Preservice Teachers’ Understandings of the Relation Between a Fraction or Integer and Its Decimal Expansion: Strength and Stability of Belief

Abstract

In an earlier study of preservice elementary and middle school teachers’ beliefs about repeating decimals, Weller, Arnon, and Dubinsky (2009) reported on a comparison of the mathematical performance of 77 preservice teachers who completed an APOS-based instructional unit with 127 preservice teachers who completed traditional instruction. The purpose of the current study, based on 47 interviews conducted 4 months after the instruction, during which time there was no further instruction on this topic, is to determine the strength and stability (over time) of the students’ beliefs, to uncover thinking that did not arise in the earlier study, and to see whether the interviews yield similar comparative results. The interviews did uncover changes in student thinking. The students who received the APOS-based instruction developed stronger and more stable (over time) beliefs that a repeating decimal is a number; a repeating decimal has a fraction or integer to which it corresponds; a repeating decimal in general equals its corresponding fraction or integer; and, in particular, In addition, a number of indices and categories were developed that may prove useful in other studies consisting of the comparison of interview and questionnaire data involving a large number of interview subjects.     

A Demonstration of High-Throughput Electrophoresis

Automating electrophoresis significantly reduces the time required for loading a large number of samples, increases the speed of electrophoresis analysis, and maximizes the resolution power (clear separation of fragments) of this technique. In addition, automation increases the precision of electrophoresis analysis. Here we demonstrate an automated, high-throughput method of loading 96 samples simultaneously onto an electrophoresis gel, using the Apogent Discoveries Tango™ system and the Invitrogen™ E-Gel® 96 system.     

Quorum-sensing Cascades Governing Bacterial Multicellular Communities

Quorum sensing (QS) is an efficient mode of intercellular communication between bacteria. This mode is regulated by self-produced small chemical signals, activating dedicated receptors once accumulated. Numerous architecturally complex QS cascades are cardinal for governing bacterial behaviors, such as pathogenicity, luminescence, and bacterial competence. Importantly, QS cascades are essential for the formation of bacterial multicellular communities. Once informed via QS cascades, motile cells often organize themselves into conspicuous multicellular structures that carry out specialized tasks. This review focuses on the major QS systems, playing an active role in the rise of complex bacterial communities in different bacterial models.     

A bacteriophage reagent for Salmonella: molecular studies on Felix 01

Felix 01 (F01) is a bacteriophage originally isolated by Felix and Callow which lyses almost all Salmonella strains and has been widely used as a diagnostic test for this genus. Molecular information about this phage is entirely lacking. In the present study, the DNA of the phage was found to be a double-stranded linear molecule of about 80 kb. 11.5 kb has been sequenced and in this region A + T content is 60%. There are relatively few restriction endonuclease cleavage sites in the native genome and clones show this is due to their absence rather than modification. A restriction map of the genome has been constructed. The ends of the molecule cannot be ligated although they contain 5' phosphates. At least 60% of the genome must encode proteins. In the sequenced portion, many open reading frames exist and these are tightly packed together. These have been examined for homology to published proteins but only 1 to 17 shows similarity to known proteins. F01 is therefore the prototype of a new phage family. On the basis of restriction sites, codon usage and the distribution of nonsense codons in the unused reading frames, a strong case can be made for natural selection that reacts to mRNA structure and function.     

Differential weighting of common and distinctive components.

We investigated possible explanations of the finding that the relative weight (W) of common components in similarity judgments is higher for verbal than for pictorial stimuli. A serial presentation of stimulus components had no effect on verbal stimuli; it increased the impact of both common and distinctive components of pictorial stimuli but did not affect their relative weight. On the other hand, W was increased by manipulations that reduced the cohesiveness of composite pictures, such as separating, scrambling, and mixing their components. Furthermore, W was decreased by manipulations that enhanced the cohesiveness of composite verbal stimuli by imposing structure on their components. Verbal and pictorial representations of the same stimuli yielded no systematic differences in W. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Self-timed is self-checking

Self-checking circuits detect (at least some of) their own faults. We describe self-timed circuits, including combinational logic and sequential machines, which either halt or generate illegal output if they include any single stuck-at faults. The self-timed circuits employ dual rail data encoding to implement ternary logic of 0, 1, andundefined states; the fourth state is used to signal illegal output and is shown to result only from certain circuit faults. The self-timed circuits also employ four-phase signaling according to a well-defined protocol of communications between the circuit and its environment; failures due to certain faults prevent the circuit from communicating properly, thus causing the circuit to halt. We show that any single stuck-at fault falls in either the first or the second category, thus providing complete fault coverage through self checking. No hardware needs to be added to our circuits to achieve the complete self-checking property; further, the circuit is guaranteed to never generate a legal but erroneous output if it contains a fault. Minimal hardware is needed to detect that a circuit has either halted or has generated an illegal output.     

Object–person discrimination and communication at 3 and 10 months.

J. Contole and R. Over's (1979, 1981) procedure for studying infant discrimination using a signal detection analysis of observers' ratings of infant behavior was used to test claims by E. Tronick et al (see record 1980-07280-001) that 3-mo-olds distinguish people from objects and nonverbally communicate with familiar caregivers. 12 observers—parents and undergraduates—judged from videotaped samples of 3- and 10-mo-old infants' behavior if the infants were alone or otherwise, if they were with something that was active or passive, and if they were greeting or withdrawing. Observers could only judge whether the infants were with their mother or an object for the 10-mo-olds. The greeting–withdrawal results seem to indicate that 3-mo-olds do communicate with their caregivers; however, observers were also able to judge greeting–withdrawal when the infants were with an object. There were no sensitivity differences between the 2 observer groups, although the parents were biased to expect the infants to be with mother and to be greeting. (18 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Encouraging collaboration and building Community in Online Asynchronous Professional Development: designing for social capital

International Journal of Computer-Supported Collaborative Learning - This research investigates a design and development approach to improving science teachers’ access to effective...     

Evaluation of peak picking quality in LC-MS metabolomics data

The output of LC-MS metabolomics experiments consists of mass-peak intensities identified through a peak-picking/alignment procedure. Besides imperfections in biological samples and instrumentation, data accuracy is highly dependent on the applied algorithms and their parameters. Consequently, quality control (QC) is essential for further data analysis. Here, we present a QC approach that is based on discrepancies between replicate samples. First, the quantile normalization of per-sample log-signal distributions is applied to each group of biologically homogeneous samples. Next, the overall quality of each replicate group is characterized by the Z-transformed correlation coefficients between samples. This general QC allows a tuning of the procedure's parameters which minimizes the inter-replicate discrepancies in the generated output. Subsequently, an in-depth QC measure detects local neighborhoods on a template of aligned chromatograms that are enriched by divergences between intensity profiles of replicate samples. These neighborhoods are determined through a segmentation algorithm. The retention time (RT)-m/z positions of the neighborhoods with local divergences are indicative of either: incorrect alignment of chromatographic features, technical problems in the chromatograms, or to a true biological discrepancy between replicates for particular metabolites. We expect this method to aid in the accurate analysis of metabolomics data and in the development of new peak-picking/alignment procedures.