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Mathematics as the reading suggests posses many characteristics, being derived from individual genius but thriving only when the culture or wider community as described by the text accepts the principles and applications surrounding it (p. 64). Individual discovery alone however, is not responsible for mathematics. The text also notes that economic and social forces can stimulate mathematical discovery. Mathematical discovery however, is something that persists regardless of the historical time or culture dominating. The text notes that many theorists favor the "doctrine of culture" so one must acknowledge the influence culture has on discovery. The text suggests the dichotomy between the individual and the doctrine of the culture is false, an argument similar to that of mind over matter; one can conclude simply that individuals may matter temporarily but culture dominates the field of mathematics over wider time periods. That culture is inextricably linked to mathematical inquiry is a fact that can't be denied (Saxe, 1991). Wang (1963) notes that it is important however,...
He notes Euclid's fifth postulate which was found later to be false, which Pasch (1882) pointed out when confirming the shortcomings in this once accepted axiomatization (Wang, 1963, p.2). Euclid's axioms were at first however, regarded as completed logical and necessary. However as times changed, especially during the Renaissance for example, controversy existed over the axiom and axiomatic systems in particular, giving rise to questions regarding the legitimacy of the axioms formulated by Euclid (Wang, 1963).
References
Merlan, P. & Shafarevitch, I.R. "Unorthodoxies." In, The Individual and the Culture.
Saxe, Geoffrey B. Culture and Cognitive Development Studies in Mathematical
Understanding. Hillsdale: Lawrence Erlbaum Associates. (1991).
Wang, Hao. A Survey of Mathematical Logic. Peking, Science Press. 1963.
Balacheff (1987) described four levels of justification, which are those as follows: (1) Native empiricism; 2) Crucial experiment; 3) Generic example; and 4) Thought experiment. (Taflin, nd) Naive empiricism is stated to be "an assertion based on a small number of cases." (Taflin, nd) Crucial experiment is stated to be "an assertion based on a particular case, but the case was used as an example of a class of objects." (Taflin, nd) the
SIAM's mission is to build cooperation between mathematics and the worlds of science and technology through its publications, research, and community. Over the last 50 years SIAM's goals have remained constant: • They want to advance the application of mathematics and computational science to engineering, industry, science, and society. • To was to promote research that will lead to effective new mathematical and computational methods and techniques for science, engineering, industry,
Mathematics Teaching Learners Studying Basic Mathematics To Enable Helping Their Children With Their Education The work of Jackson and Ginsburg (2008) reports on a series of algebra classes involving a group of African-American mother and elementary-aged children, who are low income and who "had limited and negative formal experiences with algebra." (p. 10) The women in the study who arrived to the algebra classes are reported to have had "well-informed view of
In an open-ended study of 42 teachers decided to leave with the peer assistance being a contributing factor while in another research carried out with 99 teachers, only 4 said that the peer assistance was one of the decisive factors (Billingsley et al., 1993 & 1995). Some of the factors for the variation in these studies could be the way the teachers were asked these questions (like, open-ended polls vs.
For instance, classical mathematicians by definition rely on Plato's theory of forms as the underlying basis of their mathematical worldview. The Platonist assumes the existence of true, immutable, and universal forms and structures that the mathematician approaches through the language of numbers and equations. For instance, the classical mathematician holds to the Platonic belief in the expansion of pi; to approach the expansion of pi from any other perspective
MATHEMATICS Mathematics: Career in MathematicsSlide 1: PHASE 1 (The Portfolio)Table 1: The selected career (an economist) and its relevant informationJob description: Necessary educationBachelors in Math, but some private jobs ask for higher-level degrees like Ph.D.Job description: What classes are requiredMath, Stats, Calculus, and EconomicsJob description: Tests or classes requiredThe classes required are advanced calculus, linear algebra, differential equations, and basic probability theory. No specific Math test is required other than