The functional use of a mathematical sign

The question of how a mathematics student at university-level makes sense of a new mathematical sign, presented to her or him in the form of a definition, is a fundamental problem in mathematics education. Using an analogy with Vygotsky's theory (1986, 1994) of how a child learns a new word, I argue that a learner uses a new mathematical sign both as an object with which to communicate (like a word is used) and as an object on which to focus and to organise her or his mathematical ideas (again as a word is used) even before she or he fully comprehends the meaning of this sign. Through this sign usage, I claim that the mathematical concept evolves for that learner so that it eventually has personal meaning, like the meaning of a new word does for a child; furthermore, because the usage is socially regulated, I claim that the concept evolves for the learner so that its usage concurs with its usage in the mathematical community. In line with Vygotsky, I call this usage of the mathematical sign before mature understanding, ‘functional use’. I demonstrate ‘functional use’ of signs (manipulations, imitations, template-matching and associations) through an analysis of an interview in which a mathematics university student engages with a ‘new’ mathematical sign, the improper integral, using pedagogically designed tasks and a standard Calculus textbook as resources.     

Sexuality education： Analysis of Moroccan teachers＇ and future teachers＇ conceptions

Conceptions are analyzed as being the emergences from interactions between three poles： scientific knowledge （K）, values （V） and social practices （P）. The teachers＇ beliefs and values have a direct influence on the way of understanding and teaching a topic. These beliefs must be taken into account in the content and strategies of the teacher＇s formation. In this paper, the authors discuss the importance of studying and analyzing these conceptions and present the results of the research on teachers＇ and future teachers＇ conceptions about sexual health education. In this topic, the conceptions could be deeply rooted not only in scientific knowledge but also in value systems and social practices, because teachers often refuse to teach the ethical, psychological, economic and social issues not strictly reducible to biology, such as sexuality health. The authors used a questionnaire prepared jointly within the European project Biohead-Citizen.     

Religious justification,elitist outcome: are religious schools being used to avoid integration?

Despite ongoing efforts to promote ethnic, racial and socio-economic integration, segregation continues to challenge education administrators and legal scholars. Privileged parents seeking to avoid integration employ various strategies such as attending private schools or buying houses in neighbourhoods with good school. This paper offers a combined empirical and legal research of another such strategy: the resort to religious schools. The research is conducted within one specific context, that of Israeli Religious State Schools. The empirical study examines whether “Torani” religious state schools (a category of religious schools that offer enhanced Jewish studies and a strict religious environment) induce socio-economic segregation. The findings indicate that “Torani” schools are indeed socio-economically segregated and serve children from higher socioeconomic class than regular religious state schools. It also shows that “Torani” schools are less reflective of their surroundings than regular religious state schools, and are more likely to be established by privileged parents in poor areas, where they are dissatisfied with the local state schools. The legal research offers an explanation of how legal regulation can determine whether religious schools will become a means for avoiding integration. Specifically, it points to three areas in which “Torani” schools are regulated differently than regular religious state schools – the rules regarding the establishment of new schools; the rules concerning school funding; and the rules concerning student enrolment – and argues that special treatment meant to protect religious interests is responsible for making “Torani” schools socially segregated.     

Attending to Precision: Mathematical Definitions in Courses for Pre-Service and Practicing Teachers

In this article we address the Common Core State Standard for Mathematical Practice: Attend to Precision. We describe work in mathematics content courses for pre-service and inservice teachers focused on developing teachers’ understanding of mathematical definitions. We discuss teachers’ work in developing definitions for students at various levels of mathematics, in generalizing a definition in order to extend the domain to which it may be applied, and in correcting teachers’ misconceptions. The work discussed in this article is consistent with the recommendations of the Conference Board of the Mathematical Sciences for the mathematics education of teachers. In explicit response to contemporary mathematics education research, the author presents constructive assessment prompts which lend themselves to formal study by mathematics education researchers.     

Perspectives on pedagogical change: instructor and student experiences of a newly implemented undergraduate engineering dynamics curriculum*

Engineering education has been slow to adopt research-based educational innovations. Few prior works on such adoption have investigated the combined classroom experiences of instructors and students when such innovations are being implemented. Therefore, this work focuses on the lived experiences of an instructor and her students when adopting an active, blended, and collaborative learning environment, known as Freeform, in a second-year dynamics course. Weekly reflections from the instructor were processed alongside student interviews using Thematic Analysis to discern prominent themes in their perspectives for comparison and discussion. The results indicate that the instructor navigated internal tensions between her previous instructional preferences and the philosophy and resources of Freeform. Similarly, students had to adapt to this new philosophy and suite of resources that were uncommon for their institution. Ultimately, this work highlights the contextual natures of teaching and learning, and how situational factors can influence educational innovation.     

An evaluation of the Thorndike and Lorge word count

A new emphasis on career education presents significant challenges to the speech‐communication educator. This article examines that emphasis and the accompanying challenges.     

General Mass Communications

Jerry Robinson's The Comics: An Illustrated History of Comic Strip Art (New York: Putnam, 1974—$15.00)

A History of the Comic Strip [Crown, 1968—$3.95, paper]

Perry and Aldridge's The Penguin Book of Comics [Penguin, 1967—$4.95, paper]

Reitberger and Fuchs' Comics: Anatomy of a Mass Medium Little, Brown, 1972— 6.95, paper—this last is discussed in 4:6:4 ; of which the latter appears the best competition to this new volume)

Arthur Asa Berger's The Comic-Stripped American (Baltimore: Penguin Books, 1974—$2.95, paper)

Eli M. Oboler's The Fear of the Word: Censorship and Sex (Metuchen, N.J.: Scarecrow Press, 1974—$10.00)

The Annals of the American Academy of Political and Social Science (3937 Chestnut St., Philadelphia, Pa. 19104—$4.00/3.00 per issue)

Ted Klein and Fred Danzig's How to Be Heard: Making the Media Work for You (New York: Macmillan, 1974—$9.95)

Douglas R. Berdie and John F. Anderson's Questionnaires: Design and Use (Metuchen, N.J.: Scarecrow Press, 1974—$7.50)

S.H. Steinberg's Five Hundred Years of Printing (Baltimore: Penguin Books, 1974— $3.25, paper)