Analyzes the evolution of Chinese national examinations with the "catastrophe" model. Goals, content, form, and process of exams were influenced by social and political forces. Competence over 4,000 years of Chinese history was defined as military prowess, Confucian-style scholarship, Western-style military expertise, proletarian…

The focus is on the metacognitive awareness of ten high-achieving high school pupils in mathematics in Denmark and England and their understanding of their cognitive learning processes and strategies. Mainly unstructured focus group interviews investigate how they explain that they learn a mathematical concept that is new to them. I develop the…

We first discern three different sources to describe the non-modelling-friendly environment in Taiwan: the background of mathematics teachers and students, examinations and textbooks. Under such unfriendly circumstances, how one can implement the teaching and learning of mathematical modelling is explored. In this paper, we focus on the analysis…

We noticed that when workers try to explain their mathematical practices to inquisitive outsiders, breakdowns in communication arise. We present here an example in which a worker spontaneously uses metaphors and models to facilitate explanation and communication. We analyse these, drawing on Lakoff & Johnson (1999) and Lakoff & Nunez…

Given the current and widespread practical interest in mathematical understanding, particularly with respect to higher order thinking skills, curriculum reform advocates in many countries cite the need for teaching mathematics with understanding. However, the characterization of understanding in ways that highlight its growth, as well as the…

Criticizes the current method of formalization in Italian schools and the use of tools of the mathematical method. Proposes a general three-stage formalization method which can used for physical quantities, the particular significance of certain quantities, and the description and interpretation of phenomena. (TW)

Using an input-output framework, the author derives hypotheses on wage differentials based on the assumption that human capital (in this case, education) will explain workers' wage differentials. The hypothetical wage differentials are tested on data from the Italian economy. (RW)

A powerful way of understanding something new is by analogy with something already known. An analogy is defined as a mapping from one structure, which is already known (the base or source), to another structure that is to be inferred or discovered (the target). The research community has given considerable attention to analogical reasoning in the…

Geometric axioms are discussed in terms of philosophy, history, refinements, and basic concepts. The triumphs and limitations of the formalism theory are included. Described is the status of high school geometry internationally. (KR)