Geometry

Supports for Learning to Manage Classroom Discussions: Exploring the Role of Practical Rationality and Mathematical Knowledge for Teaching

This project focuses on practicing and preservice secondary mathematics teachers and mathematics teacher educators. The project is researching, designing, and developing materials for preservice secondary mathematics teachers that enable them to acquire the mathematical knowledge and situated rationality central to teaching, in particular as it regards the leading of mathematical discussions in classrooms.

Award Number: 
0918425
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2018
Project Evaluator: 
Miriam Gamoran Sherin
Full Description: 

Researchers at the Universities of Michigan and Maryland are developing materials to survey the rationality behind secondary mathematics teaching practice and to support the development by secondary mathematics preservice teachers of specialized knowledge and skills for teaching. The project focuses on the leading of classroom discussions for the learning of algebra and geometry.

Using animations of instructional scenarios, the project is developing online, multimedia questionnaires and using them to assess practicing teachers' mathematical knowledge for teaching and their evaluations of teacher decision making. Reports and forum entries from the questionnaires are integrated into a learning environment for prospective teachers and their instructors built around these animated scenarios. This environment allows pre-service teachers to navigate, annotate, and communicate about the scenarios; and it allows their instructors to plan using those scenarios and share experiences with their counterparts.

The research on teachers' rationality uses an experimental design with embedded one-way ANOVA, while the development of the learning environment uses a process of iterative design, implementation, and evaluation. The project evaluation by researchers at Northwestern University uses qualitative methods to examine the content provided in the environment as well as the usefulness perceived by teacher educators of a state network and their students.

Geometry Assessments for Secondary Teachers (GAST)

Geometry Assessments for Secondary Teachers (GAST) represents a collaborative partnership among faculty and staff at the University of Louisville, the University of Kentucky, Florida State University, Alpine Testing Solutions, and Horizon Research, Inc. to develop a knowledge framework and assessments for secondary mathematics teachers' geometry knowledge for teaching. The framework for the assessments will be designed to collect validity evidence for predicting effective geometry teaching and improving student achievement.

Lead Organization(s): 
Award Number: 
0821967
Funding Period: 
Wed, 10/01/2008 to Fri, 09/30/2011
Project Evaluator: 
Horizon Research

The Development of Student Cohorts for the Enhancement of Mathematical Literacy in Under Served Populations

This project is developing and conducting research on the Cohort Model for addressing the mathematics education of students that perform in the bottom quartile on state and district tests. The predicted outcome is that most students will remain in the cohort for all four years and that almost all of those who do will perform well enough on college entrance exams to be admitted and will test out of remedial mathematics courses.

Lead Organization(s): 
Award Number: 
0822175
Funding Period: 
Mon, 09/01/2008 to Wed, 08/31/2011
Project Evaluator: 
Inverness Research, Inc.
Full Description: 

Project Summary

This is a Full Research and Development proposal which addresses the Contextual Challenge: How can the learning of significant STEM content be achieved to ensure public literacy and workforce readiness?  Our nation is failing to prepare millions of youth for meaningful and productive participation in an information-based society. The target population are those students performing in the bottom quartile on state and national tests, many of these are children of color living in under resourced communities, and most of these young people do not finish high school and end up diverted into an underground economy, gangs, and prisons.   

This project addresses this failure by further developing and testing an approach that the Algebra Project is developing for high school mathematics, in which students form a cohort that stays together for all four years of high school, study mathematics every day using project-designed curricular materials with teachers who participate in project professional development, and are supported by local community groups. 

The Algebra Project seeks to stimulate a demand for math literacy in those most affected by its absence -- the young people themselves.  It stresses the importance of peer culture, using lessons learned from experiences in the 1960s Civil Rights Movement, as well as in the emergence of project graduates into a group with their own perspectives and initiatives. 

In the 60s, project founders learned how to use the meeting place as a tool to engage and empower the people that the meeting was intended to serve.  In the proposed project, there are two meeting places: the students’ high school mathematics classroom and supplementary education activities; and the network of sites around the country that are communicating and learning how to develop and implement cohorts. Young peoples’ roles in each of these settings are key to creating the motivation and commitment needed for student success as well as developing local interest.  The combination of classroom and professional development work, innovative curriculum materials, and community involvement creates an intervention that can significantly transform the peer culture, even in the face of negative forces.

The Algebra Project has developed a cohort model that we predict will stimulate and enable students to pass the state and district mandated tests in mathematics, to pass the mathematics portions of any graduation test, and to score well enough on the SAT or ACT to enter college, and to place into mathematics courses for college credit (not remedial courses).  Building on previous awards, the project will continue to research and develop the cohort model, and will create a small network of cohorts to establish that our model can be widely successful.

Intellectual merit:  This project will demonstrate how students entering high school performing in the bottom quartile nationally and state-wide can be prepared for college-level mathematics, using lessons learned from many years of past experience working in such communities and in their middle schools, and more recently in their high schools and in collaboration with university mathematicians.  The research results are critical to the nation’s learning how to improve mathematics achievement for all children – to gaining a sense of what such a program “looks and feels like”, and what resources and commitments are required, from which institutions. 

Broader impact:  The results of this discovery research project will advance understanding of how to improve mathematics learning and achievement in low performing districts, so students are prepared to take college mathematics without repeating high school mathematics in early college.  It will also demonstrate the resources and commitments needed to reach this result.

Connecting Content and Pedagogical Education of Pre-service Teachers (CONCEPT)

The primary goal of the project is to enhance secondary mathematics teacher education for pre-service teachers by developing, implementing and disseminating resources from a four-course curriculum that brings together the study of mathematics content and pedagogy. Three of the courses are problem-based technology enhanced (PBTE) courses in Algebra and Calculus, Geometry, and Probability and Statistics. A fourth course is a capstone course in Teaching and Learning Secondary School Mathematics.

Lead Organization(s): 
Award Number: 
0455797
Funding Period: 
Wed, 06/01/2005 to Sun, 05/31/2009

Fostering Mathematics Success in English Language Learners

This project is an efficacy study of the Fostering Geometrical Thinking Toolkit (FGTT) previously developed with NSF support. FGTT is a 40-hour professional development intervention focusing on properties of geometric figures, geometric transformations, and measurement of length, area, and volume. The study addresses four research questions, three examining participating teachers and one examining the impact of teachers' professional development on ELL students.

Award Number: 
0821950
Funding Period: 
Fri, 08/15/2008 to Sun, 07/31/2011
Full Description: 

Education Development Center, Inc. (EDC), and Horizon Research, Inc., are conducting the DR-K12 research project, Fostering Mathematics Success of English Language Learners (ELLs): An Efficacy Study of Teacher Professional Development (FMSELL), a study of the effects of the Fostering Geometric Thinking

Toolkit professional development materials (FGTT) for teachers of ELLs. It will address four research questions:

1.     Does participation in FGTT increase teachers’ geometric content knowledge?

2.     How does teachers’ participation affect attention to students’ thinking and mathematical communication?

3.     How does participation affect instructional practices?

4.     What impact on ELLs’ problem-solving strategies is evident when teachers participate in FGTT?

FGTT is a 40-hour professional development intervention focusing on properties of geometric figures, geometric transformations, and measurement of length, area, and volume. The project tests the hypothesis that geometric problem solving invites diagramming, drawing, use of colloquial language, and gesturing to complement mathematical communication and affords teachers opportunities to support ELL learning. The research design uses a randomized block design with 25 pairs of professional development facilitators matched according to their districts’ demographic information.

Creation and Dissemination of Upper-elementary Mathematics Assessment Modules

This project has constructed, pilot tested, validated, and is now disseminating assessments of student achievement for use in upper elementary grades.
Lead Organization(s): 
Award Number: 
0831450
Funding Period: 
Fri, 05/01/2009 to Mon, 04/30/2012
Full Description: 
This project has constructed, pilot tested, validated, and is now disseminating assessments of student achievement for use in upper elementary grades. There are four equivalent forms for each of the fourth and fifth grades, with each form covering (1) number and operations, (2) pre-algebra and algebra, and (3) geometry and measurement. Items are based in the literature on student's cognitive growth and are meant to:
  • Represent central ideas in the subject matter;
  • Focus on the meaning of facts and procedures; and
  • Require more complex responses than traditional multiple-choice problems. 
These forms and associated technical materials can be accessed at: http://cepr.harvard.edu/ncte-student-assessments

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