Zobrazeno 1 - 10
of 32
pro vyhledávání: '"John S. Caughman"'
Publikováno v:
Educational Studies in Mathematics. 103:173-189
There is a longstanding conversation in the mathematics education literature about proofs that explain versus proofs that only convince. In this essay, we offer a characterization of explanatory proofs with three goals in mind. We first propose a the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f59956d4b4c7d25f2f66646e9af5988e
https://doi.org/10.1007/s10649-020-09933-8
https://doi.org/10.1007/s10649-020-09933-8
Autor:
Ari J. Herman, John S. Caughman
Publikováno v:
Symmetry
Volume 13
Issue 2
Symmetry, Vol 13, Iss 179, p 179 (2021)
Volume 13
Issue 2
Symmetry, Vol 13, Iss 179, p 179 (2021)
In this paper, we show that Zermelo&ndash
Fraenkel set theory with Choice (ZFC) conflicts with basic intuitions about randomness. Our background assumptions are the Zermelo&ndash
Fraenekel axioms without Choice (ZF) together with a fragment
Fraenkel set theory with Choice (ZFC) conflicts with basic intuitions about randomness. Our background assumptions are the Zermelo&ndash
Fraenekel axioms without Choice (ZF) together with a fragment
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6e427bf616a37287529d86359e5a2465
Publikováno v:
Discrete Mathematics. 341:138-142
Let v > k > i be non-negative integers. The generalized Johnson graph, J ( v , k , i ) , is the graph whose vertices are the k -subsets of a v -set, where vertices A and B are adjacent whenever | A ∩ B | = i . In this article, we derive general for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c11ac7a5a6f8e45e2e430a00860bdae6
https://doi.org/10.1016/j.disc.2017.08.022
https://doi.org/10.1016/j.disc.2017.08.022
Publikováno v:
Graphs and Combinatorics. 33:321-333
In Krussel et al. (ARS Comb 57:77---82, 2000), Krussel, Marshall, and Verall proved that whenever $$2n-1$$2n-1 is a prime of the form $$8m+7$$8m+7, there exists a spanning tree decomposition of $$K_{2n}$$K2n orthogonal to the 1-factorization $$GK_{2n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dd0ccd8fa85165772a78bf52e6db467e
https://doi.org/10.1007/s00373-017-1766-7
https://doi.org/10.1007/s00373-017-1766-7
Publikováno v:
International Journal of Research in Undergraduate Mathematics Education. 3:381-416
The multiplication principle serves as a cornerstone in enumerative combinatorics. The principle underpins many basic counting formulas and provides students with a critical element of combinatorial justification. Given its importance, the way in whi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7a35202e59774181a1cca3cf5a1e8c9c
https://doi.org/10.1007/s40753-016-0045-y
https://doi.org/10.1007/s40753-016-0045-y
Autor:
John S. Caughman, Elise Lockwood
Publikováno v:
PRIMUS. 26:143-157
To further understand student thinking in the context of combinatorial enumeration, we examine student work on a problem involving set partitions. In this context, we note some key features of the multiplication principle that were often not attended
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::69214f8b253ee157ce19d6dd77ab2cc6
https://doi.org/10.1080/10511970.2015.1072118
https://doi.org/10.1080/10511970.2015.1072118
Publikováno v:
International Journal of Research in Undergraduate Mathematics Education. 1:27-62
Counting problems provide an accessible context for rich mathematical thinking, yet they can be surprisingly difficult for students. To foster conceptual understanding that is grounded in student thinking, we engaged a pair of undergraduate students
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a7f6b88d34225c4bf4682646f8af323f
https://doi.org/10.1007/s40753-015-0001-2
https://doi.org/10.1007/s40753-015-0001-2
Publikováno v:
Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers ISBN: 9783319992136
The previous two chapters drew insights from studies featuring very different methodologies, but focused on very similar types of connections between abstract algebra and preservice teacher education. A central idea of each chapter was the way that p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9a269259ea2fe5fc1657a64c781f4087
https://doi.org/10.1007/978-3-319-99214-3_4
https://doi.org/10.1007/978-3-319-99214-3_4
Autor:
John S. Caughman IV1
Publikováno v:
Graphs & Combinatorics. Mar2004, Vol. 20 Issue 1, p47-57. 11p.
Publikováno v:
The Journal of Mathematical Behavior. 32:743-760
As part of an effort to scale up an instructional innovation in abstract algebra, several mathematicians have implemented an inquiry-oriented, group theory curriculum. Three of those mathematicians (co-authors here) also participated in iterative rou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e6e81dff42da9d7ebf0e97eef7735087
https://doi.org/10.1016/j.jmathb.2013.03.003
https://doi.org/10.1016/j.jmathb.2013.03.003