Revealing conceptions of rate of change

Rate of change is an important mathematical concept. Research referring to students’ difficulties with this concept spans more than twenty years. Research suggests that problems experienced by some calculus students are likely a result of pre-existing limited or incorrect conceptions of rate of change. This study investigated 23 Victorian Year 10 students’ understanding of rate as revealed by phenomenographic analysis of interviews. Eight conceptions of rate of change emerged. Four important aspects of the concept were identified and gaps in students’ thinking defined. In addition, the employment of phenomenography, to reveal conceptions of rate, is described in detail.

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.

Patterns of coronary heart disease mortality over the 20th century in England and Wales : possible plateaus in the rate of decline

Background
Coronary heart disease (CHD) rates in England and Wales between 1950 and 2005 were high and reasonably steady until the mid 1970s, when they began to fall. Recent work suggests that the rate of change in some groups has begun to decrease and may be starting to plateau or even reverse.

Methods
Data for all deaths between 1931 and 2005 in England and Wales were grouped by year, sex, age at death and contemporaneous ICD code for CHD as cause of death. CHD mortality rates by calendar year and birth cohort were produced for both sexes and rates of change were examined.

Results
The pattern of increased burden of CHD mortality within older age groups has only recently emerged in men, whereas it has been established in women for far longer. CHD mortality rates among younger people showed little variation by birth cohort. For younger women (49 and under), the rate of change in CHD mortality has reversed in the last 20 years, indicating a future plateau and possible reversal of previous improvement in CHD mortality rates. Among younger men the rate of change in CHD mortality has been consistent for the past 15 years indicating that rates in this group have continued to fall steadily.

Conclusion
Although CHD mortality rates continue to drop in older age groups the actual burden of coronary heart disease is increasing due to the ageing of the population. The rate of improvement in CHD mortality appears to be beginning to decline and may even be reversing among younger women.

Tuning the mechanical and morphological properties of self-assembled peptide hydrogels via control over the gelation mechanism through regulation of ionic strength and the rate of pH change

Hydrogels formed by the self-assembly of peptides are promising biomaterials. The bioactive and biocompatible molecule Fmoc-FRGDF has been shown to be an efficient hydrogelator via a π-β self-assembly mechanism. Herein, we show that the mechanical properties and morphology of Fmoc-FRGDF hydrogels can be effectively and easily manipulated by tuning both the final ionic strength and the rate of pH change. The increase of ionic strength, and consequent increase in rate of gelation and stiffness, does not interfere with the underlying π-β assembly of this Fmoc-protected peptide. However, by tuning the changing rate of the system's pH through the use of glucono-δ-lactone to form a hydrogel, as opposed to the previously reported HCl methodology, the morphology (nano- and microscale) of the scaffold can be manipulated.

An investigation of middle secondary students' mathematical conceptions of rate

This study identified four educationally critical aspects of ‘rate’ through analysis of phenomenographic, video-recorded interviews with Year 10 students. Further analysis indicated understandings in one representation or context were not necessarily transferable.

Variation in energy intake and basal metabolic rate of a bird migrating in a wind tunnel

1. We studied the changes in body mass, metabolizable energy intake rate (ME) and basal metabolic rate (BMR) of a Thrush Nightingale, Luscinia luscinia, following repeated 12-h migratory flights in a wind tunnel. In total the bird flew for 176 h corresponding to 6300 km. This is the first study where the fuelling phase has been investigated in a bird migrating in captivity.

2. ME was very high, supporting earlier findings that migrating birds have among the highest intake rates known among homeotherms. ME was significantly higher the second day of fuelling, indicating a build-up of the capacity of the digestive tract during the first day of fuelling.

3. Further indications of an increase in size or activity level of metabolically active structures during fuelling come from the short-term variation in BMR, which increased over the 2-day fuelling period with more than 20%, and in almost direct proportion to body mass. However, mass-specific BMR decreased over the season.

4. The patterns of mass change, ME and BMR of our focal bird following two occasions of 12-h fasts were the same as after flights, indicating that fast and flight may involve similar physiological processes.

5. The relatively low ME the first day following a flight may be a contributing factor to the well-known pattern that migrating birds during stopover normally lose mass the first day of fuelling.

Improving primary science: schools experience of change

Provides insights into the experiences of school officials in improving their method of teaching science within the School Innovation in Science (SIS) initiative. Involvement of all science teachers on the project; Management of educators and the analysis of existing teaching practices; Evidence of change in teaching methods and discussion of the stage process.

`Zealotry or nostalgic regret`? women leaders in technical and further education in Australia : agents of change, entrepreneurial educators or corporate citizens?

Education has been restructured in many Western post-industrial nation states during the 1990s. The Australian Technical and Further Education sector (TAFE) has been particularly susceptible to discourses of responsiveness to the market and the new entrepreneuralism. This article explores how women have been repositioned in contradictory and ambiguous ways as the new entrepreneurial middle managers by existing and emergent discourses that circulated in and through TAFE organizations. In turn, it points to how discourses of change management and client responsiveness took on particular readings within specific institutional and professional cultures of the eight Technical and Further Education institutions (TAFEs). At the same time, the restructuring that arose from the corporatization of TAFE, in a highly gendered process, through the twin strategies of marketization and the new managerialism produced new possibilities for individual women educators who moved up into middle management. Yet these individual women were positioned within highly masculinist 'neo-corporate bureaucratic cultures' that co-opted their passion for the capacity of education to make a difference and incorporated these new entrepeneurial work identities.

Yield, growth and mortality rate of the Thai river sprat, Clupeichthys aesarnensis, in Sirinthorn Reservoir, Thailand

The Thai river sprat, Clupeichthys aesarnensis Wongratana, is a clupeid with a short life span, and supports artisanal fisheries in a number of reservoirs in the Mekong Basin. The growth parameters, mortality rates and the status of the Thai river sprat in Sirinthorn Reservoir (28 800 ha), NE Thailand (15°N; 105°E), are presented. The fishery is based on lured lift-nets, operated 7–14 days in the new moon period, September to April each year. It was shown that the von Bertalanffy growth function (VBGF) model was L_t (mm) = 78.43[1 − exp{−0.211[t − (−0.7996)]}] and its growth conformed to an isometric pattern. Natural mortality rate (month−¹) was 0.13 month−¹. Total mortality rates ranged from 0.69 to 1.53 month−¹ depending on the weather and the fishing season. Recruitment was continuous throughout the year but peaked in June and July. The yield per recruit model indicated that the exploitation rate of this fishery is probably too high.