The Mathematical Content Knowledge of Prospective Teachers in Iceland

This study focused on the mathematical content knowledge of prospective teachers in Iceland. The sample was 38 students in the School of Education at the University of Iceland, both graduate and undergraduate students. All of the participants in the study completed a questionnaire survey and 10 were interviewed. The choice of ways to measure the mathematical content knowledge of prospective teachers was grounded in the work of Ball and the research team at the University of Michigan (Delaney, Ball, Hill, Schilling, and Zopf, 2008; Hill, Ball, and Schilling, 2008; Hill, Schilling, and Ball, 2004), and their definition of common content knowledge (knowledge held by people outside the teaching profession) and specialized content knowledge (knowledge used in teaching) (Ball, Thames, and Phelps, 2008). This study employed a mixed methods approach, including both a questionnaire survey and interviews to assess prospective teachers' mathematical knowledge on the mathematical topics numbers and operations and patterns, functions, and algebra. Findings, both from the questionnaire survey and the interviews, indicated that prospective teachers' knowledge was procedural and related to the "standard algorithms" they had learned in elementary school. Also, findings indicated that prospective teachers had difficulties evaluating alternative solution methods, and a common denominator for a difficult topic within both knowledge domains, common content knowledge and specialized content knowledge, was fractions. During the interviews, the most common answer for why a certain way was chosen to solve a problem or a certain step was taken in the solution process, was "because that is the way I learned to do it." Prospective teachers' age did neither significantly influence their test scores, nor their approach to solving problems during the interviews. Supplementary analysis revealed that number of mathematics courses completed prior to entering the teacher education program significantly predicted prospective teachers' outcome on the questionnaire survey.Comparison of the findings from this study to findings from similar studies carried out in the US indicated that there was a wide gap in prospective teachers' ability in mathematics in both countries, and that they struggled with similar topics within mathematics. In general, the results from this study were in line with prior findings, showing, that prospective elementary teachers relied on memory for particular rules in mathematics, their knowledge was procedural and they did not have an underlying understanding of mathematical concepts or procedures (Ball, 1990; Tirosh and Graeber, 1989; Tirosh and Graeber, 1990; Simon, 1993; Mewborn, 2003; Hill, Sleep, Lewis, and Ball, 2007). The findings of this study highlight the need for a more in-depth mathematics education for prospective teachers in the School of Education at the University of Iceland. It is not enough to offer a variety of courses to those specializing in the field of mathematics education. It is also important to offer in-depth mathematics education for those prospective teachers focusing on general education. If those prospective teachers teach mathematics, they will do so in elementary school where students are forming their identity as mathematics students

Teachers\u27 Of Students With Visual Impairments Perceptions And Experiences Of Teaching The Expanded Core Curriculum

The purpose of the qualitative research study was to explore the perceptions and experiences of teachers of students with visual impairments (TSVIs) in the state of North Dakota regarding the expanded core curriculum (ECC). This study included transcribed interviews from six TSVIs who taught in grades K-12. The National Agenda for the Education of Children and Youths with Visual Impairments, Including Those with Multiple Disabilities was used to frame this study. Phenomenological methods were used to analyze the interviews into codes, categories, themes, and an assertion. Following were the seven themes supported by the data collected: 1. Teachers of students with visual impairments (TSVIs) reported that the responsibility of educating students with visual impairments is “huge”; therefore, it takes a village (i.e., North Dakota Vision Services/School for the Blind [NDVS/SB] professionals, teams, and others) to ensure the unique needs of students with visual impairments are met. 2. TSVIs emphasized the importance of systematic and purposeful instruction, and ongoing and systematic checks for understanding. 3. TSVIs perceived instructors at the NDVS/SB as experts in teaching the expanded core curriculum. 4. TSVIs perceived they were primarily responsible for teaching compensatory skills and use of assistive technology. 5. TSVIs perceived the parents of students with visual impairments and the NDVS/SB were primarily responsible for teaching independent living skills of the expanded core curriculum (ECC). 6. TSVIs perceived academic curriculum takes precedence over the expanded core curriculum. 7. Limited time and limited access prohibit TSVIs from providing consistent, and systematic, instruction of the expanded core curriculum within their respective school districts. These seven themes converged into the following assertion: Educating students with visual impairments in the state of North Dakota requires an integrative approach in which academic curriculum and expanded core curriculum are addressed through collaborative efforts among all stakeholders and service providers. In summary, educating students with visual impairments is an enormous task that no one person can accomplish alone. It behooves stakeholders, associated with vision impairments, to work together to create models for teaching the expanded core curriculum that ensure equity of services throughout the state

Phases of knowledge in lexical acquisition : a developmental study into four to twelve year olds decipherment of unfamiliar words from linguistic contexts during continuous assessment

Research on the deciphering of nonsense words within the context of text, a story, or tale was conducted at various schools and day-care centres in the Stirling area of Scotland in 1985-1988. Three experiments were conducted, in which large samples of primary school children aged 4-12 were tested. The experiments resembled Werner and Kaplan's (1950) "Word-Context Task, " in which isolated sentences in a series with one nonsense word in each sentence were presented to school children. The children were asked to answer questions about the meanings of these words. The results were not in line with the rapid word learning that experience suggests happens in young children, it was not until after age 9 that the children started to give approximately correct answers, and prior to age 11 the answers did not meet up with proper adult definitions. It has been pointed out, however (Donaldson, 1978), that because these sentences were not supported by any relation to immediate context and behaviour, and because the children were required to process utterances as pure isolated language - an unnatural situation for language acquisition - the "Word-Context Task" may have given an unrealistic picture of the child's ability to acquire language naturally. In the three word-leaming studies at Stirling University in 1985-1988, in order to account for a more natural presentation, the sentences with the nonsense word were embodied in the context of a story. Children were thought to fare better (than the children in the Wemer & Kaplan study) when listening to such a story, especially if the basic theme was of interest. A methodological tool, refined in the work of Dockrell (1981), in which the full meaning of a term involves having worked out the sense, reference, and denotation of the term. was applied in each of the test batteries that followed the presentation of the story. In these tests, the children were tested on both their comprehension and production of the new term in question. Drawings were used in order to try to tap the children's denotation of the new term, and to facilitate young children's approach to the demands of the study. As regards word meaning in general. Martin Joos (1972) had argued that the common blunder was that an odd word must have an odd sense--the odder, the better. He argued that one should define words in such a fashion as to make them contribute least to the total message derivable from its passage where it is housed, rather than, e. g., defining it according to some presumed etymology of semantic history. He called this concept "a tacit principle", and argued that word learners and word users would sense the intuitive familiarity of the conveyed meaning of words and text. Words are, according to this principle, "mysterious" in their environment, their meanings are not worked out deliberately, intentionally; rather, one should make the mysterious item maximally supportive and supported in its situation, in order that redundancy would result in proper connotation of the distributed meaning. Context and knowledge of contexts reveal meaning; the text is processed holistically, and so are the instantaneous meanings of the words of which it is composed. Thus, Joos maintained that in deciphering an unknown word, the wisest course is to assume the "least meaning" consistent with the context. Tasks such as Werner and Kaplan's "Word-Context Task" (1950), force subjects to infer aspects of meaning that go well beyond this "least" meaning and, as Joos pointed out, this leads notably to errors from which recovery is difficult. In the studies at Stirling University, attempts were made to determine if different types of learning would result in different types of responses. The dichotomy, intentional/incidental or analytic/holistic was worked out into experimental and control conditions, as based on Aveling's pioneering experiment (1911, 1912) into the general and particular aspects of encoded stimuli. Later, Lee Brooks (1978) worked with the dichotomies intentional/incidental in his Lepton experiments and argued that the more complex a behaviour is (speaking or writing, for example), the more likely it is to be learned implicitly. He pointed out, however, that the dichotomies explicit/implicit, analytic/non analytic, and deliberate vs. intuitive processes need to be elaborated and not taken as a strict division. In the three experiments at Stirling, children of primary school age (ages 4 to 12) were presented with a "word-context" task and their understanding of the unknown word was probed under different conditions. In the control condition a control word was probed, but in the experimental condition the child's understanding of the target word was fully tested. All the children listened to a short story displayed by a video or read from a tape in which the unknown word occurred in several different contexts, the unknown word in each story denoted an unfamiliar natural kind. During the story's display, children in the control condition were, at certain intervals, asked questions about the story's theme. Children in the experimental group were, at these same intervals, shown a sample of objects, to one of which the unknown word referred, and they were asked to hand these objects to the experimenter as she requested the objects, or they were asked direct questions about the meaning of the target word and about other words in the story. After hearing the story, all subjects were tested on their comprehension and production of the unknown word, together with other words, and a scoring procedure based on a technique developed by Dockrell (1981) was applied. This procedure necessitated the full meaning of the term covering aspects of the sense, reference., and denotation of the new term (cf. Lyons, 1977a). The results indicate that children younger than those tested in the Wemer and Kaplan's "Word-Context Task" (ages 8.6 to 13.6) could decipher the full meaning of the new term. But individual differences within age groups showed greater differences than existed between age groups. All in all, the results indicate that working out the full meaning of a new term is a lengthy process indeed (Campbell & Dockrell, 1986), even though a sense of the given semantic domain may often be established quite early in the learning process. Performance styles also differ from younger children to older ones. The results indicate that there were significant age differences between the children in the first and second experiments, but that such differences were lacking in the third experiment, and that control subjects in the three studies seldom gave poorer responses than did experimental subjects and often did better. However, the results must be interpreted in the light of learning and recovery from error occurring, within the experimental subjects in the course of deciphering. If the initial scores of the experimental subjects on the target word as obtained during encoding are compared with the first scores obtained from the control subjects after they had heard the whole story, there is a significant difference in scores between the conditions in favour of the control subjects in all age groups. This is consistent with Joos's assumption that an interference concerning the meaning of a word that occurs too early in the learning task and not enough information of contextual cues will lead the children in the experimental groups astray in their guesses when asked too early for answers on the new word's meaning. But implied in Joos's Axiom is the likelihood for recoveries from errors, and the strategies children use in order to work them out need to be explored further. Much individual variation was found among the children's responses in the age groups. These differences were indeed more significant than were the differences between age groups. Overall, the children did very well at these tasks and that result may be related to the population from which they were selected, Stirling University Playgroup, Psychology Department, Dunblane Primary Schools Nursery and Killin playgroup and primary Schools in Central Scotland. In general, the study provided support for Joos's idea (1958, 1967, 1972) that early interference with the meaning of a new word when deciphering from a verbal context results in errors. However, recovery is possible, if not guaranteed. The study also indicated that children much younger than Werner and Kaplan's subjects (1950) could work out the full meaning of the unknown word. Earlier studies on context such as theirs may have been biased in using experimental setups with bits of isolated language and thus not tapping the real capability of the young word-learner who may come to learn words and their meanings through contexts, through the procedures that the word is linked to, through the verbal and/or nonverbal circumstance it is used in, and accompanied by actions, and exercised; what John Dewey had termed "context of use" (1910). Also, it is clear from the study that at a young age children are able to establish a sense of the given semantic domain a new word belongs to and a stable denotata, as their drawings indicate, but in order to decipher the full meaning of a new term is a lengthy process indeed for most children (Carey, 1978a, Campbell & Dockrell, 1986; Miller & Gildea, 1987). In all age groups and in all conditions there were differences between the children's comprehension and production of the new term in favour of comprehension. However, that result may be related to the nature of the experimental setup (the children gained more experience in working with comprehension than with production), and does not necessarily give support to the claim that comprehension precedes production. There were differences in the age groups between comprehension and production: children in all conditions gave more correct answers in the comprehension tasks and is in accord with earlier experimental evidence. There were children in all age groups who clearly had acquired the full meaning of the new word. its sense, reference, and denotation, whereas the average picture of the children's performance on all these three aspects was quite scattered. This is in accord with earlier work of Dockrell (1981), which suggests that to work out the full meaning of a new term is a lengthy process, even though a sense of the given semantic domain may often be established quite early. In a posttest, two to three weeks later, in which all the children were tested again on the unknown word, it was clear that learning had indeed taken place and that in most cases children who had mapped the new word's meaning in the first experimental set-up, now felt surer about the unknown word's meaning. In general, the study provided support for the view that too early interferences and constraints in the learning task lead the young word learner astray, but that children may nevertheless recover from their errors when provided with more inforination and time. The study also demonstrated that the children were motivated to work at the tasks set before them and that their drawings are a valuable experimental and educational tool for tapping young children's representations. The results indicated that the control group subjects in all age groups fared better than did the experimental subjects, and age group differences here were, in most cases, significant. That the control group subjects fared better is consistent with Joos's assumption that too early an interference on a word's meaning will lead the children astray in their process of deciphering. However, bombarding the children in the experimental groups with questions on the meaning of the unknown word while they are in the process of encoding hampers the needed reorganisation of the tacit semantic representation underlying their meaning of words. The different tests that were designed for the three experiments reveal interesting individual variations in the sample and different testing profiles. The tests show much correlation among them, such that tests that were designed in order to test forverbal coding, comprehension, and general knowledge correlate highly and tests that were designed to test for imaginal coding (depicting) show positive correlation to these verbal comprehension tests - high scores on the verbal tests usually relate to good performance in the depicting tests - and tests that were designed for the production of the new word also show positive correlation with tests that only test for comprehension, and, finally, tests of categorisation that were designed to test for linguistic definitions - for conceptual understanding and declarative skill based on the understanding of logical relationships between words in a taxonomy - show some positive correlation to the other tests (such as the ones of production) but less to others. The test results may indicate that the tests of production and the tests of linguistic definitions better reflect semantic content and true linguistic ability than tests of comprehension, general knowledge, and imaginal coding that may be broader and cover more functions and thus reflect general, cognitive knowledge. These results from the different tests confirm the idea that the meaning of a word has many phases, each of which takes time to grow and to be mastered by the child, the results also show that within the same child and between children there are differences as to their fluency in dealing with these different phases of word meaning and mastering them. Thus, the results confirm the basic notion of this thesis, namely, that different phases are involved in both the composition of a word within text, and in the deciphering of that composition from contextual to acontextual meaning

Energy Conservation By Intermittently Recirculating and Aerating an Aquaponics System with an Airlift

An airlift device providing aeration and circulation was designed to reduce electrical power requirements for aquaponics by eliminating the need for a water pump. The airlift performed better than predicted and achieved water flow rates of 10 L/min at 25 °C, in comparison to the theoretical design performance 2.65 L/min. Koi (Cyprinus carpio) and sweet basil (Ocimum basilicum) were cultured for five weeks in two identical aquaponics systems. The system was located indoors and consisted of a fish tank, a sump tank, and a soil-free growth media bed under artificial lighting. The total water volume in each system was 230 liters. Test conditions of intermittent vs. continuous aeration and recirculation were studied and growth rates of plants and fish were measured. Four week-long tests of intermittent aeration and circulation (50% on/50% off) showed net total bed growth rates per 1 KWh per day of 99.4%, while the continuous operated bed showed 50.3% growth per 1 KWh for the same period. The intermittently operated system showed 44.1% more growth for the same energy consumption. This suggests electrical power requirements for aquaponics aeration and recirculation may be reduced by as much as 75% with the use of an intermittent aeration and recirculation through an airlift. This suggests that intermittent airlift technology may be useful for reducing energy costs, and increasing the feasibility of using renewable power in commercial aquaponics farms

Topological Effects on the Magnetoconductivity in Topological Insulators

Three-dimensional strong topological insulators (TIs) guarantee the existence of a 2-D conducting surface state which completely covers the surface of the TI. The TI surface state necessarily wraps around the TI's top, bottom, and two sidewalls, and is therefore topologically distinct from ordinary 2-D electron gases (2DEGs) which are planar. This has several consequences for the magnetoconductivity $\Delta \sigma$, a frequently studied measure of weak antilocalization which is sensitive to the quantum coherence time $\tau_\phi$ and to temperature. We show that conduction on the TI sidewalls systematically reduces $\Delta \sigma$, multiplying it by a factor which is always less than one and decreases in thicker samples. In addition, we present both an analytical formula and numerical results for the tilted-field magnetoconductivity which has been measured in several experiments. Lastly, we predict that as the temperature is reduced $\Delta \sigma$ will enter a wrapped regime where it is sensitive to diffusion processes which make one or more circuits around the TI. In this wrapped regime the magnetoconductivity's dependence on temperature, typically $1/T^2$ in 2DEGs, disappears. We present numerical and analytical predictions for the wrapped regime at both small and large field strengths. The wrapped regime and topological signatures discussed here should be visible in the same samples and at the same temperatures where the Altshuler-Aronov-Spivak (AAS) effect has already been observed, when the measurements are repeated with the magnetic field pointed perpendicularly to the TI's top face

Unbranched Catacondensed Polygonal Systems Containing Hexagons and Tetragons

An algebraic solution for the isomer numbers of unbranched a-4- catafusenes is presented. An a-4-catafusene is a catacondensed polygonal system consisting of exactly o: tetragons each and otherwise only hexagons. This analysis, which makes use of certain triangular matrices including the Pascal triangle, is a continuation of a previous work on di-4-catafusenes. By serendipity, the problem was reversed in the sence that the systems were considered as possessing \u277 hexagons each and otherwise only tetragons. Under this viewpoint the enumeration problem could be solved more directly and led to explicit formulas. Finally, the resuIts are applied to catafusenes as a special case

Novel interpretation of sperm stress test and morphology for maturity assessment of young Norwegian Red bulls

The use of genomic selection significantly reduces the age of dairy bulls entering semen pro-duction compared to progeny testing. The study aimed to identify early indicators that could be used for screening bulls during their performance testing period and could give us insight into their future semen production performance, acceptance for the AI station, and prediction of their future fertility. The study population consisted of 142 young Norwegian Red bulls enrolled at the performance test station, followed until we received semen production data, semen doses, and, subsequently, non-return rates (NR56) from the AI station. A range of semen quality parameters were measured with computer-assisted sperm analysis and flow cytometry from ejaculates collected from 65 bulls (9-13 months). The population morphometry of normal spermatozoa was examined, showing that Norwegian Red bulls at 10 months of age have homogenous sperm morphometry. Norwegian Red bulls could be separated into 3 clusters according to their sperm's reaction patterns to stress test and cryopreservation. Results of semi-automated morphology assessment of young Norwegian Red bulls showed that 42% of bulls rejected for the AI station and 18% of bulls accepted had ejaculates with abnormal morphology scores. For the youngest age group at 10 months, the mean (SD) proportion of spermatozoa with normal morphology was 77.5% (10.6). Using novel interpretation of sperm stress test combined with sperm morphology analysis and consecutive cryopreservation at a young age allowed identification of the candi-date's sperm quality status. This could help breeding companies introduce young bulls earlier to the AI stations

Congenitally deaf children's care trajectories in the context of universal neonatal hearing screening: a qualitative study of the parental experiences

The objective of this study is to examine the early care trajectories of congenitally deaf children from a parental perspective, starting with universal neonatal hearing screenings. The analysis using a three-dimensional care trajectory concept is aimed at developing a basic typology of postscreening care trajectories. Children with severe/profound hearing loss, registered in the Flanders' (Belgium) universal neonatal hearing screening program, born between 1999 and 2001. Thematic content analysis of qualitative data collected retrospectively from participant's parents. Two basic types of care trajectories emerged; based on differences in care-use in the phase of further diagnosis and related parental experiences. Subtypes resulted from events related to cochlear implantation. Five trajectory phases were identified: screening, further diagnosis, care and technology, cochlear implantation, and reduction of care and were characterized by specific parental experiences such as confusion, disbelief, disappointment, and uncertainty. Those experiences relate to care professionals' acts and communication and the child's functional evolution. Early care interventions could benefit from coordinated transition between phases, parent support throughout the care trajectory, and a broad approach to deafness in professionals' communication