Geometry Module
developed by
The Rice University
School Mathematics Project
(RUSMP)
Funding for the Geometry Module was provided by the
Texas Education Agency and the Texas Higher
Education Coordinating Board.
2004
,Introduction
The Texas Education Agency and the Texas Higher Education Coordinating Board
Geometry Module
Introduction
The Rice University School Mathematics Project (RUSMP) developed the Geometry Module as a
comprehensive teacher training module with funding from the Texas Education Agency and the
Texas Higher Education Coordinating Board. The Geometry Module effectively assists teachers
in developing a deeper understanding of the underlying concepts that support the Texas Essential
Knowledge and Skills (TEKS) in Geometry and helps teachers develop the pedagogical tools
necessary to provide their students the opportunity to meet Texas’ challenging state content and
student performance standards. The Geometry Module also supports related TExES Mathematics
Competencies. The rigor of the Geometry Module is of sufficient nature as to allow participating
teachers who have not yet met the requirements of a “highly qualified” teacher, as defined by the
United States NO CHILD LEFT BEHIND ACT of 2001 (NCLB), to progress towards this goal.
Theoretical Framework for the Geometry Module
The National Council of Teachers of Mathematics (NCTM) proposed major changes in pre-college
mathematics curriculum in its Standards (1989, 1991, 1995, 2000). The National Research Council
in Adding It Up: Helping Children Learn Mathematics (2001) and Educating Teachers of Science,
Mathematics, and Technology: New Practices for the New Millennium (2001) provides research-
based recommendations for teaching and learning that support effective mathematics education.
This research indicates that active, student-centered mathematical investigations, group
cooperation, and alternative assessments are more effective in reaching diverse student populations
than the passive, teacher-centered learning methods which have dominated mathematics instruction
in the past. The Geometry Module materials are consistent with these recommendations.
The Geometry Module is based on the van Hiele model of geometric thought. NCTM in its
Standards (1989), acknowledged the importance of the van Hieles’ research.
Development of geometric ideas progresses through a hierarchy of levels. Students first
learn to recognize whole shapes and then to analyze the relevant properties of a shape.
Later they can see relationships between shapes and make simple deductions (p. 48).
Traditional geometry curriculum often fails, because there is a mismatch between geometry
instruction and a student’s van Hiele level. The hierarchy of levels in the van Hiele model consists
Geometry Module i
,Introduction
of (1) the Visual Level, (2) the Descriptive Level, (3) the Relational Level, (4) the Deductive Level,
and (5) Rigor. The Geometry Module provides van Hiele-based experiences (Crowley, 1987) to
move participants through the hierarchy from the Visual Level to Rigor. The Geometry Module
provides descriptive behavior criteria which identify the different van Hiele levels of student
performance, so that participants may identify and select corresponding activities to ensure success
for all. Throughout the Geometry Module, participants will identify the van Hiele levels within the
activities.
Tools for Learning Geometry
The Geometry Module utilizes construction tools, manipulatives, and technology: (1) to address
various learning styles, (2) to model or represent mathematical concepts, (3) to abstract from the
manipulative representations, (4) to construct and explore mathematical properties of geometric
objects, (5) to generate authentic data, and most importantly (6) to progress participants through
the van Hiele levels. The appropriate use of construction tools, manipulatives, the graphing
calculator, The Geometer’s Sketchpad, and NonEuclid is incorporated into module materials.
RUSMP’s Unique Qualifications to Write the Geometry Module
RUSMP was established in 1987, with a grant from the National Science Foundation (NSF), in
order to provide a bridge between the Rice University mathematics research community and
Houston-area mathematics teachers. In addition to the original grant, RUSMP has received funding
from a second NSF grant, the United States Department of Education Eisenhower and Teacher
Quality Programs, and from corporations, foundations and school districts. The mission of RUSMP
is to help teachers and administrators better understand the nature of mathematics, the effective
teaching and assessing of mathematics, and the importance of mathematics in today's society.
RUSMP’s major goal is to enhance the mathematical and pedagogical knowledge of Houston PreK-
12 teachers and support them in implementing more effective mathematics programs.
The RUSMP approach is founded on the belief that sustained instructional changes can best be
supported through the development of professionalism among teachers and the creation of a
network of teachers who have extensive knowledge of both mathematical content and pedagogy.
All RUSMP activities are designed to support the development of teachers’ professionalism.
RUSMP has developed an extensive array of programs and courses available to teachers and
administrators. These include long-term, intensive professional development for teachers, day-long
workshops, and opportunities for networking across schools and districts. In addition, RUSMP has
Geometry Module ii
, Introduction
undertaken several collaborative projects with districts, schools, and other community members in
the Houston area. While there is great diversity among the programs and activities offered by
RUSMP, they are all anchored by a common curriculum and approach to instruction. The
Geometry Module is the latest of RUSMP’s efforts to improve the teaching of pre-college
mathematics.
As a result of RUSMP’s eighteen-year partnership with Houston-area school districts to improve
mathematics instruction, RUSMP has the knowledge and experience necessary to develop an
effective Geometry Module that meets the needs of current and future teachers. The Geometry
Module builds upon the strengths and recommendations of prior curricula that RUSMP has
designed and implemented for Houston-area PreK-12 teachers.
The Texas Education Agency and the Texas Higher Education Coordinating Board
Geometry Module
Acknowledgements
Geometry Module iii
developed by
The Rice University
School Mathematics Project
(RUSMP)
Funding for the Geometry Module was provided by the
Texas Education Agency and the Texas Higher
Education Coordinating Board.
2004
,Introduction
The Texas Education Agency and the Texas Higher Education Coordinating Board
Geometry Module
Introduction
The Rice University School Mathematics Project (RUSMP) developed the Geometry Module as a
comprehensive teacher training module with funding from the Texas Education Agency and the
Texas Higher Education Coordinating Board. The Geometry Module effectively assists teachers
in developing a deeper understanding of the underlying concepts that support the Texas Essential
Knowledge and Skills (TEKS) in Geometry and helps teachers develop the pedagogical tools
necessary to provide their students the opportunity to meet Texas’ challenging state content and
student performance standards. The Geometry Module also supports related TExES Mathematics
Competencies. The rigor of the Geometry Module is of sufficient nature as to allow participating
teachers who have not yet met the requirements of a “highly qualified” teacher, as defined by the
United States NO CHILD LEFT BEHIND ACT of 2001 (NCLB), to progress towards this goal.
Theoretical Framework for the Geometry Module
The National Council of Teachers of Mathematics (NCTM) proposed major changes in pre-college
mathematics curriculum in its Standards (1989, 1991, 1995, 2000). The National Research Council
in Adding It Up: Helping Children Learn Mathematics (2001) and Educating Teachers of Science,
Mathematics, and Technology: New Practices for the New Millennium (2001) provides research-
based recommendations for teaching and learning that support effective mathematics education.
This research indicates that active, student-centered mathematical investigations, group
cooperation, and alternative assessments are more effective in reaching diverse student populations
than the passive, teacher-centered learning methods which have dominated mathematics instruction
in the past. The Geometry Module materials are consistent with these recommendations.
The Geometry Module is based on the van Hiele model of geometric thought. NCTM in its
Standards (1989), acknowledged the importance of the van Hieles’ research.
Development of geometric ideas progresses through a hierarchy of levels. Students first
learn to recognize whole shapes and then to analyze the relevant properties of a shape.
Later they can see relationships between shapes and make simple deductions (p. 48).
Traditional geometry curriculum often fails, because there is a mismatch between geometry
instruction and a student’s van Hiele level. The hierarchy of levels in the van Hiele model consists
Geometry Module i
,Introduction
of (1) the Visual Level, (2) the Descriptive Level, (3) the Relational Level, (4) the Deductive Level,
and (5) Rigor. The Geometry Module provides van Hiele-based experiences (Crowley, 1987) to
move participants through the hierarchy from the Visual Level to Rigor. The Geometry Module
provides descriptive behavior criteria which identify the different van Hiele levels of student
performance, so that participants may identify and select corresponding activities to ensure success
for all. Throughout the Geometry Module, participants will identify the van Hiele levels within the
activities.
Tools for Learning Geometry
The Geometry Module utilizes construction tools, manipulatives, and technology: (1) to address
various learning styles, (2) to model or represent mathematical concepts, (3) to abstract from the
manipulative representations, (4) to construct and explore mathematical properties of geometric
objects, (5) to generate authentic data, and most importantly (6) to progress participants through
the van Hiele levels. The appropriate use of construction tools, manipulatives, the graphing
calculator, The Geometer’s Sketchpad, and NonEuclid is incorporated into module materials.
RUSMP’s Unique Qualifications to Write the Geometry Module
RUSMP was established in 1987, with a grant from the National Science Foundation (NSF), in
order to provide a bridge between the Rice University mathematics research community and
Houston-area mathematics teachers. In addition to the original grant, RUSMP has received funding
from a second NSF grant, the United States Department of Education Eisenhower and Teacher
Quality Programs, and from corporations, foundations and school districts. The mission of RUSMP
is to help teachers and administrators better understand the nature of mathematics, the effective
teaching and assessing of mathematics, and the importance of mathematics in today's society.
RUSMP’s major goal is to enhance the mathematical and pedagogical knowledge of Houston PreK-
12 teachers and support them in implementing more effective mathematics programs.
The RUSMP approach is founded on the belief that sustained instructional changes can best be
supported through the development of professionalism among teachers and the creation of a
network of teachers who have extensive knowledge of both mathematical content and pedagogy.
All RUSMP activities are designed to support the development of teachers’ professionalism.
RUSMP has developed an extensive array of programs and courses available to teachers and
administrators. These include long-term, intensive professional development for teachers, day-long
workshops, and opportunities for networking across schools and districts. In addition, RUSMP has
Geometry Module ii
, Introduction
undertaken several collaborative projects with districts, schools, and other community members in
the Houston area. While there is great diversity among the programs and activities offered by
RUSMP, they are all anchored by a common curriculum and approach to instruction. The
Geometry Module is the latest of RUSMP’s efforts to improve the teaching of pre-college
mathematics.
As a result of RUSMP’s eighteen-year partnership with Houston-area school districts to improve
mathematics instruction, RUSMP has the knowledge and experience necessary to develop an
effective Geometry Module that meets the needs of current and future teachers. The Geometry
Module builds upon the strengths and recommendations of prior curricula that RUSMP has
designed and implemented for Houston-area PreK-12 teachers.
The Texas Education Agency and the Texas Higher Education Coordinating Board
Geometry Module
Acknowledgements
Geometry Module iii
