Development of fourth-grade students’ understanding of experimental and theoretical probability

Students explored variation and expectation in a probability activity at the end of the first year of a 3-year longitudinal study across grades 4-6. The activity involved experiments in tossing coins both manually and with simulation using the graphing software, TinkerPlots. Initial responses indicated that the students were aware of uncertainty, although an understanding of chance concepts appeared limited. Predicting outcomes of 10 tosses reflected an intuitive notion of equiprobability, with little awareness of variation. Understanding the relationship between experimental and theoretical probability did not emerge until multiple outcomes and representations were generated with the software.

Structuring representations of continuous data through investigations in grade 1

The study of data modelling with elementary students involves the analysis of a developmental process beginning with children’s investigations of meaningful contexts: visualising, structuring, and representing data and displaying data in simple graphs (English, 2012; Lehrer & Schauble, 2005; Makar, Bakker, & Ben-Zvi, 2011). A 3-year longitudinal study investigated young children’s data modelling, integrating mathematical and scientific investigations. One aspect of this study involved a researcher-led teaching experiment with 21 mathematically able Grade 1 students. The study aimed to describe explicit developmental features of students’ representations of continuous data...

Bhutanese eighth grade students' and teachers' perceptions of their classroom learning environment in relation to the new mathematics curriculum

This thesis examined how Bhutanese eighth grade students and teachers perceived their classroom learning environment in relation to a new standards-based mathematics curriculum. Data were gathered from administering surveys to a sample of 608 students and 98 teachers, followed by semi-structured interviews with selected participants. The findings of the study indicated that participants generally perceived their learning environments favorably. However, there were differences in terms of gender, school level, and school location. The study provides teachers, educational leaders, and policy-makers in Bhutan new insights into students' and teachers' perceptions of their mathematics classroom environments.

STEM learning through engineering design: fourth-grade students' investigations in aerospace

Background: Internationally, there is a growing concern for developing STEM education to prepare students for a scientifically and technologically advanced society. Despite educational bodies lobbying for an increased focus on STEM, there is limited research on how engineering might be incorporated especially in the elementary school curriculum. A framework of five comprehensive core engineering design processes (problem scoping, idea generation, design and construction, design evaluation, redesign), adapted from the literature on design thinking in young children, served as a basis for the study. We report on a qualitative study of fourth-grade students’ developments in working an aerospace problem, which took place during the first year of a 3-year longitudinal study. Students applied design processes together with their mathematics and science knowledge to the design and redesign of a 3-D model plane. Results: The study shows that through an aerospace engineering problem, students could complete initial designs and redesigns of a model plane at varying levels of sophistication. Three levels of increasing sophistication in students’ sketches were identified in their designs and redesigns. The second level was the most prevalent involving drawings or templates of planes together with an indication of how to fold the materials as well as measurements linked to the plane’s construction. The third level incorporated written instructions and calculations. Students’ engagement with each of the framework’s design processes revealed problem scoping components in their initial designs and redesigns. Furthermore, students’ recommendations for improving their launching techniques revealed an ability to apply their mathematics knowledge in conjunction with their science learning on the forces of flight. Students’ addition of context was evident together with an awareness of constraints and a consideration of what was feasible in their design creation. Interestingly, students’ application of disciplinary knowledge occurred more frequently in the last two phases of the engineering framework (i.e., design evaluation and redesign), highlighting the need for students to reach these final phases to enable the science and mathematics ideas to emerge. Conclusions: The study supports research indicating young learners’ potential for early engineering. Students can engage in design and redesign processes, applying their STEM disciplinary knowledge in doing so. An appropriate balance is needed between teacher input of new concepts and students’ application of this learning in ways they choose. For example, scaffolding by the teacher about how to improve designs for increased detail could be included in subsequent experiences. Such input could enhance students’ application of STEM disciplinary knowledge in the redesign process. We offer our framework of design processes for younger learners as one way to approach early engineering education with respect to both the creation of rich problem experiences and the analysis of their learning.

Confronting expectation in grade 4: Tossing two coins

This study focuses on the experiences of 91 Grade 4 students who had been introduced to expectation and variation through trials of tossing a single coin many times. They were then given two coins to toss simultaneously and asked to state their expectation of the chances for the possible outcomes, in a similar manner expressed for a single coin. This paper documents the journey of the students in discovering that generally their initial expectation for two coins was incorrect and that despite variation, a large number of tosses could confirm a new expectation.

Effect of ion nitriding on the microstructure and properties of Maraging steel (250 Grade)

In the present investigation, ion nitriding of Maraging steel (250 grade) has been carried out at three different temperatures i.e., at 435 degrees C, 450 degrees C and 465 degrees C for 10 h duration in order to achieve good wear resistance along with high strength required for the slat track component of aircraft. The microstructure of the base material and the nitrided layer was examined by optical and scanning electron microscope, and various phases present were determined by X-ray diffraction. Various properties, such as, hardness, case depth, tensile, impact, fatigue properties and corrosion resistance were investigated for both un-nitrided and ion-nitrided materials. It is observed that the microstructure of the core material remains unaltered and Fe4N is formed in the hardened surface layer after ion nitriding at all the three temperatures employed. Surface hardness increases substantially after ion nitriding. Surface hardness remains almost the same but case depth increases with the increase in ion nitriding temperature due to greater diffusivity at higher temperatures. Tensile strength, fatigue strength and corrosion resistance are improved but ductility and energy absorbed in impact test decrease on ion nitriding. These results are explained on the basis of microstructural observations. The properties obtained after ion nitriding at 450 degrees C for 10 h are found to be optimum when compared to the other two ion nitriding temperatures.

MHD Flow of a 2nd Grade Fluid in an Orthogonal Rheometer

The magnetohydrodynamics (MHD) flow of a conducting, homogeneous incompressible Rivlin-Ericksen fluid of second grade contained between two infinite, parallel, insulated disks rotating with the same angular velocity about two noncoincident axes, under the application of a uniform transverse magnetic field, is investigated. This model represents the MHD flow of the fluid in the instrument called an orthogonal rheometer, except for the fact that in the rheometer the rotating plates are necessarily finite. An exact solution of the governing equations of motion is presented. The force components in the x and y directions on the disks are calculated. The effects of magnetic field and the viscoelastic parameter on the forces are discussed in detail.

Young, gifted and spiritual -The case of Finnish sixth-grade pupils

The aim of this study was to explore the spirituality of Finnish academically gifted 12 13-year old pre-adolescents (N = 101). Their spirituality was investigated through the following three questions: (1) What is their relationship to religion? (2) How do they perceive transcendence? and (3) How does their search for meaning integrate into their lives? A total of 60 girls and 41 boys participated in the study. They attend a special school, Helsingin Suomalainen yhteiskoulu, in Helsinki, Finland. The school includes classes from grade 3 to upper secondary school and has an entrance test. This study is part of a research project called Actualizing Finnish Giftedness which is funded by the Finnish Academy between 2000 2007 and is led by Professor Tirri. The research project is based on Gardner s Multiple Intelligences theory (Gardner 1993) and on Hay s (1998) work on spirituality. The data in this study was gathered in 2003 and 2004. It includes both qualitative and quantitative material. The emphasis is on data gathered with interviews. The mixed method approach was used as the methodological framework for connecting the qualitative content analysis, phenomenological approach and the quantitative tests of this study. The results of the sub-studies are reported in full in the four original articles. First, the articles show that the pupils connect religion mainly with Christian institutions and do not consider religion and spirituality to overlap. Second, the articles show that the pupils believe in God and the interference of God in their lives and they think that reality includes a spiritual dimension. Third, the pupils had four kinds of existentially significant interests: personal, transcendental, cosmic and ethical. Cosmic interests were especially highlighted in the article concerning boys as nature and science were reported to be integral sources for their existential thinking. In addition, perceptions on God seemed to be connected to the individual s perception on the meaning of life. In RE, spiritual development has been a constant topic of interest since the late eighties. Likewise, recently in gifted education there have been discussions concerning spiritual intelligence (Gardner 1999) and spirituality of the gifted (Kerr & Cohn 2001). Based on the empirical results of the study, this study concludes that education wishing to promote spiritual development should aim at being existentially relevant to the pupils and use their existential search as an integrative framework for their individual talents and skills.

Unterprima (eleventh grade) boys school class portrait Portraits Groups Men

Digital Image

Unterprima (eleventh grade) boys school class portrait Portraits Groups Men

Digital Image

Activated carbon + HFC 134a based two stage thermal compression adsorption refrigeration using low grade thermal energy sources

A thermodynamic analysis is presented for the two stage thermal compression process for an adsorption refrigeration cycle with HFC-134a as the working fluid and activated carbon as the adsorbent. Three specimens of varying achievable packing densities were evaluated. The influence of evaporating, condensing/adsorption and desorption temperatures was assessed through three performance indicators, namely,the uptake efficiency, the coefficient of performance and the exergetic efficiency. Conditions under which a two stage thermal compression process performs better than the single stage unit are identified. It is concluded that two stage thermal compression will be a viable proposition when the heat source temperature is low or when adsorption characteristics are weak or when adequate packing densities are difficult to realize. (C) 2008 Elsevier Ltd. All rights reserved.

Veneer Grade Analysis of Early to Mid-rotation Plantation Eucalyptus Species in Australia

Processing Australian hardwood plantations into rotary veneer can produce more acceptable marketable product recoveries compared to traditional processing techniques (e.g. sawmilling). Veneers resulting from processing trials from six commercially important Australian hardwood species were dominated by D-grade veneer. Defects such as encased knots, gum pockets, gum veins, surface roughness, splits, bark pockets, and decay impacted the final assigned grade. Four grading scenarios were adopted. The first included a change to the grade limitations for gum pockets and gum veins, while the second investigated the potential impact of effective pruning on grade recovery. Although both scenarios individually had a positive impact on achieving higher face grade veneer qualities, the third and fourth scenarios, which combined both, had a substantial impact, with relative veneer values increasing up to 18.2% using conservative calculations (scenario three) or up to 22.6% (scenario four) where some of the upgraded veneers were further upgraded to A-grade, which attracts superior value. The total change in veneer value was found to depend on the average billet diameter unless defects other than those relating to the scenarios (gum or knots) restricted the benefit of pruning and gum upgrading. This was the case for species prone to high levels of growth stress and related defects.

Influence of Solvents on the MWCNT/Adhesive Grade Epoxy Nanocomposites Preparation

In this article, the effect of two solvents, namely dimethyl formamide (DMF) and N-methyl pyrrolidone (NMP), on the dispersion effectiveness and the resulting electrical and mechanical properties of multi-walled carbonanotubes (MNCNT) filled structural adhesive grade epoxy nanocomposites was studied. The solvents were used mainly to reduce the viscosity of the resin system to effectively disperse the nanofiller. The dispersion was carried out under vacuum using high energy sonic waves. SEM was undertaken to study the dispersion effectiveness. Electrical resistivity, tensile properties, and glass transition of the nanocomposites were studied. Between DMF and NMP, the former proved better in terms of dispersion effectiveness and the resulting electrical and mechanical properties of the nanocomposites. Addition of MWCNT into AV138M resulted in an increase in glass transition temperature irrespective of the solvent used and in both cases percolation threshold was found with respect to reduction in electrical resistivity of the nanocomposites. Less agglomeration and hence better interaction between CNT and epoxy was observed in the samples prepared using DMF compared with that using NMP.

Development of probabilistic understanding in fourth grade

We analyzed the development of 4th-grade students’ understanding of the transition from experimental relative frequencies of outcomes to theoretical probabilities with a focus on the foundational statistical concepts of variation and expectation. We report students’ initial and changing expectations of the outcomes of tossing one and two coins, how they related the relative frequency from their physical and computersimulated trials to the theoretical probability, and how they created and interpreted theoretical probability models. Findings include students’ progression from an initial apparent equiprobability bias in predicting outcomes of tossing two coins through to representing the outcomes of increasing the number of trials. After observing the decreasing variation from the theoretical probability as the sample size increased, students developed a deeper understanding of the relationship between relative frequency of outcomes and theoretical probability as well as their respective associations with variation and expectation. Students’ final models indicated increasing levels of probabilistic understanding.