Geometry

Engaging Students with Non-routine Geometry Proof Tasks

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 that students had turned proving into a rote task, whereby they expected to mark a diagram and prove two triangles congruent.

Author/Presenter: 
Michelle Cirillo
Lead Organization(s): 
Year: 
2018
Short Description: 

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 that students had turned proving into a rote task, whereby they expected to mark a diagram and prove two triangles congruent.

Building Mathematical Knowledge for Teaching Proof in Geometry

Presentation slides and handout from the 2019 NCTM Regional Conference in Nashville, TN.

Author/Presenter: 
Michelle Cirillo
Lead Organization(s): 
Year: 
2019
Short Description: 

Presentation slides and handout from the 2019 NCTM Regional Conference in Nashville, TN.

Linear Algebra and Geometry

Linear Algebra and Geometry is organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field. 

Author/Presenter: 
Al Cuoco
Kevin Waterman
Bowen Kerins
Elena Kaczorowski
Michelle Manes
Year: 
2019
Short Description: 

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 around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field.

Addressing Misconceptions in Secondary Geometry Proof

Cirillo, M. & Hummer, J. (2019). Addressing misconceptions in secondary geometry proof. Mathematics Teacher, 112(6).

Author/Presenter: 
Michelle Cirillo
Jenifer Hummer
Lead Organization(s): 
Year: 
2019
Short Description: 

Use these ideas to diagnose and address common conceptual obstacles that inhibit students’ success.

Thinking scientifically in a changing world

Shifting people’s judgments toward the scientific involves teaching them to purposefully evaluate connections between evidence and alternative explanations.

Lombardi, D. (2019). Thinking scientifically in a changing world. Science Brief: Psychological Science Agenda, 33(1). Retrieved from https://www.apa.org/science/about/psa/2019/01/changing-world.aspx

Author/Presenter: 
Doug Lombardi
Lead Organization(s): 
Year: 
2019
Short Description: 

Shifting people’s judgments toward the scientific involves teaching them to purposefully evaluate connections between evidence and alternative explanations.

Scaffolding scientific thinking: Students’ evaluations and judgments during Earth science knowledge construction

Critical evaluation underpins the practices of science. In a three-year classroom-based research project, we developed and tested instructional scaffolds for Earth science content in which students evaluate lines of evidence with respect to alternative explanations of scientific phenomena (climate change, fracking and earthquakes, wetlands and land use, and formation of Earth’s Moon).

Author/Presenter: 
Doug Lombardi
Janelle M. Bailey
Elliot S. Bickel
Shondricka Burrell
Lead Organization(s): 
Year: 
2018
Short Description: 

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, relational, and critical), along with measures of plausibility reappraisal and knowledge.

Teachers' Understandings of Realistic Contexts to Capitalize on Students' Prior Knowledge

The theory of realistic mathematics education establishes that framing mathematics problems in realistic contexts can provide opportunities for guided reinvention. Using data from a study group, I 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 students' prior knowledge? (b) How are the participants' perspectives of realistic contexts related to teachers' instructional obligations?

Author/Presenter: 
Gloriana González
Year: 
2017
Short Description: 

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 students' prior knowledge? (b) How are the participants' perspectives of realistic contexts related to teachers' instructional obligations? (c) How do the participants draw upon these perspectives when designing a lesson?

Teachers Extending Their Knowledge in Online Collaborative Learning Environments: Opportunities and Challenges

STEM Categorization: 
Day: 
Fri

Join two projects to discuss the challenges and opportunities afforded through online environments for providing professional development and supporting classroom implementation of mathematical practices.

Date/Time: 
9:15 am to 10:45 am
Session Materials: 

Teams of researchers from Drexel University, Rutgers University, University of Missouri, and the Math Forum have been investigating online environments for math education and math teacher professional learning communities. The Virtual Math Teams project has developed a synchronous, multi-user GeoGebra implementation and studies the learning of small groups as well as the preparation of teachers to facilitate this learning.

Session Types: 

Promoting productive mathematical discourse: Tasks in collaborative digital environments

Powell, A. B., & Alqahtani, M. M. (2015). Promoting productive mathematical discourse: Tasks in collaborative digital environments. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1246-1249). East Lansing, MI: Michigan State University.

Author/Presenter: 
Arthur B. Powell
Muteb M. Alqahtani
Lead Organization(s): 
Year: 
2015
Short Description: 

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 a larger research project. We present our task design principles that developed through an iterative research design for a project that involves secondary teachers in online courses to learn discursively dynamic geometry by collaborating on construction and problem-solving tasks in a cyber learning environment. In this study, we discuss a task and the collaborative work of a team of teachers to illustrate relationships between the task design and productive mathematical discourse. Implications suggest further investigations into interactions between characteristics of task design and learners mathematical activity.

Pages

Subscribe to Geometry