentation duration. Accuracy based measures were more informative about the underlying ANS acuity than RT based measures. Moreover, the influence of the underlying representations on accuracy data was more pronounced when participants preferred accuracy over speed after the accuracy instruction as well as for long or unlimited presentation durations. Implications regarding the diffusion model as a theoretical framework of dot comparison as well as regarding the relationship between ANS acuity and math performance are discussed.

Die Kraft der Konkretion oder: Die Rolle deskriptiver Annahmen für die Anwendung und Kontextsensitivität ethischer Theorie

ZusammenfassungDer Artikel greift die Überlegung auf, dass sich die Bioethik auch deshalb der empirischen Forschung zuwenden solle, um ihre Anwendbarkeit und Kontextsensitivität zu erhöhen. Am Beispiel der Norm, dass Schmerzen zu lindern seien, und mit Hilfe eines allgemeinen Modells ethischer Urteilsbildung werden verschiedene Bedeutungen der Anwendung und der Kontextsensitivität unterschieden und es wird untersucht, welche Rolle deskriptive Annahmen hierbei jeweils spielen können. Es wird die These vertreten, dass Kontextsensitivität in den meisten ihrer Bedeutungen von fundamentalethischen Grundannahmen unabhängig ist und dass deskriptive Annahmen einen Prozess der Spezifikation ethischer Urteilsbildung auslösen, der in dieser Form nicht von der ethischen Begründung von Normen und Werten aus initiiert und antizipiert werden kann, jedoch zu seinem (zumindest vorübergehenden) handlungsorientierenden Abschluss auf diese zurückverwiesen ist.AbstractDefinition of the problem The article takes up the idea that bioethics should consider empirical research in order to enhance its applicability and context-sensitivity. Arguments The example of the norm that pain should be eased and a general model of ethical judgement help to differentiate various meanings of applicability and context-sensitivity and help to analyze which role descriptive assumptions play for them. Conclusion It is argued that context-sensitivity is most often independent of fundamental ethical theories and that descriptive assumptions prompt a process of ethical specification that cannot be initiated and anticipated by ethical substantiation in itself but has to refer back to it if it shall succeed in guiding action.

The ethical matrix as an instrument for teaching and evaluation

This contribution presents how the Ethical Matrix was used in teaching and evaluating a course on ‘Ethics of Food and Nutrition Security’ (EFNS) at Hohenheim University in the winter semester 2010/2011 and in the winter semester 2011/12. We will first provide some information on the development of the course and present the results of the general evaluation of the course by the department. We will then introduce the newly developed instrument in which the Ethical Matrix was embedded. The instrument aims at testing individual skills necessary for identifying ethical issues. Finally, we will draw some conclusions that refer to the further development of the instrument.

Using propensity score matching to construct experimental stimuli.

Propensity score matching is widely used in various fields of research, including psychology, medicine, education, and sociology. It is usually applied to find a matched control group for a treatment group. In the present article, we suggest that propensity score matching might also be used to construct item sets matched for different parameters. We constructed stimuli to illustrate the use of propensity score matching in item construction for the exemplary cases of numerical cognition research and reading research. In particular, we provide a step-by-step approach, using the statistics software R, for how to apply propensity score matching for constructing matched stimuli. This approach involves deciding on a population of stimuli, determining and calculating the covariates, and finally applying the propensity-matching method to find a set of items matched to another predefined set. Thereby, we were able to construct well-matched item sets for both examples. Hence, we conclude that the propensity-score-matching method is useful for constructing matched stimuli. Further cases of application are discussed.

Magnitude processing of symbolic and non-symbolic proportions: an fMRI study

BackgroundRecent research indicates that processing proportion magnitude is associated with activation in the intraparietal sulcus. Thus, brain areas associated with the processing of numbers (i.e., absolute magnitude) were activated during processing symbolic fractions as well as non-symbolic proportions. Here, we investigated systematically the cognitive processing of symbolic (e.g., fractions and decimals) and non-symbolic proportions (e.g., dot patterns and pie charts) in a two-stage procedure. First, we investigated relative magnitude-related activations of proportion processing. Second, we evaluated whether symbolic and non-symbolic proportions share common neural substrates.MethodsWe conducted an fMRI study using magnitude comparison tasks with symbolic and non-symbolic proportions, respectively. As an indicator for magnitude-related processing of proportions, the distance effect was evaluated.ResultsA conjunction analysis indicated joint activation of specific occipito-parietal areas including right intraparietal sulcus (IPS) during proportion magnitude processing. More specifically, results indicate that the IPS, which is commonly associated with absolute magnitude processing, is involved in processing relative magnitude information as well, irrespective of symbolic or non-symbolic presentation format. However, we also found distinct activation patterns for the magnitude processing of the different presentation formats.ConclusionOur findings suggest that processing for the separate presentation formats is not only associated with magnitude manipulations in the IPS, but also increasing demands on executive functions and strategy use associated with frontal brain regions as well as visual attention and encoding in occipital regions. Thus, the magnitude processing of proportions may not exclusively reflect processing of number magnitude information but also rather domain-general processes.

Set size influences the relationship between ANS acuity and math performance: a result of different strategies?

Previous research has proposed that the approximate number system (ANS) constitutes a building block for later mathematical abilities. Therefore, numerous studies investigated the relationship between ANS acuity and mathematical performance, but results are inconsistent. Properties of the experimental design have been discussed as a potential explanation of these inconsistencies. In the present study, we investigated the influence of set size and presentation duration on the association between non-symbolic magnitude comparison and math performance. Moreover, we focused on strategies reported as an explanation for these inconsistencies. In particular, we employed a non-symbolic magnitude comparison task and asked participants how they solved the task. We observed that set size was a significant moderator of the relationship between non-symbolic magnitude comparison and math performance, whereas presentation duration of the stimuli did not moderate this relationship. This supports the notion that specific design characteristics contribute to the inconsistent results. Moreover, participants reported different strategies including numerosity-based, visual, counting, calculation-based, and subitizing strategies. Frequencies of these strategies differed between different set sizes and presentation durations. However, we found no specific strategy, which alone predicted arithmetic performance, but when considering the frequency of all reported strategies, arithmetic performance could be predicted. Visual strategies made the largest contribution to this prediction. To conclude, the present findings suggest that different design characteristics contribute to the inconsistent findings regarding the relationship between non-symbolic magnitude comparison and mathematical performance by inducing different strategies and additional processes.

Das Lernziel „Ethik“ in Studiengängen der Chemie: Empirische Bestandsaufnahme und Gestaltungsvorschläge

Auf der Basis einer empirischen Untersuchung chemischer Curricula an deutschen Universitaten wird am Beispiel der Ethik die Diskrepanz zwischen politischem Anspruch und Hochschulwirklichkeit aufgezeigt. In uber 80 % der Chemie-Curricula ist das Lernziel „ethische Reflexion“ nicht einmal benannt. Und dort, wo es formuliert ist, taucht es meist lediglich im unverbindlichen Wahlbereich auf. Abschliesend wird eine Reihe von praktischen Vorschlagen formuliert, um diese Diskrepanz zu uberwinden.

Welche ethischen Fragen wirft die Biogerontologie auf

Das Ziel dieser Einleitung ist es, die ethischen Fragen, die durch die Biogerontologie aufgeworfen werden, gezielt zu formulieren und zu strukturieren. Dabei geht sie theoriegeleitet vor, das heist, sie orientiert sich an einigen fundamentalen Unterscheidungen ethischer Theoriebildung, die als solche relativ unstrittig sind, wenn auch ihr genauer begrifflicher Zuschnitt, ihr Verhaltnis untereinander und ihre Bedeutung fur die ethische Urteilsbildung z. T. sehr unterschiedlich gesehen werden. Hierzu gehoren die Unterscheidungen zwischen Moral und Ethik, zwischen Fragen des guten Lebens und des Gesollten sowie zwischen Individual- und Sozial- bzw. Individual- und Institutionenethik, die in der Angewandten Ethik bereits langer als Strukturierungshilfe verwendet werden (siehe z. B. programmatisch Haker 1998).