Summary This review volume consists of a set of chapters written by leading scholars, most of them founders of their fields. Preface p.
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Gauvrit and J. Longo and C. Palamidessi and T. Paul 6 Metaphysics, Metamathematics and Metabiology p. Chaitin 7 Uncertainty in Physics and Computation p. Stay 8 Indeterminism and Randomness Through Physics p. Delahaye 10 The Road to Intrinsic Randomness p. Miller 17 Studying Randomness Through Computation p. Nies 18 Computability, Algorithmic Randomness and Complexity p.
Ten Years After p. Ferbus-Zanda and S. Kucera 22 Connecting Randomness to Computation p. Staiger 24 Randomness in Algorithms p. Calude and J. Casti and G. Chaitin and P. Davits and K. Name of resource. Problem URL. Describe the connection issue.
SearchWorks Catalog Stanford Libraries. Randomness through computation : some answers, more questions. Responsibility editor, Hector Zenil. Imprint New Jersey : World Scientific, c Physical description xviii, p. Online Available online. Science Library Li and Ma.
R Unknown. More options. Find it at other libraries via WorldCat Limited preview. Contributor Zenil, Hector. Bibliography Includes bibliographical references and indexes. Contents Is randomness necessary?
Understanding Random Variables
Rukhin Scatter and regularity imply Benford's law Gauvrit, J. Questions concerning probability as a ratio seemed quite easy for the participants. This may seem unsurprising, as pupils learn to calculate ratios in primary school KMK, b. This finding corroborates indications presented by various authors e. This is a concern, as students have to calculate and apply ratios explicitly in biology to topics such as Mendelian inheritance and Hardy-Weinberg equilibrium e.
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In the mathematical context, students found some of the single-event items challenging some were apparently easy, but responses to more than half were distributed across the scale. Even when asked about the un predictability of single events, students seemed to think about predictability in aggregate terms. Similarly, in the evolutionary context, items regarding origin of variation, either generally e.
Finally, random phenomena seemed quite challenging for our students in evolutionary contexts. When they had to explain why evolutionary change through natural selection is a nonrandom process, they often forgot that natural selection acts upon randomly generated variation. A particularly important source of new variation in the focal contexts is mutation, which is regarded as a random process, partly because the probability of mutations occurring is not affected by the selective consequences and partly because their occurrence in a given individual at a given time is far beyond our modeling capacities Gregory, ; Heams, Nevertheless, several studies have indicated that students tend to struggle with both the importance of random processes such as the origin of variation in evolutionary processes and understanding why mutations are called random e.
Our results corroborate these findings that random processes pose learning difficulties. Most studies of evolutionary knowledge focus on differences between novice and advanced students attending similar study programs e. However, possible differences between biology majors and preservice biology teachers are also potentially important, particularly as the latter will form the next generation to teach evolutionary theory.
So, it might be acceptable for preservice biology teachers to lack detailed knowledge of specific associated processes, and thus obtain lower scores in tests such as RaProEvo, but they should have similar general understanding as measured, e. Alarmingly, we found significant deficits relative to the biology majors in both their conceptual knowledge of randomness and probability in evolutionary contexts and their evolutionary knowledge.
However, we cannot exclude the possibility that these findings are simply a manifestation of differences that existed between the groups before their higher educational training.
However, most previous studies on evolutionary knowledge have solely considered biological aspects Tibell and Harms, unpublished data. Nevertheless, instruments such as RaProEvo and RaProMath have intrinsic limitations, partly because they need to be reasonably short and not require much time to complete or mark. Thus, they must include only a few items targeting each concept. Hence, the instruments should be used mainly for formative purposes, that is, for instructors to identify obstacles their students are currently facing.
The instruments were not intended to be summative evaluation tools. We also note the obvious limitation of the small sample size in our study. We obtained promising preliminary results, but the reliability measures of the instruments must be confirmed with a larger group of students. Further, the participants were all German students from a single cohort. To assess the generality of the findings and identify causes of possible variations in findings, tests of the instruments internationally and with other cohorts are required.
In addition, having developed an instrument for measuring conceptual knowledge of randomness and probability in the context of evolution RaProEvo , we found that instruction about randomness and probability connected to evolutionary concepts warrants attention. We thank the whole EvoVis group and Dr.
Special thanks to Dr John Blackwell for the language review and valuable and insightful comments on evolution aspects of the paper. We are also very thankful to the students who participated in this study and the experts for their comments on the instruments. National Center for Biotechnology Information , U. Ross Nehm, Monitoring Editor. Author information Article notes Copyright and License information Disclaimer. This article is distributed by The American Society for Cell Biology under license from the author s.
It is available to the public under an Attribution—Noncommercial—Share Alike 3.
This article has been cited by other articles in PMC. Abstract Students of all ages face severe conceptual difficulties regarding key aspects of evolution—the central, unifying, and overarching theme in biology. Research Objective Diverse instruments have been developed for measuring evolutionary knowledge e.
Procedure Participants responded to a basic demographic questionnaire including items probing their academic self-concept and completed tests on conceptual knowledge of randomness and probability in both evolutionary and mathematical contexts.
TABLE 1. M19, M30, M Open in a separate window. TABLE 2.
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Faculty Review. TABLE 3. Test of Evolutionary Knowledge. We used the following three, of five, items from this instrument: Explain why some bacteria have evolved resistance to antibiotics that is, the antibiotics no longer kill the bacteria. TABLE 4. Explanations of key concepts and alternative conceptions. Individual variation Differences in the traits of individuals are addressed e. Differential survival potential Individuals have different survival potentials due to specific traits e.