The New Sacred Math

The individual soul is an ageless idea, attested in prehistoric times by the oral traditions of all cultures. But as far as we know, it enters history in ancient Egypt. I will begin with the individual soul in ancient Egypt, then recount the birth of the world soul in the Pythagorean community of ancient Greece, and trace it through the Western Esoteric Tradition until its demise in Kepler's writings, along with the rise of modern science, around 1600 CE. Then I tell of the rebirth of the world soul recently, in new branches of mathematics.     

Teachers' Gender Stereotypes in South Africa: A Case Study

The study investigated Teachers' gender stereotypes in the Eastern Province of South Africa. Participants were 65 Junior Secondary school teachers (females= 40 and males = 25) who assembled together at a seminar organized by the Department of Education. They completed a ten-statement questionnaire on gender stereotypes that would apply to school boys and girls. Data were analysed by means for differences in proportions endorsing stereotypes in relation to school activities. Gender stereotypes were apparent in the pattern of activities endorsed for males and females.     

Putnam, Peano, and the Malin Génie: could we possibly bewrong about elementary number-theory?

This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following (along with Saul Kripke's ‘scepticalsolution’), Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a variant of Descartes' dream scenario – in order to establish the in-principle possibility that we might be deceived by the apparent self-evidence of basic arithmetical truths or that it might be ‘rational’ to doubt them under some conceivable (even if imaginary) set of circumstances. Thus Putnam assumes that mathematical realism involves a self-contradictory ‘Platonist’ idea of our somehow having quasi-perceptual epistemic ‘contact’ with truths that in their very nature transcend the utmost reach of human cognitive grasp. On this account, quite simply, ‘nothing works’ in philosophy of mathematics since wecan either cling to that unworkable notion of objective (recognition-transcendent) truth or abandon mathematical realism in favour of a verificationist approach that restricts the range of admissible statements to those for which we happen to possess some means of proof or ascertainment. My essay puts the case, conversely, that these hyperbolic doubts are not forced upon us but result from a false understanding of mathematical realism – a curious mixture of idealist and empiricist themes – which effectively skews the debate toward a preordained sceptical conclusion. I then go on to mount a defence of mathematical realism with reference to recent work in this field and also to indicate some problems – as I seethem – with Putnam's thought-experimental approach as well ashis use of anti-realist arguments from Dummett, Kripke, Wittgenstein, and others.     

Examining the Relationship Between Mathematics Anxiety and Mathematics Performance: An Instructional Hierarchy Perspective

This study investigated the relationship between mathematics anxiety, fluency, and error rates in basic mathematical operations among college students. College students were assigned to one of two groups (high anxiety or low anxiety) based on results from the Fennema-Sherman Mathematics Anxiety Scale (FSMAS). Both groups were then presented with timed tests in basic mathematical operations (addition, subtraction, multiplication, division, and linear equations). Results suggested that the higher mathematics anxiety group had significantly lower fluency levels across all mathematical operations tests. However, there were no significant differences in error rates between the two groups across any of the probes suggesting that mathematics anxiety is more related to higher levels of learning than to the initial acquisition stage of learning. Discussion focuses on a) stages of learning and their potential relationship to mathematics anxiety, b) the relationship between mathematics anxiety and mathematics performance, and c) directions for future research.     

TOPICAL EPISTEMOLOGIES

Abstract: What is the point of developing an epistemology for a topic—for example, morality? When is it appropriate to develop the epistemology of a topic? For many topics—for example, the topic of socks—we see no need to develop a special epistemology. Under what conditions, then, does a topic deserve its own epistemology? I seek to answer these questions in this article. I provide a criterion for deciding when we are warranted in developing an epistemological theory for a topic. I briefly apply this criterion to moral epistemology and argue that some approaches to moral epistemology should be abandoned. I also argue that we can develop an epistemology for a topic without committing ourselves to a specific substantive theory of justification, such as reliabilism or coherentism, if we work within a suitably neutral framework.     

Predictive model for early math skills based on structural equations

Early math skills are determined by higher cognitive processes that are particularly important for acquiring and developing skills during a child's early education. Such processes could be a critical target for identifying students at risk for math learning difficulties. Few studies have considered the use of a structural equation method to rationalize these relations. Participating in this study were 207 preschool students ages 59 to 72 months, 108 boys and 99 girls. Performance with respect to early math skills, early literacy, general intelligence, working memory, and short‐term memory was assessed. A structural equation model explaining 64.3% of the variance in early math skills was applied. Early literacy exhibited the highest statistical significance (β = 0.443, p < 0.05), followed by intelligence (β = 0.286, p < 0.05), working memory (β = 0.220, p < 0.05), and short‐term memory (β = 0.213, p < 0.05). Correlations between the independent variables were also significant (p < 0.05). According to the results, cognitive variables should be included in remedial intervention programs.     

数学等值概念获得的过渡性学习者认知发展的实验研究

就数学等值概念获得而言,一般地,过渡性学习者在解决简单问题作业时趋向于使用一种正确策略,而当题目较难时则使用几种不同的错误策略。经过针对性的指导（或输入适当信息）后极易掌握此概念,表现为使用一种正确且充分的策略。同时,“言语一手势失匹配”可能不是过渡性学习者的必然的认知特征。