Developing pre-service teachers’ noticing of students’ understanding of the derivative concept

This research study examines the development of the ability of pre-service teachers to notice signs of students’ understanding of the derivative concept. It analyses preservice teachers’ interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers’ progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0

In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form w1az1+w2az2+⋯+wnazn, with non-null complex numbers w 1,w 2,…,w n and a 1,a 2,…,a n , produces analytic solutions of the functional equation w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0 on certain domains of C, which represents an extension of some existing results in the literature on this functional equation for the case of positive coefficients a j and w j.

Students’ understanding of the function-derivative relationship when learning economic concepts

The aim of this study is to characterise students’ understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding of these economic concepts is linked to students’ capacity to perform conversions and treatments between the algebraic and graphic registers of the function-derivative relationship when extracting the economic meaning of concavity/convexity in graphs of functions using the second derivative.

Visions of the Spanish Revolution: identities and conflicts in post-welfare societies

This is a case study that analyzes photographic documents of the social protest in Spain between 2011 and 2013. The analysis is qualitative and considers the use of space, the visual expression of the messages and the orientation toward the causes or effects of political, economic and social changes. Visual sociology allows us to appreciate, in the case of the Spanish Revolution, a dynamic of “reflexivity” unrecognizable from other research approaches. Two successive waves of social mobilization in response to two different shocks can be appreciated. The first is given by political corruption, unemployment and the threat to consumer society. The second shock is caused by the savage cuts in the Welfare State. Social mobilization is expressed differently in each phase, and the forms taken by the protests show how the class structure in post industrial society shapes the reactions to the crisis of the Welfare State.

The expenses of a dinner provided at the installation of the Rev'd. Professor Williams, 1780 May 2

Handwritten one-page itemized list of costs for food and supplies purchased for the installation dinner of Samuel Williams (1743-1817) for his appointment as Hollis Professor Mathematics and Natural Philosophy at Harvard College. Signed by Caleb Gannett.

An Oration Delivered on the eighth day of May one thousand seven hundred and seventy nine. At the Funeral of the Hon'ble John Winthrop..., 1779-1780

Small pamphlet bound in brown paper containing a handwritten nine-page copy of Stephen Sewall's funeral oration for Hollis Professor Mathematics and Natural Philosophy John Winthrop delivered May 8, 1779. The title page includes the inscription: "The lips of the wise disperse knowledge,/ A Man shall be comended [sic] according to his Wisdom -- Solomon."

Rules and orders relating to a Professor of the Mathematicks, of Natural and Experimental Philosophy, in Harvard College, 18 January 1726

This folder contains a single document describing the "rules and orders" of the Hollis Professor of Mathematics and Natural Philosophy. The document begins by defining the subjects to be taught by the Hollis Professor including natural and experimental philosophy, elements of geometry, and the principles of astronomy and geography. It then outlines the number of public and private lectures to be given to students, how much extra time the professor should spend with students reviewing any difficulties they may encounter understanding class subject matter discussed, and stipulates that the professor's duties shall be restricted solely to his teaching activities and not involve him in any religious activities at the College or oblige him to teach any additional studies other than those specified for the Hollis Professor of Mathematics and Natural Philosophy. Furthermore, the rules establish the professor's salary at £80 per year and allow the professor to receive from students, except those students studying theology under the Hollis Professor of Divinity, an additional fee as determined by the Corporation and Board of Overseers, to supplement his income. Moreover, the rules assert that all professorship candidates selected by the Harvard Corporation must be approved by Thomas Hollis during his lifetime or by his executor after his death. Finally, the rules state that the Hollis professor take an oath to the civil government and declare himself a member of the Protestant reformed religion. This document is signed by Thomas Hollis and four witnesses, John Hollis, Joshua Hollis, Richard Solly, and John Williams.

Of the invention of theorems : manuscript, [17--]

Mathematical notes, equations, theorems, and definitions. Probablynot by William Winthrop (Harvard AB 1770) as it is different handwriting and language habits from other of his manuscript.

Rubbing of the gravestone of Harvard librarian Nathaniel Ward made by David S. Ferriero, October 15, 1972

Large rubbing of the gravestone of Nathaniel Ward, librarian of Harvard college for one week in 1768. The rubbing was made by David S. Ferriero, and is signed and dated October 15, 1972 in the lower right corner.

The Opportunity Costs of STEM Degrees and the Unmet Needs of the Low-Skilled: Two labour market problems explained. CEPS Policy Brief No. 295, 26 June 2013

There is general consensus that to achieve employment growth, especially for vulnerable groups, it is not sufficient to simply kick-start economic growth: skills among both the high- and low-skilled population need to be improved. In particular, we argue that if the lack of graduates in science, technology, engineering and mathematics (STEM) is a true problem, it needs to be tackled via incentives and not simply via public campaigns: students are not enrolling in ‘hard-science’ subjects because the opportunity cost is very high. As far as the low-skilled population is concerned, we encourage EU and national policy-makers to invest in a more comprehensive view of this phenomenon. The ‘low-skilled’ label can hide a number of different scenarios: labour market detachment, migration, and obsolete skills that are the result of macroeconomic structural changes. For this reason lifelong learning is necessary to keep up with new technology and to shield workers from the risk of skills obsolescence and detachment from the labour market.

A Stata implementation of the Blinder-Oaxaca decomposition

The counterfactual decomposition technique popularized by Blinder (1973) and Oaxaca (1973) is widely used to study mean outcome differences between groups. For example, the technique is often used to analyze wage gaps by sex or race. The present paper summarizes the technique and addresses a number of complications such as the identification of effects of categorical predictors in the detailed decomposition or the estimation of standard errors. A new Stata command called -oaxaca- is introduced and examples illustrating its usage are given.

Social differentiation of risk: perceptions of the future in drought-prone Central Niger

A snapshot of two Tuareg-dominated 'communes rurales' in the pastoral-agricultural transition zones of Maradi and Tahoua regions, Central Niger, shows that, despite the openly shared 'inevitable natural hazard' drought discourse, risk-taking action in response to drought-related dangers is sharply polarized according to social position. On the one hand the dominant Tuareg minority perceive drought not only as danger for their herds but also as opportunity to increase their political following through the channelling of drought relief benefits to their supporters. On the other hand, the majority of commune households, living on the brink of economic viability, cultivate social links with the dominant families in order to secure access to water, land and humanitarian aid; and household members are forced into more and more frequent and distant out-migration. Certain leaders, well-informed about national land policy and practice, focus their efforts for a better future on the consolidation of community land rights through the promotion of certain sedentarization and land privatization initiatives; however the resulting increased land pressure in key locations may unwittingly expose inhabitants to even worse drought-linked crises in the future. Bibliogr., notes, sum. in English and French