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.

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.

Implication of 3D culture system for study of prostate cancer (CaP) mediated bone metastasis

Introduction : For the past decade, three dimensional (3D) culture has served as a foundation for regenerative medicine study. With an increasing awareness of the importance of cell-cell and cell-extracellular matrix interactions which are lacking in 2D culture system, 3D culture system has been employed for many other applications namely cancer research. Through development of various biomaterials and utilization of tissue engineering technology, many in vivo physiological responses are now better understood. The cellular and molecular communication of cancer cells and their microenvironment, for instance can be studied in vitro in 3D culture system without relying on animal models alone. Predilection of prostate cancer (CaP) to bone remains obscure due to the complexity of the mechanisms and lack of proper model for the studies. In this study, we aim to investigate the interaction between CaP cells and osteoblasts simulating the natural bone metastasis. We also further investigate the invasiveness of CaP cells and response of androgen sensitve CaP cells, LNCaP to synthetic androgen.----- Method : Human osteoblast (hOB) scaffolds were prepared by seeding hOB on medical grade polycaprolactone-tricalcium phosphate (mPLC-TCP) scaffolds and induced to produce bone matrix. CaP cell lines namely wild type PC3 (PC3-N), overexpressed prostate specific antigen PC3 (PC3k3s5) and LNCaP were seeded on hOB scaffolds as co-cultures. Morphology of cells was examined by Phalloidin-DAPI and SEM imaging. Gelatin zymography was performed on the 48 hours conditioned media (CM) from co-cultures to determine matrix metalloproteinase (MMP) activity. Gene expression of hOB/LNCaP co-cultures which were treated for 48 hours with 1nM synthetic androgen R1881 were analysed by quantitative real time PCR (qRT-PCR).----- Results : Co-culture of PCC/hOB revealed that the morphology of PCCs on the tissue engineered bone matrix varied from homogenous to heterogenous clusters. Enzymatically inactive pro-MMP2 was detected in CM from hOBs and PCCs cultured on scaffolds. Elevation in MMP9 activity was found only in hOB/PC3N co-culture. hOB/LNCaP co-culture showed increase in expression of key enzymes associated with steroid production which also corresponded to an increase in prostate specific antigen (PSA) and MMP9.----- Conclusions : Upregulation of MMP9 indicates involvement of ECM degradation during cancer invasion and bone metastases. Expression of enzymes involved in CaP progression, PSA, which is not expressed in osteoblasts, demonstrates that crosstalk between PCCs and osteoblasts may play a part in the aggressiveness of CaP. The presence of steroidogenic enzymes, particularly, RDH5, in osteoblasts and stimulated expression in co-culture, may indicate osteoblast production of potent androgens, fuelling cancer cell proliferation. Based on these results, this practical 3D culture system may provide greater understanding into CaP mediated bone metastasis. This allows the role of the CaP/hOB interaction with regards to invasive property and steroidogenesis to be further explored.

Impact response and parametric studies of reinforced concrete circular columns

This paper presents a detailed description of the influence of critical parameters that govern the vulnerability of columns under lateral impact loads. Numerical simulations are conducted by using the Finite Element program LS-DYNA, incorporating steel reinforcement, material models and strain rate effects. A simplified method based on impact pulse generated from full scale impact tests is used for impact reconstruction and effects of the various pulse loading parameters are investigated under low to medium velocity impacts. A constitutive material model which can simulate failures under tri-axial state of stresses is used for concrete. Confinement effects are also introduced to the numerical simulation and columns of Grade 30 to 50 concrete under pure axial loading are analysed in detail. This research confirmed that the vulnerability of the axially loaded columns can be mitigated by reducing the slenderness ratio and concrete grade, and by choosing the design option with a minimal amount of longitudinal steel. Additionally, it is evident that approximately a 50% increase in impact capacity can be gained for columns in medium rise buildings by enhancing the confinement effects alone. Results also indicated that the ductility as well as the mode of failure under impact can be changed with the volumetric ratio of lateral steel. Moreover, to increase the impact capacity of the vulnerable columns, a higher confining stress is required. The general provisions of current design codes do not sufficiently cover this aspect and hence this research will provide additional guidelines to overcome the inadequacies of code provisions.

Elementary school students’ learner self-concept, academic self-concepts and approaches to learning

The present study investigated the relationships between academic selfconcepts, learner self-concept, and approaches to learning in elementary school students. A sample of 580 Australian Grade 6 and 7 school students with a mean age of 10.7 years participated in the study. Weak negative correlations between learner self-concepts and surface approaches to learning were identiŽ ed. In contrast, deep approaches for both boys and girls showed the highest positive correlations with school self-concept and learning self-concept. Only slight variations in these Ž gures were found between boys and girls.

Evaluation of polycaprolactone scaffold degradation for 6 months in vitro and in vivo

The use of polycaprolactone (PCL) as a biomaterial, especially in the fields of drug delivery and tissue engineering, has enjoyed significant growth. Understanding how such a device or scaffold eventually degrades in vivo is paramount as the defect site regenerates and remodels. Degradation studies of three-dimensional PCL and PCL-based composite scaffolds were conducted in vitro (in phosphate buffered saline) and in vivo (rabbit model). Results up to 6 months are reported. All samples recorded virtually no molecular weight changes after 6 months, with a maximum mass loss of only about 7% from the PCL-composite scaffolds degraded in vivo, and a minimum of 1% from PCL scaffolds. Overall, crystallinity increased slightly because of the effects of polymer recrystallization. This was also a contributory factor for the observed stiffness increment in some of the samples, while only the PCL-composite scaffold registered a decrease. Histological examination of the in vivo samples revealed good biocompatibility, with no adverse host tissue reactions up to 6 months. Preliminary results of medical-grade PCL scaffolds, which were implanted for 2 years in a critical-sized rabbit calvarial defect site, are also reported here and support our scaffold design goal for gradual and late molecular weight decreases combined with excellent long-term biocompatibility and bone regeneration. (C) 2008 Wiley Periodicals, Inc. J Biomed Mater Res 90A: 906-919, 2009

Authentic and conventional assessment in Singapore schools : an empirical study of teacher assignments and student work

This is an empirical examination of the quality of teacher assignments and student work in Singapore schools. Using a theoretical framework based on principles of authentic assessment and intellectual quality, two sets of criteria and scoring rubrics were developed for the training of expert teachers to judge the quality of assignments and student work. Following rigorous training, the inter-rater reliability of expert teacher scoring was high. Samples of teacher assignments and student work were collected in English, social studies, mathematics, and science subject areas from a random stratified sample of 30 elementary schools and 29 high schools. For both grade levels, there were significant differences for the authentic intellectual quality of teachers’ assignments by subject area. Likewise, the differences of authentic intellectual quality for student work were significant and varied by subject area. Subject area effect was large. The correlations between the quality of teachers’ assignment tasks and student work were strong and significant at both grade levels. Where teachers set more intellectually demanding tasks, students were more likely to generate work or artefacts judged to be of higher quality. The findings suggest that teacher professional development in authentic intellectual assessment task design can contribute to the improvement of student learning and performance. It is argued that this will be a key requisite of educational systems like Singapore that are seeking to expand pedagogy and student outcomes beyond a focus on factual and rote knowledge.

Identifying effective leadership practices for implementing a new mathematics curriculum in Taipei

This study explores successful junior high school principals’ leadership practices for implementing the reformed mathematics curriculum in Taipei. Avolio and Bass’s (2002) full range leadership theory was used to record data through interviews and observations of five Taipei “Grade A” junior high school principals. Findings revealed that specific leadership practices linked to management by exception-active and contingent reward (transaction leadership), and individualised consideration and idealised influence (transformational) were considered effective for implementing reform measures. Ensuring principals are aware of effective measures may further assist reform agendas.

Self-talk in upper primary school children : its relationship with irrational beliefs, self-esteem and depression

Self-talk, irrational beliefs, self-esteem and depression were measured in a sample of 105 elementary school children in Grades 4 to 7. Sex and grade differences in positive self-talk were found. The pattern of correlation coefficients for positive self-talk supported the substantive position that positive self-talk is positively related to self-esteem and negatively related to irrational beliefs and depression in a non-clinical sample of children. However, the same support was not forthcoming for the reverse relationships for negative self-talk. Therapeutic implications are outlined as are suggestions for future research in the area of children's self-talk.

Re-imagining school through young people’s drawings

Children’s drawings provide rich qualitative data (Walker, 2008) and “valuable information for the assessment of children's environmental perceptions” (Barraza, 1999, p. 49). They are the primary data source being used to re-imagine school from a student perspective (Schratz & Steiner-Löffler, 1998) in a research project being carried out with primary school students in Queensland, Australia. This paper will report on the progress of this project which addresses a mostly unmet need for students’ perspectives to be included in school design (Rudduck & Flutter, 2004). Grade 5/6 students in a number of primary schools have been invited to submit annotated drawings with up to 200 words of text illustrating their ideal educational spaces. Using purpose-designed analytical tools, the submissions will be compared across student backgrounds and school types to obtain a better understanding of the needs and educational desires of young people in relation to changing learning environments. The findings will inform consideration of the design and use of educational spaces with all work exhibited through a dedicated website. The term ‘educational spaces’ avoids restrictive notions of what the concept of ‘school’ means, referring to any real or virtual space in which teaching and learning may occur or, as Ferguson and Seddon (2007) have referred to it, “the shifting imagery of education” that includes red brick schools and dispersed learning networks. The theoretical framework for this study is grounded in the work of Greene (1995) and Wright-Mills (2001) who cited the deployment of critical and empathic imagination in addressing education reform.

Amniotic fluid stem cells produce robust mineral deposits on biodegradable scaffolds

Insufficient availability of osteogenic cells limits bone regeneration through cell-based therapies. This study investigated the potential of amniotic fluid–derived stem (AFS) cells to synthesize mineralized extracellular matrix within porous medical-grade poly-e-caprolactone (mPCL) scaffolds. The AFS cells were initially differentiated in two-dimensional (2D) culture to determine appropriate osteogenic culture conditions and verify physiologic mineral production by the AFS cells. The AFS cells were then cultured on 3D mPCL scaffolds (6-mm diameter9-mm height) and analyzed for their ability to differentiate to osteoblastic cells in this environment. The amount and distribution of mineralized matrix production was quantified throughout the mPCL scaffold using nondestructive micro computed tomography (microCT) analysis and confirmed through biochemical assays. Sterile microCT scanning provided longitudinal analysis of long-term cultured mPCL constructs to determine the rate and distribution of mineral matrix within the scaffolds. The AFS cells deposited mineralized matrix throughout the mPCL scaffolds and remained viable after 15 weeks of 3D culture. The effect of predifferentiation of the AFS cells on the subsequent bone formation in vivo was determined in a rat subcutaneous model. Cells that were pre-differentiated for 28 days in vitro produced seven times more mineralized matrix when implanted subcutaneously in vivo. This study demonstrated the potential of AFS cells to produce 3D mineralized bioengineered constructs in vitro and in vivo and suggests that AFS cells may be an effective cell source for functional repair of large bone defects