Math-Towers: Online Interactive Collaborative Mathematics Explorations & Problem-Solving for Students Ages 11 to 15 years (Grades 6 to 10)

Math-Towers (www.math-towers.ca) is an online resource for students in grades 6 to 10 that supports collaborative problem-solving and investigations. This paper presents the philosophical position motivating the development of Math-Towers and describes how the site presents and motivates the mathematical challenges and supports participants' exploration and collaboration.

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.

Amphibian skin peptides and their corresponding cDNAs from single lyophilized secretion samples: identification of novel brevinins from three species of Chinese frogs

Brevinins are peptides of 24 amino acid residues, originally isolated from the skin of the Oriental frog, Rana brevipoda porsa, by nature of their microbicidal activity against a wide range of Gram-positive and Gram-negative bacteria and against strains of pathogenic fungi. cDNA libraries were constructed from lyophilized skin secretion of three, unstudied species of Chinese frog, Odorrana schmackeri, Odorrana versabilis and Pelophylax plancyi fukienensis, using our recently developed technique. In this report, we describe the “shotgun” cloning of novel brevinins by means of 3'-RACE, using a “universal” degenerate primer directed towards a highly conserved nucleic acid sequence domain within the 5'-untranslated region of previously characterized frog skin peptide cDNAs. Novel brevinins, deduced from cloned cDNA open-reading frames, were subsequently identified as mature peptides in the same samples of respective species skin secretions. Bioinformatic analysis of both prepro-brevinin nucleic acid sequences and translated open-reading frame amino acid sequences revealed a highly conserved signal peptide domain and a hypervariable anti-microbial peptide-encoding domain. The experimental approach described here can thus rapidly provide robust structural data on skin anti-microbial peptides without harming the donor amphibians.

Cloning from tissue surrogates: antimicrobial peptide (esculentin) cDNAs from the defensive skin secretions of Chinese ranid frogs

The defensive skin secretions of amphibians are a rich source of bioactive peptides. Here we describe a rapid technique for skin granular gland transcriptome cloning from a surrogate tissue-the secretion itself. cDNA libraries were constructed from lyophilized skin secretion from each of the Chinese frogs (Rana schmackeri, Rana versabilis, and Rana plancyi fukienensis) using magnetic oligo(dT) bead-captured polyadenylated mRNA as templates. Specific esculentin cDNAs were amplified by 3'-RACE using a degenerate primer designed for a consensus nucleotide sequence in the 5' untranslated region of previously characterized ranid frog peptide cDNAs. The cloned cDNAs were found to encode the antimicrobial peptides esculentins 1 and 2 from each of the species examined. The presence of predicted peptide structures in skin secretions was confirmed by MALDI-TOF mass spectrometry and automated Edman degradation. This experimental approach can thus rapidly expedite parallel transcriptome and peptidome analysis of amphibian granular gland secretions without harming or sacrificing donor animals.