Classical Business Cycles in America: Are National Business Cycles Synchronised?

This paper provides further evidence on the synchronization between business cycle regimes in seven American countries by using a classical business cycles approach. Despite recent increasing international economic transactions within this continent, our results suggest that national business cycles are largely idiosyncratic, except for the United States and Canada. Thus, international coordination of macroeconomic policies may not be effective, at least in the short-run. Also, as a by product, we find evidence of asymmetries between expansions and recessions in mean, volatility and duration in most countries.Business cycle regimes, international synchronization, North America, South America

The accuracy of farmer-generated data in an agricultural citizen science methodology.

Over the last decades, participatory approaches involving on-farm experimentation have become more prevalent in agricultural research. Nevertheless, these approaches remain difficult to scale because they usually require close attention from well-trained professionals. Novel large-N participatory trials, building on recent advances in citizen science and crowdsourcing methodologies, involve large numbers of participants and little researcher supervision. Reduced supervision may affect data quality, but the “Wisdom of Crowds” principle implies that many independent observations from a diverse group of people often lead to highly accurate results when taken together. In this study, we test whether farmer-generated data in agricultural citizen science are good enough to generate valid statements about the research topic. We experimentally assess the accuracy of farmer observations in trials of crowdsourced crop variety selection that use triadic comparisons of technologies (tricot). At five sites in Honduras, 35 farmers (women and men) participated in tricot experiments. They ranked three varieties of common bean (Phaseolus vulgaris L.) for Plant vigor, Plant architecture, Pest resistance, and Disease resistance. Furthermore, with a simulation approach using the empirical data, we did an order-of-magnitude estimation of the sample size of participants needed to produce relevant results. Reliability of farmers’ experimental observations was generally low (Kendall’s W0.174 to 0.676). But aggregated observations contained information and had sufficient validity (Kendall’s tau coefficient 0.33 to 0.76) to identify the correct ranking orders of varieties by fitting Mallows-Bradley-Terry models to the data. Our sample size simulation shows that low reliability can be compensated by engaging higher numbers of observers to generate statistically meaningful results, demonstrating the usefulness of the Wisdom of Crowds principle in agricultural research. In this first study on data quality from a farmer citizen science methodology, we show that realistic numbers of less than 200 participants can produce meaningful results for agricultural research by tricot-style trials

The effect of authority on the persuasiveness of mathematical arguments

Three experiments are reported which investigate the extent to which an authority figure influences the level of persuasion undergraduate students and research-active mathematicians invest in mathematical arguments. We demonstrate that, in some situations, both students and researchers rate arguments as being more persuasive when they are associated with an expert mathematician than when the author is anonymous. We develop a model which accounts for these data by suggesting that, for both students and researchers, an authority figure only plays a role when there is already some uncertainty about the argument’s mathematical status. Implications for pedagogy, and for future research, are discussed

How persuaded are you? A typology of responses

Several recent studies have suggested that there are two different ways in which a person can proceed when assessing the persuasiveness of a mathematical argument: by evaluating whether it is personally convincing, or by evaluating whether it is publicly acceptable. In this paper, using Toulmin’s (1958) argumentation scheme, we produce a more detailed theoretical classification of the ways in which participants can interpret a request to assess the persuasiveness of an argument. We suggest that there are (at least) five ways in which such a question can be interpreted. The classification is illustrated with data from a study that asked undergraduate students and research-active mathematicians to rate how persuasive they found a given argument. We conclude by arguing that researchers interested in mathematical conviction and proof validation need to be aware of the different ways in which participants can interpret questions about the persuasiveness of arguments, and that they must carefully control for these variations during their studies

Semantic contamination and mathematical proof: can a non-proof prove?

The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Hereweargue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to argument evaluation tasks suggest that students may hold two different and contradictory conceptions of proof: one related to conviction, and one to validity. We demonstrate that these two conceptions can be preferentially elicited by making apparently irrelevant linguistic changes to task instructions. After analyzing the occurrence of “proof” and “prove” in natural language, we report two experiments that suggest that the noun form privileges evaluations related to validity, and that the verb form privileges evaluations related to conviction. In short, we show that (what is judged to be) a non-proof can sometimes (be judged to) prove

“Explanatory” talk in mathematics research papers

In this paper we explore the ways in which mathematicians talk about explanation in their research papers. We analyze the use of the words explain/explanation (and various related words) in a large corpus of text containing research papers in both mathematics and physical sciences. We found that mathematicians do not frequently use this family of words and that their use is considerably more prevalent in physics papers than in mathematics papers. In particular, we found that physicists talk about explaining why disproportionately more often than mathematicians. We discuss some possible accounts for these differences