Semantic and Syntactic Proof Productions

In this paper, we distinguish between two ways that an individual can construct a formal proof. We define a syntactic proof production to occur when the prover draws inferences by manipulating symbolic formulae in a logically permissible way. We define a semantic proof production to occur when the prover uses instantiations of mathematical concepts to guide the formal inferences that he or she draws. We present two independent exploratory case studies from group theory and real analysis that illustrate both types of proofs. We conclude by discussing what types of concept understanding are required for each type of proof production and by illustrating the weaknesses of syntactic proof productions.     

Is There a Downside to Anticipating the Upside? Children's and Adults’ Reasoning About How Prior Expectations Shape Future Emotions

Four- to 10-year-olds and adults (N = 205) responded to vignettes involving three individuals with different expectations (high, low, and no) for a future event. Participants judged characters’ pre-outcome emotions, as well as predicted and explained their feelings following three events (positive, attenuated, and negative). Although adults rated high-expectation characters more negatively than low-expectation characters after all outcomes, children shared this intuition starting at 6–7 years for negative outcomes, 8–10 years for attenuated, and never for positive. Comparison to baseline (no expectation) indicated that understanding the costs of high expectations emerges first and remains more robust across age than recognition that low expectations carry benefits. Explanation analyses further clarified this developing awareness about the relation between thoughts and emotions over time.     

“From the Beginning,I Felt Empowered”: Incorporating an Ecological Approach to Learning in Elementary Science Teacher Education

Research in Science Education - While a renewed national dialog promotes the importance of science education for future technological and economic viability, students must find science personally...     

Multimedia resources designed to support learning from written proofs: an eye-movement study

This paper presents two studies of an intervention designed to help undergraduates comprehend mathematical proofs. The intervention used multimedia resources that presented proofs with audio commentary and visual animations designed to focus attention on logical relationships. In study 1, students studied an e-Proof or a standard written proof and their comprehension was assessed in both immediate and delayed tests; the groups performed similarly at immediate test, but the e-Proof group exhibited poorer retention. Study 2 accounted for this unexpected result by using eye-movement analyses to demonstrate that participants who studied an e-Proof exhibited less processing effort when not listening to the audio commentary. We suggest that the extra support offered by e-Proofs disrupts the processes by which students organise information, and thus restricts the extent to which their new understanding is integrated with existing knowledge. We discuss the implications of these results for evaluating teaching innovations and for supporting proof comprehension.     

The Role of Attention in the Development of Short-Term Memory: Age Differences in the Verbal Span of Apprehension

In previous studies of memory span, participants have attended to the stimuli while they were presented, and therefore have had the opportunity to use a variety of mnemonic strategies. In the main portion of the present study, participants (first- and fourth-grade children, and adults; 24 per age group) carried out a visual task while hearing lists of spoken digits and received a post-list digit recall cue only occasionally, for some lists. Under these conditions, list information presumably must be extracted from a passively held store such as auditory sensory memory. The results suggest that each individual has a core memory capacity limit that can be observed clearly in circumstances in which it cannot be supplemented by mnemonic strategies, and that the capacity limit appears to increase with age during childhood. Other, attention-demanding processes also contribute to memory for attended lists.     

Verification policies in Croatian medical biochemistry laboratories: a survey of the practice

IntroductionThe aim of this study was to screen practices used in verification procedures for methods/analysers among medical biochemistry laboratories (MBLs) in Croatia. We hypothesized that these procedures differ widely from laboratory to laboratory and wanted to gather specific data on steps used in the verification workflow.Materials and methodsIn order to obtain data, an online survey was conducted. The survey, divided in two sections, contained 29 questions and statements addressing general characteristics and specific steps of the verification workflow of each individual MBL. The survey was disseminated among managers of all MBLs in Croatia.ResultsA total of 108/196 (55%) laboratories participated in the survey. Forty nine MBLs were excluded from the second part of the survey: 14 have not implemented verification procedures, and 35 MBLs due to the absence of answers. The most relevant results of the second part of the survey showed that: 18/59 (0.31) of the responding MBLs have difficulties when defining acceptance criteria, 27/59 (0.46) used the Clinical and Laboratory Standards Institute protocol for precision estimation; the majority of MBLs used a median of 20 samples for method/analyser comparisons and estimated bias using internal quality control samples; reference intervals provided by external sources are mainly adopted; 60% of MBLs do not include linearity verification in their protocol and do not use the national document for the estimation of measurement uncertainty.ConclusionsHeterogeneous verification protocols are routinely utilized across Croatian MBLs which clearly confirms that a national document might help in the harmonization of verification procedures.     

Synchronous and asynchronous interactions of bilingual Hispanic pre‐ and in‐service teachers in distance learning

Abstract

This study investigated differences in online written interactions of bilingual Hispanic pre‐ and in‐service teachers across two types of online discussion groups: synchronous and asynchronous. Participants were exposed to a shortened version of a wholly online special education course and participated in instructional activities as well as synchronous and asynchronous discussion groups over a six‐week period. The research used both an alternating treatment design to gather quantitative data, and interviews and questionnaires for qualitative data. The results support the contention that synchronous discussion group interactions are an important feature of successful online courses with Hispanic students.     

“Do you want an idea of what they’re doing?” Transgressive data generation and analysis within a bilingual writers workshop

We consider how research participants engage alongside researchers as choreographers of data generation and highlight the everyday practices of researchers and participants in motion within and across time and space. Data for this case analysis were generated during a two-year qualitative study investigating multimodal literacies, multilingualism, and literacy teacher development. We utilized microethnographic discourse analysis to analyze a video excerpt from a classroom observation during writers workshop in a fourth-grade bilingual classroom. We sought to understand how the teacher’s and students’ discursive moves during the event tactically disrupted the researchers’ agenda in the moment and complicated attempts at data analysis. Our analyses illustrate how the teacher multiply situated herself in ways that trouble dichotomous framings of teachers’ work, such as traditional or nontraditional, as well as dominant conceptualizations of qualitative research, such as data “collection.” We end with implications for interpreting and representing research findings.     

ePortfolios and Reflective Practice for Food Science Students

The study investigated students’ perceptions and attitudes toward the use of ePortfolios for reflective practice as a learning and teaching strategy. A mixed‐method approach was applied to the study in a first‐year food science unit, at a regional Australian university. Data were generated via 3 sources, in order to provide the evidential basis for the investigation, including: a mixed method survey, access to student's exam results, and students’ ePortfolio reflections. The findings identified 3 key positive aspects. First, a variety of assessment methods was key to enhancing the overall learning of 1st‐year food science students. Second, ePortfolio reflective writing can be a key aspect for improved student engagement. Finally, structured ePortfolio sessions can help food science students consolidate knowledge, while also allowing them to encounter new ideas related to food science theory and develop technical knowledge. However, technological issues with using an ePortoflio can cloud the value of the reflective task for some students. Recommendations are made for how to better support and implement reflective practice using ePortfolios to enhance the learning of food science students.     

The effect of a structured story reading intervention,story retelling and higher order thinking for English language and literacy acquisition

The purpose of this study was to investigate the effectiveness of structured story reading intervention, Story reTelling and higher order thinking for English Language and Literacy Acquisition (STELLA), delivered to 38 Hispanic English language learners (ELL) placed in an enhanced transitional bilingual programme over 2 years from first to second grade as compared with 34 control students placed in a typical practice transitional bilingual programme during the same time period. Both treatment and comparison ELL students' retellings of two stories in Spanish and English were measured by five story elements. Findings were that (a) students receiving intervention outperformed their comparison peers in all five story elements in English and Spanish of both stories; (b) students showed stronger ability in their native language in four of five story elements; and (c) students performed at a higher level in the narrative‐informational story than a narrative story in both languages. Educational implications are discussed.