What do error patterns tell us about Hong Kong Chinese and Australian students’ understanding of decimal numbers?

Mathematics educators have had a long standing interest in students’ understanding of decimal numbers. Most studies of students’ understanding of decimals have been conducted within Western cultural settings. The present study sought to gain insight into Chinese Hong Kong students’ and regional Australian students’ general performance on a variety of decimals tasks and to investigate students’ error patterns

Extending the notion of Specialized Content Knowledge: Proposing constructs for SCK

While it is widely believed that Specialized Content Knowledge (SCK) is essential to effective and quality mathematics teaching, the specific constructs that compose SCK remain underspecified. This paper describes the development and use of a new framework that extends the notion of SCK. The framework was trialled with a cohort of 90 first year Bachelor of Education (Primary) pre-service teachers who enrolled in a regional Australian university. The pre-service teachers undertook a mathematics test, which required them to address school students’ misconceptions and to explain specific mathematical concepts. Resultant data (i.e., the pre-service teachers’ responses to the written test) provided an empirical basis for the proposed constructs of SCK. The analysis of the data allowed insight into the central question: whether the proposed framework enables researchers to identify the constructs of SCK in the pre-service teachers’ responses to a written test which examines their SCK. Ultimately, we aim to conceptualise the constructs of SCK through elaborating the theoretical and empirical basis

Visual perceptual abilities of Chinese-speaking and English-speaking children

This paper reports an investigation of Chinese-speaking and English- speaking children's general visual perceptual abilities. The Developmental Test of Visual Perception was administered to 41 native Chinese-speaking children of mean age 5 yr. 4 mo. in Hong Kong and 35 English-speaking children of mean age 5 yr. 2 mo. in Melbourne. Of interest were the two interrelated components of visual perceptual abilities, namely, motor-reduced visual perceptual and visual-motor integration perceptual abilities, which require either verbal or motoric responses in completing visual tasks. Chinese-speaking children significantly outperformed the English-speaking children on general visual perceptual abilities. When comparing the results of each of the two different components, the Chinese-speaking students' performance on visual-motor integration was far better than that of their counterparts (ES = 2.70), while the two groups of students performed similarly on motor-reduced visual perceptual abilities. Cultural factors such as written language format may be contributing to the enhanced performance of Chinese-speaking children's visual-motor integration abilities, but there may be validity questions in the Chinese version. © Perceptual and Motor Skills 2012

Social Psychology Meets School Mathematics in PISA 2012: An Application of the Theory of Planned Behaviour in Australia

Educators and government administrators are keen to find interventions to change the rapidly declining enrollments in senior high school mathematics. In 2012, PISA introduced measures to examine the Theory of Planned Behaviour (TPB), a prominent theory from social psychology for encouraging changes in behavior (and perhaps mathematics enrollments). This paper sought to examine the applicability of the TPB for predicting the relationship between students’ intentions, their mathematics attitudes, subject norms, perceived controllability and self-efficacy as well as their mathematics behaviour, using items created by PISA 2012 question designers to assess these TPB constructs. Australian PISA 2012 data from 14,481 students found that the hypothesized TPB antecedents for studying mathematics were very poor predictors of mathematical intentions and indirectly, weak predictors of mathematical behaviour. The Attitudes factor i.e. an interest in mathematics, was found to be the strongest predictor of mathematical intentions. The poor predictive capacity of the TPB was proposed to have been due to ill-defined indicator items in the PISA 2012 measuring instruments, which did not comply with the TPB’s principles of compatibility and aggregation. Future studies testing the TPB in the context of studying mathematics would benefit from undertaking Elicitation studies to identify appropriate TPB antecedents and indicators of the mathematics behaviour being targeted

HONG KONG GRADE 6 STUDENTS’ PERFORMANCE AND MATHEMATICAL REASONING IN DECIMALS TASKS: PROCEDURALLY BASED OR CONCEPTUALLY BASED?

© 2014, National Science Council, Taiwan. Most studies of students’ understanding of decimals have been conducted within Western cultural settings. The broad aim of the present research was to gain insight into Chinese Hong Kong grade 6 students’ general performance on a variety of decimals tasks. More specifically, the study aimed to explore students’ mathematical reasoning for their use of ‘rules’ and algorithms and to determine whether connections exist between students’ conceptual and procedural knowledge when completing decimals tasks. Results indicated that conceptual understanding for rules and procedures were built into the students’ knowledge system for most of the items concerned with place value in decimals—ordering decimals, translating fractions into decimals, the representation of place value in decimals, the concept of place value in decimals on number line and the concept of continuous quantity in decimals. However, the students were not able to provide such clear explanations for the use of algorithms for the multiplication and division items. The findings are discussed in the light of Chinese perspectives on procedural and conceptual understanding

Teaching with procedural variation: A Chinese way of promoting deep understanding of mathematics

In mathematics education, there has been tension between deep learning and repetitive learning. Western educators often emphasize the need for students to construct a conceptual understanding of mathematical symbols and rules before they practise the rules (Li, 2006). On the other hand, Chinese learners tend to be oriented towards rote learning and memorization (Marton, Watkins & Tang, 1997). One aspect of the criticism is that rote learning is known to lead to poor learning outcomes (Watkins & Biggs, 2001). However, Chinese students consistently outperform their Western counterparts in many international comparative studies on mathematics achievement such as TIMSS (Beaton, Mullis, Martin, Gonzalez, Kelly & Smith, 1997; Mullis, Martin, & Foy, 2008) and PISA (OECD, 2004; OECD, 2010). This paper aims to contribute to an understanding of the “paradox of the Chinese learners” (Marton, Dall‟ Alba & Lai, 1993) by exploring the procedural variation and its place in the development of mathematical understanding

Distinctive patterns of macrolide-lincosamide-streptogramin resistance phenotypes and determinants amongst Staphylococcus aureus populations in Hong Kong

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XRand: Differentially Private Defense against Explanation-Guided Attacks

Recent development in the field of explainable artificial intelligence (XAI) has helped improve trust in Machine-Learning-as-a-Service (MLaaS) systems, in which an explanation is provided together with the model prediction in response to each query. However, XAI also opens a door for adversaries to gain insights into the black-box models in MLaaS, thereby making the models more vulnerable to several attacks. For example, feature-based explanations (e.g., SHAP) could expose the top important features that a black-box model focuses on. Such disclosure has been exploited to craft effective backdoor triggers against malware classifiers. To address this trade-off, we introduce a new concept of achieving local differential privacy (LDP) in the explanations, and from that we establish a defense, called XRand, against such attacks. We show that our mechanism restricts the information that the adversary can learn about the top important features, while maintaining the faithfulness of the explanations.Comment: To be published at AAAI 202

Impact of dye interlayer on the performance of organic photovoltaic devices

The influences of buffer interlayer at the donor/acceptor interface on the open circuit voltage (VOC) of typical copper phthalocyanine (CuPc) / C60 organic photovoltaic devices are studied. Six fluorescent dyes with progressively increasing ionization potentials (I P) were used to investigate the factors influencing the VOC. The short-circuit current and fill factor of CuPc/ C60 device incorporating dye interlayer are lower than those of standard bilayer device. On the other hand, the VOC increases linearly with the I P of dye material and falls off when the I P is equal to or greater than 5.6 eV, in which the energy offset between the highest occupied molecular orbitals at the interlayer/ C60 heterojunction is smaller than the C60 exciton binding energy. The findings underscore the importance of energy offsets in photovoltaic responses. © 2009 American Institute of Physics.published_or_final_versio

Active Membership Inference Attack under Local Differential Privacy in Federated Learning

Federated learning (FL) was originally regarded as a framework for collaborative learning among clients with data privacy protection through a coordinating server. In this paper, we propose a new active membership inference (AMI) attack carried out by a dishonest server in FL. In AMI attacks, the server crafts and embeds malicious parameters into global models to effectively infer whether a target data sample is included in a client's private training data or not. By exploiting the correlation among data features through a non-linear decision boundary, AMI attacks with a certified guarantee of success can achieve severely high success rates under rigorous local differential privacy (LDP) protection; thereby exposing clients' training data to significant privacy risk. Theoretical and experimental results on several benchmark datasets show that adding sufficient privacy-preserving noise to prevent our attack would significantly damage FL's model utility.Comment: Published at AISTATS 202