# Geometry

## Animated Contrasting Cases in Geometry

In this collection of materials, four geometric topics are covered in animated, digital materials.

Author/Presenter:
Erin Krupa
Jon Star
Brianna Bentley
Josh Mannix
Year:
2019
Short Description:

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 Volume. These topics are discussed in scenarios of contrasting cases, where two fictional students each present a unique method or solution strategy to the same problem. The goal is then to analyze both methods and discuss similarities and differences, strengths and weaknesses of each.

## Competencies and Behaviors Observed When Students Solve Geometry Proof Problems: An Interview Study with Smartpen Technology

This peer-reviewed research journal publication addresses one of the grant goals with respect to how students performed on a set of proof tasks. Student work was documented through the use of smartpen technology which allowed the researchers to "track" students' written work on the proof tasks as well as hear the students' explanations of their thinking about the tasks. Although the two tasks highlighted in this paper were relatively routine triangle congruent proofs, only 7 out of 23 of the sampled students were successful on both proofs.

Author/Presenter:
Michelle Cirillo
Jenifer Hummer
Year:
2021
Short Description:

This peer-reviewed research journal publication addresses one of the grant goals with respect to how students performed on a set of proof tasks.

Resource(s):

## 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
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
Year:
2019
Short Description:

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

Resource(s):

## 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
Year:
2019
Short Description:

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

Resource(s):

## 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
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
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?