Geometry

Linear Algebra and Geometry

Algebra
Geometry
Mathematics
Curriculum

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. 

Access Link: 
https://bookstore.ams.org/text-46/
Author/Presenter: 
Al Cuoco
Kevin Waterman
Bowen Kerins
Elena Kaczorowski
Michelle Manes
Lead Organization(s): 
Education Development Center, Inc. (EDC)
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

Geometry
Mathematics
Assessment

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

Access Link: 
https://www.nctm.org/Publications/Mathematics-Teacher/2019/Vol112/Issue6/Address...
Author/Presenter: 
Michelle Cirillo
Jenifer Hummer
Lead Organization(s): 
University of Delaware (UD)
Year: 
2019
Short Description: 
Use these ideas to diagnose and address common conceptual obstacles that inhibit students’ success.

Thinking scientifically in a changing world

Algebra
Astronomy
Geometry
Science

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

Access Link: 
Author/Presenter: 
Doug Lombardi
Lead Organization(s): 
Temple University
Year: 
2019
Short Description: 
Shifting people’s judgments toward the scientific involves teaching them to purposefully evaluate connections between evidence and alternative explanations.
Resource(s): 
PDF icon Lombardi 2019-Thinking scientifically in a changing world.pdf

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

Astronomy
Geometry
Science

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).

Access Link: 
Author/Presenter: 
Doug Lombardi
Janelle M. Bailey
Elliot S. Bickel
Shondricka Burrell
Lead Organization(s): 
Temple University
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.
Resource(s): 
PDF icon Lombardi et al. 2018-Instructional Scaffold Comparison.pdf

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

Geometry
Mathematics

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?

Access Link: 
http://onlinelibrary.wiley.com/doi/10.1111/ssm.12249/full
Author/Presenter: 
Gloriana González
Lead Organization(s): 
University of Illinois at Urbana-Champaign
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

21st Century Skills
Assessment
Cyberlearning
Disciplinary Content Knowledge
Discourse
Educational Technology
Geometry
Pedagogical Content Knowledge
Pedagogy
Professional Development
Standards
Teacher Attitudes/Beliefs
Teacher Practice
Elementary School
Middle School
High School
Post-secondary
Course
Software
Website
STEM Categorization: 
Math
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
Presenters: 
Arthur Powell
Jason Silverman
Stephen Weimar
Location: 
Taft
Session Materials: 
PDF icon Slides

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: 
Concurrent Session

Promoting productive mathematical discourse: Tasks in collaborative digital environments

Cyberlearning
Discourse
Educational Technology
Geometry

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.

Access Link: 
http://cadrek12.org/sites/default/files/webform/Powell%20%26%20Alqahtani%20%2820...
Author/Presenter: 
Arthur B. Powell
Muteb M. Alqahtani
Lead Organization(s): 
Rutgers University (RU)
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.

Instrumental development of teachers’ reasoning in dynamic geometry

Cyberlearning
Discourse
Educational Technology
Geometry
Teacher Practice

Alqahtani, M. M., & Powell, A. B. (2015, March). Instrumental development of teachers’ reasoning in dynamic geometry. Paper presented at the 2015 annual meeting of the American Educational Research Association, Chicago, IL.

Access Link: 
http://cadrek12.org/sites/default/files/webform/Alqahtani%20%26%20Powell%20%2820...
Author/Presenter: 
Muteb M. Alqahtani
Arthur B. Powell
Lead Organization(s): 
Rutgers University (RU)
Year: 
2015
Short Description: 
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 online dynamic geometry environment (DGE). Using the theory of instrument-mediated activity, we analysis the discourse and DGE actions of a group of middle and high school mathematics teachers who participated in a semester-long, professional development course. Working in small teams, they collaborated to solve geometric problems. Our results show that as teachers appropriate DGE artifacts and transform its components into instruments, they develop their geometrical knowledge and reasoning in dynamic geometry. Our study contributes to a broad understanding of how teachers develop mathematical knowledge for teaching.

Tasks promoting productive mathematical discourse in collaborative digital environments

Cyberlearning
Discourse
Educational Technology
Geometry

Powell, A. B., & Alqahtani, M. M. (2015). Tasks promoting productive mathematical discourse in collaborative digital environments. In N. Amado & S. Carreira (Eds.), Proceedings of the 12th International Conference on Technology in Mathematics Teaching. (pp. 68-76). Faro, Portugal: Universidade do Algarve.

Access Link: 
http://cadrek12.org/sites/default/files/webform/Powell%20%26%20Alqahtani%20%2820...
Author/Presenter: 
Arthur B. Powell
Muteb M. Alqahtani
Lead Organization(s): 
Rutgers University (RU)
Year: 
2015
Short Description: 
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 from a larger research project. We present the theoretical foundations of 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 cyberlearning environment. In this study, we discuss a task and the collaborative work of a team of teachers to illustrate relationships between the task design, productive mathematical discourse, and the development of new mathematics knowledge for the teachers. Implications of this work suggest further investigations into interactions between characteristics of task design and learners mathematical activity.

Teachers’ support of students’ instrumentation in a collaborative, dynamic geometry environment

Discourse
Geometry
Teacher Practice

Alqahtani, M. M., & Powell, A. B. (2015). Teachers’ support of students’ instrumentation in a collaborative, dynamic geometry environment. In N. Amado & S. Carreira (Eds.), Proceedings of the 12th International Conference on Technology in Mathematics Teaching. (pp. 268-276). Faro, Portugal: Universidade do Algarve.

Access Link: 
http://cadrek12.org/sites/default/files/webform/Alqahtani%20%26%20Powell%20%2820...
Author/Presenter: 
Muteb M. Alqahtani
Arthur B. Powell
Lead Organization(s): 
Rutgers University (RU)
Year: 
2015
Short Description: 
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 teacher engaged a class of students in the Virtual Math Teams with GeoGebra environment (VMTwG) to solve geometrical tasks. The VMTwG allows users to share both GeoGebra and chat windows to engage in joint problem solving. Our analysis of the teacher’s implementation and students’ interactions in VMTwG shows that his instrumental orchestration (Trouche, 2004, 2005) supported students’ instrumentation (Rabardel & Beguin, 2005) and shaped their movement between empirical explorations and deductive justifications. This study contributes to understanding the interplay between a teacher’s instrumental orchestration and students’ instrumentation and movement towards more deductive justifications.

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