Teacher Practice

Improving Student Learning and Teacher Practice in Mathematics: A Focus on Formative Assessment

STEM Categorization: 
Day: 
Thu

Join a discussion with panelists from several projects about project model designs, initial findings, and implementation challenges associated with formative assessment in mathematics.

Date/Time: 
2:15 pm to 3:45 pm
Session Materials: 

In this session, four projects will share their work on formative assessment and mathematics learning trajectories, and participants will discuss the implications for formative assessment practices in mathematics.

Session Types: 

Professional Development Approaches to Strengthen Collaboration among Educators with Different Roles to Improve Student Math Learning

STEM Categorization: 
Day: 
Thu

Discuss the benefits and challenges of creating mathematics professional development that brings together educators with different roles to build knowledge, practices, and collaboration for teaching students with diverse needs.

Date/Time: 
9:30 am to 11:00 am
Session Materials: 

In order to broaden the participation of underrepresented student groups, such as students with disabilities and English Language Learners (ELL), mathematics professional development (PD) programs need to include educators with different areas of expertise, not just mathematics teachers. This session will focus on the benefits and challenges of creating effective PD programs that bring together educators with different roles to build knowledge, practices, and collaboration for improving the mathematics learning of all students.

Session Types: 

Problematizing and Assessing Secondary Mathematics Teachers’ Ways of Thinking

STEM Categorization: 
Day: 
Thu

Engage with presenters as they discuss assessment and rubrics designed to measure secondary teachers’ mathematical habits of mind.

Date/Time: 
9:30 am to 11:00 am
Session Materials: 

Work in secondary mathematics education takes many approaches to content, pedagogy, professional development and assessment. This session aims to illuminate the richness of hte content of secondary mathematics and the field of secondary mathematics education by sharing two such approaches and reflecting on the differences and commonalities between the two.   

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Perspectives on Solution Diversity and Divergent Thinking in K–12 Engineering Design Learning Experiences

STEM Categorization: 
Day: 
Thu

Consider multiple approaches to valuing, supporting, and studying the diversity of students’ solutions to design problems through poster presentations and small-group discussion.

Date/Time: 
9:30 am to 11:00 am
Session Materials: 

“Solution diversity” has been proposed as one key characteristic that distinguishes engineering design from other disciplinary pursuits. Engineering designers recognize that for any design problem, there will be multiple acceptable solutions, and informed designers have been found to strive for “idea fluency” through divergent thinking techniques that assist them in exploring the design space (Crismond & Adams, 2012).

Session Types: 

On the Design and Implementation of Practical Measures to Support Instructional Improvement at Scale

STEM Categorization: 
Day: 
Thu

Learn about two efforts to design and implement practical measures of science and mathematics teaching to inform school and district instructional improvement efforts.

Date/Time: 
9:30 am to 11:00 am
Session Materials: 

In contrast to evaluative research that uses accountability measures, improvement science research (Bryk, Gomez, Grunow, & LeMahieu, 2015), using practical measures is designed to provide practitioners with frequent, rapid feedback that enables them to assess and adjust instruction during the process of implementation. The resulting data is potentially of use to multiple stakeholders. For example, practical measures can orient teachers to attend to key aspects of the classroom that might be invisible to them.

Session Types: 
References: 

Bryk, A. S., Gomez, L. M., Grunow, A., & LeMahieu, P. (2015). Learning to improve: How America's schools can get better at getting better.
       Cambridge, MA: Harvard Education Press.
Yeager, D., Bryk, A. S., Muhich, J., Hausman, H., & Morales, L. (2013). Practical measurement. Carnegie Foundation for the Advancement of
       Teaching. Stanford, CA.

Kara Jackson, Jessica Thompson

Elementary Mathematical Writing Task Force Recommendations: Implications for Research and Classroom Implementation

STEM Categorization: 
Day: 
Thu

Learn about types of and purposes for elementary mathematical writing, and discuss implications for research and classroom implementation.

Date/Time: 
9:30 am to 11:00 am
Session Materials: 

Although the mathematics education community long has emphasized the importance of discourse in teaching and learning mathematics, mathematical writing has not been clearly defined. Questions remain about how writing can leverage elementary students’ learning of mathematics. In October 2015, the Elementary Mathematical Writing Task Force came together and recommended four types of writing (exploratory, informative/explanatory, argumentative, and mathematically creative) and their respective purposes.

Session Types: 

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.

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.

Mathematics Curriculum, Teacher Professionalism, and Supporting Policies in Korea and the United States: Summary of a Workshop

On July 15-17, 2012 the United States National Commission on Mathematics Instruction and Seoul National University held a joint Korea-U.S. workshop on Mathematics Teaching and Curriculum. The workshop was organized to address questions and issues related to math teaching and curriculum that were generated by each country, including the following: What are the main concerns in the development of the curriculum? What issues have been discussed or debated among curriculum developers, teachers, teacher educators, and scholars regarding the curriculum?

Author/Presenter: 
Ana Ferreras
Cathy Kessel
Myong-Hi Kim
Lead Organization(s): 
Year: 
2015
Short Description: 

On July 15-17, 2012 the United States National Commission on Mathematics Instruction and Seoul National University held a joint Korea-U.S. workshop on Mathematics Teaching and Curriculum. The workshop was organized to address questions and issues related to math teaching and curriculum that were generated by each country. This report summarizes the presentations and discussions at the workshop.

Why a Digital Teacher Guide?

Inquiry-based educative curricula and teachers who use these curricula as intended are major factors in achieving successful student learning outcomes in science. Educative curricula can also bring about significant change in teacher practice. Educative curricula are generally accompanied by carefully designed print teacher guides that facilitate the implementation of curricula, encourage new instructional strategies, and accommodate curriculum modifications while retaining fidelity to the developers’ content sequencing and pedagogy.

Author/Presenter: 
Jacqueline S. Miller
Katherine F. Paget
Year: 
2016
Short Description: 

An electronic teacher guide (eTG) was developed to determine whether a digital guide could better support teachers in implementing an inquiry-based curriculum and in enhancing their practice. Developed as a proof-of-concept exemplar, features of the eTG support high school teachers in planning, implementing, and modifying innovative instructional materials and in developing more ambitious teaching practices.

Resource(s): 

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