Which Potential Linguistic Challenges do Pre-Service Teachers Identify in a Mathematical Expository Text?

Language is a crucial aspect of mathematical thinking and learning, and it is therefore essential for teachers to be equipped with the skills required for linguistically responsive teaching. This includes the ability to identify potential linguistic challenges in expository texts. In the present study, we investigated the ability of pre-service teachers (N = 115) to identify potential linguistic challenges in a mathematical expository text for ninth graders. Participants identified about 12% of the potential linguistic challenges that were previously identified by a reference expert group. They identified challenges more frequently that were on the word level and considered to be mathematics-specific by the experts. Subjective judgements of disciplinarity of the challenges differed between participants, and between participants and experts. No differences in the ability to identify potential linguistic challenges were found between participants who studied language arts (German or English) or mathematics as a subject. Our results indicate that pre-service teachers may not be adequately prepared to identify and respond to linguistic challenges in mathematical expository texts.

A new bioinspired method for pressure and flow sensing based on the underwater air-retaining surface of the backswimmer Notonecta.

In technical systems, static pressure and pressure changes are usually measured with piezoelectric materials or solid membranes. In this paper, we suggest a new biomimetic principle based on thin air layers that can be used to measure underwater pressure changes. Submerged backswimmers (Notonecta sp.) are well known for their ability to retain air layers on the surface of their forewings (hemelytra). While analyzing the hemelytra of Notonecta, we found that the air layer on the hemelytra, in combination with various types of mechanosensitive hairs (clubs and pins), most likely serve a sensory function. We suggest that this predatory aquatic insect can detect pressure changes and water movements by sensing volume changes of the air layer under water. In the present study, we used a variety of microscopy techniques to investigate the fine structure of the hemelytra. Furthermore, we provide a biomimetic proof of principle to validate our hypothesis. The suggested sensory principle has never been documented before and is not only of interest for sensory biologists but can also be used for the development of highly sensitive underwater acoustic or seismographic sensory systems.

The peregrine falcon's rapid dive: on the adaptedness of the arm skeleton and shoulder girdle.

During a dive, peregrine falcons (Falco peregrinus) can reach a velocity of up to 320 km h- 1. Our computational fluid dynamics simulations show that the forces that pull on the wings of a diving peregrine can reach up to three times the falcon's body mass at a stoop velocity of 80 m s- 1 (288 km h- 1). Since the bones of the wings and the shoulder girdle of a diving peregrine falcon experience large mechanical forces, we investigated these bones. For comparison, we also investigated the corresponding bones in European kestrels (Falco tinnunculus), sparrow hawks (Accipiter nisus) and pigeons (Columba livia domestica). The normalized bone mass of the entire arm skeleton and the shoulder girdle (coracoid, scapula, furcula) was significantly higher in F. peregrinus than in the other three species investigated. The midshaft cross section of the humerus of F. peregrinus had the highest second moment of area. The mineral densities of the humerus, radius, ulna, and sternum were highest in F. peregrinus, indicating again a larger overall stability of these bones. Furthermore, the bones of the arm and shoulder girdle were strongest in peregrine falcons.

The impact of infrared radiation in flight control in the Australian "firebeetle" Merimna atrata.

Infrared (IR) receptors are rare in insects and have only been found in the small group of so-called pyrophilous insects, which approach forest fires. In previous work the morphology of the IR receptors and the physiology of the inherent sensory cells have been investigated. It was shown that receptors are located on the thorax and the abdomen respectively and show an astounding diversity with respect to structure and the presumed transduction mechanism. What is completely missing, however, is any behavioral evidence for the function of the IR receptors in pyrophilous insects. Here we describe the responses of the Australian "firebeetle", Merimna atrata to IR radiation. Beetles in a restrained flight were laterally stimulated with IR radiation of an intensity 20% above a previously determined electrophysiological threshold of the IR organs (40 mW/cm2). After exposure, beetles always showed an avoidance response away from the IR source. Reversible ablation experiments showed that the abdominal IR receptors are essential for the observed behavior. Tests with weaker IR radiation (11.4 mW/cm2) also induced avoidance reactions in some beetles pointing to a lower threshold. In contrast, beetles were never attracted by the IR source. Our results suggest that the IR receptors in Merimna atrata serve as an early warning system preventing an accidental landing on a hot surface. We also tested if another fire specific stimulus, the view of a large smoke plume, influenced the flight. However, due to an unexpected insensitivity of the flying beetles to most visual stimuli results were ambiguous.

Respiration in spiders (Araneae).

Spiders (Araneae) are unique regarding their respiratory system: they are the only animal group that breathe simultaneously with lungs and tracheae. Looking at the physiology of respiration the existence of tracheae plays an important role in spiders with a well-developed tracheal system. Other factors as sex, life time, type of prey capture and the high ability to gain energy anaerobically influence the resting and the active metabolic rate intensely. Most spiders have metabolic rates that are much lower than expected from body mass; but especially those with two pairs of lungs. Males normally have higher resting rates than females; spiders that are less evolved and possess a cribellum have lower metabolic rates than higher evolved species. Freely hunting spiders show a higher energy turnover than spiders hunting with a web. Spiders that live longer than 1 year will have lower metabolic rates than those species that die after 1 year in which development and reproduction must be completed. Lower temperatures and starvation, which most spiders can cope with, will decrease the metabolic rate as well.

Functional morphology of the respiratory organs in the cellar spider Pholcus phalangioides (Arachnida, Araneae, Pholcidae).

Morphometric evaluation of the lungs of male and female cellar spiders (Pholcus phalangioideus) was carried out in 2 test groups with different body masses (mean value 10.8, males, and 26.6 mg, females). Males have significant higher lung volume to body mass ratios (2.49 vs. 2.13 × 10(-3) cm(3) g(-1)), which might result from the differences in body mass between sexes. Moreover, males have slightly more respiratory surface area per body mass (8.2 vs. 7.7 cm(2) g(-1)) and a little bit larger morphological diffusing capacities for oxygen (9.3 vs. 8.2 nmol s(-1) g(-1) kPa(-1)) than females, but both values were not significant. Metabolic rates were measured using flow through respirometry under video tracking: the CO2 release of male and female spiders was measured. Resting rates were 1.7 (males) and 1.5 nmol s(-1) g(-1) (females). Gluing of one spiracle did not influence the resting metabolic rate. Factorial scopes during stimulation to maximum metabolic rates were about 12 in intact animals, while elimination of one spiracle reduced the factorial scope to 5.2. Comparison with other araneomorph spiders strengthens the hypothesis that tracheae in spiders increase the metabolic rates of the tracheated species and do not only replace reduced lung capacity.

Morphological properties of the last primaries, the tail feathers, and the alulae of Accipiter nisus, Columba livia, Falco peregrinus, and Falco tinnunculus.

We investigated the mechanical properties (Young's modulus, bending stiffness, barb separation forces) of the tenth primary of the wings, of the alulae and of the middle tail feathers of Falco peregrinus. For comparison, we also investigated the corresponding feathers in pigeons (Columba livia), kestrels (Falco tinnunculus), and sparrowhawks (Accipiter nisus). In all four species, the Young's moduli of the feathers ranged from 5.9 to 8.4 GPa. The feather shafts of F. peregrinus had the largest cross-sections and the highest specific bending stiffness. When normalized with respect to body mass, the specific bending stiffness of primary number 10 was highest in F. tinnunculus, while that of the alula was highest in A. nisus. In comparison, the specific bending stiffness, measured at the base of the tail feathers and in dorso-ventral bending direction, was much higher in F. peregrinus than in the other three species. This seems to correlate with the flight styles of the birds: F. tinnunculus hovers and its primaries might therefore withstand large mechanical forces. A. nisus has often to change its flight directions during hunting and perhaps needs its alulae for this maneuvers, and in F. peregrinus, the base of the tail feathers might need a high stiffness during breaking after diving.

Concept of an Active Amplification Mechanism in the Infrared Organ of Pyrophilous Melanophila Beetles.

Jewel beetles of the genus Melanophila possess a pair of metathoracic infrared (IR) organs. These organs are used for forest fire detection because Melanophila larvae can only develop in fire killed trees. Several reports in the literature and a modeling of a historic oil tank fire suggest that beetles may be able to detect large fires by means of their IR organs from distances of more than 100 km. In contrast, the highest sensitivity of the IR organs, so far determined by behavioral and physiological experiments, allows a detection of large fires from distances up to 12 km only. Sensitivity thresholds, however, have always been determined in non-flying beetles. Therefore, the complete micromechanical environment of the IR organs in flying beetles has not been taken into consideration. Because the so-called photomechanic sensilla housed in the IR organs respond bimodally to mechanical as well as to IR stimuli, it is proposed that flying beetles make use of muscular energy coupled out of the flight motor to considerably increase the sensitivity of their IR sensilla during intermittent search flight sequences. In a search flight the beetle performs signal scanning with wing beat frequency while the inputs of the IR organs on both body sides are compared. By this procedure the detection of weak IR signals could be possible even if the signals are hidden in the thermal noise. If this proposed mechanism really exists in Melanophila beetles, their IR organs could even compete with cooled IR quantum detectors. The theoretical concept of an active amplification mechanism in a photon receptor innervated by highly sensitive mechanoreceptors is presented in this article.

Diving-flight aerodynamics of a peregrine falcon (Falco peregrinus).

This study investigates the aerodynamics of the falcon Falco peregrinus while diving. During a dive peregrines can reach velocities of more than 320 km h⁻¹. Unfortunately, in freely roaming falcons, these high velocities prohibit a precise determination of flight parameters such as velocity and acceleration as well as body shape and wing contour. Therefore, individual F. peregrinus were trained to dive in front of a vertical dam with a height of 60 m. The presence of a well-defined background allowed us to reconstruct the flight path and the body shape of the falcon during certain flight phases. Flight trajectories were obtained with a stereo high-speed camera system. In addition, body images of the falcon were taken from two perspectives with a high-resolution digital camera. The dam allowed us to match the high-resolution images obtained from the digital camera with the corresponding images taken with the high-speed cameras. Using these data we built a life-size model of F. peregrinus and used it to measure the drag and lift forces in a wind-tunnel. We compared these forces acting on the model with the data obtained from the 3-D flight path trajectory of the diving F. peregrinus. Visualizations of the flow in the wind-tunnel uncovered details of the flow structure around the falcon's body, which suggests local regions with separation of flow. High-resolution pictures of the diving peregrine indicate that feathers pop-up in the equivalent regions, where flow separation in the model falcon occurred.

The lateral line receptor array of cyprinids from different habitats.

The lateral line system of teleost fishes consists of an array of superficial and canal neuromasts (CN). Number and distribution of neuromasts and the morphology of the lateral line canals vary across species. We investigated the morphology of the lateral line system in four diurnal European cyprinids, the limnophilic bitterling (Rhodeus sericeus), the indifferent gudgeon (Gobio gobio), and ide (Leuciscus idus), and the rheophilic minnow (Phoxinus phoxinus). All fish had lateral line canals on head and trunk. The total number of both, CN and superficial neuromasts (SN), was comparable in minnow and ide but was greater than in gudgeon and bitterling. The ratio of SNs to CNs for the head was comparable in minnow and bitterling but was greater in gudgeon and ide. The SN-to-CN ratio for the trunk was greatest in bitterling. Polarization of hair cells in CNs was in the direction of the canal. Polarization of hair cells in SNs depended on body area. In cephalic SNs, hair cell polarization was dorso-ventral or rostro-caudal. In trunk SNs, it was rostro-caudal on lateral line scales and dorso-ventral on other trunk scales. On the caudal fin, hair cell polarization was rostro-caudal. The data show that, in the four species studied here, number, distribution, and orientation of CNs and SNs cannot be unequivocally related to habitat.

Evolution of air breathing: oxygen homeostasis and the transitions from water to land and sky.

Life originated in anoxia, but many organisms came to depend upon oxygen for survival, independently evolving diverse respiratory systems for acquiring oxygen from the environment. Ambient oxygen tension (PO2) fluctuated through the ages in correlation with biodiversity and body size, enabling organisms to migrate from water to land and air and sometimes in the opposite direction. Habitat expansion compels the use of different gas exchangers, for example, skin, gills, tracheae, lungs, and their intermediate stages, that may coexist within the same species; coexistence may be temporally disjunct (e.g., larval gills vs. adult lungs) or simultaneous (e.g., skin, gills, and lungs in some salamanders). Disparate systems exhibit similar directions of adaptation: toward larger diffusion interfaces, thinner barriers, finer dynamic regulation, and reduced cost of breathing. Efficient respiratory gas exchange, coupled to downstream convective and diffusive resistances, comprise the "oxygen cascade"-step-down of PO2 that balances supply against toxicity. Here, we review the origin of oxygen homeostasis, a primal selection factor for all respiratory systems, which in turn function as gatekeepers of the cascade. Within an organism's lifespan, the respiratory apparatus adapts in various ways to upregulate oxygen uptake in hypoxia and restrict uptake in hyperoxia. In an evolutionary context, certain species also become adapted to environmental conditions or habitual organismic demands. We, therefore, survey the comparative anatomy and physiology of respiratory systems from invertebrates to vertebrates, water to air breathers, and terrestrial to aerial inhabitants. Through the evolutionary directions and variety of gas exchangers, their shared features and individual compromises may be appreciated.

Infrared receptors in pyrophilous ("fire loving") insects as model for new un-cooled infrared sensors.

Beetles of the genus Melanophila and certain flat bugs of the genus Aradus actually approach forest fires. For the detection of fires and of hot surfaces the pyrophilous species of both genera have developed infrared (IR) receptors, which have developed from common hair mechanoreceptors. Thus, this type of insect IR receptor has been termed photomechanic and shows the following two special features: (i) The formation of a complex cuticular sphere consisting of an outer exocuticular shell as well as of a cavernous microfluidic core and (ii) the enclosure of the dendritic tip of the mechanosensitive neuron inside the core in a liquid-filled chamber. Most probably a photomechanic IR sensillum acts as a microfluidic converter of infrared radiation which leads to an increase in internal pressure inside the sphere, which is measured by a mechanosensitive neuron.A simple model for this biological IR sensor is a modified Golay sensor in which the gas has been replaced by a liquid. Here, the absorbed IR radiation results in a pressure increase of the liquid and the deflection of a thin membrane. For the evaluation of this model analytical formulas are presented, which permits the calculation of the pressure increase in the cavity, the deformation of the membrane and the time constant of an artificial leak to compensate ambient temperature changes. Some organic liquids with high thermal expansion coefficients may improve the deflection of the membrane compared to water.

Distribution and functional morphology of photomechanic infrared sensilla in flat bugs of the genus Aradus (Heteroptera, Aradidae).

Globally the flat bug genus Aradus comprises about 200 species. About half a dozen Aradus species can be primarily found on burnt areas and, therefore, have been called pyrophilous. Bugs and their offspring feed on fungi growing on burnt wood. Recently, prothoracic infrared (IR) receptors have been described in the pyrophilous Australian species Aradus albicornis. In our study we investigated 10 Aradus species, once again including A. albicornis, and found prothoracic as well as hitherto unknown mesothoracic IR sensilla in A. albicornis, Aradus lugubris and Aradus fuscicornis. In Aradus flavicornis only prothoracic IR receptors were found. Currently the latter two species are not known as pyrophilous. However, there is considerable evidence that these flat bugs also approach forest fires. In all four species where IR receptors were identified, the dome-shaped IR sensilla look very similar. An IR sensillum consists of an internal exocuticular sphere reinforced by consecutive layers of chitin fibres. In the center of the sphere, a microfluidic core is located which consists of a cup-shaped plug of cuticle and an underlying fluid filled annular channel surrounding the tip of the dendrite of a mechanosensitive neuron. Like the IR receptors of buprestid beetles of the genus Melanophila, the IR sensilla found in Aradus species can be classified as photomechanic IR receptors.

Organization of the superficial neuromast system in goldfish, Carassius auratus.

Distribution, morphology, and orientation of superficial neuromasts and polarization of the hair cells within superficial neuromasts of the goldfish (Carassius auratus) were examined using fluorescence labeling and scanning electron microscopy. On each body side, goldfish have 1,800-2,000 superficial neuromasts distributed across the head, trunk and tail fin. Each superficial neuromast had about 14-32 hair cells that were arranged in the sensory epithelium with the axis of best sensitivity aligned perpendicular to the long axis of the neuromast. Hair cell polarization was rostro-caudal in most superficial neuromasts on trunk scales (with the exception of those on the lateral line scales), or on the tail fin. On lateral line scales, the most frequent hair cell polarization was dorso-ventral in 45% and rostro-caudal in 20% of the superficial neuromasts. On individual trunk scales, superficial neuromasts were organized in rows which in most scales showed similar orientations with angle deviations smaller than 45 degrees . In about 16% of all trunk scales, groups of superficial neuromasts in the dorsal and ventral half of the scale were oriented orthogonal to each other. On the head, most superficial neuromasts were arranged in rows or groups of similar orientation with angle deviations smaller than 45 degrees . Neighboring groups of superficial neuromasts could differ with respect to their orientation. The most frequent hair cell polarization was dorso-ventral in front of the eyes and on the ventral mandible and rostro-caudal below the eye and on the operculum.

Microfluidic photomechanic infrared receptors in a pyrophilous flat bug.

Infrared (IR) receptors are so far known only in boid and crotalid snakes and in three genera of pyrophilous beetles that seek out forest fires. Pyrophilous insects can also be found in other orders, however, so it can be hypothesised that IR receptors also occur in some of these species. We investigated the pyrophilous Australian flat bug Aradus albicornis and found a small number of dome-shaped sensilla (diameter 13 microm) on the prothorax, which have previously not been described. Ultrastructural investigations revealed that the sensilla are characterised by a fluid-filled inner compartment enclosed in a round cuticular shell. The cuticular apparatus is innervated by the dendrite of a ciliary mechanoreceptor, which is fluidically coupled to the inner compartment. Electrophysiological recordings demonstrated that the sensilla respond to brief warming by red laser light or to broadband IR radiation. Depending on the radiation intensity (4.4-549 mW/cm(2) tested, threshold measured as 11.3 mW/cm(2)), first spike latencies varied between 3.4 and 7.5 ms. Thus, our findings demonstrate that A. albicornis most probably possesses photomechanic IR sensilla resembling the metathoracic IR sensilla of buprestid beetles of the genus Melanophila. In the Melanophila sensillum, IR radiation causes thermal expansion of a fluid, which rapidly deforms the dendritic membrane of a mechanosensory cell. The existence of photomechanic IR receptors in both beetles and bugs demonstrates a remarkable convergent evolution towards this particular biophysical transduction mechanism and suggests that it provides selective advantages over other possible solutions.

The analysis of the mechanosensory origin of the infrared sensilla in Melanophila acuminata (Coeloptera; Buprestidae) adduces new insight into the transduction mechanism.

The thoracic infrared (IR) sensilla of the pyrophilous jewel beetle Melanophila acuminata most likely have evolved from hair mechanoreceptors (sensilla trichodea). To further elucidate the sensory transduction mechanism, the morphology of IR sensilla and of neighbouring hair mechanoreceptors was investigated by using conventional electron microscopical techniques (SEM, TEM) in combination with focused ion beam milling (FIB). It was assumed that any deviation from the bauplan of a sensillum trichodeum is of particular concern for the transduction of IR radiation into a mechanical stimulus. Thus, the structures supposed to be relevant for stimulus uptake and transduction were homologized. Compared to a hair mechanoreceptor, an IR sensillum shows the following special features: (i) the formation of a complex cuticular sphere instead of the bristle; the sphere consists of an outer exocuticular shell as well as of an inner porous mesocuticular part. (ii) The enclosure of the dendritic tip of the mechanosensitive neuron inside the sphere in a fluid-filled inner pressure chamber which is connected with a system of microcavities and nanocanals in the mesocuticular part. Hence we propose that an IR sensillum most probably acts as a microfluidic converter of infrared radiation into an increase in internal pressure inside the sphere which is measured by the mechanosensitive neuron.

Stereological estimation of surface area and barrier thickness of fish gills in vertical sections.

Previous morphometric methods for estimation of the volume of components, surface area and thickness of the diffusion barrier in fish gills have taken advantage of the highly ordered structure of these organs for sampling and surface area estimations, whereas the thickness of the diffusion barrier has been measured orthogonally on perpendicularly sectioned material at subjectively selected sites. Although intuitively logical, these procedures do not have a demonstrated mathematical basis, do not involve random sampling and measurement techniques, and are not applicable to the gills of all fish. The present stereological methods apply the principles of surface area estimation in vertical uniform random sections to the gills of the Brazilian teleost Arapaima gigas. The tissue was taken from the entire gill apparatus of the right-hand or left-hand side (selected at random) of the fish by systematic random sampling and embedded in glycol methacrylate for light microscopy. Arches from the other side were embedded in Epoxy resin. Reference volume was estimated by the Cavalieri method in the same vertical sections that were used for surface density and volume density measurements. The harmonic mean barrier thickness of the water-blood diffusion barrier was calculated from measurements taken along randomly selected orientation lines that were sine-weighted relative to the vertical axis. The values thus obtained for the anatomical diffusion factor (surface area divided by barrier thickness) compare favourably with those obtained for other sluggish fish using existing methods.

Coping with cyclic oxygen availability: evolutionary aspects.

Both the gradual rise in atmospheric oxygen over the Proterozoic Eon as well as episodic fluctuations in oxygen over several million-year time spans during the Phanerozoic Era, have arguably exerted strong selective forces on cellular and organismic respiratory specialization and evolution. The rise in atmospheric oxygen, some 2 billion years after the origin of life, dramatically altered cell biology and set the stage for the appearance of multicelluar life forms in the Vendian (Ediacaran) Period of the Neoproterozoic Era. Over much of the Paleozoic, the level of oxygen in the atmosphere was near the present atmospheric level (21%). In the Late Paleozoic, however, there were extended times during which the level of atmospheric oxygen was either markedly lower or markedly higher than 21%. That these Paleozoic shifts in atmospheric oxygen affected the biota is suggested by the correlations between: (1) Reduced oxygen and the occurrences of extinctions, a lowered biodiversity and shifts in phyletic succession, and (2) During hyperoxia, the corresponding occurrence of phenomena such as arthropod gigantism, the origin of insect flight, and the evolution of vertebrate terrestriality. Basic similarities in features of adaptation to hyopoxia, manifest in living organisms at levels ranging from genetic and cellular to physiological and behavioral, suggest the common and early origin of a suite of adaptive mechanisms responsive to fluctuations in ambient oxygen. Comparative integrative approaches addressing the molecular bases of phenotypic adjustments to cyclic oxygen fluctuation provide broad insight into the incremental steps leading to the early evolution of homeostatic respiratory mechanisms and to the specialization of organismic respiratory function.

Spiders on a treadmill: influence of running activity on metabolic rates in Pardosa lugubris (Araneae, Lycosidae) and Marpissa muscosa (Araneae, Salticidae).

The CO2 release of the well-tracheated jumping spider, Marpissa muscosa, and the poorly tracheated, Pardosa lugubris, was tested while animals were running on a treadmill at three different speeds and under a selective elimination of lungs or tracheae. Thus, the influence of a well-developed tracheal system on the metabolism during physical exercise was examined. The CO2 release in intact animals increased with the running speed in both species. The costs of transport (COT) running at the maximal sustainable speed were nearly twice as big in M. muscosa as in P. lugubris. Elimination of one lung by sealing resulted in reduced COT and running times, and increasing anaerobic proportions in metabolism. Effects were greater in P. lugubris than in M. muscosa, indicating that tracheae compensate partly for the lacking lung capacity. Sealing of the tracheae in M. muscosa reduced the COT and the running times only at the highest speed. Results indicate that tracheae in M. muscosa support the aerobic metabolism only at the most intense physical exercise. At low and medium activity, tracheae may play their main role in the local supply of organs that are not involved in running activity.