## Building Mathematical Knowledge for Teaching Proof in Geometry

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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# Geometry

## Building Mathematical Knowledge for Teaching Proof in Geometry

## CAREER: Proof in Secondary Classrooms: Decomposing a Central Mathematical Practice

## Linear Algebra and Geometry

## Addressing Misconceptions in Secondary Geometry Proof

## Thinking scientifically in a changing world

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

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

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

## Promoting productive mathematical discourse: Tasks in collaborative digital environments

## Instrumental development of teachers’ reasoning in dynamic geometry

## Pages

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

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Year:

2019

Short Description:

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

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Target Audience:

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.

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Year:

2019

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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 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.

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

Lead Organization(s):

Year:

2019

Short Description:

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

Resource(s):

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

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Year:

2019

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

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).

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2018

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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, relational, and critical), along with measures of plausibility reappraisal and 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?

Lead Organization(s):

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?

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

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Location:

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:

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.

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.

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.

Lead Organization(s):

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.

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