Accelerating the Mathematics Learning of Low Socio-Economic Status Junior Secondary Students : an early report

The Accelerating the Mathematics Learning of Low Socio-Economic Status Junior Secondary Students project aims to address the issues faced by very underperforming mathematics students as they enter high school. Its aim is to accelerate learning of mathematics through a vertical curriculum to enable students to access Year 10 mathematics subjects, thus improving life chances. This paper reports upon the theory underpinning this project and illustrates it with examples of the curriculum that has been designed to achieve acceleration.

A conceptual framework for the cultural integration of cooperative learning : a Thai primary mathematics education perspective

The Thailand education reform adopted cooperative learning to improve the quality of education. However, it has been reported that the introduction and maintenance of cooperative learning has been difficult and uncertain because of the cultural differences. The study proposed a conceptual framework developed based on making a connection between Thai cultures and cooperative learning elements, and implemented a small-scale research project in a Thai primary mathematics class with a teacher and thirty-two Grade 4 students. The results uncovered that the three components including preparation of teachers, instructional strategies and preparation of students can be vehicles for the culture integration in cooperative learning.

Modelling as a vehicle for philosophical inquiry in the mathematics curriculum

Philosophical inquiry in the teaching and learning of mathematics has received continued, albeit limited, attention over many years (e.g., Daniel, 2000; English, 1994; Lafortune, Daniel, Fallascio, & Schleider, 2000; Kennedy, 2012a). The rich contributions these communities can offer school mathematics, however, have not received the deserved recognition, especially from the mathematics education community. This is a perplexing situation given the close relationship between the two disciplines and their shared values for empowering students to solve a range of challenging problems, often unanticipated, and often requiring broadened reasoning. In this article, I first present my understanding of philosophical inquiry as it pertains to the mathematics classroom, taking into consideration the significant work that has been undertaken on socio-political contexts in mathematics education (e.g., Skovsmose & Greer, 2012). I then consider one approach to advancing philosophical inquiry in the mathematics classroom, namely, through modelling activities that require interpretation, questioning, and multiple approaches to solution. The design of these problem activities, set within life-based contexts, provides an ideal vehicle for stimulating philosophical inquiry.

An evaluation of the Australian ‘reconceptualising early mathematics learning’ project : key findings and implications

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 (AMPS) enables mathematical thinking and simple forms of generalization from an early age. This paper provides an overview of key findings of the Reconceptualizing Early Mathematics Learning empirical evaluation study involving 316 Kindergarten students from 4 schools. The study found highly significant differences on PASA scores for PASMAP students. Analysis of structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a short period of time.

Starting out in STEM : a study of young men and women in first year science, technology, engineering and mathematics courses

In late 2011, first year university students in science, technology, engineering and mathematics (STEM) courses across Australia were invited to participate in the international Interests and Recruitment in Science (IRIS) study. IRIS investigates the influences on young people's decisions to choose university STEM courses and their subsequent experiences of these courses. The study also has a particular focus on the motivations and experiences of young women in courses such as physics, IT and engineering given the low rates of female participation in these fields. Around 3500 students from 30 Australian universities contributed their views on the relative importance of various school and non-school influences on their decisions, as well as insights into their experiences of university STEM courses so far. It is hoped that their contributions will help improve recruitment, retention and gender equity in STEM higher education and careers.

Successful outcomes in vocational education and training courses and mathematics: how pedagogy and expectations influence achievement

This paper reports on a four year Australian Research Council funded Linkage Project titled Skilling Indigenous Queensland, conducted in regional areas of Queensland, Australia from 2009 to 2013. The project sought to investigate Vocational Education and Training (VET) and teaching, Indigenous learners’ needs, employer culture and expectations and community culture and expectations to identify best practice in numeracy teaching for Indigenous VET learners. Specifically it focused on ways to enhance the teaching and learning of courses and the associated mathematics in such courses to benefit learners and increase their future opportunities of employment. To date thirty - nine teachers/trainers/teacher aides and two hundred and thirty - one students consented to participate in the project. Nine VET courses offered in schools and Technical and Further Education Institutes (TAFE) were nominated to be the focus on the study. This paper focuses on student questionnaire responses and interview responses from teachers/trainers one high school principal and five students as a result of these processes, the findings indicated that VET course teachers work hard to adopt contextualising strategies to their teaching; however this process is not always straight forward because of the perceptions of how mathematics has been taught and learned by trainers and teachers. Further teachers, trainers and students have high expectations of one another with the view to successful outcomes from the courses.

Connectivity of workflow nets : the foundations of stepwise verification

Behavioral models capture operational principles of real-world or designed systems. Formally, each behavioral model defines the state space of a system, i.e., its states and the principles of state transitions. Such a model is the basis for analysis of the system’s properties. In practice, state spaces of systems are immense, which results in huge computational complexity for their analysis. Behavioral models are typically described as executable graphs, whose execution semantics encodes a state space. The structure theory of behavioral models studies the relations between the structure of a model and the properties of its state space. In this article, we use the connectivity property of graphs to achieve an efficient and extensive discovery of the compositional structure of behavioral models; behavioral models get stepwise decomposed into components with clear structural characteristics and inter-component relations. At each decomposition step, the discovered compositional structure of a model is used for reasoning on properties of the whole state space of the system. The approach is exemplified by means of a concrete behavioral model and verification criterion. That is, we analyze workflow nets, a well-established tool for modeling behavior of distributed systems, with respect to the soundness property, a basic correctness property of workflow nets. Stepwise verification allows the detection of violations of the soundness property by inspecting small portions of a model, thereby considerably reducing the amount of work to be done to perform soundness checks. Besides formal results, we also report on findings from applying our approach to an industry model collection.

The biconnected verification of workflow nets

Formal representations of business processes are used for analysis of the process behavior. Workflow nets are a widely used formalism for describing the behavior of business processes. Structure theory of processes investigates the relation between the structure of a model and its behavior. In this paper, we propose to employ the connectivity property of workflow nets as an angle to their structural analysis. In particular, we show how soundness verification can be organized using biconnected components of a workflow net. This allows for efficient identification and localization of flaws in the behavior of workflow nets and for supporting process analysts with diagnostic information

ORIGO stepping stones common core mathematics Grade 5 practice book

ORIGO Stepping Stones is written and developed by a team of experts to provide teachers with a world-class elementary math program. Our expert team of authors and consultants are utilizing all available educational research to create a unique program that has never before been available to teachers. The full color Student Practice Book provides practice pages that support previous and current lessons.

The continuing decline of science and mathematics enrolments in Australian high schools

Is there a crisis in Australian science and mathematics education? Declining enrolments in upper secondary Science and Mathematics courses have gained much attention from the media, politicians and high-profile scientists over the last few years, yet there is no consensus amongst stakeholders about either the nature or the magnitude of the changes. We have collected raw enrolment data from the education departments of each of the Australian states and territories from 1992 to 2012 and analysed the trends for Biology, Chemistry, Physics, two composite subject groups (Earth Sciences and Multidisciplinary Sciences), as well as entry, intermediate and advanced Mathematics. The results of these analyses are discussed in terms of participation rates, raw enrolments and gender balance. We have found that the total number of students in Year 12 increased by around 16% from 1992 to 2012 while the participation rates for most Science and Mathematics subjects, as a proportion of the total Year 12 cohort, fell (Biology (-10%), Chemistry (-5%), Physics (-7%), Multidisciplinary Science (-5%), intermediate Mathematics (-11%), advanced Mathematics (-7%) in the same period. There were increased participation rates in Earth Sciences (+0.3%) and entry Mathematics (+11%). In each case the greatest rates of change occurred prior to 2001 and have been slower and steadier since. We propose that the broadening of curriculum offerings, further driven by students' self-perception of ability and perceptions of subject difficulty and usefulness, are the most likely cause of the changes in participation. While these continuing declines may not amount to a crisis, there is undoubtedly serious cause for concern.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Analysis of two authorization protocols using Colored Petri Nets

To prevent unauthorized access to protected trusted platform module (TPM) objects, authorization protocols, such as the object-specific authorization protocol (OSAP), have been introduced by the trusted computing group (TCG). By using OSAP, processes trying to gain access to the protected TPM objects need to prove their knowledge of relevant authorization data before access to the objects can be granted. Chen and Ryan’s 2009 analysis has demonstrated OSAP’s authentication vulnerability in sessions with shared authorization data. They also proposed the Session Key Authorization Protocol (SKAP) with fewer stages as an alternative to OSAP. Chen and Ryan’s analysis of SKAP using ProVerif proves the authentication property. The purpose of this paper was to examine the usefulness of Colored Petri Nets (CPN) and CPN Tools for security analysis. Using OSAP and SKAP as case studies, we construct intruder and authentication property models in CPN. CPN Tools is used to verify the authentication property using a Dolev–Yao-based model. Verification of the authentication property in both models using the state space tool produces results consistent with those of Chen and Ryan.

Interrupting malaria transmission: quantifying the impact of interventions in regions of low to moderate transmission

Malaria has been eliminated from over 40 countries with an additional 39 currently planning for, or committed to, elimination. Information on the likely impact of available interventions, and the required time, is urgently needed to help plan resource allocation. Mathematical modelling has been used to investigate the impact of various interventions; the strength of the conclusions is boosted when several models with differing formulation produce similar data. Here we predict by using an individual-based stochastic simulation model of seasonal Plasmodium falciparum transmission that transmission can be interrupted and parasite reintroductions controlled in villages of 1,000 individuals where the entomological inoculation rate is <7 infectious bites per person per year using chemotherapy and bed net strategies. Above this transmission intensity bed nets and symptomatic treatment alone were not sufficient to interrupt transmission and control the importation of malaria for at least 150 days. Our model results suggest that 1) stochastic events impact the likelihood of successfully interrupting transmission with large variability in the times required, 2) the relative reduction in morbidity caused by the interventions were age-group specific, changing over time, and 3) the post-intervention changes in morbidity were larger than the corresponding impact on transmission. These results generally agree with the conclusions from previously published models. However the model also predicted changes in parasite population structure as a result of improved treatment of symptomatic individuals; the survival probability of introduced parasites reduced leading to an increase in the prevalence of sub-patent infections in semi-immune individuals. This novel finding requires further investigation in the field because, if confirmed, such a change would have a negative impact on attempts to eliminate the disease from areas of moderate transmission.

Making meaning in mathematics problem solving using the Reciprocal Teaching approach

This paper examines the application of the Reciprocal Teaching instructional approach to Mathematical word problems in the middle years. The Reciprocal Teaching process is extended from the four traditional strategies of predicting, clarifying, questioning and summarising, to include further cognitive reading comprehension strategies applied to the context of solving Mathematical word problems.