Beyond questionnaires – Exploring adult education teachers' mathematical beliefs with pictures and interviews

Because of the impact that mathematical beliefs have on an individual’s behaviour, they are generally well researched. However, little mathematical belief research has taken place in the field of adult education. This paper presents preliminary results from a study conducted in this field in Switzerland. It is based on Ernest’s (1989) description of mathematics as an instrumental, Platonist or problem solving construct. The analysis uses pictures drawn by the participants and interviews conducted with them as data. Using a categorising scheme developed by Rolka and Halverscheid (2011), the author argues that adults’ mathematical beliefs are complex and especially personal aspects are difficult to capture with said scheme. Particularly the analysis of visual data requires a more refined method of analysis.

When language of instruction and language of application differ: Cognitive costs of bilingual mathematics learning

Bilingual education programs implicitly assume that the acquired knowledge is represented in a language-independent way. This assumption, however, stands in strong contrast to research findings showing that information may be represented in a way closely tied to the specific language of instruction and learning. The present study aims to examine whether and to which extent cognitive costs appear during arithmetic learning when language of instruction and language of retrieving differ. Thirty-nine high school students participating in a bilingual education program underwent a four-day training on multiplication and subtraction problems in one language (German or French), followed by a test session in which they had to solve trained as well as untrained problems in both languages. We found that cognitive costs related to language switching appeared for both arithmetic operations. Implications of our findings are discussed with respect to bilingual education as well as to cognitive mechanisms underlying different arithmetic operations.

Functional neuroimaging of emotional learning and autonomic reactions

This article provides a selective overview of the functional neuroimaging literature with an emphasis on emotional activation processes. Emotions are fast and flexible response systems that provide basic tendencies for adaptive action. From the range of involved component functions, we first discuss selected automatic mechanisms that control basic adaptational changes. Second, we illustrate how neuroimaging work has contributed to the mapping of the network components associated with basic emotion families (fear, anger, disgust, happiness), and secondary dimensional concepts that organise the meaning space for subjective experience and verbal labels (emotional valence, activity/intensity, approach/withdrawal, etc.). Third, results and methodological difficulties are discussed in view of own neuroimaging experiments that investigated the component functions involved in emotional learning. The amygdala, prefrontal cortex, and striatum form a network of reciprocal connections that show topographically distinct patterns of activity as a correlate of up and down regulation processes during an emotional episode. Emotional modulations of other brain systems have attracted recent research interests. Emotional neuroimaging calls for more representative designs that highlight the modulatory influences of regulation strategies and socio-cultural factors responsible for inhibitory control and extinction. We conclude by emphasising the relevance of the temporal process dynamics of emotional activations that may provide improved prediction of individual differences in emotionality.

Imaging emotional brain functions: conceptual and methodological issues

This article reviews the psychophysiological and brain imaging literature on emotional brain function from a methodological point of view. The difficulties in defining, operationalising and measuring emotional activation and, in particular, aversive learning will be considered. Emotion is a response of the organism during an episode of major significance and involves physiological activation, motivational, perceptual, evaluative and learning processes, motor expression, action tendencies and monitoring/subjective feelings. Despite the advances in assessing the physiological correlates of emotional perception and learning processes, a critical appraisal shows that functional neuroimaging approaches encounter methodological difficulties regarding measurement precision (e.g., response scaling and reproducibility) and validity (e.g., response specificity, generalisation to other paradigms, subjects or settings). Since emotional processes are not only the result of localised but also of widely distributed activation, a more representative model of assessment is needed that systematically relates the hierarchy of high- and low-level emotion constructs with the corresponding patterns of activity and functional connectivity of the brain.

Evaluating retraining rules for semi-supervised learning in neural network based cursive word recognition

Training a system to recognize handwritten words is a task that requires a large amount of data with their correct transcription. However, the creation of such a training set, including the generation of the ground truth, is tedious and costly. One way of reducing the high cost of labeled training data acquisition is to exploit unlabeled data, which can be gathered easily. Making use of both labeled and unlabeled data is known as semi-supervised learning. One of the most general versions of semi-supervised learning is self-training, where a recognizer iteratively retrains itself on its own output on new, unlabeled data. In this paper we propose to apply semi-supervised learning, and in particular self-training, to the problem of cursive, handwritten word recognition. The special focus of the paper is on retraining rules that define what data are actually being used in the retraining phase. In a series of experiments it is shown that the performance of a neural network based recognizer can be significantly improved through the use of unlabeled data and self-training if appropriate retraining rules are applied.