NOMAD, June 2008

As we are about to shift from June to July, it is time to point your attention to the June issue of NOMAD (Nordic Studies in Mathematics Education). The issue contains an interesting editorial concerning the development of the journal, some information from Barbro Grevholm about the Nordic graduate school in mathematics education, and three research articles:

• Matematikopfattelser hos 2g’ere: fokus på de ‘tre aspekter‘ by Uffe Thomas Jankvist. Abstract: Based on the so-called ‘three aspects‘ from the 1987-regulations for the Danish upper secondary mathematics programme this article discusses second-year upper secondary students’ beliefs about the nature of mathematics. That is to say, it investigates the students’ beliefs concerning the historical evolution of mathematics, the application of mathematics in society, and the inner structures of mathematics as a scientific discipline. Firstly, the article examines the origin of the ‘three aspects‘ as well as the role they play in both the KOM-project of 2002 and the new regulations for the Danish upper secondary mathematics programme of 2007. Secondly, it discusses how the students in a concrete second-year class of upper secondary level seem to fulfil the goals of the ‘three aspects’. Thirdly, the results of this study are compared to a similar study from 1980 and differences and similarities between the two are discussed. It is concluded that there still is room for improvement concerning the fulfilment of the three aspects, and that the students’ beliefs in the 1980-study and in the 2007-study are very similar. In the end, the article speculates upon why the ‘three aspects’ do not seem to have had a larger impact on the mathematics teaching on upper secondary level when they have been in the regulations for twenty years now.
• Interrater reliability in a national assessment of oral mathematical communication by Torulf Palm. Abstract: Mathematical communication, oral and written, is generally regarded as an important aspect of mathematics and mathematics education. This implies that oral mathematical communication also should play a part in various kinds of assessments. But oral assessments of subject matter knowledge or communication abilities, in education and elsewhere, often display reliability problems, which render difficulties with their use. In mathematics education, research about the reliability of oral assessments is comparably uncommon and this lack of research is particularly striking when it comes to the assessment of mathematical communication abilities. This study analyses the interrater reliability of the assessment of oral mathematical communication in a Swedish national test for upper secondary level. The results show that the assessment does suffer from interrater reliability problems. In addition, the difficulties to assess this construct reliably do not seem to mainly come from the communication aspect in itself, but from insufficiencies in the model employed to assess the construct.
  
• Finnish mathematics teacher students’ informal and formal arguing skills in the case of derivative by Antti Viholainen. Abstract: In this study, formal and informal reasoning skills of 146 Finnish subject-teacher students in mathematics are investigated. The students participated in a test in which they were asked to argue two claims concerning derivative both informally and formally. The results show that the success in the formal tasks and the success in the informal tasks were dependent. However, there were several students who did well in the formal tasks despite succeeding poorly in the informal tasks. The success both in the formal tasks and in the informal tasks was dependent also on the amount of passed studies in mathematics and on the success in these studies. Moreover, these factors could have a stronger effect on the formal than on the informal reasoning skills.