Developing Learning Trajectory For Enhancing Students’ Relational Thinking

Algebra is part of Mathematics learning in Indonesian curriculum. It takes one half of the teaching hours in senior high school, and one third in junior high school. However, the learning trajectory of Algebra needs to be improved because teachers teach computational thinking by applying paper-and-pencil strategy combining with the concepts-operations-example-drilling approach. Mathematics textbooks do not give enough guidance for teachers to conduct good activities in the classroom to promote algebraic thinking especially in the primary schools. To reach Indonesian Mathematics teaching goals, teachers should develop learning trajectories based on pedagogical and theoretical backgrounds. Teachers need to have knowledge of student’s developmental progressions and understanding of mathematics concepts and students’ thinking. Research shows that teachers’ knowledge of student’s mathematical development is related to their students’ achievement. In fostering a greater emphasis on algebraic thinking, teachers and textbooks need to work more closely together to develop a clearer learning trajectory. Having this algebraic thinking, students developed not only their own character of learning and thinking but also their attitude, attention and discipline. Key Words: Learning Trajectory, Relational Thinkin

The Model Builder: A Multi-Fidelity Structural Modeling Tool for Seismic Hazard Analysis

Earthquakes affect millions of people across the earth. Earthquakes cause billions of dollars of damage and hundreds of thousands of deaths per year. For these reasons that seismic resilience is a field of immense concern for government, stakeholders and researchers. As the field of earthquake engineering has advanced, higher levels of analysis have been developed, both in terms of fidelity and complexity, capable of capturing complex non-linear structural response. However, regional assessment frameworks, which estimate structural performance at regional scale, do not commonly use building-level structural modeling to capture structural response. Many of these frameworks instead use a fragility-based approach where seismic intensity measures (such as peak ground acceleration) are related to probabilistic levels of damage. The fragility functions used in this approach are based on the response of structural archetypes such as a steel moment frames or concrete shear walls. Thus, the response and damage estimations generated using these methodologies are not that of the actual structure in question, but rather that of an archetypical representation of the structure. While this approach can roughly predict the dominant characteristics of vulnerable structures subjected to seismic hazards, it is difficult to pinpoint critical deficiencies for immediate retrofit or evacuation and inspection. The objective of this research is to develop a framework to provide building-specific nonlinear response predictions within regional structural simulation. First, existing regional response prediction frameworks for natural disasters and structural analysis are introduced. Next, the opensource finite element analysis software OpenSeesPy is introduced along with the multi-fidelity Model Builder tool capable of rapidly developing building-level structural models using the software. This software uses the OpenSEES framework to create the models, apply ground motions, and assess levels of damage of the structural system. The Model Builder was then validated using several recorded structural response histories. Based on the findings here, the Model Builder can be applied to develop models for regional response simulation

Modern statistical literacy, data science, dashboards, and automated analytics and its applications

With regard to the internationalization of statistics education, this paper considers first a global context concerning modern statistical literacy, data science, and dashboards. Then, it examines data discovery using automated analytics, whereby data insights may be indicated by suitable signals generated by the computer environment used. This theoretical paper, directed towards statistics educators, as well as other educators in relevant high school subjects, should make them (more) aware of this context and such analytics, supporting them to identify issues that need be considered in their teaching (and research) in order to have their students better prepared for the jobs of tomorrow

From research to practice: The case of mathematical reasoning

Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, international assessments of mathematical literacy suggest that mathematical reasoning and problem solving are areas of difficulty for Australian students. Given the efficacy of teaching informed by quality assessment data, a recent study focused on the development of evidence-based Learning Progressions for Algebraic, Spatial and Statistical Reasoning that can be used to identify where students are in their learning and where they need to go to next. Importantly, they can also be used to generate targeted teaching advice and activities to help teachers progress student learning. This paper explores the processes involved in taking the research to practice

An empirically based practical learning progression for generalisation, an essential element of algebraic reasoning

Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is then elaborated and validated by reference to a large range of assessment tasks acquired from a previous project Reframing Mathematical Futures II (RMFII). In the RMFII project, Rasch modelling of the responses of over 5000 high school students (Years 7–10) to algebra tasks led to the development of a Learning Progression for Algebraic Reasoning (LPAR). Our learning progression in generalisation is more specific than the LPAR, more coherent regarding algebraic generalisation, and enabling teachers to locate students’ performances within the progression and to target their teaching. In addition, a selection of appropriate teaching resources and marking rubrics used in the RMFII project is provided for each level of the learning progression

High-Level Macrolide Resistance Due to the Mega Element [mef(E)/mel] in Streptococcus pneumoniae

Transferable genetic elements conferring macrolide resistance in Streptococcus pneumoniae can encode the efflux pump and ribosomal protection protein, mef(E)/mel, in an operon of the macrolide efflux genetic assembly (Mega) element- or induce ribosomal methylation through a methyltransferase encoded by erm(B). During the past 30 years, strains that contain Mega or erm(B) or both elements on Tn2010 and other Tn916-like composite mobile genetic elements have emerged and expanded globally. In this study, we identify and define pneumococcal isolates with unusually high-level macrolide resistance (MICs > 16 μg/ml) due to the presence of the Mega element [mef(E)/mel] alone. High-level resistance due to mef(E)/mel was associated with at least two specific genomic insertions of the Mega element, designated Mega-2.IVa and Mega-2.IVc. Genome analyses revealed that these strains do not possess erm(B) or known ribosomal mutations. Deletion of mef(E)/mel in these isolates eliminated macrolide resistance. We also found that Mef(E) and Mel of Tn2010-containing pneumococci were functional but the high-level of macrolide resistance was due to Erm(B). Using in vitro competition experiments in the presence of macrolides, high-level macrolide-resistant S. pneumoniae conferred by either Mega-2.IVa or erm(B), had a growth fitness advantage over the lower-level, mef(E)/mel-mediated macrolide-resistant S. pneumoniae phenotypes. These data indicate the ability of S. pneumoniae to generate high-level macrolide resistance by macrolide efflux/ribosomal protection [Mef(E)/Mel] and that high-level resistance regardless of mechanism provides a fitness advantage in the presence of macrolides

The importance of understanding large data, context, conventions and uncertainty in a pandemic

Background: The coronavirus disease 2019 (COVID-19) pandemic has provided rich data displays informing the public about the spread of infection, risks for certain population groups and the effectiveness of vaccines. These data sources offer opportunities for students and teachers to explore and discuss data of high relevance to their lives and their communities. Aim: This article argues that in the teaching of statistics and probability, greater attention needs to be given to understand the three key elements of statistical literacy, namely context, conventions and uncertainty. The article also identifies several key areas linking theory and practice. Setting: This article draws on different data displays using COVID-19-related websites internationally; nationally in Africa and South Africa; and locally in the State of Victoria in Australia. Methods: By investigating and analysing different data displays, the article shows the importance of assisting students to understand context, data conventions, uncertainty and risk–benefit to understand COVID-19 data. The article examines pertinent ‘frontier’ areas in the teaching of probability and statistics. Results: The article identifies important opportunities and challenges for the teaching of statistics in schools and for teacher education, including greater attention to frequentist expressions of probability, risk–benefit analysis, the importance of time series analyses and critical approaches to the evaluation of available data sets. Conclusion: For schools, greater attention needs to be given to the different conventions by which data are expressed, including the use of dynamic dashboard representations. Contribution: The article shows how available COVID-19 data can be used to enhance students’ statistical literacy and enrich teacher education