Project Narrative

Demonstration of Need

This project grows from the No Child Left Behind federal legislation combined with low performance data locally in student mathematics achievement in grades 3-5. The No Child Left Behind mathematics challenge is to produce "the math excellence required for global economic leadership and homeland security in the 21st century" (U.S. Department of Education, 2002). Given the results of international studies, such as TIMSS (Michigan State University, n.d.), and national studies, such as the 2000 National Assessment of Educational Progress (National Center for Education Statistics, 2002), we know that mathematics continues to be an academic stumbling block for many children and adults. Though test results have improved slightly, No Child Left Behind reports that "only a quarter of our fourth- and eighth-graders are performing at or above proficient levels in math." This project partnership between a university and a school district with a large, underserved student population, will provide the No Child Left Behind mandated "urgency, tested methods, and high level expertise to rebuilding math excellence."

Academic student performance data for Tennessee school systems for the 2001-2002 academic year is available on the web (Tennessee Department of Education, 2002a, 2002b). Data for the Hamilton County Department of Education schools show several elementary schools with at least two of the three grades' TCAP mathematics achievement scores, grades 3-5, below the 40th percentile (median national percentile), as presented in Table 1. All percentile scores fall at least 20 percentile points below the state average for that grade, and at least 15 percentile points below the Hamilton County average for that grade. All of these schools are located in urban settings, with a large majority of students from underserved and/or underrepresented groups.

Table 1. TCAP mathematics scores (median national percentile) for low-performing Hamilton County elementary schools.

The above-listed elementary schools feed into several middle schools, which have low TCAP scores, as well, as presented in Table 2. Again, all percentile scores fall at least 20 percentile points below the state average for that grade, and at least 16 percentile points below the Hamilton County average for that grade. All of these schools are located in urban settings, with a large majority of students from underserved and/or underrepresented groups.

Table 2. TCAP mathematics scores (median national percentile) for Hamilton County middle schools into which low-performing elementary schools feed.

Performance varies greatly across schools within the same district, with median national percentile scores as low as 15, as seen in the Elementary School table. The achievement scores of students in suburban school settings are off-setting the scores from urban settings in overall district performance. The achievement score results of students in the district's urban schools exemplify the mathematics need of the students targeted by No Child Left Behind. They also allow ample room for growth in professional development experiences targeting inservice training as a means to improve student academic performance.

This project is aligned with Hamilton County's Project MaSS (Math and Science Synergy), funded through the National Science Foundation. The focus of the professional development area of the grant is for teachers to engage in at least 60 hours of professional development in mathematics and science each year of the grant. Professional development data for the 2000-2001 academic year is available on the web (Hamilton County Department of Education, 2001). Table 3 shows the number of teachers that engaged in the given number of hours of professional development in mathematics and science. Built-in professional development days in the academic calendar would account for several of the hours within the category of 0-19.99 hours.

Table 3. Number of hours of professional development in mathematics and science engaged in by Hamilton County elementary teachers from selected schools.

For elementary teachers in the entire district overall, 83.24% engaged in fewer than the NSF grant's goal of 60 hours of professional development. For the selected schools, 41% of the teachers engaged in fewer than 20 hours of professional development for an entire academic year. There are 3 inservice days for professional development built into the academic calendar. Disregarding other content areas, at best, each teacher would receive inservice training for 1-2 days on mathematics topics and 1-2 days on science topics, approximately 5 hours per day. An additional 25 hours over 5 days of professional development through this project, if funded, would substantially increase the amount of professional development experiences engaged in by 30 elementary school teachers.

The 60-hour mark of yearly professional development appears to be somewhat of a standard number. Llamas (1997) reports that in a National Science Foundation Rural Systemic Initiative grant targeting Hispanic and Native American populations, 25% of mathematics and science teachers at each of 102 schools received at least 60 hours of professional development during the 2nd year of the grant. Hamilton County teachers in the targeted elementary schools are lagging slightly behind this mark, with 22% of the teachers receiving 60 or more hours of professional development. Madsen and Gallagher (1992) describe a professional development program in science in which 8 junior high school teachers from 4 schools in Toledo were provided with over 60 hours of professional development. Teachers were then able to improve the quality of instruction at the departmental level, received a positive response from students toward new techniques and ideas, and demonstrated increased confidence and competence in their teaching.

Recruitment and Selection Plan

This project will serve teachers in the Hamilton County Department of Education schools, with an emphasis on serving teachers in urban schools. The single grade band of Grades 3-5, as defined by the National Council of Teachers of Mathematics (NCTM, 2000), has been selected. In a previously funded THEC workshop, Implementing Mathematics Standards through Computer and Calculator Technologies, presented summer 2000, participants stated on the workshop evaluation that they would have preferred a more narrow focus, rather than elementary, middle grades, and secondary teachers in the same workshop.

Two to three teachers of grades 3-5 will be sought from each of the 10 elementary schools listed above. Given the rezoning of schools due to the opening of two new downtown schools, Brown Academy and Battle Academy, workshop participation by teachers from these two schools will be important. Private school participants will also be recruited from schools such as The Lutheran School, Our Lady of Perpetual Help, St. Jude, Brainerd Baptist, Bright School, etc. UTC maintains a good working relationship with both public and private schools. A total of 30 inservice teachers will participate. School district personnel, school principals, and UTC faculty will assist in the participant selection process. Effort will be made to recruit teacher participants from underrepresented groups. Teachers from underrepresented groups can effectively be recruited as evidenced in previous THEC projects. Of the 20 teacher participants in the summer 2000 THEC workshop, 10 were from underrepresented groups.

Local Education Agency Collaboration

This project will be conducted in cooperation with the Hamilton County Department of Education which has an established working relationship with UTC. The project provides professional development opportunities available to teachers in additional to those provided through the NSF-funded Math and Science Synergy project, and those provided (for a fee) through the Eisenhower Regional Consortium for Mathematics and Science Education at Appalachia Education Laboratory. Hamilton County schools use the Everyday Mathematics series (SRA/McGraw-Hill, 2002) for grades K-5, which is correlated with the NCTM standards, and promotes innovative practices. In Everyday Mathematics, learning is promoted as summarized below:

Each topic is designed to reappear throughout the curriculum to ensure that ideas become integrated into the children's learning experiences. This curriculum organization emphasizes that mathematical concepts and ideas are visited and revisited in a wide variety of activities and in a variety of contexts.

The NCTM (2000, p. 168) states that in algebra, "students in grades 3–5 often work with geometric problems to explore patterns and functions," as seen in problems in which segments are added, as with towers or trains. Therefore, participation in this project will help teachers with the work they are already doing in the classroom, especially in the topics covered that are related to algebra and geometry.

Hamilton County will be providing 2 days of professional development for Grade 3 teachers in the geometry Navigations this academic year. Ava Warren, Co-director of Project MaSS, believes that this project, if funded, is exactly what is necessary to meet Hamilton County's needs as a professional development opportunity for teachers of elementary mathematics (personal communication, September 11, 2002). The project will be able to provide more in-depth training for teachers, as well as serving a larger grade band of teachers, than what the County currently has planned. It was agreed that if this project is funded, a few participants will be identified and prepared to lead workshops for additional Hamilton County teachers, further extending the reach of this project. Hamilton County will provide a stipend for these identified teachers for a 2-day preparation workshop after the close of the 5-day workshop.

Letters of support are contained in Appendix B.

Plan of Operation

Time Commitments. Thirty participants will attend a 5-day summer 2003 workshop, 5 hours per day, totaling 25 contact hours (Table 4).

Table 4. Summer Workshop Schedule (tentative dates).

Activities are listed under the content and pedagogy outline.

Instructional Plan. Goal and objectives.

Goal. The teacher will gain mathematics content knowledge and process skills as a result of project participation.

Measurable objectives:

1. There will be a statistically significant increase in participants' scores on the mathematics quiz between pre-test and post-test assessments.

2. There will be a statistically significant increase in participants' scores on the algebra portion of the mathematics quiz between pre-test and post-test assessments.

3. There will be a statistically significant increase in participants' scores on the geometry portion of the mathematics quiz between pre-test and post-test assessments.

Quiz items will be drawn from the publicly released TIMSS items that are relevant to the algebra and geometry topics under study in the workshop. To insure subject anonymity, teachers will use a self-selected code to pair pre-test and post-test forms. Paired scores, not names, are needed for data analysis.

In addition, overall workshop effectiveness will be assessed through a brief evaluation (strengths, weaknesses, and areas for improvement) which will be administered at the close of each day and at the close of the workshop. Evaluation material is contained in Appendix C.

Curriculum objectives for algebra that will be met through workshop activities include the following (NCTM, 2001a):

• recognize patterns in a variety of mathematical and real-life contexts; (p. 7)

• verbalize the rules that produce patterns; (p. 7)

• extend and make generalizations about patterns; (p. 7)

• analyze patterns given orally, in tables, and in graphs; (p. 7)

• use mathematical symbols as tools to communicate mathematical ideas; (p. 37)

• solve problems containing equations and inequalities with variables as unknowns, variables as quantities that vary, and variables in generalizations of patterns; (p, 43)

• extend the ideas of pattern rules and the representation of patterns to the notion of functional relationships. (p. 55)

Curriculum objectives for geometry that will be met through workshop activities include the following (NCTM, 2001b):

• developing the mathematics of shapes; (p. 10)

• compare and contrast a variety of two- and three-dimensional shapes and list the attributes and defining characteristics of the shapes; (p. 10)

• interpreting directions for moving from one location to another; (p. 35)

• finding and labeling points on the coordinate plane; (p. 35)

• explore and design figures with more than one line of symmetry; (p. 47)

• use precise and sophisticated language for rotations and angles when describing rotational symmetry; (p. 47)

• transform figures in their mind's eye and use the images to help construct new understandings of the figures. (p. 75)

Content and pedagogy outline. Through an immersed approach and concentrated study of elementary-school topics in algebra and geometry, this project will focus on inservice teacher professional development as an agent to effect change in the Grades 3-5 classroom. Content will be studied through the use of two publications from the National Council of Teachers of Mathematics: Navigating through Algebra in Grades 3-5 (NCTM, 2001a) and Navigating through Geometry in Grades 3-5 (NCTM, 2001b). Mathematics activities will be enhanced through the use of computer technology, in the form of software packaged with the Navigations books and relevant Internet sites.

Workshop activities will be drawn from the Navigations books, which themselves are activities by which the national standards for mathematics are implemented. Tennessee standards are based on national standards; local standards are based on state standards. Navigations promote both important mathematics for all students and innovative practices. Constructivist strategies will be used for teaching and learning. They include the following: focusing on learning through posing problems; exploring possible answers; focusing on global goals that specify general abilities, such as problem solving; stressing group work; and exploring open-ended questions (Roblyer, 2003). Hands-on activities using a variety of mathematics manipulatives will be emphasized. Manipulatives used will include those available commercially and those that can be made from inexpensive materials, such as paper photocopies. The activities specifically target two of the content standards, algebra and geometry. Activities will be drawn from Navigations topics, as presented in Table 5.

Table 5. Navigations lessons from which project activities will be drawn

In a document summarizing what is know about teaching and learning mathematics, Mid-continent Research for Education and Learning (2002) states the following:

Interesting contexts stimulate learning and retention. Cooperative group interactions and social construction of knowledge contribute positively to student engagement and attainment. Multiple approaches that allow students of different learning dispositions to gain access to problems engage students. Students will feel more capable in mathematics if they attribute success to their abilities and effort and if they feel that their success is meaningful, than if they attribute success to luck or external influences. (p. 18)

Technology, including use of the Internet, has become more commonplace in the P-12 classroom, and is addressed in the NCTM standards as demanded by the needs of society. It is one of the six principles woven throughout the national standards.

Workshop activities will occur in large and small groups, as individual work and presentations, within same-grade groups or same-school groups, and with and without the use of technology. Small group work will allow for extended study on particular topics, guided by an individual facilitator. Participants will focus on each standard and activity through hands-on activity, using manipulatives, collecting data, communicating mathematics, and making connections to other content areas.

Each teacher will receive the following: (a) the book Navigating through Algebra in Grades 3-5 ($27.95); (b) the book Navigating through Geometry in Grades 3-5 ($32.95); (c) Hands-on Teaching Strategies for Using Math Manipulatives Grades K-6 kit ($69.95); and (d) a $50 per day stipend ($250 total). Lunch and snacks, and a parking pass will be provided. The ETA kit (Thornton & Lowe-Parrino, 1998) contains transparent versions of manipulatives for use with an overhead projector. Teachers may then use the materials for classroom presentation. An activity book is included in the kit, extending the reach of the workshop with additional materials to be used during the school year. Kit activities are correlated with the NCTM standards.

Project faculty. Deborah McAllister, a tenured Associate Professor with responsibilities in Mathematics Education and Educational Technology, and will serve as the Project Director. This is her 10th year at UTC. She recently attended several of NCTM's conference sessions that discussed implementation of the Navigations series in the classroom. Four teacher consultants, Kaye McClanahan, Lisa Richardson, Shirley McDonald, and one teacher selected in conjunction with Hamilton County Department of Education personnel, will serve as workshop facilitators. Project faculty have participated as facilitators for previous Eisenhower (THEC and AEL) workshops. Their areas of expertise include mathematics and technology. Each of the project faculty provide a current knowledge base and particular technical expertise in standards and topics under study, such as (a) doing and communicating mathematics, (b) using technology, (c) teaching through developmentally appropriate practices, and (d) including multicultural approaches. Workshop activities will be lead and modeled according to current practice.

A spring 2003 graduate assistant will provide a curriculum mapping of workshop activities to national, state, and local curriculum standards for mathematics and will order workshop materials. Curriculum mapping will be done in the style of a Curriculum Crosswalk, as detailed by Jordan and Audet (2002). Two summer graduate assistants will assist with workshop implementation by unpacking and assembling materials for workshop activities, photocopying, assembling participant notebooks, interfacing with food services, and assisting with data analysis of participants' test scores and session evaluations. Technology skills required include expertise with word processing, spreadsheet, and statistical software. Peggy Moyer, Dr. McAllister's current graduate assistant, will likely serve as one of the summer graduate assistants for the project. Faculty vita are contained in Appendix A.

Management Plan. Timeline of project activities. The timeline of project activities, December 1, 2002 - September 30, 2003, with optional course credit through December 21, 2003, is presented in Table 6.

Table 6. Project timeline.

Institutional commitment. Project activities will be conducted in UTC's classroom space and technology classroom in Hunter Hall. The technology classroom contains 26 Dell (Windows-compatible) computers with Internet access. Two of Dr. McAllister's previously funded THEC/Eisenhower workshops were held in the previous 21st Century Classroom. UTC also houses an Access Center for the Eisenhower National Clearinghouse.

Collaboration. Through prior grants, workshops, and UTC courses Dr. McAllister has worked with teachers and administrators from most of the schools in Hamilton County. Some of the schools' faculty received ConnecTEN and federally-funded training for various programs at UTC in the 21st Century Classroom. School personnel have earned advanced degrees from UTC. UTC faculty have a presence in many of the Hamilton County schools through the Professional Development School programs, as well as other grants and partnerships, including the partnership with the two new downtown schools, one of which was funded through private donation. Private school participation will be encouraged. If participation is lower than expected, two strategies may be used for further recruitment of participants. The project is flexible enough to be modified to include (a) Grade 2 teachers from participating schools, or Grade 3-5 teachers from other schools; or (b) Grade 6 teachers with low-performing students.

Upon funding, principals will be contacted for input on the participant selection process. The project director will prepare a brief PowerPoint (Microsoft Corporation, 1998) overview of the project to be distributed in paper and/or electronic form.

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