Students’ geometric thinking with cube representations: Assessment framework and empirical evidence

ArticleThis is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.While representations of 3D shapes are used in the teaching of geometry in lower secondary school, it is known that such representations can provide difficulties for students. In order to assess students’ thinking about 3D shapes, we constructed an assessment framework based on existing research studies and data from G7-9 students (aged 12-15). We then applied our framework to assess students’ geometric thinking in lessons. We report two cases of qualitative findings from a classroom experiment in which Grade 7 students (aged 12-13) tackled a problem in 3D geometry that was, for them, quite challenging. We found that students who failed to answer given problems did not mentally manipulate representations effectively, while others could mentally manipulate representations and reason about them in order to reach correct solutions. We conclude with the proposition that this finding shows the framework can be used by teachers in instruction to assess their students' 3D geometric thinking

Spatial reasoning skills about 2D representations of 3D geometrical shapes in grades 4 to 9

This is the final version. Available on open access from the Mathematics Education Research Group of Australasia via the DOI in this recordGiven the important role played by students’ spatial reasoning skills, in this paper we analyse how students use these skills to solve problems involving 2D representations of 3D geometrical shapes. Using data from in total 1357 grades 4 to 9 students, we examine how they visualise shapes in the given diagrams and make use of properties of shapes to reason. We found that using either spatial visualisation or property-based spatial analytic reasoning is not enough for the problems that required more than one step of reasoning, but also that these two skills have to be harmonised by domain-specific knowledge in order to overcome the perceptual appearance (or “look”) of the given diagram. We argue that more opportunities might be given to both primary and secondary school students in which they can exercise not only their spatial reasoning skills but also consolidate and use their existing domain-specific knowledge of geometry for productive reasoning in geometry

Identifying Japanese students’ core spatial reasoning skills by solving 3D geometry problems: An exploration

This is the final version. Available on open access from SAGE Publications via the DOI in this recordTaking the importance of spatial reasoning skills, this article aims to identify “core” spatial reasoning skills which are likely to contribute to successful problem-solving in three-dimensional (3D) geometry. “Core” spatial skills are those which might be particularly related to students’ successful problem-solving in 3D geometry. In this article, spatial reasoning skills are malleable and can be improved with teaching/interventions with mental rotation, spatial orientation, spatial visualization, and property-based reasoning. To achieve the study aim, we conducted a survey in total of 2,303 Japanese Grade 4–9 students (10–15 years old). We take the following stages of the procedures in this article: (a) Descriptive statistics; (b) 2 parameter logistic model (2PLM) analysis; and (c) Experiments with the Pearson correlation coefficient. As a result, we identified that a set of a few tasks can be used to check if students have “core” spatial skills in 3D geometry. For both primary and secondary, rotating given representations mentally, and imagining and drawing 3D shapes, are important, and for secondary schools, property-based reasoning is also crucial for further problem-solving skills. Our findings and methodological approach have implications for mathematics education research and practice as our results provide clear, and promising principles for task/units/curriculum design for spatial reasoning in which more robust teaching intervention is necessary

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion

PERSPECTIVAS DEL PROCESO DE GLOBALIZACIÓN Y SU INFLUENCIA SOBRE LOS DERECHOS HUMANOS ECONÓMICOS, SOCIALES Y CULTURALES

El escenario internacional se encuentra en constante transformación debido a lo que se ha denominado el proceso de “globalización”. Este afecta las relaciones internaciones interestatales e influye en la vida cotidiana de los individuos. El Derecho Internacional y más específicamente el Derecho Internacional de los Derechos Humanos no es ajeno a este proceso. La investigación afirma que nos encontramos frente a una etapa de transnacionalización de los Derechos Humanos, que permite que los individuos cuenten con mayor protección en ámbitos supranacionales. También hace especial mención a los derechos Económicos Sociales y Culturales, analiza el debate sobre el pluralismo jurídico y la eficacia diferencial. En la metodología empleada se revisan fuentes documentales y se realiza un análisis de algunos derechos particulares previstos en el Pacto de Derechos Económicos, Sociales y Culturales. Los planteamientos permiten afirmar que el proceso de globalización ha determinado la transnacionalización de los Derechos Humanos, surgiendo de dicho fenómeno consecuencias positivas y negativas en cuanto a su cumplimiento

Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: towards a theoretical framing

Defining and classifying quadrilaterals, though an established component of the school mathematics curriculum, appears to be a difficult topic for many learners. The reasons for such difficulties relate to the complexities in learning to analyse the attributes of different quadrilaterals and to distinguish between critical and non-critical aspects. Such learning, if it is to be effective, requires logical deduction, together with suitable interactions between concepts and images. This paper reports on an analysis of data from a total of 263 learners. The main purpose of the paper is to present a theoretical framing that is intended to inform further studies of this important topic within mathematics education research. This theoretical framing relates prototype phenomenon and implicit models to common cognitive paths in the understanding of the relationship between quadrilaterals

Supplementary Material for: Combination Assay of Methylated HOXA1 with Tumor Markers Shows High Sensitivity for Detection of Early-Stage Hepatocellular Carcinoma

Background: Patients with hepatitis virus-related hepatocellular carcinoma (viral HCC) are decreasing as hepatitis control improves, but those with non-viral-related HCC (non-viral HCC) are increasing in Japan. No established surveillance system exists for patients with non-viral HCC, so they are often diagnosed at an advanced stage. To address this, we performed this study. Methods: We collected serum samples from 516 participants (154 healthy subjects, 93 chronic liver disease [CLD] patients without HCC, and 269 HCC patients). Participants were divided into a control group comprising healthy subjects and patients with CLD and an HCC group. We evaluated serum methylated HOXA1 (m-HOXA1) copy numbers using modified combined restriction digital PCR (CORD) assay (1-step CORD assay). We assessed diagnostic performance of m-HOXA1 compared to HCC tumor markers alpha-fetoprotein (AFP) and des-gamma-carboxy prothrombin (DCP) and created a novel index to improve HCC prediction. Results: Serum m-HOXA1 level was significantly higher in each HCC stage group versus the control group. Its sensitivity was 69.1% and specificity was 78.5% for diagnosing HCC. The area under the curve (AUC) of m-HOXA1 was superior to that of AFP and equal to that of DCP. Multivariate logistic regression analysis revealed independent contributions of m-HOXA1, DCP, and AFP, in that order of strength, to diagnose HCC after adjustment for age and sex. We designated the predictive probability of HCC based on the regression model as the ASDAm-H1 (Age, Sex, DCP, AFP, and m-HOXA1) index. Its diagnostic accuracy was 0.96 by AUC with a sensitivity of 86.2% and specificity of 93.9%. Sensitivity was identical for viral and non-viral HCCs. When limited to early-stage HCC, sensitivity of the ASDAm-H1 index was 76.3%. Conclusions: We showed distinguished performance of the ASDAm-H1 index to detect viral and non-viral HCC even at an early stage. This index might have potential as a non-viral HCC surveillance system