Predicting long-term growth in students' mathematics achievement: the unique contributions of motivation and cognitive strategies

This research examined how motivation (perceived control, intrinsic motivation, and extrinsic motivation), cognitive learning strategies (deep and surface strategies), and intelligence jointly predict long-term growth in students' mathematics achievement over 5 years. Using longitudinal data from six annual waves (Grades 5 through 10; Mage = 11.7 years at baseline; N = 3,530), latent growth curve modeling was employed to analyze growth in achievement. Results showed that the initial level of achievement was strongly related to intelligence, with motivation and cognitive strategies explaining additional variance. In contrast, intelligence had no relation with the growth of achievement over years, whereas motivation and learning strategies were predictors of growth. These findings highlight the importance of motivation and learning strategies in facilitating adolescents' development of mathematical competencies.

Diversity in mathematics assessment equals diversity in opinion?

We undertook a study to investigate the views of both students and staff in our department towards assessment in mathematics, as a precursor to considering increasing the diversity of assessment types. In a survey and focus group there was reasonable agreement amongst the students with regards major themes such as mode of assessment. However, this level of agreement was not seen amongst the staff, where discussions regarding diversity in mathematics assessment definitely revealed a difference of opinion. As a consequence, we feel that the greatest barriers to increasing diversity may be with staff, and so more efforts are needed to communicate to staff the advantages and disadvantages, in order to give them greater confidence in trying a range of assessment types.

Relationship between classroom authority and epistemological beliefs as espoused by primary school mathematics teachers from the very high and very low socio-economic regions in Thailand

This article presents findings of a larger single-country comparative study which set out to better understand primary school teachers’ mathematics education-related beliefs in Thailand. By combining the interview and observation data collected in the initial stage of this study with data gathered from the relevant literature, the 8-belief / 22-item ‘Thai Teachers’ Mathematics Education-related Beliefs’ (TTMEB) Scale was developed. The results of the Mann-Whitney U Test showed that Thai teachers in the two examined socio-economic regions espouse statistically different beliefs concerning the source and stability of mathematical knowledge, as well as classroom authority. Further, these three beliefs are found to be significantly and positively correlated.

Inclusive approaches to teaching and learning mathematics

This chapter explores the role of mentors in supporting pre-service teachers to include all children in mathematics teaching, no matter what their individual needs.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Spatio-temporal variations of ozone and nitrogen dioxide concentrations under urban trees and in a nearby open area

The evergreen Quercus ilex L. is one of the most common trees in Italian urban environments and is considered effective in the uptake of particulate and gaseous atmospheric pollutants. However, the few available estimates on O3 and NO2 removal by urban Q. ilex originate from model-based studies (which indicate NO2/O3 removal capacity of Q. ilex) and not from direct measurements of air pollutant concentrations. Thus, in the urban area of Siena (central Italy) we began long-term monitoring of O3/NO2 concentrations using passive samplers at a distance of 1, 5, 10 m from a busy road, under the canopies of Q. ilex and in a nearby open-field. Measurements performed in the period June 2011-October 2013 showed always a greater decrease of NO2 concentrations under the Q. ilex canopy than in the open-field transect. Conversely, a decrease of average O3 concentrations under the tree canopy was found only in autumn after the typical Mediterranean post-summer rainfalls. Our results indicate that interactions between O3/NO2 concentrations and trees in Mediterranean urban ecosystems are affected by temporal variations in climatic conditions. We argue therefore that the direct measurement of atmospheric pollutant concentrations should be chosen to describe local changes of aerial pollution.

Trees for development? Articulating the ambiguities of power, authority and legitimacy in governing Ghana’s mineral rich forests

The growth of mining activities in Africa in the last decade has coincided with increased attention on the fate of the continent’s forests, specifically in the contexts of livelihoods and climate change. Although mining has serious environmental impacts, scant attention has been paid to the processes which shape decision-making in contexts where minerals and forests overlap. Focussing on the illustrative case of Ghana, this paper articulates the dynamics of power, authority and legitimacy of private companies, traditional authorities and key state institutions in governing mining activities in forests. The analysis highlights how mining companies and donors promote a neoliberal model of resource management which entrenches their ability to benefit from mineral exploitation and marginalises the role of state institutions and traditional authorities in decision-making. This subsequently erodes state authority and legitimacy and compounds the contested nature of traditional authorities’ legitimacy. A more nuanced examination of foundational governance questions concerning the relative role of the state, traditional authorities and private interests is needed.

Don’t aim too high for your kids: parental over-aspiration undermines students’ learning in mathematics

Previous research has suggested that parents’ aspirations for their children’s academic attainment can have a positive influence on children’s actual academic performance. Possible negative effects of parental over-aspiration, however, have found little attention in the psychological literature. Employing a dual-change score model with longitudinal data from a representative sample of German schoolchildren and their parents (N = 3,530; grades 5 to 10), we showed that parental aspiration and children’s mathematical achievement were linked by positive reciprocal relations over time. Importantly, we also found that parental aspiration that exceeded their expectation (i.e., over-aspiration) had negative reciprocal relations with children’s mathematical achievement. These results were fairly robust after controlling for a variety of demographic and cognitive variables such as children’s gender, age, intelligence, school type, and family SES. The results were also replicated with an independent sample of US parents and their children. These findings suggest that unrealistically high parental aspiration can be detrimental for children’s achievement.

An assessment of the impact of trees upon archaeology within a relict wetland

An evaluation of a surviving stretch of the Abbot's Way, in the Somerset Levels and Moors, was undertaken to assess the consequences of the previous management regime and inform future management of the site. The scheduled site appeared to have been dewatered and desiccated as a consequence of tree planting and the effects of a deep, adjacent drainage ditch during the previous decade. The evaluation considered the condition of the Neolithic timbers and associated palaeoenvironmental record from three trenches and, where possible, compared the results with those obtained form the 1974 excavation (Girling, 1976). The results of this analysis suggest that the hydrological consequences of tree planting and colonization had a detrimental effect on both the condition of the timbers and insect remains. However, pollen and plant macro-fossils survived well although there was modern contamination. A trench opened outside the scheduled area. where the ground was waterlogged and supported a wet acid grassland flora, revealed similar problems of survival and condition. This almost certainly reflects a period of peat extraction and an associated seasonally fluctuating water table in the 1950s and 1960s; in fact pollen survived better in the scheduled dewatered area. These results are compared with those recovered from the Sweet Track which was evaluated in 1996. Both sites have been subject to recent tree growth but the Sweet Track has been positively managed in terms of hydrology. The most notable difference between the two sites is that insects and wood survived better at the Sweet Track sites than at the Abbot's Way. Insects seem to be a more sensitive indicator of site desiccation than plant remains. It is recommended that any programme of management of wetland for archaeology should avoid deliberate tree planting and natural scrub and woodland generation. It should also take into account past as well as present land use.