Taking away and determining the difference—a longitudinal perspective on two models of subtraction and the inverse relation to addition

Subtraction can be understood by two basic models—taking away (ta) and determining the difference (dd)—and by its inverse relation to addition. Epistemological analyses and empirical examples show that the two models are not relevant only in single-digit arithmetic. As curricula should be developed in a longitudinal perspective on mathematics learning processes, the article highlights some exemplary steps in which the inverse relation is discussed in light of the two models, namely mental subtraction, the standard algorithms for subtraction, negative numbers and manipulations for solving algebraic equations. For each step, the article presents educational considerations for fostering a flexible use of the two models as well as of the inverse relation between subtraction and addition. In each section, a mathe-didactical analysis is conducted, empirical results from literature as well as from our own case studies are presented and consequences for teaching are sketched.     

The dream of education

Due to the indeterminacy inherent to anthropology and the necessity of human selfdesign, the dream of education is as necessary as education itself. The dream swirls about the realities of life and education; the dream supplements reality, corrects it, satisfies its unfulfilled desires; the dream penetrates reality, evades it, transcends it; it designs contrafactual modifications and alternatives. Yet, the question remains open as to what dreams are dreamed and which forms of education are realized in a particular society, and in a historical period. The difference between the dream and educational reality is irrevocable; it corresponds with the difference between the imaginary and the real. There is a tangible hiatus between imagination and reality, which, by exposing the limits of the possibilities of education to change human reality, and by revealing the limits to which humans can be educated, gives rise to ever-new compensatory dreams as well as nightmares of education.     

Learning styles and their impact on cross-cultural training: An international comparison in France, Germany and Quebec

Every person has his or her own individual way to learn and to solve problems in day-to-day situations. These personal cognitive strategies, acquired in a long socialization process are called “learning styles” and may differ depending on gender, age or culture.In this study, the learning styles of over 300 students in business administration in France, Germany and Quebec are examined with the Learning Style Inventory (LSI). Representative and significant learning differences where found. This is why the LSI can be used in a first step for the illustration and comparison of typical patterns of learning. In a second step the results may be of use to international trainers in making decisions about course design and methods of cross-cultural training in relation to the learning profiles of the participants.     

Faecal calprotectin in the diagnosis of inflammatory bowel disease

Suspicion of inflammatory bowel disease should be raised in any patient with chronic or recurrent abdominal pain and diarrhoea. However, symptoms of inflammatory bowel disease (IBD) overlap with functional gastrointestinal disorders and those patients may not need endoscopy. Currently, colonoscopy with multiple biopsies is considered the gold standard to establish the diagnosis of IBD. Unfortunately, patient selection for endoscopy based on symptoms is not reliable. The use of guidelines of appropriateness for endoscopy yields significantly more significant findings but the selection criteria suffer from low specificity. Calprotectin is a calcium binding protein of neutrophil granulocytes that correlates well with neutrophil infiltration of the intestinal mucosa when measured in faeces. In the last decade, a large body of evidence on the diagnostic value of faecal calprotectin has accumulated and measurement of calprotectin in faeces has been suggested as a surrogate marker of intestinal inflammation. Testing of faecal calprotectin has been highly useful to distinguish organic from functional intestinal disorders in patients with abdominal complaints. Additionally, faecal calprotectin has reliably identified colonic inflammation in patients with suspected IBD. The use of this inexpensive and widely available test in the evaluation and risk stratification in patients with abdominal complaints is likely to increase in the future.     

Adolescent Learning in the Zoo: Embedding a Non-Formal Learning Environment to Teach Formal Aspects of Vertebrate Biology

The aim of this study was to assess the outcome of a zoo visit in terms of learning and retention of knowledge concerning the adaptations and behavior of vertebrate species. Basis of the work was the concept of implementing zoo visits as an out-of-school setting for formal, curriculum based learning. Our theoretical framework centers on the self-determination theory, therefore, we used a group-based, hands-on learning environment. To address this questions, we used a treatment—control design (BACI) with different treatments and a control group. Pre-, post- and retention tests were applied. All treatments led to a substantial increase of learning and retention knowledge compared to the control group. Immediately after the zoo visit, the zoo-guide tour provided the highest scores, while after a delay of 6 weeks, the learner-centered environment combined with a teacher-guided summarizing scored best. We suggest incorporating the zoo as an out-of-school environment into formal school learning, and we propose different methods to improve learning in zoo settings.