The notion of a chainable continuum was introduced by R. L. Moore in [10] (see also [11]); and, in [12], J. H. Roberts showed that any chainable plane continuum has uncountably many disjoint images in the plane. More recently, Moise and Bing used a certain chainable continuum, the pseudo arc, as an example to settle two questions of considerable interest, ([3] and [9]). In [5] Bing defines the notion of a snakelike continuum and shows that it is equivalent to the earlier notion of chainable plane continuum and makes a study of some of the properties of snakelike continua. Recently, Henderson, [7], makes use of the structure of decomposable snakelike continuum to obtain the result that the only decomposable continuum homeomorphic to each of its proper subcontinua is the arc. However, all but one of the fifteen theorems in his paper contain the hypothesis that the set considered is (by his result) an arc.13. W. A. WILSON, On the structure of a continuum, limited and irreducible between two points,
Constructivism is currently a hotly debated topic, with proponents and opponents equally adamant and emotional with respect to their viewpoints. Many misconceptions exist on both sides of the debate, and misuses of terminology and attribution are rampant. Constructivism is a theory of learning, not a particular approach to instruction and not a curriculum. Proponents, the majority of whom are involved in K-12 education, argue that reaching more students with a deeper understanding of mathematics requires an appreciation of how knowledge is constructed and an instructional approach that more fully acknowledges the students' roles as active participants in the classroom instruction, rather than the lecture method which has worked well for some but poorly for others. The opponents, many of whom are mathematicians, tend to equate constructivism with "discovery" learning and deem it as inefficient at best, and tolerating inaccurate mathematics at worst. However, many mathematicians, including those who criticize constructivism, revere R. L. Moore as an outstanding teacher of mathematics. The Moore Method and the Modified Moore Method are frequently cited [2] as exemplary in the literature on teaching undergraduate-and graduate-level mathematics. An analysis of his method of teaching, however, indicates adherence to a theory of learning which he did not necessarily articulate, and might even have disputed. The goal of this article is to show that Moore's method aligned with a constructivist approach.
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