Geometry

Mathematics Discourse in Secondary Classrooms (M-DISC): A Case-Based Professional Development Curriculum

This project is developing, designing, and testing materials for professional development leaders (e.g., teacher educators, district mathematics specialists, secondary mathematic department chairs) to use in their work with secondary mathematics teachers. The aim is to help those teachers analyze the discourse patterns of their own classrooms and improve their skills in creating discourse patterns that emphasize high-level mathematical explanation, justification, and argumentation.

Award Number: 
0918117
Funding Period: 
Sat, 08/01/2009 to Thu, 07/31/2014
Project Evaluator: 
Horizon

PUM (PhysicsUnionMathematics) Exploration

The PuM project develops and conducts research on a learning continuum for seamless instruction in middle school physical science and high school physics. The ultimate goal is to use physics as the context to develop mathematics literacy, particularly with students from underrepresented populations and special needs students. The research component analyzes the effects of the curriculum on students' learning while simultaneously investigating teachers' pedagogical content knowledge in a variety of forms.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0733140
Funding Period: 
Sat, 09/01/2007 to Tue, 08/31/2010

Dynamic Geometry in Classrooms

This project is conducting repeated randomized control trials 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 with standard instruction that does not make use of computer drawing tools.

Project Email: 
Lead Organization(s): 
Award Number: 
0918744
Funding Period: 
Tue, 09/01/2009 to Sat, 08/31/2013
Project Evaluator: 
Ed Dickey
Full Description: 

The project is conducting repeated randomized control trials 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 with standard instruction that does not make use of computer drawing/exploraction tools. The basic hypothesis of the study is that use of DG software to engage students in constructing mathematical ideas through experimentation, observation, data recording, conjecturing, conjecture testing, and proof results in better geometry learning for most students. The study tests that hypothesis by assessing student learning in 76 classrooms randomly assigned to treatment and control groups. Student learning is assessed by a geometry standardized test, a conjecturing-proving test, and a measure of student beliefs about the nature of geometry and mathematics in general. Teachers in both treatment and control groups receive relevant professional development, and they are provided with supplementary resource materials for teaching geometry. Fidelity of implementation for the experimental treatment is monitored carefully. Data for answering the several research questions of the study are analyzed by appropriate HLM methods. Results will provide evidence about the effectiveness of DG approach in high school teaching, evidence that can inform school decisions about innovation in that core high school mathematics course. The main research question of the project is: Is the dynamic geometry approach better than the business-as-usual approach in facilitating the geometric learning of our students (and more specifically our economically disadvantaged students) over the course of a full school year?

The main resources/products include geometry teachers’ professional development training materials, suggested dynamic geometry instructional activities to supplement current high school geometry curriculum, instruments such as Conjecturing-Proving Test, Geometry Belief Instrument, Classroom Observation Protocols, DG Implementation Questionnaire and Student Interview Protocols. 

The general plan for the four-year project is as follows:

Year 1: Preparation (All research instruments, professional development training and resource materials, recruitment and training of participants, etc.); 

Year 2: The first implementation of the dynamic geometry treatment, and related data collection and initial data analysis; 

Year 3: The second implementation of the DG treatment, and related data collection and data analysis; 

Year 4: Careful and detailed data analysis and reporting.

We are now in project year 3. Data are collected for the second implementation of the DG treatment. For data collected during project year 2, some initial analysis (the analysis on the geometry pretest and posttest data and the psychometric analysis on the project developed instruments) has been conducted. More thorough analysis of the collected data is still on going. The analysis on the geometry test shows that the experimental group significantly outperformed the control group on geometry performance.

The evaluation will be implemented throughout the project’s four-year duration, with an evolving balance of formative and summative evaluation activities.  In the project’s first three years, the evaluation will emphasize formative functions, designed to inform the project research team of the relative strengths and weaknesses of the research design and execution, and target corrections and improvements of the research components. Summative evaluation activities will also take place in these years with the collection of data on student achievement and teacher change. Evaluation activities for year 4 will focus on the summative evaluation of the project’s accomplishment and especially its impact on participating teachers and students. Evaluation reports will be issued annually with a final summative report presented at the end of year 4.

The research results will be disseminated via the following efforts: 1) Creating and constantly updating the project web site; 2) Publishing the related research articles in research journals such as Journal for Research in Mathematics Education; 3) Presenting at state, regional, national, and international research and professional meetings; 4) Meeting with state and local education agencies, schools, and mathematics teacher educators at other universities for presenting the research findings and using the DG approach in more schools and more mathematics teacher education programs; and 5) Contacting more school districts, with a view to developing relationships and ties that would smooth the way to disseminate the research results.

Project M2: Maturing Mathematicians -- Advanced Curriculum for Primary Level Students

Project M2 is producing and disseminating curriculum materials in geometry and measurement for students in grades K-2. This builds on success of the M3 U.S. Department of Education curriculum grant for students in Grades 3-5. (www.projectm3.org). Project M2 units are advanced units for all students designed using research-based practices in mathematics, early childhood, and gifted education. Curricular materials focus on promising discourse and hands-on inquiry of rich problem-situations.  

Project Email: 
Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0733189
Funding Period: 
Wed, 08/15/2007 to Sun, 07/31/2011
Full Description: 

Project Publications and Presentations:

Gavin, M. K.; Casa, Tuita, M.; Chapin, S. & Sheffield, L. (2010). Designing a Shape Gallery: Geometry with Meerkats.

Gavin, M. K.; Casa, Tuita, M.; Chapin, S. & Sheffield, L. (2010). Designing a Shape Gallery: Geometry with the Meerkats Student Mathematician's Journal. Student Mathematician's Journal.

Casa, T.; Firmender, J. & Gavin, M. K. (2010, April). Designing a Shape Gallery: Making Geometry Connections for Primary Students. Presented at National Council of Teachers of Mathematics Annual Meeting, San Diego, CA.

Casa, T. & Gavin, M. K. (2010, March). Exploring Shapes in Space: Geometry with the Frogonauts. Presented at Keefe Bruyette Symposium, Saint Joseph College, West Hartford, CT.

Gavin, M. K. (2009, November). Mentoring Young Mathematicians: New Advanced Curriculum for Primary-level Students. Presented at the National Association for Gifted Children Annual Meeting, St. Louis, MO.

Gavin, K. M. (2010, April). Nurturing Mathematically Promising and Creative Students, Project M2: Mentoring Young Mathematicians. Presented at National Council of Supervisors of Mathematics Annual Conference, San Diego, CA.

Gavin, M. K.; Firmender, J. M. & Casa, Tuita, M. (2010, April). Project M2's Approach: Connecting Math and Language Arts through Communication. Presented at the National Council of Teachers of Mathematics Annual Meeting, San Diego, CA.

Gavin, M. K.; Casa, T. M., Chapin, S. & Sheffield, L. (2011). Using Everyday Measures: Measuring with the Meerkats.

Learning and Teaching Geometry: VideoCases for Mathematics Professional Development

This project is creating five video-case modules for use in professional development of middle school mathematics teachers. The materials are designed to develop teachers' understanding of mathematics knowledge for teaching similarity. In total, 18-24 video cases will be produced, which, taken together, form the curriculum of a 45- to 60-hour professional development course.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0732757
Funding Period: 
Sat, 09/01/2007 to Fri, 08/31/2012
Project Evaluator: 
Horizon Research

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.

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