Student and expert perceptions of the role of mathematics within physics

Students’ perceptions of the role of mathematics within physics were examined. I propose that the identification of physics as a science based ultimately on experiment is a threshold concept: transformation from a naïve view that physics is based upon mathematics to an expert view that physics is based on experiment is difficult for students. Seven students taking first-year university physics were interviewed in two focus groups; nine practising physicists from academia and industry (considered as experts) were interviewed as six individuals plus one focus group of three participants. Of particular interest was the ‘expert’ view emphasizing the conceptual nature of physics. This was a threshold in understanding that had not been crossed by students. Rather, students viewed mathematics and physics as being more strongly connected than did practising physicists; specifically that “maths explains physics”. Experts consider this view as holding back a student’s understanding of the subject and preventing them from becoming effective physicists. It is troublesome to students because they are less able to identify the relevant concepts before trying to tackle a problem with mathematics, making their approach less likely to be effective, however, both groups (physicists and students) identified physics as belonging to ‘the real world’ and that mathematics shows how physical entities can be combined or related, indicating student responses are not completely naïve. Opinions on how best to teach mathematical concepts in physics varied considerably across participants

Preservationism, or The Elephant in the Room: How Opponents of Same-Sex Marriage Deceive Us into Establishing Religion

The overwhelming majority of support for bans on same-sex civil marriage has come from religious believers, and the so-called secular justifications for these bans are mere pretexts for religious beliefs that homosexuality, homosexuals, and same-sex couples are evil or sinful. Courts should take a hard look at the substantive justifications offered in support of same-sex marriage bans, bearing in mind that (1) these justifications are universally offered by religious believers but are infrequently offered by credentialed Secularists, and (2) they are the result of a studied use of pretextual, secular-sounding language to cloak a religiously-motivated bias against homosexuals and same-sex couples

Knots with infinitely many incompressible Seifert surfaces

We show that a knot in $S^3$ with an infinite number of distinct incompressible Seifert surfaces contains a closed incompressible surface in its complement.Comment: 16 pages, 6 figure