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We report on a case study that seeks to understand how teachers’ pedagogical interventions influence students’ instrumentation and mathematical reasoning in a collaborative, dynamic geometry environment. A high school…
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Rich tasks can be vehicles for productive mathematical discussions. How to support such discourse in collaborative digital environments is the focus of our theorization and empirical examination of task design that emerges…
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To contribute to understanding how teachers can develop geometrical understanding, we report on the discursive development of teachers’ geometrical reasoning through instrument appropriation while collaborating in an…
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Tasks can be vehicles for productive mathematical discussions. How to support such discourse in collaborative digital environments is the focus of our theorization and empirical examination of task design that emerges from…
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This article examine geometry teachers' perspectives regarding realistic contexts during a lesson study cycle. I ask the following. (a) What are the participants' perspectives regarding realistic contexts that elicit…
Scaffolding Scientific Thinking: Students’ Evaluations and Judgments During Earth Science Knowledge Construction
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The present paper documents a quasi-experimental study where high school Earth science students completed these instructional scaffolds, including an explanation task scored for evaluative levels (erroneous, descriptive,…
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Shifting people’s judgments toward the scientific involves teaching them to purposefully evaluate connections between evidence and alternative explanations.
Shifting people’s judgments toward the…
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Use these ideas to diagnose and address common conceptual obstacles that inhibit students’ success.
Cirillo, M. & Hummer, J. (2019). Addressing misconceptions in secondary geometry proof.…
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Linear Algebra and Geometry is aimed at preservice and practicing high school mathematics teachers and advanced high school students looking for an addition to or replacement for calculus. The materials are organized…
Poster
High School
Geometry
Mathematics
Michelle Cirillo
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Presentation slides and handout from the 2019 NCTM Regional Conference in Nashville, TN.
Presentation slides and handout from the 2019 NCTM Regional Conference in Nashville, TN…
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Students who earned high marks during the proof semester of a geometry course were interviewed to understand what high-achieving students actually took away from the treatment of proof in geometry. The findings suggest…
Competencies and Behaviors Observed When Students Solve Geometry Proof Problems: An Interview Study with Smartpen Technology
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This peer-reviewed research journal publication addresses one of the grant goals with respect to how students performed on a set of proof tasks.
This peer-reviewed research journal publication addresses…
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In this collection of materials, four geometric topics are covered in animated, digital materials. There are also paper-based materials for the four geometric topics: Angles, Transformations, Pythagorean Theorem, and…
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There is strong empirical evidence in support of learning from comparisons in mathematics education research. The Animated Contrasting Cases in Geometry project seeks to extend this research and transform the learning of…
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This study examines technology-enhanced teacher responses and students’ written mathematical explanations to understand how to support effective teacher responding and the centering of students’ mathematical ideas.…
Speak Up or Stay Silent: How Does Teachers’ Verbal Participation in a Professional Development Programme Relate to Instructional Outcomes?
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Like classrooms, professional development (PD) workshops can be organised as dialogic and inclusive spaces, where the verbal contributions of the participants are critical for driving the inquiry and meeting the intended…
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Jiang, Z., White, A. & Rosenwasser, A. (2011). Randomized Control Trials on the Dynamic Geometry Approach. Journal of Mathematics Education at Teachers College, Vol. 2, No. 2.
ABSTRACT:
The project reported…
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A four-year research project funded by NSF examines the efficacy of an approach to high school geometry that utilizes dynamic geometry (DG) software and supporting instructional materials to supplement ordinary…
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A symmetric polynomial is a polynomial in one or more variables in which swapping any pair of variables leaves the polynomial unchanged. For example, f(x, y, z) = xy +xz + yz is a symmetric polynomial. If we interchange…