Evaluation of the "reconceptualising early mathematics learning" project

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure enables mathematical thinking and simple forms of generalisation from an early age. The project aims to promote a strong foundation for mathematical development by focusing on critical, underlying features of mathematics learning. This paper provides an overview of key aspects of the assessment and intervention, and analyses of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas. A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in the evaluation throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ assessment and a Pattern and Structure Assessment (PASA) interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a relatively short period of time.

Growth of confined cancer spheroids : a combined experimental marker, critical modelling approach

A critical step in the dissemination of ovarian cancer is the formation of multicellular spheroids from cells shed from the primary tumour. The objectives of this study were to apply bioengineered three-dimensional (3D) microenvironments for culturing ovarian cancer spheroids in vitro and simultaneously to build on a mathematical model describing the growth of multicellular spheroids in these biomimetic matrices. Cancer cells derived from human epithelial ovarian carcinoma were embedded within biomimetic hydrogels of varying stiffness and grown for up to 4 weeks. Immunohistochemistry, imaging and growth analyses were used to quantify the dependence of cell proliferation and apoptosis on matrix stiffness, long-term culture and treatment with the anti-cancer drug paclitaxel. The mathematical model was formulated as a free boundary problem in which each spheroid was treated as an incompressible porous medium. The functional forms used to describe the rates of cell proliferation and apoptosis were motivated by the experimental work and predictions of the mathematical model compared with the experimental output. This work aimed to establish whether it is possible to simulate solid tumour growth on the basis of data on spheroid size, cell proliferation and cell death within these spheroids. The mathematical model predictions were in agreement with the experimental data set and simulated how the growth of cancer spheroids was influenced by mechanical and biochemical stimuli including matrix stiffness, culture duration and administration of a chemotherapeutic drug. Our computational model provides new perspectives on experimental results and has informed the design of new 3D studies of chemoresistance of multicellular cancer spheroids.

Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

Chemistry, Raman and infrared spectroscopic characterization of the phosphate mineral reddingite: (MnFe)3(PO4)2(H2O,OH)3, a mineral found in lithium-bearing pegmatite

Detailed investigation of an intermediate member of the reddingite–phosphoferrite series, using infrared and Raman spectroscopy, scanning electron microcopy and electron microprobe analysis, has been carried out on a homogeneous sample from a lithium-bearing pegmatite named Cigana mine, near Conselheiro Pena, Minas Gerais, Brazil. The determined formula is (Mn1.60Fe1.21Ca0.01Mg0.01)∑2.83(PO4)2.12⋅(H2O2.85F0.01)∑2.86 indicating predominance in the reddingite member. Raman spectroscopy coupled with infrared spectroscopy supports the concept of phosphate, hydrogen phosphate and dihydrogen phosphate units in the structure of reddingite-phosphoferrite. Infrared and Raman bands attributed to water and hydroxyl stretching modes are identified. Vibrational spectroscopy adds useful information to the molecular structure of reddingite–phosphoferrite.

A comparison of Chinese and Australian early childhood mathematics

In the 21st century mathematics proficiency is synonymous with a numerate citizenry. In the past few decades young children’s ability to reason mathematically and develop mathematical proficiencies has been recognised. This paper explores the history of early childhood mathematics (ECME) that may explicate differences in Chinese and Australian contexts. Results of this review established that China and Australia are diametrically positioned in ECME. Influencing each countries philosophies and practices are their cultural beliefs. ECME in China and Australia must be culturally sustainable to achieve excellent outcomes for young children. Ongoing critique and review is necessary to ensure that ECME is meeting the needs of all teachers and children in their particular context. China and Australia with their rich contrasting philosophies can assist each other in their journeys to create exemplary ECME for the 21st century.

Mathematics learning in prep

Most teachers recognise the importance of mathematics teaching and learning in early years but there is not consensus on how and when this learning should occur. Young-Loveridge (cited in de Vries, Thomas, and Warren, 2010) suggests that quality early mathematical experiences are a key determinant to later achievement.

Embedding environmental sustainability in the undergraduate chemistry curriculum : a case study

In spite of increasing attention devoted to the importance of embedding sustainability in university curricula, few Australian universities include specific green chemistry units, and there is no mention of green or sustainable chemistry concepts in the majority of units. In this paper, an argument is posited that all universities should embed sustainable chemistry within all Chemistry courses because it is the morally correct stance to minimise the harm of climate change. Attitudes of chemistry lecturers towards integrating sustainability into their teaching have been probed and it was found, using an established model, that personal environmental perspectives are critical to their attitude. Importantly, academic staff whose research has an environmental component were more likely to incorporate sustainability into their teaching while others struggled to find ways to do so even when they believed it to be important. This paper will recommend that resources are required to assist academic staff without a green chemistry research program to incorporate sustainability into their teaching and several suggestions are provided.

A comparative study on the mineralogy, chemistry and chronology of the Apollo 16 crystalline impact melt breccias. Part II: Chronology.

The controversy on how to interpret the ages of lunar highland breccias has recently been discussed by James [1]. Are the measured ages testimony of true events in lunar history; do they represent the age of the ancient crustal rocks, mixed ages of unequilibrated matrix-phenocryst relationships, or merely thermal events subsequent to the formational event ? It is certain from analyses of terrestrial impact melt breccias that the melt matrix of whole impact melt sheets is isotopically equilibrated due to the extensive mixing process of the early cratering stage [2,3]. It has been shown that isotopic equilibration takes place between impact melt matrix and target rock clasts therein, with the intensity of isotopic exchange depending on the degree of shock metamorphism, thermal metamorphism and the size of the clasts [4]. Therefore, impact melt breccias - if they are relatively clast-poor and mineralogically well studied - can be considered to be the most reliable source for information on the impact history of the lunar highland.

Assessing the potential of mathematics textbooks to promote deep learning

Curriculum documents for mathematics emphasise the importance of promoting depth of knowledge rather than shallow coverage of the curriculum. In this paper, we report on a study that explored the analysis of junior secondary mathematics textbooks to assess their potential to assist in teaching and learning aimed at building and applying deep mathematical knowledge. The method of analysis involved the establishment of a set of specific curriculum goals and associated indicators, based on research into the teaching and learning of a particular field within the mathematics curriculum, namely proportion and proportional reasoning. Topic selection was due to its pervasive nature throughout the school mathematics curriculum at this level. As a result of this study, it was found that the five textbook series examined provided limited support for the development of multiplicative structures required for proportional reasoning, and hence would not serve well the development of deep learning of mathematics. The study demonstrated a method that could be applied to the analysis of junior secondary mathematics in many parts of the world.

Academic success in context-based chemistry : Demonstrating fluid transitions between concepts and context

Curriculum developers and researchers have promoted context-based programmes to arrest waning student interest and participation in the enabling sciences at high school and university. Context-based programmes aim for student connections between scientific discourse and real-world contexts to elevate curricular relevance without diminishing conceptual understanding. This interpretive study explored the learning transactions in one 11th grade context-based chemistry classroom where the context was the local creek. The dialectic of agency/structure was used as a lens to examine how the practices in classroom interactions afforded students the agency for learning. The results suggest that first, fluid transitions were evident in the student–student interactions involving successful students; and second, fluid transitions linking concepts to context were evident in the students’ successful reports. The study reveals that the structures of writing and collaborating in groups enabled students’ agential and fluent movement between the field of the real-world creek and the field of the formal chemistry classroom. Furthermore, characteristics of academically successful students in context-based chemistry are highlighted. Research, teaching, and future directions for context-based science teaching are discussed.

Higher order thinking in chemistry curriculum and its assessment

Higher-order thinking has featured persistently in the reform agenda for science education. The intended curriculum in various countries sets out aspirational statements for the levels of higher-order thinking to be attained by students. This study reports the extent to which chemistry examinations from four Australian states align and facilitate the intended higher-order thinking skills stipulated in curriculum documents. Through content analysis, the curriculum goals were identified for each state and compared to the nature of question items in the corresponding examinations. Categories of higher-order thinking were adapted from the OECD’s PISA Science test to analyze question items. There was considerable variation in the extent to which the examinations from the states supported the curriculum intent of developing and assessing higher-order thinking. Generally, examinations that used a marks-based system tended to emphasize lower-order thinking, with a greater distribution of marks allocated for lower-order thinking questions. Examinations associated with a criterion-referenced examination tended to award greater credit for higher-order thinking questions. The level of complexity of chemistry was another factor that limited the extent to which examination questions supported higher-order thinking. Implications from these findings are drawn for the authorities responsible for designing curriculum and assessment procedures and for teachers.

Using formative feedback to identify and support first year chemistry students with missing or misconceptions. A Practice Report

Students entering tertiary studies possess a diverse range of prior experiences in their academic preparation for tertiary chemistry so academics need tools to enable them to respond to issues in diversity in conceptual models possessed by entering students. Concept inventories can be used to provide formative feedback to help students identify concepts that they need to address to improve construction of subsequent understanding enabling their learning. Modular, formative learning activities that can be administered inside or outside of class in first year chemistry courses have been developed. These activities address key missing and mis-conceptions possessed by incoming student. Engagement in these learning activities by students and academics will help shift the culture of diagnostic and formative assessment within the tertiary context and address issues around the secondary/tertiary transition. This diagnostic/intervention framework is currently being trialed across five Australian tertiary institutions encompassing a large heterogeneous sample of students.

Comprehensive study of surface chemistry of MCM-41 using 29Si CP/MAS NMR, FTIR, pyridine-TPD, and TGA

A comprehensive study was conducted on mesoporous MCM-41. Spectroscopic examinations demonstrated that three types of silanol groups, i.e., single, (SiO)3Si-OH, hydrogen-bonded, (SiO)3Si-OH-OH-Si(SiO)3, and geminal, (SiO)2Si(OH)2, can be observed. The number of silanol groups/nm2, ?OH, as determined by NMR, varies between 2.5 and 3.0 depending on the template-removal methods. All these silanol groups were found to be the active sites for adsorption of pyridine with desorption energies of 91.4 and 52.2 kJ mol-1, respectively. However, only free silanol groups (involving single and geminal silanols) are highly accessible to the silylating agent, chlorotrimethylsilane. Silylation can modify both the physical and chemical properties of MCM-41.