Geometry

Tasks promoting productive mathematical discourse in collaborative digital environments

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.

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

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.

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

Illuminating Coordinate Geometry with Algebraic Symmetry

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.

Author/Presenter: 
Ryota Matsuura
Sarah Sword
Year: 
2015
Short Description: 

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 the variables x and y, we obtain yx + yz + xz, which is the same as f(x, y, z); likewise, swapping x and z (or y and z) returns the original polynomial. These polynomials arise in many areas of mathematics, including Galois theory and combinatorics, but they are rarely taught in a high school curriculum. In this article, we describe an application of symmetric polynomials to a familiar problem in coordinate geometry, thus introducing this powerful tool in a context that is accessible to high school students.

An Efficacy Study on the Use of Dynamic Geometry Software

Jiang, Z. & White, A. (2012). An efficacy study on the use of dynamic geometry software. In the Proceedings of the 12th International Congress on Mathematical Education.

Author/Presenter: 
Zhonghong Jiang
Alexander White
Lead Organization(s): 
Year: 
2012
Short Description: 

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 instructional practices. It compares effects of that intervention (the DG approach) with standard instruction that does not make use of computer tools. This paper reports a study conducted during the second year of the project. Student learning is assessed by a geometry test and other tests. Data for answering the research questions of the study are analyzed mainly by appropriate HLM methods. The analysis on the geometry test data is discussed in detail. The experimental group significantly outperformed the control group in geometry performance.

Professional Development Materials to Support Geometry Learning and Instruction, the Common Core Standards, and English Language Learners

Day: 
Fri

Two projects that are investigating how middle school geometry professional development materials support teachers’ learning. Presenters compare approaches, present preliminary results, and discuss strengths and challenges.

Date/Time: 
10:30 am to 12:30 pm
Session Type: 
PI-organized Discussion

This session focuses on two professional development projects, both aimed at increasing geometric content knowledge of middle school mathematics teachers and their students. The goal is to engage grantees in considering what the presenters are learning about the impact of these projects and to consider next steps in advancing the field. The two participating projects are:

Randomized Control Trials on the Dynamic Geometry Approach

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:

Author/Presenter: 
Zhonghong Jiang
Alexander White
Alana Rosenwasser
Lead Organization(s): 
Year: 
2011

Training Teachers in the Effective Mathematical and Pedagogical Uses of Software: Perspectives from the Dynamic Number and Dynamic Geometry in Classrooms Projects

Day: 
Thu

This presentation explores technology training in relation to two DR K-12 projects with a focus on increasing the mathematical and pedagogical content knowledge of teachers.

Date/Time: 
2:00 pm to 4:00 pm
Session Type: 
Panel
Session Materials: 

How can professional development that is focused on technology move beyond the nuts and bolts of the particular tool to a deeper look into the mathematical and pedagogical opportunities afforded by the technology?     This presentation explores technology training in relation to two DR K–12 projects with a focus on increasing the mathematical and pedagogical content knowledge of teachers.

NCSM Conference

Event Date: 
Mon, 04/19/2010 - 6:00am to Wed, 04/21/2010 - 10:30am
Associated Dates and Deadlines: 
March 26, 2010 - Advanced Registration Deadline

Whether you're a first-timer or a veteran of NCSM Annual Conferences, join us for three exciting days focused on important issues for leaders in mathematics education.

NCSM's Program Committee has lined up a terrific slate of speakers who will help us focus on "Charting a Course to Mathematics Leadership."

Conference sessions will be led by experts in their field-people at the forefront of change in mathematics education.

The six strands featured at this exciting and educational NCSM event are:

2011 NCTM Annual Meeting and Exposition

Event Date: 
Wed, 04/13/2011 - 7:00am to Sat, 04/16/2011 - 12:00pm
Associated Dates and Deadlines: 
Proposals accepted beginning February 2010

For more information on the 2011 NCTM Annual Meeting and Exposition, visit the NCTM website.

For more information on proposal submission, click here.

Look for these DR K-12 grantees who are presenting:

Event Type: 

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