Potential of technology and a familiar context to enhance students' concept of rate of change

Students' concept image of rate of change may be incomplete or erroneous. This paper reports a pilot study, with secondary school students, which explores the potential of technology (JavaMathWorlds), depicting a familiar context of motion, to develop students' existing schema of informal understandings of rate of change to more formal mathematical representations. Students developed numerous 'models of' rate of change in a motion context which then transferred to serve as a 'model for' rate of change in other contexts.

Video evidence : what gestures tell us about students' understanding of rate of change

This paper reports on insights into students’ understanding of the concept of rate of change, provided by examining the gestures made, by 25 Year 10 students, in videorecorded interviews. Detailed analysis, of both the sound and images, illuminates the meaning of rate-related gestures. Findings indicate that students often use the symbols and metaphors of gesture to complement, supplement, or even contradict verbal descriptions. Many students demonstrated, by the combination of their words and gestures, a sound qualitative understanding of constant rate, with a few attempting to quantify rate. The interpretation of gestures may provide teachers with a better understanding of the progress in their students’ thinking.

An 'emergent model' for rate of change

Does speed provide a ‘model for’ rate of change in other contexts? Does JavaMathWorlds (JMW), animated simulation software, assist in the development of the ‘model for’ rate of change? This project investigates the transference of understandings of rate gained in a motion context to a non-motion context. Students were 27 14–15 year old students at an Australian secondary school. The instructional sequence, utilising JMW, provided rich learning experiences of rate of change in the context of a moving elevator. This context connects to students’ prior knowledge. The data taken from pre- and post-tests and student interviews revealed a wide variation in students’ understanding of rate of change. The variation was mapped on a hypothetical learning trajectory and interpreted in the terms of the ‘emergent models’ theory (Gravemeijer, Math Think Learn 1(2):155–177, 1999) and illustrated by specific examples from the data. The results demonstrate that most students were able to use the ‘model of’ rate of change developed in a vertical motion context as a ‘model for’ rate of change in a horizontal motion context. A smaller majority of students were able to use their, often incomplete, ‘model of’ rate of change as a ‘model for’ reasoning about rate of change in a non-motion context.

It's the economy : the effect of macroeconomic variables of the rate of suicide

Background. There are a large number of factors mediating suicide. Many studies have searched for a direct causal relationship between economic hardship and suicide, however, findings have been varied.

Method. Suicide data was obtained from the Australian Bureau of Statistics for the period between January 1968 and August 2002. These were correlated with a suite of macroeconomic data including housing loan interest rates, unemployment rates, days lost to industrial disputes, Consumer Price Index, gross domestic product, and the Consumer Sentiment Index.

Results. A total of 51 845 males and 16 327 females committed suicide between these dates. There were significant associations between suicide rates and eleven macroeconomic indicators for both genders in at least one age range. Data was divided into male and female and five age ranges and pooled ages. Analyses were conducted on these 132 datasets resulting in 80 significant findings. The data was generally stronger for indices measuring economic performance than indices measuring consumers’ perceptions of the state of the economy. A striking difference between male and female trends was seen. Generally, male suicide rates increased with markers of economic adversity, while the opposite pattern was seen in females. There were significantly different patterns in age-stratified data, with for example higher housing loan interest rates having a positive association with suicide in younger people and a negative association in older age groups.

Conclusion. Macroeconomic trends are significantly associated with suicide. The patterns in males and females are very different, and there are further substantial age-related differences.

The impact of ionic liquids on amyloid fibrilization of AB16-22 : tuning the rate of fibrilization using a reverse Hofmeister strategy

We have shown that the amyloid fibrilization of Aß16-22 follows a reverse hofmeister trend in pILs. Fast fibrilization rates of seconds can be achieved.

A phase II multicentered, single-blind, randomized, controlled trial of the stroke self-management program

Background and Purpose—The benefits of chronic disease self-management programs for stroke survivors are uncertain because individuals with severe impairments have been excluded from previous research. We undertook a phase II randomized controlled trial to determine whether a self-management program designed for survivors (SSMP; 8 weeks) was safe and feasible compared to standard care (control) or a generic self-management program (generic; 6 weeks).
Methods—Stroke survivors were recruited from 7 South Australian hospitals via a letter or indirectly (eg, newspapers). Eligible participants were randomized at a 1:1:1 ratio of 50 per group. Primary outcomes were recruitment, participation, and participant safety. Secondary outcomes were positive and active engagement in life using the Health Education Impact Questionnaire and characteristics of quality of life and mood at 6 months from program completion.
Results—Of 315 people screened, 149 were eligible and 143 were randomized (48 SSMP, 47 generic, 48 control); mean age was 69 years (SD, 11) and 59% were female. Demographic features were similar between groups and 41% had severe cognitive impairment; 57% accessed the interventions, with 52% SSMP and 38% generic completing >50% of sessions (P=0.18). Thirty-two participants reported adverse events (7 control, 12 generic, 13 SSMP; P=0.3; 34% severe); however, none was attributable to the interventions. Potential benefits for improved mood were found.
Conclusions—SSMP was safe and feasible. Benefits of the stroke-specific program over the generic program included greater participation and completion rates. An efficacy trial is warranted given the forecast growth in the stroke population and improved survival trends.

Age- and gender-specific rate of fractures in Australia : a population-based study

There is little population-based data concerning fracture rates in Australia. We ascertained all fractures occurring during 2 years in adults aged 35 years and over residing within a defined region (population 218 000), representative of the Australian population. The major strength of this study is the comprehensive ascertainment of fractures, which was ensured by regular searches of the only two radiologic providers in the Geelong Osteoporosis Study region. Nevertheless, vertebral fractures are likely to be underestimated since our ascertainment relied on a clinical indication for a medical imaging procedure. Among those aged 35 – 55 years, the fracture rate (persons per 10 000/year) in men was about double the rate in women (65 vs 35). The fracture rate was almost 7 times higher in women over 60 years versus women less than 55 years of age. In contrast, the fracture rate in men over 60 years was only 50% higher than in men less than 55 years of age (72 vs 104). Fracture rates in women and men were highest at the hip (28 and 10 respectively), spine (21 and 7), distal forearm (Colles’) (18 and 4) and humerus (11 and 3), and were 3–4 times higher in women than men. These fractures accounted for 63% of all fractures in women and 32% in men. By contrast, the rate of lower leg and ankle fractures was less than 10 per 10 000 in both women and men and did not increase to the same extent with age. Hip fracture rates appear high, particularly among the older age strata, compared with retrospective ascertainment in other populations. In Australia, as in many other countries, there is an increasing longevity of the population. The number of women aged 90 years and over increased by 32% and the number of men of this age increased by 48% in the 5 years between the Australian national census of 1991 and 1996. Given stable fracture rates, the substantial health burden imposed by age-related fractures, particularly hip fractures, will continue to escalate in both women and men.

Does the rate of foraging attempts predict ingestion rate for young-of-the-year brook trout (Salvelinus fontinalis) in the field?

To assess the costs and benefits of young fish adopting different behavioural tactics, field studies of juvenile salmonines have assumed that (but did not test whether) the rate of foraging attempts predicts ingestion rate. We tested this assumption by quantifying capture, ingestion, and rejection rates of potential prey items for individual young-of-the-year brook trout (Salvelinus fontinalis) in a lake. Overall, capture rate (a conservative estimate of the rate of foraging attempts) was only a fair predictor of overall ingestion rate (Kendall's 1 = 0.54) and only 46% of captured items (number/minute) were ingested. Surface capture rate was a poor predictor of surface ingestion rate (T = 0.27) and only 1% of captured items were ingested. In contrast, subsurface capture rate was an excellent predictor of subsurface ingestion rate (T = 0.75) and 93% of captured items were ingested. No benthic prey captures were observed. Fish that ingested a low proportion of captured items spent a greater proportion of time moving, moved faster, and pursued prey further than fish that ingested a higher proportion of captured items. Rejection of captured items can represent a significant and little appreciated component of the foraging cycle for young salmonid fishes.

Incorporating differences in marginal utilities of time across activities in a time allocation model

Most existing activity time allocation models assume that individuals allocate their time to different activities over a period in such a way that the marginal utilities of time across activities are equal. Their argument is that, if not equal, an individual is free to allocate more time to those activities whose marginal utilities of time are higher and, finally allocates the optimal time to each activity with equal marginal utility. However, such an ideal situation may not always prevail in reality, especially when an individual is under income constraint and/or under intense time pressure. In order to incorporate such differences in marginal utilities of time across activities, we enrich the traditional activity time allocation model by explicitly including income constraint and by adding marginal extension activity choice model. As an application, the developed integrated model is used to estimate the value of activity time during weekends in Tokyo. The results are encouraging in that they forecast the individual time allocation more accurately and estimate realistically the value of activity time for each activity in a set of different activities than do by existing traditional models.