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Preface

This second edition of IMAGES makes use of the experience gained during the 2002 and 2003 IMAGES Institutes, held in Pennsylvania and Maryland for 343 educators. Observing how they made use of the materials presented was extremely valuable as we continually revisit how to best support the teaching of geometry and measurement. As a result of these Institutes, secondary workshops were conducted by these participants, and to date more than 2,000 teachers have had some training with the IMAGES program. We also sought to show evidence of effectiveness since the first printing of the book in 2002.

Part of this effort was to measure change in content knowledge by administering pre- and post-tests at each of the five IMAGES Institutes conducted since the summer of 2002. The pre-tests from each of these five institutes indicated that teachers had misunderstandings of basic geometry and measurement concepts, and in the post-tests teachers showed statistically significant growth in their knowledge of these concepts. Furthermore, after engaging in the IMAGES professional development training:

• 88 percent of participants stated that they had an increased knowledge of geometry and measurement
• 82 percent of participants reported feeling more competent in their ability to teach geometry and measurement
• 90 percent of participants agreed they were comfortable using manipulatives to teach geometry and measurement concepts
• 93 percent of participants reported being more aware of places to find appropriate technologies (e.g., the Web and appropriate software) to help them plan and teach geometry and measurement.1
  

We are proud to know that our efforts are having a positive impact. One elementary principal who attended the IMAGES 2002 Institute wrote, "All 3 of my fifth grade teachers attended IMAGES last summer. . . . I was thrilled that my 5th grade PSSA math scores continued to rise this year. . . . I couldn't help but note that my building was the only elementary building in our district with scores well above the state average in measurement and geometry. Proof to me that the IMAGES workshop we attended was well worth the time."2

With the publication of this second edition, we are continuing to gather evidence of effectiveness of the IMAGES program.

Rationale

The Pennsylvania State Team of the Mid-Atlantic Eisenhower Consortium at Research for Better Schools (RBS) has developed IMAGES (Improving Measurement and Geometry in Elementary Schools) to assist teachers and students in grades K-5 in improving their concepts and skills in these areas. Through this publication we hope to play a part in inspiring teachers to provide a firm foundation in mathematics that integrates geometry and measurement with sound teaching strategies that make use of the best educational research and teaching experience.

The Third International Mathematics and Science Study (TIMSS), conducted in 1995, clearly indicated that American students need to improve their understanding of geometric concepts and improve their basic knowledge in measurement and proportionality.3 This problem has been recognized by state educational agencies, the U.S. Department of Education, the National Council of Teachers of Mathematics (NCTM), institutions of higher education, school districts, and many educational publishers.4 Since the release of the TIMSS 1995 data, some mathematics projects have been highlighted as being exemplary or promising and have begun to be used in schools throughout the country.5 In addition, other publishers have examined these programs and have begun to develop standards-based mathematics textbooks and resource materials with strong content and an emphasis on big ideas. A review of states' test scores, the Third International Mathematics and Science Study-Repeat (TIMSS-R, conducted in 1999), and the Nation's Report Card 6 shows that the need for improvement in geometry and measurement continues. Additional time and more intensive professional development for teachers is needed to have the desired impact on student learning and achievement in these areas.

The Pennsylvania Governor's Institutes and Urban Academy programs during the summer of 2001 revealed many elementary teachers' limited knowledge of geometry. When it was announced by the Pennsylvania Department of Education that the Governor's summer professional development programs for teachers would focus on geometry, the number of applications for admission to those institutes doubled and tripled.7 Additionally, instructors' records indicate that participants who took the pre-test performed very poorly. In the Urban Academy for kindergarten through eighth grade teachers, only a few achieved a passing grade in the pre-test. In one group of 28 elementary teachers, only one passed the pre-test.8

While many educational agencies are striving to determine the causes for the lack of improvement in these areas, it is becoming clearer that many elementary teachers (through no fault of their own) have limited and faulty knowledge of geometric concepts and skills. Furthermore, research needs to inform instructional strategies and curriculum content for geometry and measurement in the classroom.

The benefits of geometry and measurement skills for students go beyond these specific content areas, and also help students with broader cognitive tasks, such as organization, problem solving, enhancing visualization, and even following directions.

To fulfill its goal of improving the quality of the teaching of geometry and measurement, IMAGES addresses elements that are integral to developing local school capacity:

• rich, rigorous academic content in geometry and measurement for K-5 teachers
• strategies to develop the skills and concepts students must have to meet or exceed state measurement and geometry standards
• a trained cohort of educators to share the program content with teachers in their district and surrounding districts
• support for the trained cohort after the initial summer institutes
• continuing professional education hours or graduate credit needed for recertification requirements
• a dynamic presence on the Web, with a site that will continue to grow and change, based on feedback and use of the materials.

IMAGES differs from other resources in that it comprehensively covers the geometry and measurement content expectations for teachers and for students in kindergarten through grade five. It also provides a broad collection of varying print and non-print resources addressing issues such as cognition and development, brain research, children's literature, assessment, and software.

IMAGES will continue to improve teachers' content knowledge, increase their use of best practices, change attitudes toward geometry and measurement, and provide a better understanding of how students learn. Our hope is that this will make a difference in classroom instruction as well as on students' performance in measurement and geometry.

How to Use IMAGES

This print version of IMAGES has been created in conjunction with a Web site, http://images.rbs.org, which will continue to grow as the program evolves. The resources are intended for: classroom teachers to use in furthering their own knowledge and in planning lessons; school administrators conducting professional development; other leaders within a school; and mathematics specialists and coordinators in a school or school district. IMAGES resources are keyed to both national and state standards. The relevant mathematics standards of several states appear in the appendices to this book; others are available on the IMAGES Web site.

The IMAGES team encourages educators to use these materials:

• as a resource to help implement state and national standards
• as a guide to determine what big ideas in geometry and measurement content are most important for students
• as a reminder that their own understanding of geometry and measurement is critical to their students' learning
• as sample lessons and activities, both to use as is and as the basis for creating new classroom experiences
• as a source for finding useful manipulatives, videos, technology, children's literature, and links to research and curricula that can improve the teaching and learning of geometry and measurement
• as a source of resources for teachers to improve their own content knowledge in geometry and measurement
• as a means to foster collaboration with other teachers in their schools and school districts, as well as with those in other districts.

One of the most important aspects of these materials is that they make it easier for teachers to see how to implement standards, as well as reinforce the big ideas related to geometry and measurement. This publication begins with an investigation of how children learn (cognitive and developmental issues), then presents what children should learn (geometry and measurement content) and how to teach and assess what children learn (teaching strategies, lesson plans, and assessment). The book finishes with multiple print and non-print resources.

1. Analysis of IMAGES Institutes, conducted August 2002-February 2004.
2. E-mail from Linda Lemmon, then Principal of Dillsburg Elementary School in Dillsburg, Pa., to Janie Zimmer, July 23, 2003.
3. U.S. Department of Education, National Center for Education Statistics, Pursuing Excellence: A Study of U.S. Fourth-Grade Mathematics and Science Achievement in International Context (Washington, D.C.: U.S. Government Printing Office, 1997), pp. 28-29; U.S. Department of Education, National Center for Education Statistics, Pursuing Excellence: A Study of U.S. Eighth-Grade Mathematics and Science Teaching, Learning, Curriculum, and Achievement in International Context (Washington, D.C.: U.S. Government Printing Office, 1996), pp. 28-29. Both are available online at http://nces.ed.gov/timss.
4. U.S. Department of Education, National Commission on Mathematics and Science Teaching for the 21st Century, Before It's Too Late: A Report on the Nation (Washington, D.C.: U.S. Government Printing Office, September 2000), available online at http://www.ed.gov/inits/Math/glenn/index.html; Tom Loveless and Paul Diperna, The Brown Center Report on American Education: How Well Are American Students Learning? Focus on Math Achievement (Washington, D.C.: Brookings Institution, 2000); National Council of Teachers of Mathematics, Principles and Standards for School Mathematics (Reston, Va.: National Council of Teachers of Mathematics, 2000).
5. U.S. Department of Education's Math and Science Education Expert Panel, Exemplary and Promising Mathematics Programs (Washington, D.C.: U.S. Department of Education, 1999), available online at http://www.enc.org/professional/federalresources/exemplary/promising.
6. National Center for Education Statistics, Nation's Report Card (Washington, D.C.: National Center for Education Statistics, 2003), available online at http://nces.ed.gov/nationsreportcard/.
7. Telephone interview with Linda Benedetto, Higher Education Associate at the Pennsylvania Department of Education, conducted by Janie Zimmer, October 2001.
8. Telephone interview with Linda Benedetto, October 2001.