Department of Mathematical Sciences
http://udspace.udel.edu/handle/19716/203
2017-12-12T14:36:57ZChallenges to Teaching Authentic Mathematical Proof in School Mathematics
http://udspace.udel.edu/handle/19716/17350
Challenges to Teaching Authentic Mathematical Proof in School Mathematics
Cirillo, Michelle
As pointed out by Stylianides (2007), a major reason that proof and proving have
been given increased attention in recent years is because they are fundamental to
doing and knowing mathematics and communicating mathematical knowledge.
Thus, there has been a call over the last two decades to bring the experiences of
students in school mathematics closer to the work of practicing mathematicians.
In this paper, I discuss the challenges that a beginning teacher faced as he
attempted to teach authentic mathematical proof. More specifically, I argue that
his past experiences with proof and the curriculum materials made available to
him were obstacles to enacting a practice that was more like what he called “real
math.”
2009-01-01T00:00:00Z“I’m like the Sherpa guide”: On Learning to Teach Proof in School Mathematics
http://udspace.udel.edu/handle/19716/17334
“I’m like the Sherpa guide”: On Learning to Teach Proof in School Mathematics
Cirillo, Michelle
This article describes the experiences of a beginning mathematics teacher, Matt,
across his first three years of teaching proof in a high school geometry course.
Matt’s past experiences with mathematics influenced his beliefs about what he could
and could not do to help his students learn how to prove. During his first year of
teaching proof, Matt claimed that you cannot teach someone to write a proof. Over
time, however, Matt eventually developed some strategies for teaching proof to his
students. Within this work is an interest in learning more about how a teacher learns
to teach proof to students who are just learning how to construct a formal proof. This
case highlights the importance of pedagogical content knowledge.
2011-01-01T00:00:00ZSupporting the Introduction to Formal Proof
http://udspace.udel.edu/handle/19716/17333
Supporting the Introduction to Formal Proof
Cirillo, Michelle
In this study, a tool that worked to support teachers with the introduction to formal proof in geometry is discussed. The tool helped teachers navigate the “shallow end” of proof. More specifically, the tool was shown to support teachers with introducing and scaffolding proof. Findings from this study suggest that the tool may be useful for supporting formal reasoning in geometry as well as other areas.
2014-01-01T00:00:00ZConceptions and Consequences of What We Call Argumentation, Justification, and Proof
http://udspace.udel.edu/handle/19716/17243
Conceptions and Consequences of What We Call Argumentation, Justification, and Proof
Cirillo, Michelle; Kosko, Karl W.; Newton, Jill; Staples, Megan; Weber, Keith
Argumentation, justification, and proof are conceptualized in many ways in extant mathematics
education literature. At times, the descriptions of these objects and processes are compatible or
complementary; at other times, they are inconsistent and even contradictory. The inconsistencies in
definitions and use of the terms argumentation, justification, and proof highlight the need for
scholarly conversations addressing these (and other related) constructs. Collaboration is needed to
move toward, not one-size-fits-all definitions, but rather a framework that highlights connections
among them and exploits ways in which they may be used in tandem to address overarching research
questions. Working group leaders aim to facilitate discussions and collaborations among
researchers and to advance our collective understanding of argumentation, justification and proof,
particularly the relationships among these important mathematical constructs. Working group
sessions will provide opportunities to engage with a panel of researchers and other participants who
approach these aspects of reasoning from different perspectives, as well as to: hear findings from a
recent analysis of these constructs in research; reflect on one’s own work and position it with respect
to the field; and contribute to moving the field forward in this area.
2015-01-01T00:00:00Z