Semantic structures of one-step word problems involving multiplication or division

From classifications of word problems in international discussion of elementary mathematics instruction as well as from conceptual elaborations of didactical analyses in Germany, a classification of semantic structures of one-step word problems involving multiplication or division is proposed, comprehending four main classes: Forming the n-th multiple of measurers, combinatorial multiplication, composition of operators, and multiplication by formula. This classification is more comprehensive and differentiated than the classifications of Vergnaud (1983), Nesher (1988), and Bellet al. (1989) — aiming at a better assignment between diverse contextual circumstances and conceptual demands of mathematics and at compatibility with the well-known semantic structures of addition and subtraction word problems.     

Delayed discriminations in the pigeon: The role of within-trial location of conditional cues

Four pigeons were trained in a delayed conditional discrimination in which color and line cues jointly indicated trial outcome. These were either combined in advance of a retention interval (RI) or separately presented before and after the RI. The former procedure resulted in less forgetting over the RI, the difference increasing with longer RIs. In a second study, the line cue was presented redundantly before and after the RI, and then selectively omitted from either temporal location during probe tests. In general, the results indicated that the birds relied upon the line as a cue to a greater extent when it was compounded with the color in advance of the RI than when it was presented after the RI. The data support an interpretation based on anticipatory processing in working memory, which leads to better retention than retrospective remembering.     

Mechanismen der Elitebildung im deutschen Bildungssystem

The German education system is currently experiencing two contrasting trends: On the one hand, social opening, e.g. through the introduction of a partially-integrated secondary school system, compensatory all-day-schooling. On the other hand, an increasing vertical hierarchy in certain educational phases, e.g. through the explicitly encouraged introduction of private kindergartens and primary schools and the establishment of prime (academic track) Gymnasien and elite universities. In line with these structural changes, next to equality, the principle of excellence is gaining an increasing significance as a justification argument. This contribution will present the situation from an education-policy perspective, discuss theoretical discourses, and the national and international state of research on the topic of elitism and education. It will close with future research challenges.     

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Ohne Zusammenfassung     

ICMI Study 14: Applications and modelling in mathematics education – Discussion document

This paper is the Discussion Documentfor a forthcoming ICMI Study on Applications and Modelling in MathematicsEducation. As will be well-known, fromtime to time ICMI (the InternationalCommission on Mathematical Instruction)mounts specific studies in order toinvestigate, both in depth and in detail,particular fields of interest inmathematics education. The purpose of thisDiscussion Document is to raise someimportant issues related to the theory andpractice of teaching and learningmathematical modelling and applications,and in particular to stimulate reactionsand contributions to these issues and tothe topic of applications and modelling asa whole (see Section 4). Based onthese reactions and contributions, alimited number (approximately 75) ofparticipants will be invited to aconference (the Study Conference)which is to take place in February 2004 inDortmund (Germany). Finally, using thecontributions to this conference, a bookwill be produced (the Study Volume)whose content will reflect thestate-of-the-art in the topic ofapplications and modelling in mathematicseducation and suggest directions for futuredevelopments in research and practice.The authors of this Discussion Document are themembers of the International ProgrammeCommittee for this ICMI Study. Thecommittee consists of 14 people from 12countries, listed at the end of Section4. The structure of the Document isas follows. In Section 1, we identifysome reasons why it seems appropriate tohold a study on applications and modelling.Section 2 sets a conceptual frameworkfor the theme of this Study, and Section3 contains a selection of importantissues, challenges and questions related tothis theme. In Section 4 we describepossible modes and ways of reacting to theDiscussion Document, and in the finalSection 5 we provide a shortbibliography relevant to the theme of thisStudy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations

In this study which was part of the DISUM-project, 224 ninth graders from 14 German classes from middle track schools (Realschule) were asked about their enjoyment, interest, value and self-efficacy expectations concerning three types of mathematical problems: intra-mathematical problems, word problems and modelling problems. Enjoyment, interest, value and self-efficacy were assessed before and after a ten-lesson teaching unit promoting modelling competency related to the topics “Pythagoras’ theorem” and “linear functions”. The study aimed to answer the following research questions: (1) Do students’ enjoyment, value, interest and self-efficacy expectations differ depending on the type of task? (2) Does the treatment of modelling problems in classroom instruction influence these variables? (3) Are there any differential effects for different ways of teaching modelling problems, including a “directive”, teacher-centred instruction and an “operative-strategic”, more student-centred instruction emphasising group work and strategic scaffolding by the teacher? The findings show that there were no differences in students’ enjoyment, interest, value and self-efficacy between the three types of tasks. However, teaching oriented towards modelling problems had positive effects on some of the student variables, with the student-centred teaching method producing the most beneficial effects.     

Knowledge management supporting education and research at a university cleanroom

At the university, each institute or chair can be seen as a small independent enterprise in respect of education and research. For this reason, the efficiency of management as well as the improvement of education and research within this unit is more and more at a premium. The students need a good working environment and the opportunity to gain and share information in order to carry out successful research and course work. This paper shows how education at a university semiconductor laboratory can be improved by using a content management system to build a knowledge management system. The structuring and implementation will be shown as well as students’ rating of it. The results support the conclusion that the knowledge base is a great step forward for improving education and research in a complex environment.     

The relative age effect in youth soccer across Europe

The potential asymmetries in the birth-date distributions of youth soccer players across ten European countries (2175 age citations) were considered. First, we examined the birth-dates of players representing national youth teams in international competitions. Second, the birth-dates of players representing professional club teams in international youth tournaments were analysed. Kolmogorov-Smirnov tests were used to assess differences between observed and expected birth-date distributions. Regression analyses were employed to examine the relationship between month of birth and number of players in the different samples. The results showed an over-representation of players born in the first quarter of the selection year (from January to March) for all the national youth selections at the under-15 (U-15), U-16, U-17 and U-18 age categories, as well as for the UEFA U-16 tournaments and Meridian Cup. Players with a greater relative age are more likely to be identified as "talented" because of the likely physical advantages they have over their "younger" peers. Some options for reducing the relative age effect are offered.