Examining the reciprocal relations of mathematics anxiety to quantitative reasoning and number knowledge in Chinese children

This study aimed to examine the longitudinal relations of mathematics anxiety to quantitative reasoning and number knowledge in Chinese children. Three hundred and sixteen 6-year-old Chinese children in Hong Kong participated in two waves of assessments, eight months apart. Cross-lagged panel analyses showed that prior quantitative reasoning and number knowledge predicted lower mathematics anxiety, even after the effects of gender, mothers’ educational levels, and general anxiety were taken into account. However, earlier mathematics anxiety did not predict later quantitative reasoning and number knowledge. Our findings were consistent with the Deficit Theory, which postulates that mathematics anxiety comes from poor mathematical competence but not vice versa. We also found a reciprocal association between quantitative reasoning and number knowledge, in which initial quantitative reasoning had a stronger prediction on later number knowledge. Taken together with previous research, this result highlights the importance of quantitative reasoning in children’s mathematics learning and its role in mathematics education.     

Auditing fairness under unawareness through counterfactual reasoning

Artificial intelligence (AI) is rapidly becoming the pivotal solution to support critical judgments in many life-changing decisions. In fact, a biased AI tool can be particularly harmful since these systems can contribute to or demote people’s well-being. Consequently, government regulations are introducing specific rules to prohibit the use of sensitive features (e.g., gender, race, religion) in the algorithm’s decision-making process to avoid unfair outcomes. Unfortunately, such restrictions may not be sufficient to protect people from unfair decisions as algorithms can still behave in a discriminatory manner. Indeed, even when sensitive features are omitted (fairness through unawareness), they could be somehow related to other features, named proxy features. This study shows how to unveil whether a black-box model, complying with the regulations, is still biased or not. We propose an end-to-end bias detection approach exploiting a counterfactual reasoning module and an external classifier for sensitive features. In detail, the counterfactual analysis finds the minimum cost variations that grant a positive outcome, while the classifier detects non-linear patterns of non-sensitive features that proxy sensitive characteristics. The experimental evaluation reveals the proposed method’s efficacy in detecting classifiers that learn from proxy features. We also scrutinize the impact of state-of-the-art debiasing algorithms in alleviating the proxy feature problem.     

Drawing to reason and learn in science

Despite mixed results in research on student learning from drawing in science, there is growing interest in the potential for this visual mode, in tandem with other modes, to enact and enable student reasoning in this subject. Building on current research in this field, and using a micro-ethnographic approach informed by socio-semiotic perspectives, we aimed to identify how and why student drawing can contribute to student reasoning and learning. In our study, secondary school students were challenged to explore and collaboratively create explanatory representations of phenomena including through drawing. Data were generated using multiple wall- and ceiling-mounted cameras capable of continuously tracking groups of students negotiating these representational challenges. Our analysis proceeded through active and iterative viewing of the extensive video record, and the identification of themes to establish possible relationships between drawing and reasoning. Through this process, we (a) identify multiple necessary conditions and varied opportunities for student drawing to enact and enable reasoning, and (b) extend current understandings of how the particular affordances of this mode interact with these conditions to contribute to student learning in science.     

基于本体与规则的语义推理研究

为解决本体相关概念的共享和信息集成,发现本体间的语义关联,提出了本体与规则整合下的语义推理模型ORRM,构建了家庭本体FO。将推理集中在两个不同层次,第一层的推理使用Racer推理机进行描述逻辑的推理,检测本体的冲突。第二层使用本体中表示的概念和属性制定成员规则库,采用基于XML的SWRL呈现规则和Jess推理引擎,增加了本体概念问语义的关联。该模型在本体中引入规则表示,弥补了OWL DL在推理机制上的不足,推导出的新本体在原本体的基础上实现了本体成员间隐含关系的语义推理,完善了本体知识库的内容。在语义Web领域,该模型的应用能够提高本体知识的利用率。     

Diagnosing Teachers’ Understandings of Rational Numbers: Building a Multidimensional Test Within the Diagnostic Classification Framework

We report a multidimensional test that examines middle grades teachers’ understanding of fraction arithmetic, especially multiplication and division. The test is based on four attributes identified through an analysis of the extensive mathematics education research literature on teachers’ and students’ reasoning in this content area. We administered the test to a national sample of 990 in‐service middle grades teachers and analyzed the item responses using the log‐linear cognitive diagnosis model. We report the diagnostic quality of the test at the item level, mastery classifications for teachers, and attribute relationships. Our results demonstrate that, when a test is grounded in research on cognition and is designed to be multidimensional from the onset, it is possible to use diagnostic classification models to detect distinct patterns of attribute mastery.     

Promoting teachers’ algebraic reasoning and self-regulation with metacognitive guidance

This study investigates algebraic reasoning and self-regulation skills among elementary school teachers who participated in a professional development program either with IMPROVE metacognitive questioning (PD + Meta) or with no metacognitive guidance (PD). Sixty-four Israeli teachers participated in a 3-year program designed to enhance mathematical knowledge. Results indicated that the PD + Meta teachers outperformed the PD teachers on various algebraic procedural and real-life tasks regarding conceptual mathematical explanations. In addition, the PD + Meta group outperformed the PD group in using self-monitoring and evaluation strategies in algebraic problem solving. We discuss educational and practical implications.     

Biology instruction using a generic framework of scientific reasoning and argumentation

We investigated biology instruction—using a generic framework of scientific reasoning and argumentation (SRA) with eight epistemic activities—on how to foster student learning in biological literacy which had not been clarified in previous studies. Our analysis of videotaped biology lessons and student achievement showed varying frequencies in using these activities and their effects on achievement. Those students taught with more epistemic activities had higher achievement. We believe that the SRA framework can be a worthwhile methodical tool for teaching biology to foster student learning. Therefore, we draw practically orientated implications for educational research, practitioners, teacher educators, and curriculum developers.     

如何利用“破”与“立”建立牢固的科学的概念

从教育学的角度出发,通过“破”学生错误的前科学概念,以便“立”正确的科学概念,进而掌握良好的学习方法．     

推理链：科学发现的逻辑新论

科学发现有没有逻辑的争论,由来已久.有人称其无,有人说其有,还有归纳派和演绎派的形同水火.究其实,争论是由逻辑观--传统形式逻辑和现代数理逻辑的不同引起的.其实,归纳派和演绎派各执一端,各有长短,彼此是相通的,类比、归纳和演绎整合的推理链,才是科学发现的逻辑.     

Threats to student evaluative judgement and their management

ABSTRACT

Students’ capacity for making evaluative judgements of their own work is widely acknowledged as central to their learning within programmes as well as being vital to their subsequent professional practice. In higher education literature, the act of evaluative judgement is usually portrayed as a process of deliberative, analytical reasoning requiring student agency and objectivity, typically scaffolded by points of reference such as explicit criteria, rubrics or exemplars. This article challenges this common portrayal of judgement by drawing attention to research from outside higher education on the role of unconscious factors in judgement and decision-making. Drawing from the field of heuristics and bias studies, the article outlines six unconscious factors that have the potential to distort students’ analytical judgement of their work. A recent challenge to the heuristics and bias approach that radically repositions the place of reasoning in judgement is also considered. Since these unconscious factors have received scant attention in higher education literature, the purpose of this article is to draw attention to them, to identify the challenges they pose to current understandings of evaluative judgement, and to outline their implications for enhancing assessment practice.