Strategies and Skills Used by Middle School Students During the Solving of Non-routine Mathematics Problems

This study was conducted to determine the processes and strategies selected middle school students use during the solving of non-routine mathematics problems. Qualitative research methods were used to identify the cognitive and metacognitive skills and processes used in problem solving and to determine the affective influences on the problem solving process. Six middle grade students were selected to participate in the study. Each student was interviewed four times. The first interview was conducted in order to develop student profiles by obtaining information about each student\u27s family, school, and mathematics background. The second and third interviews consisted of two phases. First, students solved problems for twenty minutes and verbally explained their thoughts and work. Afterwards, a follow-up interview was conducted in order to clarify and enhance information collected during the twenty minute problem solving session. The fourth and final interview was conducted using a grid technique in order to determine student perceptions of the problem solving process. The interviews were audiotaped, and the problem solving sessions were videotaped. The transcriptions were analyzed using a constant comparative method. Themes emerged from the data analysis, and findings were identified. The themes and findings led the researcher to the following conclusions. 1. Students are not aware of the various alternatives available to help them understand a non-routine mathematics problem when they first read it. 2. The only skills which students perceive as mathematics skills are the basic computations of addition, subtractions, multiplications, and division. 3. Students are unwilling to take risks when presented with a problem solving situation. They are hesitant to try a strategy unless they have seen a teacher use that particular strategy. 4. Students have been told that various heuristics exist to help them solve problems. Even though they have been instructed to use them, they have not been adequately informed concerning how and when to use the heuristics. 5. Students model the problem solving strategies and behaviors of their teachers. The study demonstrates that teachers need to concentrate on fostering students\u27 self-esteem and positive attitudes toward problem solving in mathematics. Non-routine problems should become a regular part of the mathematics which students are exposed to in school, and teachers should focus on modeling their successful problems solving behaviors

The Contribution of Io-Raised Tides to Europa's Diurnally-Varying Surface Stresses

Europa's icy surface records a rich history of geologic activity, Several features appear to be tectonic in origin and may have formed in response to Europa's daily-varying tidal stress [I]. Strike-slip faults and arcuate features called cycloids have both been linked to the patterns of stress change caused by eccentricity and obliquity [2J[3]. In fact, as Europa's obliquity has not been directly measured, observed tectonic patterns arc currently the best indicators of a theoretically supported [4] non-negligible obliquity. The diurnal tidal stress due to eccentricity is calculated by subtracting the average (or static) tidal shape of Europa generated by Jupiter's gravitational field from the instantaneous shape, which varies as Europa moves through its eccentric orbit [5]. In other words, it is the change of shape away from average that generates tidal stress. One might expect tidal contributions from the other large moons of Jupiter to be negligible given their size and the height of the tides they raise on Europa versus Jupiter's mass and the height of the tide it raises on Europa, However, what matters for tidally-induced stress is not how large the lo-raised bulge is compared to the Jupiter-raised bulge but rather the differences bet\Veen the instantaneous and static bulges in each case. For example, when Europa is at apocenter, Jupiter raises a tide 30m lower than its static tide. At the same time, 10 raises a tide about 0.5m higher than its static tide. Hence, the change in Io's tidal distortion is about 2% of the change in the Jovian distortion when Europa is at apocente

The Frustration with Utilization: Why Have Improvements in Internal Phosphorus Utilization Efficiency in Crops Remained so Elusive?

Despite the attention internal phosphorus utilization efficiency (PUE) of crops has received in the literature, little progress in breeding crop cultivars with high PUE has been made. Surprisingly few studies have specifically investigated PUE; instead, genotypic variation for PUE has been investigated in studies that concurrently assess phosphorus acquisition efficiency (PAE). We hypothesized that genotypic differences in PAE confound PUE rankings because genotypes with higher PAE suffer a lower degree of P stress, resulting in lower PUE. The hypothesis was tested by comparing soil-based screening to a modified technique whereby rice genotypes were grown in individual containers with a single dose of solution P, to eliminate differences in P uptake among genotypes. Genotypic differences in PUE were apparent in root and shoot tissue using the modified nutrient solution technique, but PUE rankings showed no correlation with those from traditional soil-based screening. We conclude that PUE in soil-based screening systems is unavoidably linked with genotypic PAE, resulting in PUE rankings confounded by differences in P uptake. Only screening techniques assuring equal P uptake are suitable for the exploitation of genotypic variation for PUE

Dynamics of a quantum reference frame undergoing selective measurements and coherent interactions

We consider the dynamics of a quantum directional reference frame undergoing repeated interactions. We first describe how a precise sequence of measurement outcomes affects the reference frame, looking at both the case that the measurement record is averaged over and the case wherein it is retained. We find, in particular, that there is interesting dynamics in the latter situation which cannot be revealed by considering the averaged case. We then consider in detail how a sequence of rotationally invariant unitary interactions affects the reference frame, a situation which leads to quite different dynamics than the case of repeated measurements. We then consider strategies for correcting reference frame drift if we are given a set of particles with polarization opposite to the direction of drift. In particular, we find that by implementing a suitably chosen unitary interaction after every two measurements we can eliminate the rotational drift of the reference frame.Comment: 9 pages, 5 figure

Clinicians’ Perceptions of Telemedicine for Conducting Family Conferences Prior to Transfer to a Tertiary Care Center Intensive Care Unit

Objectives: Critically ill patients are often transferred from rural to tertiary care medical centres for further higher levels of care. The transportation process may delay family conferences during which prognosis and goals of care are discussed. These conferences typically occur when family members meet the treating physicians for the first time in person after transport. Telemedicine is a tool that may be used to bridge this gap in communication by enabling these family conferences before transport. There are no data on perceptions of telemedicine used in this setting. We conducted a qualitative study assessing provider perceptions regarding the use of telemedicine for conducting family conferences prior to transport. Methods: Critical care physicians and nurses were invited to view an educational video demonstrating the process of conducting a family conference via telemedicine. Immediately following viewing of the video, physicians and nurses filled out an open-ended questionnaire regarding their thoughts and perceptions of the video and the telemedicine family conference approach. Results: There was a 68% response rate to the surveys. Responses were categorised into two major themes: benefits and barriers. Within the theme of benefits, three sub-themes were identified: satisfaction, knowledge and quality of care. We identified four domains within the theme of barriers: time, perception, technology and logistics. Conclusions: Respondents believe that there may be several benefits including increased satisfaction, improved communication and empowerment of families by dissemination of knowledge. Barriers to the use of this intervention identified include costs, time, technology and negative perceptions of the telemedicine conference

Phosphorus Efficient Phenotype of Rice

The ideal phenotype to cope with P deficiency is suggested to be a larger root system, both in terms of length and foraging area, coupled with a high capacity for P solubilization from compounds exuded from roots. Greater soil exploration results in a large number of roots in the top soil, longer roots in general with more cortical aerenchyma, more and longer root hairs, and a shift in mycorrhizal and bacterial colonization. However, these assumptions often result from experiments in highly controlled, sterile and soil-free conditions using model plants or single ecotypes where results are then extrapolated to all genotypes and plant species. In recent years this generalization has been questioned. Here, we summarize recent rice research analyzing the natural diversity of rice root systems under P deficiency. Interestingly, while some of the high yielding genotypes do show the expected, large root system phenotype, some have a surprisingly small root system—as little as a quarter of that of the large root system varieties—but achieve similar yield and P uptake under P deficiency. This effect has recently been termed root efficiency, which we discuss in this chapter in conjunction with root foraging traits