Browsing by Author "Cirillo, Michelle"
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Item Area and Perimeter Geogebra Applet(2015-05-04) Cirillo, MichelleThis applet was designed to be used with the "Mathematics Discourse in Secondary Classrooms" professional development materials. The applet allows the user to explore questions about how the area and perimeter of a triangle interact with one another. The applet works with free Geogrebra open source software which may be downloaded from this site: https://www.geogebra.org/Item Challenges to Teaching Authentic Mathematical Proof in School Mathematics(The Department of Mathematics, National Taiwan Normal University Taipei, Taiwan, 2009) Cirillo, MichelleAs 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.”Item Conceptions and Consequences of What We Call Argumentation, Justification, and Proof(East Lansing, MI: Michigan State University, 2015) Cirillo, Michelle; Kosko, Karl W.; Newton, Jill; Staples, Megan; Weber, Keith; Cirillo, MichelleArgumentation, 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.Item Exploring Side-Side-Angle Triangle Congruence Criterion(2015-05-04) Cirillo, Michelle; Todd, Rachael; Obrycki, JoeWe describe an exploratory task intended to support students’ conceptual understandings of triangle congruence with particular emphasis on the Side-Side-Angle (SSA) case. We reveal how SSA, often dismissed, is actually a challenging an interesting case for exploration.Item “I’m like the Sherpa guide”: On Learning to Teach Proof in School Mathematics(The International Group for the Psychology of Mathematics Education, 2011) Cirillo, MichelleThis 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.Item Supporting the Introduction to Formal Proof(The International Group for the Psychology of Mathematics Education (PME), 2014) Cirillo, MichelleIn 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.