The Nctm Standards and the Philosophy of Mathematics

It is argued that the philosophical and epistemological beliefs about the nature of mathematics have a significant influence on the way mathematics is taught at school. In this paper, the philosophy of mathematics of the NCTM's Standards is investigated by examining is explicit assumptions regarding the teaching and learning of school mathematics. The main conceptual tool used for this purpose is the model of two dichotomous philosophies of mathematics-absolutist versus- fallibilist and their relation to mathematics pedagogy. The main conclusion is that a fallibilist view of mathematics is assumed in the Standards and that most of its pedagogical assumptions and approaches are based on this philosophy.     

A computerized test for the assessment of mild cognitive impairment subtypes in sentence processing

This study examines thesentence processing ability of mild cognitive impairment (MCI) subtypes. In addition to standard MCI neuropsychological tests, an experimental approach was applied to assess language. 133 people (93 MCI/40 controls) participated in novel computerized sentence processing tasks. Results presented statistically significant differences between MCI/controls andMCI subtypes (ANOVA):(a) duration F(2,92) = 19.259,p < .001) in sentence construction; (b) correct answers (F(2, 89) = 8.560,p < .001) and duration (F2,89) = 15.525,p < .001)in text comprehension; (c) correct answers (F(2, 92) = 8.975,p < .001) andduration (F(2, 92) = 4.360,p = .016) in metaphoric sentences comprehension; (d) correct answers (F(2, 92) = 12.836,p < .001) andduration (F(2, 92) = 10.974,p < .001) in verb form generation. Subtle changes in MCIsubtypes could affect sentence processing and provide useful information for cognitive decline risk estimation and screening purposes.     

Emotional and learning behaviour in mice overexpressing heat shock protein 70

The effects of inducible heat shock protein 70 (HSP70) on emotional and learning behaviour as well as hippocampal long-term potentiation was investigated in transgenic HSP70 overexpressing mice. In active two-way avoidance learning (shuttle box) as well as spatial 8-arm radial maze learning, the HSP70 overexpressing mice showed diminished learning performance. In several tests there was no indication of differences in anxiety behaviour between transgenic mice and wild-type mice. This suggests that impairment in learning behaviour is unrelated to the learning task and motivational aspects of behaviour. To investigate the neurophysiological correlate of learning, long-term potentiation experiments were performed. In transversal hippocampal slices, an enhanced amplitude of the population spike was found in HSP70 overexpressing mice. It was hypothesised that enhanced potentiation in conjunction with potentiation effects due to learning led to learning impairment.     

Anxiety and depression in cataract surgery: a pilot study in the elderly

To assess anxiety induced by a planned cataract surgery and to evaluate the correlations of rated anxiety and depression with optical acuity pre- and post-operatively, 278 patients ages 65 years or older were tested. Patients were divided into two groups: first-eye and second-eye cataract surgery. Anxiety and depression were evaluated using the Hamilton's Rating Scales for Anxiety and Depression, respectively. Pre-operatively, first-eye patients showed significantly higher anxiety than second-eye patients (F1,251 = 75.39, p < .001). First-eye patients rated peak anxiety on the day of the surgery, while patients scheduled for second-eye cataract surgery presented no fluctuations in rated anxiety (F1,251 = 49.60, p < .001). There was no correlation of preoperative anxiety or depression with the outcome of surgery (F(1,251)s = .83 and .58, respectively, p > .05). Postoperatively, anxiety and depression in patients without any improvement in their vision were rated significantly higher than in those presenting improved visual acuity after surgery (F1,251 = 566.17 and 300.25, respectively, p < .001).     

Ideas and processes in mathematics: A course on history and philosophy of mathematics

This paper describes an attempt to develop a program for teaching history and philosophy of mathematics to inservice mathematics teachers. I argue briefly for the view that philosophical positions and epistemological accounts related to mathematics have a significant influence and a powerful impact on the way mathematics is taught. But since philosophy of mathematics without history of mathematics does not exist, both philosophy and history of mathematics are necessary components of programs for the training of preservice as well as inservice mathematics teachers.