The case for a sub-element ‘measuring matter’ within the Australian national numeracy learning progression

Australia has a National Numeracy Learning Progression (NNLP) that is strongly aligned with the Australian Curriculum: Mathematics. This article examines how a sub-element within this progression could be impacting students’ learning of Science. This sub-element is firmly based on Mathematics education research as to how students build their understanding of geometric measurement (the structure of length, area and volume). Mathematics educators subsequently researched children’s measurement of mass and included it within the same sub-element of the NNLP. The contexts in which mass and volume are measured in Mathematics are different to those used in teaching Science. This article presents two studies that used variation theory and task-based interviews of children in Years 5 and 6, to explore their thinking about mass and volume in a Science context. The findings suggest that mathematical constructs in geometric measurement could be constraining the development of scientific ideas about matter. This research has implications for furthering the development of the NNLP to encompass scientific aspects of measuring matter.

Vocalization with semi-occluded airways is favorable for optimizing sound production

Vocalization in mammals, birds, reptiles, and amphibians occurs with airways that have wide openings to free-space for efficient sound radiations, but sound is also produced with occluded or semi-occluded airways that have small openings to free-space. It is hypothesized that pressures produced inside the airway with semi-occluded vocalizations have an overall widening effect on the airway. This overall widening then provides more opportunity to produce wide-narrow contrasts along the airway for variation in sound quality and loudness. For human vocalization described here, special emphasis is placed on the epilaryngeal airway, which can be adjusted for optimal aerodynamic power transfer and for optimal acoustic source-airway interaction. The methodology is three-fold, (1) geometric measurement of airway dimensions from CT scans, (2) aerodynamic and acoustic impedance calculation of the airways, and (3) simulation of acoustic signals with a self-oscillating computational model of the sound source and wave propagation.

Research and evaluation of the measurement uncertainty with the two-dimensional optical calibration plate

As a portable standard, two-dimensional optical calibration plate is playing an increasingly important role in precision industry measurement. Therefore, it is of great scientific significance and obvious socioeconomic benefits to carry out the research of comparator. This paper was based on rich experience with the institute in the field of the geometric measurement technology for a long time, the measurement uncertainty of the optical calibration plate was studied, and the measurement uncertainty of the instrument has been researched. The measurement uncertainty of the error of the calibration plate’s setting and marking value was U= (0.14+ 0.015L) m k=2 L: mm.

How can the concept of perimeter and area be developed in 7th grade?

Learning and teaching measurement have a central role in school geometry. In this study, we are focusing on two physical quantities: perimeter (length) and area. We compare the results of two surveys. The first was written at the beginning of the 7th school year, in September, while completed the second one in December of the same year, two weeks after the geometric measurement topic. On the one hand, we were curious about the students' previous knowledge before receiving the new learning material related to the topic under study. On the other hand, we wanted to know how to change students' understanding after focusing on the concepts studied for a few weeks. The characteristics of the concept formation process were also of interest to us.

Standards for Evaluating the Influence of Materials on the Performance of X-Ray Computed Tomography in Measuring Geometric Variability

The industrial use of X-ray Computed Tomography (known briefly as XCT, or sometimes simply as CT) is on the rise because a single XCT scan can measure an arbitrary number of features, and XCT instruments can measure features inaccessible to contact or optical instruments — even features that are completely encased in material. This makes XCT a natural metrological companion to additive manufacturing where internal features (e.g., lattice structures) can be produced. But this advantage of being able to measure through material is somewhat mitigated by the fact that the obstructing material has a strong influence on the geometric measurement and is a dominant source of error. This problem is addressed by two emerging documentary standards in ASME and ISO (International Organization for Standardization). These documents define standardized tests for metrological accuracies of an XCT system, where accuracies — now unambiguously defined — can be expressed as Maximum Permissible Errors (MPEs). These tests rely on calibrated artifacts that are designed to reveal various XCT error sources when the system measures these artifacts in prescribed manners. This paper gives the general philosophy behind Coordinate Measuring System standards and then applies them to XCT systems in particular. Rationale is given for the artifact choices contained within these standards, with particular emphasis on material effects, and clarifies the metrological coverage of these standards.