Mathematical Communication, Conceptual Understanding, and Students' Attitudes Toward Mathematics

This action research study of my 8th grade classroom investigated the use of mathematical communication, through oral homework presentations and written journals entries, and its impact on conceptual understanding of mathematics. This change in expectation and its impact on students’ attitudes towards mathematics was also investigated. Challenging my students to communicate mathematics both orally and in writing deepened the students’ understanding of the mathematics. Levels of understanding deepened when a variety of instructional methods were presented and discussed where students could comprehend the ideas that best suited their learning styles. Increased understanding occurred through probing questions causing students to reflect on their learning and reevaluate their reasoning. This transpired when students were expected to write more than one draft to math journals. By making students aware of their understanding through communicating orally and in writing, students realized that true understanding did not come from mere homework completion, but from evaluating and assessing their own and other’s ideas and reasoning. I discovered that when students were challenged to communicate their reasoning both orally and in writing, students enjoyed math more and thought math was more fun. As a result of this research, I will continue to require students to communicate their thinking and reasoning both orally and in writing.

Mathematical Communication through Written and Oral Expression

In this action research study of my classroom of sixth grade mathematics, I investigated the use of communication of mathematics through both written and oral expression. Giving my students the opportunity to communicate mathematics both in writing and orally helped to deepen the students’ understanding of mathematics. The students’ levels of comprehension were increased when they were presented with a variety of instructional methods. Through discussion and reflection the students were able to find methods that worked best for them and their learning ability. Students’ understanding increased from probing questions that made the students reflect and re-evaluate their solutions. This learning took place when students were made aware of different solutions or ways of doing things from the class discussions that were held. I discovered that when students are challenged to express their thinking both in writing and orally, the students found that they could communicate their thinking in a new way. Some of my students were only comfortable expressing their thoughts in one of the two ways but by the time the project was completed, they all expressed that they enjoyed both ways, and maybe changed the original way they preferred doing mathematics. As a result of this research, I will continue to require students to communicate their thinking and reasoning both in writing and orally.

Generalizing the dynamic field theory of spatial cognition across real and developmental time scales

Within cognitive neuroscience, computational models are designed to provide insights into the organization of behavior while adhering to neural principles. These models should provide sufficient specificity to generate novel predictions while maintaining the generality needed to capture behavior across tasks and/or time scales. This paper presents one such model, the Dynamic Field Theory (DFT) of spatial cognition, showing new simulations that provide a demonstration proof that the theory generalizes across developmental changes in performance in four tasks—the Piagetian A-not-B task, a sandbox version of the A-not-B task, a canonical spatial recall task, and a position discrimination task. Model simulations demonstrate that the DFT can accomplish both specificity—generating novel, testable predictions—and generality—spanning multiple tasks across development with a relatively simple developmental hypothesis. Critically, the DFT achieves generality across tasks and time scales with no modification to its basic structure and with a strong commitment to neural principles. The only change necessary to capture development in the model was an increase in the precision of the tuning of receptive fields as well as an increase in the precision of local excitatory interactions among neurons in the model. These small quantitative changes were sufficient to move the model through a set of quantitative and qualitative behavioral changes that span the age range from 8 months to 6 years and into adulthood. We conclude by considering how the DFT is positioned in the literature, the challenges on the horizon for our framework, and how a dynamic field approach can yield new insights into development from a computational cognitive neuroscience perspective.

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle

A total of 46,089 individual monthly test-day (TD) milk yields (10 test-days), from 7,331 complete first lactations of Holstein cattle were analyzed. A standard multivariate analysis (MV), reduced rank analyses fitting the first 2, 3, and 4 genetic principal components (PC2, PC3, PC4), and analyses that fitted a factor analytic structure considering 2, 3, and 4 factors (FAS2, FAS3, FAS4), were carried out. The models included the random animal genetic effect and fixed effects of the contemporary groups (herd-year-month of test-day), age of cow (linear and quadratic effects), and days in milk (linear effect). The residual covariance matrix was assumed to have full rank. Moreover, 2 random regression models were applied. Variance components were estimated by restricted maximum likelihood method. The heritability estimates ranged from 0.11 to 0.24. The genetic correlation estimates between TD obtained with the PC2 model were higher than those obtained with the MV model, especially on adjacent test-days at the end of lactation close to unity. The results indicate that for the data considered in this study, only 2 principal components are required to summarize the bulk of genetic variation among the 10 traits.

Surface ecophysiological behavior across vegetation and moisture gradients in tropical South America

Surface ecophysiology at five sites in tropical South America across vegetation and moisture gradients is investigated. From the moist northwest (Manaus) to the relatively dry southeast (Pé de Gigante, state of São Paulo) simulated seasonal cycles of latent and sensible heat, and carbon flux produced with the Simple Biosphere Model (SiB3) are confronted with observational data. In the northwest, abundant moisture is available, suggesting that the ecosystem is light-limited. In these wettest regions, Bowen ratio is consistently low, with little or no annual cycle. Carbon flux shows little or no annual cycle as well; efflux and uptake are determined by high-frequency variability in light and moisture availability. Moving downgradient in annual precipitation amount, dry season length is more clearly defined. In these regions, a dry season sink of carbon is observed and simulated. This sink is the result of the combination of increased photosynthetic production due to higher light levels, and decreased respiratory efflux due to soil drying. The differential response time of photosynthetic and respiratory processes produce observed annual cycles of net carbon flux. In drier regions, moisture and carbon fluxes are in-phase; there is carbon uptake during seasonal rains and efflux during the dry season. At the driest site, there is also a large annual cycle in latent and sensible heat flux.

Common parietal activation in musical mental transformations across pitch and time

We previously observed that mental manipulation of the pitch level or temporal organization of melodies results in functional activation in the human intraparietal sulcus (IPS), a region also associated with visuospatial transformation and numerical calculation. Two outstanding questions about these musical transformations are whether pitch and time depend on separate or common processing in IPS, and whether IPS recruitment in melodic tasks varies depending upon the degree of transformation required (as it does in mental rotation). In the present study we sought to answer these questions by applying functional magnetic resonance imaging while musicians performed closely matched mental transposition (pitch transformation) and melody reversal (temporal transformation) tasks. A voxel-wise conjunction analysis showed that in individual subjects, both tasks activated overlapping regions in bilateral IPS, suggesting that a common neural substrate subserves both types of mental transformation. Varying the magnitude of mental pitch transposition resulted in variation of IPS BOLD signal in correlation with the musical key-distance of the transposition, but not with the pitch distance, indicating that the cognitive metric relevant for this type of operation is an abstract one, well described by music-theoretic concepts. These findings support a general role for the IPS in systematically transforming auditory stimulus representations in a nonspatial context. (C) 2013 Elsevier Inc. All rights reserved.

The Mountain Research Initiative Reaches Outward and Clombs Upward

Mountain regions provide a multitude of goods and services for much of humanity (Price and Butt 2000; Becker and Bugmann 2001), especially in the realms of water supply, biodiversity, and other ecosystem services (Schimel et al 2002; Körner et al 2005; Viviroli et al 2007; Viviroli et al 2011). However, the future ability of mountain regions to provide goods and services to both highland and lowland residents is seriously threatened by climatic changes, environmental pollution, unsustainable management of natural resources, and serious gaps in understanding of mountain systems (Huber et al 2005). Disciplinary, interdisciplinary, and transdisciplinary research is required to maintain these goods and services in the face of these forces. The global mountain research community, however, has historically operated at a suboptimal level because of insufficient communication across geographic and linguistic barriers, less than desirable coordination of research frameworks, and a lack of funding.

DCLK1 variants are associated across schizophrenia and attention deficit/hyperactivity disorder

Doublecortin and calmodulin like kinase 1 (DCLK1) is implicated in synaptic plasticity and neurodevelopment. Genetic variants in DCLK1 are associated with cognitive traits, specifically verbal memory and general cognition. We investigated the role of DCLK1 variants in three psychiatric disorders that have neuro-cognitive dysfunctions: schizophrenia (SCZ), bipolar affective disorder (BP) and attention deficit/hyperactivity disorder (ADHD). We mined six genome wide association studies (GWASs) that were available publically or through collaboration; three for BP, two for SCZ and one for ADHD. We also genotyped the DCLK1 region in additional samples of cases with SCZ, BP or ADHD and controls that had not been whole-genome typed. In total, 9895 subjects were analysed, including 5308 normal controls and 4,587 patients (1,125 with SCZ, 2,496 with BP and 966 with ADHD). Several DCLK1 variants were associated with disease phenotypes in the different samples. The main effect was observed for rs7989807 in intron 3, which was strongly associated with SCZ alone and even more so when cases with SCZ and ADHD were combined (P-value = 4 × 10(-5) and 4 × 10(-6), respectively). Associations were also observed with additional markers in intron 3 (combination of SCZ, ADHD and BP), intron 19 (SCZ+BP) and the 3'UTR (SCZ+BP). Our results suggest that genetic variants in DCLK1 are associated with SCZ and, to a lesser extent, with ADHD and BP. Interestingly the association is strongest when SCZ and ADHD are considered together, suggesting common genetic susceptibility. Given that DCLK1 variants were previously found to be associated with cognitive traits, these results are consistent with the role of DCLK1 in neurodevelopment and synaptic plasticity.

Dynamic Languages and Applications. Report on the Workshop Dyla 07 at ECOOP 2007

Following last two years’ workshop on dynamic languages at the ECOOP conference, the Dyla 2007 workshop was a successful and popular event. As its name implies, the workshop’s focus was on dynamic languages and their applications. Topics and discussions at the workshop included macro expansion mechanisms, extension of the method lookup algorithm, language interpretation, reflexivity and languages for mobile ad hoc networks. The main goal of this workshop was to bring together different dynamic language communities and favouring cross communities interaction. Dyla 2007 was organised as a full day meeting, partly devoted to presentation of submitted position papers and partly devoted to tool demonstration. All accepted papers can be downloaded from the workshop’s web site. In this report, we provide an overview of the presentations and a summary of discussions.