Preservice Elementary Teachers’ Beliefs toward Mathematics and Mathematics Teaching

As they began their one-year teacher education program 138 elementary school teacher candidates completed a questionnaire designed to measure their beliefs concerning the nature of mathematics, measured on a scale from absolutist to fallibilist, and their beliefs concerning effective mathematics instruction, measured on a scale from traditional to constructivist. Interviews were conducted with volunteer questionnaire participants, with selection based on the questionnaire results and using two sets of criteria. Study 1. involved 8 teacher candidates showing distinct absolutist or fallibilist views of mathematics and individual interviews explored participants' beliefs concerning the use of information and communication technology, particularly interactive whiteboards (IWB), in the teaching and learning of mathematics. Participants with absolutist beliefs about the nature of mathematics tended to focus on the IWB as a presentation tool, while those with fallibilist beliefs appreciated the use of the IWB to support student exploration. Study 2. involved 8 teacher candidates with apparently misaligning absolutist beliefs concerning the nature of mathematics and constructivist beliefs concerning teaching. Interviews exploring participants' favoured instructional approaches, particularly those involving the use of manipulatives, showed that constructivist views involved essentially surface beliefs and that in fact manipulatives would be employed to support traditional direct instruction.

Engineering passive bioreactive barriers: risk-managing the legacy of industrial soil and groundwater pollution

Permeable reactive barriers are a technology that is one decade old, with most full-scale applications based on abiotic mechanisms. Though there is extensive literature on engineered bioreactors, natural biodegradation potential, and in situ remediation, it is only recently that engineered passive bioreactive barrier technology is being considered at the commercial scale to manage contaminated soil and groundwater risks. Recent full-scale studies are providing the scientific confidence in our understanding of coupled microbial (and genetic), hydrogeologic, and geochemical processes in this approach and have highlighted the need to further integrate engineering and science tools.

Adaptation of a questionnaire to assess the epistemological beliefs of mathematics in secondary school teachers

The objective of the study is to determine the psychometric properties of the Epistemological Beliefs Questionnaire on Mathematics. 171 Secondary School Mathematics Teachers of the Central Region of Cuba participated. The results show acceptable internal consistency. The factorial structure of the scale revealed three major factors, consistent with the Model of the Three Constructs: beliefs about knowledge, about learning and teaching. Irregular levels in the development of the epistemological belief system about mathematics of these teachers were shown, with a tendency among naivety and sophistication poles. In conclusion, the questionnaire is useful for evaluating teacher’s beliefs about mathematics.

Comparison of elicitation methods for moral and affective beliefs in the theory of planned behaviour

Although the theory of planned behaviour (TPB) has been applied successfully in the area of food choice, it has been criticized for its pure utilitarian approach to the factors determining behaviour. Despite the increase in predictive power of the model with added components such as affective attitude and moral and ethical concerns, in most studies the elicitation process still only addresses people's utilitarian beliefs about the behaviour with little attention paid to other aspects. This study compares the traditional method of elicitation of advantages and disadvantages with two other methods (word association and open-ended) in the elicitations of beliefs, attitudes and moral concerns in relation to the consumption of organic foods. Results show the traditional method to be best for eliciting cognitive beliefs, open-ended emotion task for eliciting emotional beliefs and open-ended beliefs task best for moral concerns. The advantages and disadvantages of each method are discussed.

Valuing the cultural monuments of Armenia: Bayesian updating of prior beliefs in contingent valuation

The most appropriate way to measure the social benefits of conserving built cultural heritage sites is to ask the beneficiaries of conservation interventions how much they would be willing to pay for them. We use contingent valuation - a survey-based approach that elicits willingness to pay (WTP) directly from individuals - to estimate the benefits of a nationwide conservation of built cultural heritage sites in Armenia. The survey was administered to Armenian nationals living in Armenia, and obtained extensive information about the respondents' perceptions of the current state of conservation of monuments in Armenia, described the current situation, presented a hypothetical conservation program, elicited WTP for it, and queried individuals about what they thought would happen to monument sites in the absence of the government conservation program. We posit that respondents combined the information about the fate of monuments provided by the questionnaire with their prior beliefs, and that WTP for the good, or program, is likely to be affected by these updated beliefs. We propose a Bayesian updating model of prior beliefs, and empirically implement it with the data from our survey. We found that uncertainty about what would happen to monuments in the absence of the program results in lower WTP amounts. © 2008 Pion Ltd and its Licensors.

Background beliefs and evidence interpretation

In this paper we argue that it is often adaptive to use one’s background beliefs when interpreting information that, from a normative point of view, is incomplete. In both of the experiments reported here participants were presented with an item possessing two features and were asked to judge, in the light of some evidence concerning the features, to which of two categories it was more likely that the item belonged. It was found that when participants received evidence relevant to just one of these hypothesised categories (i.e. evidence that did not form a Bayesian likelihood ratio) they used their background beliefs to interpret this information. In Experiment 2, on the other hand, participants behaved in a broadly Bayesian manner when the evidence they received constituted a completed likelihood ratio. We discuss the circumstances under which participants, when making their judgements, consider the alternative hypothesis. We conclude with a discussion of the implications of our results for an understanding of hypothesis testing, belief revision, and categorisation.