Discourse

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.

Instrumental development of teachers’ reasoning in dynamic geometry

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.

Author/Presenter: 
Muteb M. Alqahtani
Arthur B. Powell
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.

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.

Perspectives on Mathematics Classroom Discourse

Day: 
Wed

In this session, presenters describe three different approaches to studying mathematics classroom discourse. Participants analyze discourse and discuss benefits and potential drawbacks of various approaches to analysis.

Date/Time: 
9:45 am to 11:45 am
2014 Session Types: 
Collaborative Panel Session
Session Materials: 

In the past 20 years, mathematics education research has seen a turn toward the social and, consequently, discursive aspects of learning (Kieran, Forman, & Sfard, 2001; Ryve, 2011). A heightened attention to discursive features of instruction is seen in the recent publication Principles to Actions (NCTM, 2014), which describes an ambitious image of mathematics teaching and learning for the 21st century.

Perspectives for Advancing the Effectiveness of Elementary Science Instruction for Student Learning: Importance and Challenges

Day: 
Wed

Presenters discuss how their projects contribute systemically to the design, implementation, and evaluation of quality elementary science programs.

Date/Time: 
9:45 am to 11:45 am
2014 Session Types: 
Collaborative Panel Session

Quality elementary science programs are faced with the challenge of adapting and/or building upon the Next Generation Science Standards (NGSS) in order to provide an essential foundation for student learning and interest in science. As such, these science programs must address how the practices of science can be linked with cross-cutting concepts through meaningful learning contexts that, of necessity, evolve progressively across grades.

Using Learning Progressions for Classroom Assessment and Teaching

Day: 
Tues

Join a discussion addressing how learning progression-based frameworks, assessments, and instruction can support teachers and students in developing increasingly sophisticated scientific knowledge and practice.

Date/Time: 
9:45 am to 11:45 am
2014 Session Types: 
Collaborative Panel Session

The goal of this session is to discuss possibilities, progress, and problems in using learning progression research to support improved assessment and instruction in middle school and high school classrooms.

In this session, several learning progression-related DR K–12 projects share findings and discuss questions around two issues:

Professional Development Materials: Supporting Facilitators at Different Levels

Day: 
Tues

Participants provide feedback on materials from a professional development program developed to help elementary teachers promote mathematics discourse, with attention to the design of facilitation support.

Date/Time: 
9:45 am to 11:45 am
2014 Session Types: 
Feedback Session (Work in Development)
Presenters: 
Session Materials: 

The main goal of this session is to share and get feedback on materials from a 40-hour professional development program for elementary mathematics, focusing in particular on the organization of facilitation supports included in these materials. The PD was designed to help teachers promote discourse in elementary mathematics classrooms. In particular, it defines and helps teachers implement “responsive” discourse in the classroom, that is, discourse in which all students are responsible for learning and engaged in probing each other’s mathematical ideas.

Meaningful Support for Teachers: Specific Ways to Encourage Game-Based Learning in the Classroom

Day: 
Tues

Panelists from three projects share lessons learned in guiding game use in classroom learning, highlighting specific examples of effective resources.

Date/Time: 
9:45 am to 11:45 am
2014 Session Types: 
Collaborative Panel Session
Session Materials: 

The three panelists in this session are in the last one or two years of their game-based learning projects, and all have done extensive work in supporting use of their games in classroom learning. As their work has progressed, each has discovered valuable ways to support teachers as well as encountered surprises in what teachers wanted (and didn’t want), and now recognize things they wished they had learned in the beginning of their projects. Session participants leave with recommendations they can use in their current projects, including:

How Can Tools for Teachers Foster High-leverage Classroom Discourse and Assessment Practices

Day: 
Thu

Presenters will enlist audience’s help to expand their thinking about how a suite of Web-based tools that support ambitious forms of science teaching might be adapted for use beyond current research contexts and in more innovative ways. Classroom video of tool-supporting teaching will be shown. 

Date/Time: 
8:30 am to 9:45 am
Session Type: 
Product Feedback Session

How can tools for teachers foster high-leverage classroom discourse and assessment practices?

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