What makes a space have large weight?

We formulate several conditions (two of them are necessary and sufficient) which imply that a space of small character has large weight. In section 3 we construct a ZFC example of a first countable 0-dimensional space X of size 2^omega with w(X)=2^omega and nw(X)=omega, we show that CH implies the existence of a 0-dimensional space Y of size omega_1 with w(Y)=nw(Y)=omega_1 and chi(Y)=R(Y)=omega, and we prove that it is consistent that 2^omega is as large as you wish and there is a 0-dimensional space Z of size 2^omega such that w(Z)=nw(Z)=2^omega but chi(Z)=R(Z^omega)=omega

On a parity based group testing algorithm

In traditional Combinatorial Group Testing the problem is to identify up to d defective items from a set of n items on the basis of group tests. In this paper we describe a variant of the group testing problem above, which we call parity group testing. The problem is to identify up to d defective items from a set of n items as in the classical group test problem. The main difference is that we check the parity of the defective items in a subset. The test can be applied to an arbitrary subset of the n items with two possible outcomes. The test is positive if the number of defective items in the subset is odd, otherwise it is negative. In this paper we extend Hirschberg et al.’s method to the parity group testing scenario

Guided inquiry-based learning in secondary-school chemistry classes: a case study

Guided inquiry-based learning has been shown to be a promising method for science education; however, despite its advantages it is rarely used in chemistry teaching in Hungary. One of the reasons for this is the lack of tried-and-tested inquiry-based teaching materials with detailed guides that teachers can readily use in their classrooms. As part of a four-year research project, new teaching materials were designed to foster scientific reasoning and scientific process skills in chemistry education in Hungary. From these materials, in this study, a guided inquiry-based chemistry task was tested with 9th-grade students ( N = 88) who had no previous experience with the method. Before the activity, the students’ mid-term grades were collected, and the Lawson Classroom Test of Scientific Reasoning (LCTSR) was administered to describe the sample. During the activity, students worked in groups ( n = 21). Data were collected through content analysis of the student worksheets, classroom observations using a rubric, and student questionnaires to explore the learning paths and identify possible obstacles. Our findings support that guided inquiry learning is suitable for students who are new to the method if appropriate scaffolding is given. The data showed the phases of the inquiry cycle in which more guidance is necessary. Formulating hypotheses, recording observations, and evaluating the hypotheses based on the evidence were found to be the most critical steps in the learning process. More than half of the groups disregarded the collected evidence and accepted their original hypotheses, despite their unproven validity, suggesting that they did not understand the true nature of the scientific inquiry. Chemistry grades and the LCTSR scores could not predict reliably the students’ success in solving the inquiry task. The results of the student questionnaire showed that the students enjoyed the inquiry session. They mostly found their work successful, but they overestimated the level of their inquiry skills in some cases