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					                              Promising Math Practices

Arizona: Statewide Instructional Technology Project

Two years ago the Statewide Instructional Technology (SIT) project was implemented to
promote staff development that teaches teachers to integrate technology into all curriculum areas.
Mathematics Workshops within the project are linked to Arizona Standards and use of current
technologies. The project follows Best Practices for the NETS standards and the NSDC
Standards. The project addresses all students but individual workshops are geared towards
specific grade levels and topic areas. Within each workshop standards alignment is highlighted
and the level of teacher expertise dealing with technology is taken into consideration. Within the
lesson the needs of the students within each teachers' classroom is addressed by varying the
curriculum and by allowing the participants to share their real life experiences. The teachers
brain storm ways to accommodate all student learning needs. Each teacher is presented with
classroom techniques and technology skills that will help them integrate the technology into
Mathematics.

Role of Technology: Within each workshop the technology used emphasizes hands on learning,
problem solving, and correlation with Mathematical concepts. The alignment of these three is
Best Practices. As mentioned earlier, workshops align with state and national technology
standards as well as the Math Academic Standards for Arizona. This is stated in the workshop
materials and is also evaluated at the end of the workshops by the participants. The workshop
projects promote the use of technology tools for problem solving and research such as using
spreadsheets to verify the “Guess and Check problem solving strategy.” Student research can be
shared by Power Points of geometric shapes, or video taping of integer operations. The project
offers students a variety of technologies to use and shows them the benefits and draw backs of
each for the required tasks.

Grade Level: Yes

Cross Curricular Connections: Cross curricular connections can be found throughout the
project. In the Geometry PowerPoint students must story board each slide which promotes
sequencing and process writing. The graphic organizers that are used with each of the Discrete
Math concepts

Classroom Observers View Students: Yes, the students work in teams to hypothesize a
solution to a problem. Students use technology to determine the accuracy of their guess. They
also use technology tools to share their findings with their classmates and explain their
reasoning. Products such as student Power Points, student spreadsheets, student graphs, and
student drawings all would be evidence of this active engagement.

Data or Formal Evaluations: Each workshop has an evaluation that participants need to
complete for internal review. Adjustments to the project workshops are made based on these
evaluations. We have formative assessment through the Technology Assessment Project from
Learning.com. The TLC from Learning.com assessment is not only multiple choice but also a
process assessment where students need to demonstrate proficiency on a certain skill. The
technology integration specialists also collect anecdotal data.
                              Promising Math Practices
Best Practices: The project has an external review process. There is internal monitoring of the
project and the workshops to ensure alignment with project goals and state initiatives and
standards. The project is replicated throughout the State of Arizona for all schools. The project
was designed so that all counties would have technology integration specialist and all schools
(public, private and charters) would have access to integration training and workshops.

How does the project or initiative tie with federal or state requirements? The project is
aligned to EETT Title IID project goals and encompasses state initiatives and academic
standards within the scope of the project.

Estimated Cost: Year 1 $1.5 million dollars. Year 2 $890,000.

Funding Source: EETT Title IID

Number of Each Impacted by Project: All districts and schools in the state have access to
these resources and workshops, which would impact all teachers and students. Not all schools
and districts chose to participate.

Other Resources: The technology integration specialists use their ASSET websites to share
lesson plans and workshop strategies. The ASSET portal is a free resource for Arizona schools
and educators.

Project Contact:
Denise Ryan
Technology Integration Specialist
Pima County Regional Support Center
dryan@pimaregionalsupport.org
(520) 745-4588
                               Promising Math Practices

California: EETT Competitive Grant Math Project

The Clovis Unified EETT Math grant is serving 2600 7th and 8th grade math students at four
intermediate schools. The program included two math/technology coaches who worked one on
one with 32 math teachers, provided quarterly day long professional development and a four-
day summer math institute for the intermediate school math teachers. The daily coaching
included demonstration lessons in math classrooms. Sets of 15 computers in carts, teacher
projectors and teacher computers provided daily computer based lessons for students provided by
these teachers.

Professional development has been offered through a combined approach, infusing technology
and math by integrating the Lesson Study Model for professional development with the
Technology Coach Model. Through this approach, teachers not only learned to become more
proficient at creating math instructional plans, but learn to do so using a technology-supported
curriculum.

Role of Technology: Two math teachers created a web site (www.cusd.com/math), which is a
repository for all the teacher developed lesson plans, PowerPoint presentations and on-line
resources such as self-directed student tutorials. These online tutorials helped math teachers
differentiate their instruction by directing their students to these tutorials to work on problem
areas. Resources such as PowerPoint presentations, handouts and worksheets, were also
developed to aid teaching each particular lesson plan.

Grade Level: Grade 7-8

Cross Curricular Connections: Yes

Classroom Observers View Students:

Data or Formal Evaluations: Annual program performance report provides data for students in
the target group. This data shows 84.3 percent of students had increase proficiency in math
content standards as measured by district pre-algebra diagnostic and post test.

The impact the grant is having on student achievement will be determined by District Benchmark
Testing and California Standards Testing in Math. District benchmark testing is conducted at the
conclusion of each math unit. A total of 9 benchmark tests will be given during the school year.
The results have yet to be disaggregated for target students only.

Best Practices: Cross curricular and interschool collaboration utilizing technology.

How does the project or initiative tie with federal or state requirements? The program is
based on state standards and district curricular goals as defined in the district technology plan.

Estimated Cost: Implemented using the EETT-C grant funds over a three year period,
$1,821,396.
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Funding Source: Title II D, EETT-Competitive grant

Number of Each Impacted by Project: 1

Other Resources: Two math teachers provided all the staff development and created a web site
(www.cusd.com/math), which became a repository for all the teacher developed lesson plans,
PowerPoint presentations and on-line resources such as self-directed student tutorials. All these
resources were developed by using a Japanese strategy called Lesson Study. Using the Lesson
Study process, the math teachers came together several times over the course of the grant for a
full day of collaborating to develop lesson plans that addressed specific standards that were
problematic for the district. Resources such as PowerPoint presentations, handouts and
worksheets, were also developed to aid teaching each particular lesson plan. Teachers were then
observed teaching the lessons in their by other teachers in order to determine the student mastery
of the material. Target teachers were also required to attend a week long summer math institute.

Project Contact Person
Raylene Paustian
Clovis Unified School District
Project Specialist
Raylenepaustian@cusd.com
(559) 327-9635
www.cusd.com/math
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Indiana: Beyond the Textbook & Community Link
The EVSC EdTech grant, in its 4th year, targets 3rd, 4th, and 5th grade teachers and their
students. Five public schools and 2 non-public schools participate in this grant. The grant
focuses on helping teachers to have a better knowledge of mathematical concepts and to
construct concept-based lessons using a hands-on approach. The results have shown
increased student understanding of math concepts.

The iCATS provide frequent workshops on mathematical concepts addressed in the
Indiana State Standards. Teachers use ideas, activities, and resources presented in these
workshops to write hands-on concept based math lessons that include Indiana Academic
Standards. Each lesson includes the Standards that are addressed, prior concept
knowledge and an engagement activity. Lessons are tested in the classroom before they
are posted to the Lesson Plan page. As part of each lesson students are encouraged to use
math journals as a means to increase understanding or for assessment of an activity.
iCATS are also available to model math skills in the classroom and give support in
technology as needed.

Students are assessed three times a year. These assessments are based on the state
standards and help teachers determine students' strengths and weaknesses. The
assessments are graded by an outside evaluator and are then returned to the teachers.
Error patterning is used to evaluate the assessments and determine how to further
students' learning and understanding.

Role of Technology: Expanding teachers' use of technology is another goal of this
EdTech grant. To level the playing field in the first year of the grant, iCATS made sure
that all teachers had a way to use their computers in the classroom as a teaching tool.
iCATS made sure that teachers' televisions were connected to a scan converter so they
could project websites as well as programs to the class. During this grant, teachers have
been surveyed three times a year to ascertain their levels of expertise in technology areas.
iCATS then have helped teachers build upon their technology levels.This has been done
by modeling technology during the math workshops and also by scheduling technology
workshops afterschool or by meeting with teachers on an individual basis during their
plan periods or before or after school. Teachers were given instruction the first year in
technologies that would be helpful in writing and teaching the new math lessons that they
were creating. A few of the technologies that were taught during the first year were
Microsoft Word, PowerPoint, GraphMaster and the use of digital cameras. To accomplish
the technology goals of this grant, each EVSC school has a "My Cat" assigned to their
building. This has been helpful for communications and to ensure that teachers know who
to call for help.

Grade Level: Grade 3-5

Cross Curricular Connections: Yes

Classroom Observers View Students: Yes
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Data or Formal Evaluations: Yes, see
http://www.evscicats.com/edtech/academics/data/
Teachers administer math assessments three times a year to their students. These
assessments are based on the state standards and help teachers determine students'
strengths and weaknesses. The assessments are created and graded by an outside
evaluator, University of Evansville Assistant Professor of Education Amy McBride
Martin . The tests are then returned to the teachers for review and error patterning. Error
patterning is used to evaluate the assessments and determine how to further students'
learning and understanding. By evaluating the students' assessments together during a
team plan period, grade level teachers help each other form instructional strategies that
will give students the experiences necessary to become successful in math. Student
iSTEP math scores are increasing.

Best Practices: This projected is predicated on Best Practices in mathematics education.
Kay Tolliver's Hands-On Math and Liping Ma provided part of the theoretical construct
of this project. Indiana Ed Tech Schools must adhere to grant guidelines as follows:
     Year 1 - project is up and running by beginning of school year
            o Student and teacher data is submitted Nov, April and June each year
     Year 2 – same requirements as Year 1, additionally:
            o Project must demonstrate student achievement gains with intervention
                population
            o Project must be scaled vertically or horizontally
            o All project teams must present at regional, state and/or national
                conferences
     Year 3 – same requirement as Year 1 & 2, additionally:
            o LEA must provide electronic dissemination (website) of results to data
                with supporting templates, lessons, professional development strategies
                and documents to allow other LEAs to replicate project.
     Year 4 – same requirement as Year 1, 2 & 3, additionally:
            o LEA must serve as an outreach site for other LEAs to visit (virtually or
                face-to-face) and begin replication of the project.
     Year 5 – same requirement as Year 1, 2, 3 & 4, additionally:
            o LEA must serve as a mentor (both virtually or face-to-face) for other
                LEAs to begin replication of the project.
            o Evansville will be required to mentor a site in Year 5.

How does the project or initiative tie with federal or state requirements?

Estimated Cost:

Funding Source: Title II, Part D and local funds are used.

Number of Each Impacted by Project: 1 district, 7 schools, approx 60 teachers per
year, approx 1200 intervention students per year, approx 250 control students per year,
approx 1450 total students per year
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Other Resources: Video, Lesson Plans, modeling,
http://www.evscicats.com/edtech/sorter

Project Contact: Mike Russ - Director of Technology for the EVSC
mkruss@evsc.k12.in.us
Phone: (812) 435-5290
Fax: 812.435.8387
http://www.evscicats.com/edtech
                   Math Best Practices Survey Results

Iowa: E2T2 - Keystone

ALEKS is a web-based, artificially intelligent assessment and learning system. ALEKS
uses adaptive questioning to quickly and accurately determine exactly what a student
knows and doesn't know in a course. ALEKS then instructs the student on the topics she
is most ready to learn. As a student works through a course, ALEKS periodically
reassesses the student to ensure that topics learned are also retained. ALEKS courses are
very complete in their topic coverage and ALEKS avoids multiple choice questions. A
student who shows a high level of mastery of an ALEKS course will be successful in the
actual course she is taking.

ALEKS also provides the advantages of one-on-one instruction, 24/7, from virtually any
web-based computer for a fraction of the cost of a human tutor. ALL fourth, fifth, and
sixth grade students throughout Keystone AEA will have FREE individual access to an
online personal mathematics tutor program called ALEKS. This Internet delivered
software will cover specific skills and benchmarks that are connected to the standards
recommended by the Iowa Department of Education. ALEKS will supplement your
classroom instruction and compliment the existing curriculum and texts your district is
currently using.

This E2T2 grant was written to address improving student achievement in mathematics
for all students in the targeted grades. E2T2 has been in practice four years.

Role of Technology: The system involves the delivery of professional development
activities and support and the determination of the accountability and impact of the
professional development on student achievement. This will be accomplished using the
ICN for two-way audio-video transmission and data delivery. In addition, the
dissemination and support of the research model and the professional development model
is made through conferences and Internet II (IP-based video conferencing and web
pages). The course content is based on scientifc evidence. The project does not
incorportate state education technology standards or components form the National
Education Technology Standards for Students (NETS*S) from ISTE. The project
includes the use of technology tools for research and problem solving activities and as
communication devices for presenting information and/or sharing work completed.

Grade Level:

Cross Curricular Connections: Probably but not currently being done.

Classroom Observers View Students: Yes

Data or Formal Evaluations: Yes

Best Practices: External evaluator at Iowa State University.
http://perl.hs.iastate.edu/E2T2-800.htm
                   Math Best Practices Survey Results
How does the project or initiative tie with federal or state requirements? The
impetus for this project is the need: 1) to address the NCLB requirements within the
context of the federal government’s educational entitlement programs in a rural state, 2)
to discuss the problem of evaluating the effectiveness of technology and teacher fidelity
in implementing pedagogy and the nature of change in classroom instruction in meeting
the NCLB requirements, 3) to evaluate the effectiveness of elements of the IPDM as
implemented in the Area Education Agencies professional development activities and
teacher practices in the classroom, 4) to evaluate the effectiveness of elements of the
IDMM, and 5) to develop and evaluate a communication plan and support system as
related to the issues of sustainability of effective strategies and best practices in the
classroom.

Estimated Cost: approximately $600,000 per year including federal, state, AEA and
LEA resources and dollars

Funding Source: Federal, state, AEA and LEA

Number of Each Impacted by Project: 24 districts, 50 schools, 300 teachers, and 3,500
students

Other Resources: A complete list of resources can be found at
http://www.aea1.k12.ia.us/e2t2/e2t2hp.html

Project Contact:
Rhonda Sheeley,
Director of Media & Technology Services
AEA 1 Keystone
sheeley@aea1.k12.ia.us
563-245-1480
                    Math Best Practices Survey Results

Kansas – Technology Rich Classrooms

The Kansas Technology Rich Clasroom program, which began in KS in 2003, focuses on
providing technology rich learning opoprtunities for students/teachers in Gr 3-6 within
content area focuses of reading/math and or science. Of the $7.14 million funded to date,
$1.96m has been targeted specifically at Math related projects to directly support state
math standards. The program specifically outlines required technologies, required
professional development--which is provided through a .5 facilitator who directly
supports the TRC teachers--along with program required activities/events. The program
stems from blending best practice approaches for classroom instructional strategies and
instructional technology implementations.

Regarding the question on scientific research, TRC incorporates a variety of research-
based best practices including Marzano's "What Works"research, Brain-
based/Cooperative Learning/Student Engagement research, ISTE NETS, Partnership of
21st Century Skills, LoTi framework, INTEL Teach Program and Buck Institute (BIE)
Project-Based Learning, Leadership Training (Kal-Tech and other), in addition to basic
technology literacies etc. A formal external evaluation (thru Wexford) provides ongoing
feedback &recommendations for program improvement. Additional information is
available at:
http://take.ksde.org/TechnologyPlanning/Funding/EnhancingEducationThroughTechnolo
gyGrants/TechnologyRichClassroomProject36/tabid/125/Default.aspx

Role of Technology: Technology is a major required component of the TRC program.
Specific technology is required and NETS and 21st Century Skills (including problem-
solving) are incorporated. The project-based learning professional development provided
through INTEL, and ALTEC (Buck institute PBL resources) specifically targets how to
teach with technology, how to structure learning activities that focus on teamwork,
collaboration and communication, as well as supporting student initiative and self-
directedness in supporting the project outcomes (all of which are 21st century skills).

Grade Level: 3-6

Cross Curricular Connections: Many of the projects are actually 'integrated'==meaning
they address more than 1 content area (as they should). Students are involved in geo-
caching activities in some projects, telecollaborative projects, e-field trips, etc.. Helping
provide teachers

Classroom Observers View Students: We recognize that it is an 'ebb and flow'
approach--we correlate it to a 'lava lamp', as there are times where direct teacher
instruction has to occur. Regularly/frequently students would be activitely engaged in
these types of student-centered learning opporutnities (but not 100% of the time).

Data or Formal Evaluations: Wexford provides a formal, external program evaluation,
which primarily addresses our capacity to support teacher professional development and
instructional technology impelementation and skills. The program does not include
                    Math Best Practices Survey Results
specific student outcomes (although the local evaluation component incoporates student
level data). The local evaluation usually includes student achievement information. We
do not collect student work samples, although many are published on their local project
websites linked from the TRC page.....

Best Practices: The TRC program was originally modeled after Missouri's eMints
program, with the exception that the local project facilitator is hired by the participating
district (not a state department employee/contractor). The project is considered
replicable, and we are in the process of developing a professional development
framework which could be used by districts implementing laptop intiatives or other
classroom related technology intiatives.

How does the project or initiative tie with federal or state requirements? NCLB
EETT requirements; support student achievement/standards focused instruction.

Estimated Cost:

Funding Source: EETT Title IID and some local dollars

Number of Each Impacted by Project: 42 grants have been awarded to date impacting
64 school districts, 168 classrooms in 70 schools. Approx. 170 teachers have been
directly involved, with many schools including additional staff at professional
development opportunities.

Other Resources: A variety of resources are available via the TRC website at
http://trc.altec.org

Project Contact:
Melinda Stanley
KSDE
TRC Project Director
mstanley@ksde.org
785.296.1204
                    Math Best Practices Survey Results

Louisiana: Louisiana Virtual School/Algebra I Online Project

The Louisiana Algebra I Online Project, a part of the Louisiana Virtual School (LVS), is
a Department of Education initiative in its fifth year of implementation that provides
Louisiana students with a certified Algebra I instructor and a high quality Algebra I
curriculum through a web-based course.

The project targets rural and urban districts having schools with one or more classes of
Algebra I which are taught by an uncertified mathematics teacher. A hybrid model of a
combination of online and face-to-face instruction is used. An in-class teacher who works
closely with the secondary mathematics certified online teacher in providing online
instruction to students. The in-class teacher receives support/mentoring throughout the
project and participates in a strong professional development program (face-to-face and
online) that will build capacity for strong mathematics instruction.

The Algebra I Online course is technology-rich and aligned to NCTM and state standards
and Louisiana Grade 9 GLEs (Grade-Level Expectations). It focuses on an inquiry-
learning and an investigative approach with various interactive applets, viewlets, popups,
and other interactive tools that promote development of conceptual understanding.
Activity labs are included that encourage student collaboration beneficial to students of
all academic levels. Students utilize technologies, such as the graphing calculator,
cbls/probes, digital tablet and pen, e-mail, etc.

Role of Technology: The Algebra I Online course is technology-rich and aligned to
NCTM and state standards and Louisiana Grade 9 GLEs (Grade-Level Expectations).
During course development, state standards and scientific research were considered. The
course focuses on an inquiry-learning and an investigative approach with various
interactive applets, viewlets, popups, and other interactive tools that promote
development of conceptual understanding. Activity labs are included that encourage
student collaboration beneficial to students of all academic levels. Students utilize
technologies, such as the graphing calculator, cbls/probes, digital tablet and pen, e-mail,
etc. In addition, optional activity labs are given to the teachers for the course focus areas.

Grade Level: Grade 8-10

Cross Curricular Connections: All course activities are based on real world
applications that cross curriculum areas.

Classroom Observers View Students: In each chapter, the Algebra I students are
collaboratively discussing solutions of problems that will be posted on the discussion
board problem-solving forums and team activity labs where students are actively
involved in providing evidence in support of their hypothesis.

Data or Formal Evaluations: The Algebra I Online Project final report by external
evaluators provides statistical data that demonstrates effectiveness of the program in
                   Math Best Practices Survey Results
terms of student and in-class teacher outcomes and recommendations for continued
improvement.

Best Practices: The external evaluators use data collection and analysis to help identify
best practices. The hybrid model has proven to be successful and will be used as a best
practice instructional model for other specific distance learning programs.

How does the project or initiative tie with federal or state requirements? The
Algebra I Online course meets NCTM requirements and state standards. The provision
of ongoing professional development for in-class teachers helps these teachers become
highly qualified and with their pursuit of certification.

Estimated Cost: N/A

Funding Source: The project is funded by the Louisiana Legislature and offered at no
cost to the districts.

Number of Each Impacted by Project: There are 13 districts, 18 schools, 21 teachers,
and 325 students in the Algebra I Online Project this 2006-2007 year.

Other Resources: Teachers are provided with additional online and offline resources, i.e.
website licenses with focus areas of specific math content, Praxis exam preparation, and
instructional technology and technology and math content based workbook resources.

Project Contact:
Dianne Gauthier
Louisiana Department of Education
Educational Technology Consultant
dianne.gauthier@la.gov
225-763-8604
                   Math Best Practices Survey Results

Maryland Eastern Shore Math Consortium (ESMC) II

The second Eastern Shore Math Consortium professional develoment program will serve
60 classroom, special education, and ELL mathematics teachers, grades 4-8, from 6
counties, the Maryland State Department of Education, and institues of higher education
including: Wicomico County, Caroline County, Dorchester County, Kent County,
Somerset County, Worcester County and Salisbury University Henson School of Science
ant Technology (Math Department) and Salisbury University Seidel School of Education.
This two-year program will include MSDE online algebra modules, a five-day summer
institute, Praxis preparation, an online discussion board, lesson plan development, and
attendance at a professional conference. Participants will receive resource materials and
technology. County supervisors and coaches will provide classroom follow-up. The goal
of the project is to improve the mathematics acheivement of the participating teachers'
students and increase the effective use of technology. The project will also increase the
number of highly qualified mathematics teachers on the Eastern Shore.

Role of Technology: Technology is an intregral role in effective mathematics instruction.
The teachers receive "technology bundels" including a graphing calculator, document
camera, LCD projector and a tablet PC. The professional development follows the
guidelines of the Maryland Professional Development Standards and the Maryland
Technology Literacy Standards for PK-8. Teachers receive extensive professional
development with job-embedded follow-up support from coaches. They also participate
in the Online Algebra Data Analysis Course and a professional learning community in
Desire 2 Learn.

Grade Level: 4-8

Cross Curricular Connections:

Classroom Observers View Students: Yes and we have data collected by an external
evaluator and district curriculum coordinators.

Data or Formal Evaluations: This project is made possible through the Title IIB and
Title IID grant funds. It is evaluated by MACRO International. Teacher and student
impact must be measured. The report is available upon request.

Best Practices: This project is in the second funding cycle. Adjustments to the grant
were made between the first and second funding cycle to include additional job-
embedded support for teachers and more accountability of the online learning. A similar
structure is in place for Science in Western Maryland.

How does the project or initiative tie with federal or state requirements? It is
supported by Title IIB and Title IID. Having highly-qualified math teachers is a concern
in Maryland and this grant is increasing the number of highly qualified regular, special
education, and ELL teachers on the Eastern Shore. It also infuses effective instructional
practices and increases the teachers content knowledge to enable them to differentiate
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their instruction. It supports the Maryland Voluntary State Curriculum for Mathematics,
the Maryland Technology Literacy Standards PK-8, and the Professional Development
Standards.

Estimated Cost: $618,000

Funding Source: Title IIB and Title IID

Number of Each Impacted by Project: 6 districts, 60 teachers, and 1,200 students

Other Resources:

Project Contact:
Nancy Carey
Coordinator of Professional Development
200 West Baltimore Street
Baltimore, MD 21201-2595
410-767-0441
ncarey@msde.state.md.us

Bonnie Ennis
Mathematics Coordinator PK-8
Wicomico County Public Schools
P.O. box 1538
Salisbury, MD
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Michigan - Middle School Mathematics Initiative (99b Funds)
With our 99b funds (Middle School Mathematics Money) we provided professional
development for middle school mathematics teachers. That included AlgeBlocks,
Geometers Sketchpad, TinkerPlots, TI -73. Along with the 1/2 day of professional
development each participant received a single user kit of that software for their
classroom. Each school received 10 graphing calculators. We also provided scholarships
to 12 middle school teachers to attend the Texas Instrument Teacher Leader Cadre that
focuses on Algebra & Geometry instruction with the TI-84. Along with the professional
development of the teachers, the MISD will host 300 students for 8 (1/2) day sessions as
a Summer Math Camp that will encourage technology usage in all the strands of Number
Sense, Algebra, Geometry, and Data & Statistics. The camp will have two sites, one on
the north end of the county and one on the south. Along with this, we are using funding
to write additional professional development for the integration of technology in each of
the strands. We call this project M-GLAnCE as it focuses on good instruction around the
state Grade Level Content Expectations.

Role of Technology: Teachers and students will be exposed to the power of the graphing
calculator as a method to communicate mathematics in the middle school. The
constructivist approach to instruction is the focus on the Geometers Sketchpad,
TinkerPlots, & graphing calculator professional development. Because several districts
cannot support the technology with complete student labs, teachers are given the
opportunity to see and develop lessons with one single user kit. Students will be
exposed to technology

Grade Level: Middle school

Cross Curricular Connections: Yes

Classroom Observers View Students:

Data or Formal Evaluations: We will monitor the MEAP scores of our 5 lowest scoring
districts as well as other schools who participated in the professional development.
We have had an overwhelming interest from both teachers and students in this project.
Enrollment in our training programs has vastly increased. We will watch for this affect
on overall county MEAP data.

Best Practices: All instruction is based on the discovery/constructivist approach to
education. Writing in the content area and technology are supported by lessons.

How does the project or initiative tie with federal or state requirements? The project
follows the guidelines of the state 99b fund money distribution. We have also put an
emphasis on training the teachers and students of our 5 lowest scoring (MEAP) districts.
We have analyzed their MEAP data with them and encouraged training in weak areas.

Estimated Cost: Approximatel $300,000
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Funding Source: Michigan 99b-Middle School Mathematics Money

Number of Each Impacted by Project: 21

Other Resources: We have also created a website for parents to sustain the summer
camp experience. When students are finished with the summer camp, we have written
additional lessons available on our website to sustain the experience, complete with
lesson plans, activities, and answer sheets in each of the four strands.

Project Contact:
Middle School Mathematics 99b
Macomb Intermediate School District
Marianne Srock (director), Nancy Searing (asst)
msrock@misd.net
586.228.3482
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New Jersey Bridge Project

For the past three years, Wharton Borough Public Schools has participated in a Title II,
Part D discretionary grant program entitled Math Achievement To Realize Individual
eXcellence (MATRIX). The grant has focused on integrating technology into the middle
grades math curriculum (grades 6-8). The Bridge Project is a lesson plan developed due
to the grant program.

In the Bridge Project, students are to plan for the construction of a new bridge over the
Hudson River to meet the needs of the expected increase in traffic in the future. As bridge
designers, students plan and design new bridges to connect New York and New Jersey.
They then construct models of their bridges.

Seventh grade special education students involved in the MATRIX grant progam took
first place for their bridge designs and models at the middle school level during the
National Council of Teachers of Mathematics (NCTM’s) National Conference in Atlantic
City on October 19, 2006. The teaching team and district administrators were especially
proud of this achievement because the students competed without the judges’ knowledge
of their special math needs.

Role of Technology: Technology was used by the teachers for the creation of the lesson
plan as well as for classroom instruction on the project. Students used technology for
research, problem solving with data analysis as they investigated the plane geometric
figures used in bridge construction, reporting, and presenting their work.
The Bridge Project incorporates components of New Jersey's Technological Literacy
Standards which are aligned with ISTE.

Grade Level: 6-8

Cross Curricular Connections: Cross curricular connections could be made with
Science, Technology Education (engineering), and Social Studies.

Classroom Observers View Students: The Bridge Project created a student centered
learning environment. Students had to investigate types of bridges, the plane geometric
figures used in bridge construction and be able to explain the pros and cons associated
with each bridge type/geometric figure. They then had to apply this content knowledge
by designing their own bridge and constructing a model of it.

Data or Formal Evaluations: Wharton Borough has realized increases in student
achievement in Math on state assessments. Teachers report students are highly engaged,
spend more time on task, and are reluctant to leave/miss Math class for other activities.
Integrating technology into the math curriculum has provided students with an
opportunity to gain a deeper understanding of math content and to demonstrate their
proficiency in math as is evidenced by the awards received by their seventh grade math
students. It should be noted that two groups of students from Wharton's MATRIX grant
                    Math Best Practices Survey Results
won awards: special education students were awarded first place and gifted and talented
students were awarded second place at the NCTM National Conference.

Best Practices: The National Council of Teachers of Mathematics at their national
conference reviewed the student work submitted by Wharton Borough and awarded these
students first and second place.

As part the of the requirements of the MATRIX grant, Wharton teachers will be
replicating this lesson with another school district. The need to replicate the successes of
the grant program were built into its design from the very beginning.

How does the project or initiative tie with federal or state requirements? The
MATRIX grant ties into both federal as well as state goals of creating new learning
environments through the integration of technology into the curriculum. It also addresses
the need to improve student achievement in mathematics.

Estimated Cost:

Funding Source: The MATRIX grant is funded by Title II, Part D discretionary funds
from NCLB.

Number of Each Impacted by Project: The MATRIX grant has impacted sixty (60)
public school districts in New Jersey and 34 nonpublic schools.

Other Resources: Bridge Project PowerPoint:
http://wharton.nj.k12us.com/_tools/?u=13188
Photos of Project/Awards: http://mcubed4.tripod.com/id44.html
Wharton MATRIX Web Site: http://mcubed4.tripod.com/index.html
New Jersey Department of Education MATRIX Web Site:
http://www.state.nj.us/njded/techno/grants/matrix/

Project Contact:
Joseph Seaman
Wharton Borough Public Schools
Debra Leary
Wharton Borough Public Schools
MATRIX Coordinator
Alfred C. MacKinnon Middle School
137 E. Central Avenue, Whaton, NJ 07885
973-361-1253 x388
dleary@wbps.org
                    Math Best Practices Survey Results

Ohio Title II D – Enhancing Education Through Technology (EETT)

Winton Hills K-8 Academy (WHA) in Cincinnati, OH, applied for and was awarded the
2004-2005 Ohio Enhancing Education Through Technology (EETT) grant, which is a
two year initiative. Grant applicants were required to explain what they plan to do, how it
related to relevant research, how they planned to implement the program, what data they
gathered and how they planned to use the data to evaluate the program/grant activities.
Applicants were required to develop process and accountability measures that would be
used to evaluate the extent to which activities funded under the program are effective in:
1) integrating technology into curricula and instruction; 2) increasing the ability of
teachers to teach using technology; and 3) enabling students to meet or exceed State
Board-adopted academic standards.

For WHA the EETT grant provided advanced technology in hardware and
implementation of a web-based learning management system (LMS) addressing
Mathematics and English/Language Arts standards, and staff development. These
programs align with the district’s Continuous Improvement Plan (CIP) and WHA’s
Technology Plan to provide all students with effective technology based curricula in
support of meeting the reading, math and technology standards. The program was
implemented school wide providing equal access to all students, school staff and parent
leaders. Students worked with the program daily. Grades 4-6 were targeted for statistical
analysis.

Role of Technology: Applicants must demonstrate how the project will incorporate
Scientifically Based Research (SBR). Applicants should cite evidence that ensures that
SBR materials and strategies are being used in the project. Students participated in
additional technology literacy training using technology literacy software. This software
supports ISTE's National Educational Technology Standards for Students (NETSs) and
reinforces the standards of the National Council of Teachers of Mathematics (NCTM)
and the National Council of Teachers of English (NCTE). In which the following ISTE
standards were addressed:

      Use technology tools for individual and collaborative writing, communication,
       and publishing activities to create knowledge products for audiences inside and
       outside the classroom. (3, 4)
      Use telecommunications efficiently and effectively to access remote information,
       communicate with others in support of direct and independent learning, and
       pursue personal interests. (4)
      Use telecommunications and online resources to participate in collaborative
       problem-solving activities for the purpose of developing solutions or products for
       audiences inside and outside the classroom. (4, 5)
      Use technology resources for problem solving, self-directed learning, and
       extended learning activities. (5, 6)
      Determine which technology is useful and select the appropriate tool(s) and
       technology resources to address a variety of tasks and problems. (5, 6)
                   Math Best Practices Survey Results
Grade Level: K-8

Cross Curricular Connections: No

Classroom Observers View Students: 11. Would classroom observers see students
actively engaged in problem solving, including asking questions, finding solutions,
explaining concepts and justifying reasoning. Evaluation reports from Winton Hill state
“Students are showing signs of problem solving with the computers. If someone is having
a problem, they will work together to try and fix it. The students that are more
comfortable help the students that are behind.” (WHA 2004-2005 final evaluation report).
"All in all, student have made appreciable gains in computer/technology literacy over the
course of the two year EETT grant implementation. With such a solid start in the basics
and with the hardware and software still available for several more years Winton Hills
students will continue to progress.” (WHA 2005-2006 final evaluation report).

Data or Formal Evaluations: The Winton Hill Academy Technology Leadership Team
(TLT) along with the Technologist in Residence (TIR) measured the success of the 3
main goals of the EETT grant (1. Student improvement in Math/Reading, 2. Student
technology literacy and 3. Teacher technology literacy) by using many different
formative and summative assessments. Students in the target group were given a pre &
post test in the LMS to show measured Math/Reading achievement. Monthly reports
were taken from the assessment scores to show diagnostic output of each student.

Students were required to keep a usage log. The target group is meeting the 2-hrs/wk .
Statistical information from 4th & 6th grade Proficiency Test results was analyzed for
measured change. CPS Benchmark tests based on the Pacing Guides of Standards are
given in Math & Reading in Quarters 1, 2, and 4. With the software provided, teachers
will be able to assign lessons from the LMS that will align with the Pacing Guides.
Student technology literacy will be evaluated through use of the technology literacy
software program. Results from these evaluations were submitted to eTech Ohio in
Winton Hills 2004-2005 and 2005-2006 final evaluation reports.

Best Practices: Review of evaluation data, both internal and external observations and
reports. The project is similar to those being implemented at EETT recipient districts
around the State of Ohio.

How does the project or initiative tie with federal or state requirements? In
compliance with Title II Part D requirements, applicants were required to complete the
questions posed in the Ohio Comprehensive Continuous Improvement Plan (CCIP) by
providing a narrative description addressing each of the following points: Strategies for
using technology to improve academic achievement and teacher effectiveness;
educational goals; steps to increase students’ and teachers’ access to technology; plans
for identifying and promoting curricula and teaching strategies that integrate technology;
delivery of relevant professional development; Technology types and costs associated
with the proposed project, in addition to selected vendor tools; efforts to coordinate
technology-related activities and funding to maximize resources; strategies and timeline
                    Math Best Practices Survey Results
for integrating technology into curricula and instruction through the use of web-based
curriculum management and instructional design tools. WHA addressed each item in
their application.

Estimated Cost: Winton Hills Academy received: $213,660.00, $162,000 in 2004-2005,
$51,660 in 2005-2006.

Funding Source: Title II-D

Number of Each Impacted by Project: Districts - 1, Schools - 1, Teachers - 70,
Students - 150

Other Resources: The following resources are available at
http://tlcf.osn.state.oh.us/eett/portfolio. The site includes:
     Lesson Models
     Teacher Journals
     Student and Teacher videos
     Evaluation Reports
     Scott Kane
     Cincinnati Public Schools

Project Contact:
Gini (Virginia) Browsh
Cincinnati Public School District
EETT Project Manager
browshg@cps-k12.org
Office Phone: 513-363-0371
                   Math Best Practices Survey Results

South Carolina Curriculum Technology Coaching Initiative

This project is an outgrowth of the Mathematics and Science Coaching Initiative that has
been in existence for four years. The project's theory of action includes five elements:
research-based curriculum, assessment, professional development, curriculum materials
support, and engaged school and community. The project is aligned to state content
standards in mathematics and in science. The focus is on grades K-5 and includes all
teachers teaching mathematics and or science as well as all students in those grades. The
central strategy is for a well-trained coach to work with teachers in a planning,
observation, reflection cycle. The individual coach is supported by a mathematics or
science specialist from one of eight regional centers.

Role of Technology: The initiative has begun with the research on the use of technology
in the classroom. How can teachers be supported so that they will plan, implement, and
evaluate their instruction so that most students will be able to achieve the mandated
educational objectives (i.e., the state standards). The key to the effective use of
technology tools is that teachers view their work as providing the students with important
work to accomplish. The technology tools become important.

Grade Level: K-5

Cross Curricular Connections: One of the strategies in the training has been
"notebooking." This opens cross curricular connections to ELA and social studies.
Science and mathematics are integral to the initiative.

Classroom Observers View Students: Teachers report (four years of survey data) that
their students engage in data collection, organization, presentation, and discussion more
than their students did before the initiative.

Data or Formal Evaluations: The criterion outcome is the increase of scores on the
South Carolina accountability test, the Palmetto Achievement Challenge Test (PACT).
There is data suggesting that students whose teachers have been coached perform better
on PACT than similar students whose teachers have not had the benefit of a coach.

Best Practices: The Mathematics and Science Coaching Initiative (the parent project) is
evaluated by external review against specific criteria for success.

How does the project or initiative tie with federal or state requirements? The project
is tied to school achievement of state standards.

Estimated Cost:

Funding Source: Funding is from state and district resources.

Number of Each Impacted by Project: Over the four years, approximately 50 districts,
144 schools, 3,500 teachers, and 60,000 students have been involved.
                  Math Best Practices Survey Results
Other Resources: There are videos documenting coaching work as well as survey and
outcome data.

Project Contact:
John Holton
SC Department of Education
Coordinator, Mathematics and Science Unit
jholton@ed.sc.gov
803-734-8311
                    Math Best Practices Survey Results

South Dakota AIMS (Achieve Improvement in Math)

This project is a two-year extension of the math component of the original AIMS work--
with a new twist. While AIMS focused on individual teacher professional development
in inquiry-based math, AIMS II Math will focus on standards-based, technology-rich
mathematics curriculum review, selection, implementation and professional development
at the school and/or district level. School-based support and follow-up--customized to
the needs of each participating school or district--will take place during the school year.
Vertical teams from each participating district will be provided professional development
to move through the process and individual teacher professional development will also be
provided to support the transition to standards-based inquiry math. The project started in
2004. The project uses and defines standard mathematical terms. The project aligns to
recognized mathematics standards. The project is based upon scientific evidence. The
project is designed for teachers to affect all students.

Role of Technology: The use of technology is based upon scientific evidence. The
project incorporates state education technology standards. The project includes the use of
technology tools for research and problem-solving activities and as communication
devices for presenting information, and/or sharing work

Grade Level:

Cross Curricular Connections: See website http://aims.tie.net/content/default.htm

Classroom Observers View Students: Yes

Data or Formal Evaluations: Contact project coordinator for this information.

Best Practices: Some parts have been replicated

How does the project or initiative tie with federal or state requirements? Improving
math instruction through the use of technology- state RFP requirement for NCLB-II-D
competitive awards- the funding source of this grant

Estimated Cost: not answered

Funding Source: Title II part D competitive Dollars

Number of Each Impacted by Project: http://aims.tie.net/content/default.htm

Other Resources: http://aims.tie.net/content/default.htm

Project Contact:
Marcia Torgrude – TIE AIMS Director
Phone: 394-1876
Email: mtorgrude@tie.net
                    Math Best Practices Survey Results

Texas: Teaching Mathematics TEKS (Texas Essential Knowledge and Skills)
Through Technology (TMT3)

The Teaching Mathematics TEKS through Technology (TMT3) Professional
development is designed to provide teachers an opportunity to increase their depth of
understanding about the judicious use of technology in the mathematics classroom.
Expected learning outcomes for participants include an understanding of how technology
can:
     Provide access to a deeper understanding of mathematical content;
     Provide access to “real world” mathematical topics;
     Improve the economy and efficiency of teaching mathematics TEKS relative to
        time;
     Facilitate the use of various instructional tools in a mathematical setting.
The structure of the professional development is designed around the inquiry-based 5E
instructional model. This model has a strong foundation in research and has been shown
to be highly effective in instructional settings. Modules exist for the following: grades 6-8
mathematics, Algebra I, Algebra II and Geometry.

Grades 6-8
      The components of the “5E” Instructional Model are:

       ENGAGE:
       The presenter initiates this phase by asking well-chosen questions, posing a
       problem to be solved, or showing something intriguing. The activity should be
       designed to interest participants in the problem and to make connections between
       past and present learning.

       The goal of the Engage phase is to begin conversations about data. As the
       participants see the value of data and the mathematics that can be explored and
       reinforced through the use of data, they will begin to seek data. Technology offers
       the tools to make sense of data efficiently. Technology also offers effective means
       for representing data so that analysis may take place. Participants work with data
       from the Internet, data collection devices, and basic measuring tools.
       They compare the different methods and determine similarities and differences as
       well as the benefits of each method.

       The presenter’s role is to ask well-chosen questions to guide the activity but to
       allow participants to proceed in a nonjudgmental fashion. These questions are
       provided in the leader notes of the training.

       EXPLORE/EXPLAIN:
       Explore
       The exploration phase provides the opportunity for participants to become directly
       involved with the key concepts of the lesson through guided exploration that
       requires them to probe, inquire, and question. As we learn, the puzzle pieces
       (ideas and concepts necessary to solve the problem) begin to fit together or have
            Math Best Practices Survey Results
to be broken down and reconstructed several times. In this phase, presenters
observe and listen to participants as they interact with each other and the activity.
Presenters ask probing questions to help participants clarify their understanding of
major concepts and redirect the participants when necessary.

Explain
In the explanation phase, collaborative learning teams begin to logically sequence
events and facts from the investigation and communicate these findings to each
other and the presenter. The presenter, acting in a facilitation role, uses this phase
to offer further explanation and provide additional meaning or information, such
as formalizing correct terminology. Giving labels or correct terminology is far
more meaningful and helpful in retention if it is done after the participant has had
a direct experience. The explanation phase is used to record the participant’s
development and grasp of the key ideas and concepts of the lesson.

There are 3 Explore/Explain cycles in this module.

In the first Explore/Explain cycle, participants will measure attributes to gather
data. They will create stem and leaf plots using web-based tools to represent the
center and the spread of this data. Participants will use a web-based tool to create
a box and whisker plot to explore in greater detail the shape and the spread of the
data. Participants will also use hand-held graphing technology to create box and
whisker plots. They will gather additional data to explore how such changes
impact measures of central tendency.

In the second Explore/Explain cycle, participants will be given descriptive
statements about a set of data. Different groups of participants will receive
different statements. Each group of participants will create a set of possible data
and a graphical representation of the data based on these statements. Participants
will also be given a graphical representation of a set of data. They will create a set
of possible data and write descriptive statements about the data.

In the third Explore/Explain cycle, participants will conduct sets of experiments
that have the same number of outcomes. They will create graphical
representations that compare the experimental results and the theoretical results
using spreadsheet technology and hand-held graphing technology. Participants
will compare and contrast the use of these two technologies and their
effectiveness in representing the data.

The presenter’s role in the Explore/Explain phases is to ask well-chosen questions
to guide participants and clarify their understandings. These questions are
provided in the leader notes of the training.

ELABORATE:
The elaboration phase allows for participants to extend and expand what they
have learned in the first three phases and connect this knowledge with their prior
                    Math Best Practices Survey Results
       learning to create understanding. It is critical that presenters verify participants’
       understanding during this phase.

       In the Elaborate phase, a problem is posed to the participants. Based on this
       problem, participants will collect reaction time data. They will analyze their data
       using both hand-held technology and spreadsheet technology to determine
       generalizations about their data sets. Participants will identify the strengths and
       weaknesses of each technology. These tasks will take place within the structure of
       the problem-solving model: understand the problem; make a plan; carry out the
       plan; evaluate the plan and the solution; and extend the problem.

       Participants may use any of the technologies presented during the professional
       development. Participants will then apply or extend their understandings acquired
       in the professional development by generating a list of attributes to guide
       judicious use of technology.

       The presenter’s role in the Elaborate phase is to ask well-chosen questions to
       guide participants and extend their understandings. These questions are provided
       in the leader notes of the training.

       EVALUATE:
       Throughout the learning experience, the ongoing process of evaluation allows the
       presenter to determine whether or not the participant has reached the desired level
       of understanding of the key ideas and concepts. More formal evaluation can be
       conducted at this phase.

       Participants will review the instructional phases of this professional development
       and the student lessons according to the list of attributes generated in the
       Elaborate phase of the professional development. Revisions to the list of attributes
       may occur. Participants will engage in discussion about how each lesson exhibits
       a judicious use of technology; i.e., participants will address the question, “How
       does the use of technology in this student lesson help me teach the concepts and
       skills more effectively and efficiently?”

       The presenter’s role in the Evaluate phase is to ask well-chosen questions to
       assess participants’ understandings as they evaluate student lessons for judicious
       use of technology. These questions are provided in the leader notes of the
       training.

       STUDENT LESSONS
       This training is specifically designed for adult learners. Student lessons with
       detailed teacher notes and resources are provided to facilitate the implementation
       of the knowledge acquired by participants in the professional development.

Algebra I
      The components of the “5E” Instructional Model are:
            Math Best Practices Survey Results

ENGAGE:
The presenter initiates this phase by asking well-chosen questions, posing a
problem to be solved, or showing something intriguing. The activity should be
designed to interest participants in the problem and to make connections between
past and present learning.

The goal of the Engage phase is to begin conversations about data. As the
participants see the value of data and the mathematics that can be explored and
reinforced through the use of data, they will begin to seek data. Technology offers
the tools to make sense of data efficiently. Technology also offers effective means
for representing data so that analysis may take place. Participants work with data
from the Internet, an almanac, data collection devices, and basic measuring tools.
They compare the different methods and determine similarities and differences as
well as the benefits of each method.

The presenter’s role is to ask well-chosen questions to guide the activity but to
allow participants to proceed in a nonjudgmental fashion. These questions are
provided in the leader notes of the training.

EXPLORE/EXPLAIN:
Explore
The exploration phase provides the opportunity for participants to become directly
involved with the key concepts of the lesson through guided exploration that
requires them to probe, inquire, and question. As we learn, the puzzle pieces
(ideas and concepts necessary to solve the problem) begin to fit together or have
to be broken down and reconstructed several times. In this phase, presenters
observe and listen to participants as they interact with each other and the activity.
Presenters ask probing questions to help participants clarify their understanding of
major concepts and redirect the participants when necessary.

Explain
In the explanation phase, collaborative learning teams begin to logically sequence
events and facts from the investigation and communicate these findings to each
other and the presenter. The presenter, acting in a facilitation role, uses this phase
to offer further explanation and provide additional meaning or information, such
as formalizing correct terminology. Giving labels or correct terminology is far
more meaningful and helpful in retention if it is done after the participant has had
a direct experience. The explanation phase is used to record the participant’s
development and grasp of the key ideas and concepts of the lesson.

There are 3 Explore/Explain cycles in this module.

In the first Explore/Explain cycle, participants design experiments using a
calculator, common objects, and a CBR to collect linear, quadratic, and other
            Math Best Practices Survey Results
nonlinear motion data. Participants are asked to make conjectures and design their
experiment to test their conjectures.

In the second Explore/Explain cycle, participants collect quadratic motion data
using a model of a zip-line, the calculator and a CBR. They then analyze the data
using the calculator, spreadsheets, and TI-Interactive.

In the third Explore/Explain cycle, participants analyze tree ring data (both linear
and quadratic) from the internet to formulate predictive models using TI-
Interactive, the graphing calculator, and spreadsheets.

The presenter’s role in the Explore/Explain phases is to ask well-chosen questions
to guide participants and clarify their understandings. These questions are
provided in the leader notes of the training.

ELABORATE:
The elaboration phase allows for participants to extend and expand what they
have learned in the first three phases and connect this knowledge with their prior
learning to create understanding. It is critical that presenters verify participants’
understanding during this phase.

In the Elaborate phase a problem is posed to the participants. The problem uses
bottles, vases, cylinders, or prisms that each have a constant cross section to
generate a function that shows the relationship between the volume of the water in
a vessel and the height of the water. Participants are asked to estimate the surface
area of the water without measuring. They may measure and calculate the surface
area of the water after gathering all of their data. Participants may use any of the
technologies presented during the professional development. Participants will
then apply or extend their understandings acquired in the professional
development by generating a list of attributes to guide judicious use of
technology.

The presenter’s role in the Elaborate phase is to ask well-chosen questions to
guide participants and extend their understandings. These questions are provided
in the leader notes of the training.

EVALUATE:
Throughout the learning experience, the ongoing process of evaluation allows the
presenter to determine whether or not the participant has reached the desired level
of understanding of the key ideas and concepts. More formal evaluation can be
conducted at this phase.

Participants will review the instructional phases of this professional development
and the student lessons according to the list of attributes generated in the
Elaborate phase of the professional development. Revisions to the list of attributes
may occur. Participants will engage in discussion about how each lesson exhibits
                   Math Best Practices Survey Results
       a judicious use of technology; i.e., participants will address the question, “How
       does the use of technology in this student lesson help me teach the concepts and
       skills more effectively and efficiently?”

       The presenter’s role in the Evaluate phase is to ask well-chosen questions to
       assess participants’ understandings as they evaluate student lessons for judicious
       use of technology. These questions are provided in the leader notes of the
       training.

       STUDENT LESSONS
       This training is specifically designed for adult learners. Student lessons with
       detailed teacher notes and resources are provided to facilitate the implementation
       of the knowledge acquired by participants in the professional development.

Algebra II
      The components of the “5E” Instructional Model are:

       ENGAGE:
       The instructor initiates this phase by asking well-chosen questions, posing a
       problem to be solved, or showing something intriguing. The activity should be
       designed to interest participants in the problem and to make connections between
       past and present learning.

       The goal of the Engage phase is to begin conversations about data. As participants
       see the value of data and the mathematics that can be explored and reinforced
       through the use of data, they will begin to seek data. Technology offers the tools
       to make sense of data efficiently. Technology also offers effective means for
       representing data so that analysis may take place. Participants work with data
       from the Internet, an almanac, data collection devices, and basic measuring tools.
       They compare the different methods and determine similarities and differences as
       well as the benefits of each method.

       The presenter’s role is to ask well-chosen questions to guide the activity but allow
       participants to proceed in a nonjudgmental fashion. These questions are provided
       in the leader notes of the training.

       EXPLORE/EXPLAIN:
       Explore
       The exploration phase provides the opportunity for participants to become directly
       involved with the key concepts of the lesson through guided exploration that
       requires them to probe, inquire, and question. As we learn, the puzzle pieces
       (ideas and concepts necessary to solve the problem) begin to fit together or have
       to be broken down and reconstructed several times. In this phase, presenters
       observe and listen to participants as they interact with each other and the activity.
       Presenters ask probing questions to help participants clarify their understanding of
       major concepts and redirect the participants when necessary.
            Math Best Practices Survey Results

Explain
In the explanation phase, collaborative learning teams begin to logically sequence
events and facts from the investigation and communicate these findings to each
other and the presenter. The presenter, acting in a facilitation role, uses this phase
to offer further explanation and provide additional meaning or information, such
as formalizing correct terminology. Giving labels or correct terminology is far
more meaningful and helpful in retention if it is done after the learner has had a
direct experience. The explanation phase is used to record the learner’s
development and grasp of the key ideas and concepts of the lesson.

There are 3 Explore/Explain cycles in this module.

In the first Explore/Explain cycle, participants roll a marble down a ramp and
collect data to describe the location of the marble along its projectile path at any
given moment in time. Participants then use this model to predict (using a variety
of methods) where to locate a cup on a stack of textbooks in order for the marble
to roll down the ramp then land inside the cup.

In the second Explore/Explain cycle, participants collect exponential data using a
Geometer’s Sketchpad sketch containing a sequence of golden triangles. They
then analyze the data using the calculator, spreadsheets, and TI-Interactive. This
cycle also demonstrates to participants how geometry can be used as a context to
explore Algebra 2 functions.

In the third Explore/Explain cycle, participants collect light intensity data using a
CBL and a light sensor. Participants then generate a model using an inverse-
square parent function.

The presenter’s role in the Explore/Explain phases is to ask well-chosen questions
to guide participants and clarify their understandings. These questions are
provided in the leader notes of the training.

ELABORATE:
The elaboration phase allows for participants to extend and expand what they
have learned in the first three phases and connect this knowledge with their prior
learning to create understanding. It is critical that presenter verify participants’
understanding during this phase.

In the elaborate phase a problem is posed to the participants. Participants are
given a simplified form of the 1960 University of Illinois “Doomsday” population
model in which it is predicted that the Earth’s population will exceed its resources
in 2026. Participants collect population data since 1960 to verify the accuracy of
the model then use population data to construct a more accurate model.
                   Math Best Practices Survey Results
       The presenter’s role in the Elaborate phase is to ask well-chosen questions to
       guide participants’ and extend their understandings. These questions are provided
       in the leader notes of the training.

       EVALUATE:
       Throughout the learning experience, the ongoing process of evaluation allows the
       instructor to determine whether or not the participant has reached the desired level
       of understanding of the key ideas and concepts. More formal evaluation can be
       conducted at this phase.

       Participants will review the instructional phases of this professional development
       and the classroom-ready lessons according to the list of attributes generated in the
       elaborate phase of the professional development. Revisions to the list of attributes
       may occur. Participants will engage in discussion about how each lesson exhibits
       a judicious use of technology; i.e., participants will address the question, “How
       does the use of technology in this student lesson help me teach the concepts and
       skills more effectively and efficiently?”

       The presenter’s role in the Evaluate phase is to ask well-chosen questions to
       assess participants’ understandings as they evaluate student lessons for judicious
       use of technology. These questions are provided in the leader notes of the
       training.

       STUDENT LESSONS
       This training is specifically designed for adult learners. Student lessons with
       detailed teacher notes and resources are provided to facilitate the implementation
       of the knowledge acquired by teachers in the professional development.

Geometry
     ENGAGE:
     The instructor initiates this phase by asking well-chosen questions, posing a
     problem to be solved, or showing something intriguing. The activity should be
     designed to interest participants in the problem and to make connections between
     past and present learning.

       The goal of the Engage phase is to begin conversations about data. As participants
       see the value of data and the mathematics that can be explored and reinforced
       through the use of data, they will begin to seek data. Technology offers the tools
       to make sense of data efficiently. Technology also offers effective means for
       representing data so that analysis may take place. Participants work with data
       from the Internet, an almanac, data collection devices, and basic measuring tools.
       They compare the different methods and determine similarities and differences as
       well as the benefits of each method.
            Math Best Practices Survey Results
The presenter’s role is to ask well-chosen questions to guide the activity but allow
participants to proceed in a nonjudgmental fashion. These questions are provided
in the leader notes of the training.

EXPLORE/EXPLAIN:
Explore
The exploration phase provides the opportunity for participants to become directly
involved with the key concepts of the lesson through guided exploration that
requires them to probe, inquire, and question. As we learn, the puzzle pieces
(ideas and concepts necessary to solve the problem) begin to fit together or have
to be broken down and reconstructed several times. In this phase, presenters
observe and listen to participants as they interact with each other and the activity.
Presenters ask probing questions to help participants clarify their understanding of
major concepts and redirect the participants when necessary.

Explain
In the explanation phase, collaborative learning teams begin to logically sequence
events and facts from the investigation and communicate these findings to each
other and the presenter. The presenter, acting in a facilitation role, uses this phase
to offer further explanation and provide additional meaning or information, such
as formalizing correct terminology. Giving labels or correct terminology is far
more meaningful and helpful in retention if it is done after the learner has had a
direct experience. The explanation phase is used to record the learner’s
development and grasp of the key ideas and concepts of the lesson.

There are 3 Explore/Explain cycles in this module.

In the first Explore/Explain cycle, participants manipulate sketches created in
dynamic geometric software. Problem-solving strategies of breaking a large
problem into smaller components and working backwards are utilized to facilitate
the constructions and development of geometry concepts.

In the second Explore/Explain cycle, participants use digital images to explore
geometric properties such as parallel and perpendicular lines and planes,
congruence, similarity, transformations, etc. Participants will then collect
information to formulate and test conjectures about geometric properties.
Participants will then compare and contrast traditional exploration methods with
technological exploration.

In the third Explore/Explain cycle, participants will create a sketch using dynamic
geometric software and collect and analyze data collected from their sketch using
a variety of technologies. Problem-solving strategies of breaking a large problem
into smaller components and working backwards are utilized to facilitate the
constructions and development of geometry concepts.
            Math Best Practices Survey Results
The presenter’s role in the Explore/Explain phases is to ask well-chosen questions
to guide participants and clarify their understandings. These questions are
provided in the leader notes of the training.

ELABORATE:
The elaboration phase allows for participants to extend and expand what they
have learned in the first three phases and connect this knowledge with their prior
learning to create understanding. It is critical that presenter verify participants’
understanding during this phase.

In the Elaborate phase a problem is posed to the participants. Participants will
utilize technology to plane, construct, and analyze a complex geometric figure.
They will compare and contrast a pencil and paper approach to a technology
based approach. Participants will then apply or extend their understandings
acquired in the professional development by generating a list of attributes to guide
judicious use of technology.

The presenter’s role in the Elaborate phase is to ask well-chosen questions to
guide participants’ and extend their understandings. These questions are provided
in the leader notes of the training.



EVALUATE:
Throughout the learning experience, the ongoing process of evaluation allows the
instructor to determine whether or not the participant has reached the desired level
of understanding of the key ideas and concepts. More formal evaluation can be
conducted at this phase.

Participants will review the instructional phases of this professional development
and the classroom-ready lessons according to the list of attributes generated in the
elaborate phase of the professional development. Revisions to the list of attributes
may occur. Participants will engage in discussion about how each lesson exhibits
a judicious use of technology; i.e., participants will address the question, “How
does the use of technology in this student lesson help me teach the concepts and
skills more effectively and efficiently?”

The presenter’s role in the Evaluate phase is to ask well-chosen questions to
assess participants’ understandings as they evaluate student lessons for judicious
use of technology. These questions are provided in the leader notes of the
training.

STUDENT LESSONS
This training is specifically designed for adult learners. Student lessons with
detailed teacher notes and resources are provided to facilitate the implementation
of the knowledge acquired by teachers in the professional development.
                    Math Best Practices Survey Results

Role of Technology: Each phase of the professional development incorporates the
judicious use of one or more forms of technology, including hand-held graphing
technology, graphing software, dynamic geometry software, spreadsheets, and web-based
applets. These technologies are integrated into the classroom-ready lessons that reflect
the implementation of technology-based strategies acquired during the professional
development.

Grade Level: Grades 6-8, High school coursework: Algebra I, Algebra II, and Geometry

Cross Curricular Connections: Yes

Classroom Observers View Students:

Data or Formal Evaluations: Because the emphasis is on facilitating the development
of teachers’ content knowledge and pedagogical content knowledge related to
technology, the impact on student achievement at the classroom level takes place as
individual school districts analyze their data and resulting changes in student
achievement.

Best Practices: Inquiry-based experiences supported by technology use within the 5E
Instructional Model; judicious use of technology; collaborative learning; development of
concept-based vocabulary; use of technology to explore multiple representations of
problem-solving contexts, use of technology to present findings, generalizations, and
justifications of small groups of learners to the whole group.

How does the project or initiative tie with federal or state requirements? This project
is based on the TEKS, the state curriculum standards and aligns to content assessed on
the Texas Assessment of Knowledge and Skills (TAKS), the measure of accountability
for state and federal requirements. It is part of the Governor's Math Initiative, a statewide
initiative to improve mathematics teaching and student achievement.

Estimated Cost: Private entities or persons located in Texas that are not Texas public
school districts or Texas charter schools or any entity, whether public or private,
educational or non-educational, located outside the state of Texas must obtain written
approval from the Texas A&M - Commerce and will be required to enter into a license
agreement that may involve the payment of a licensing fee or a royalty fee.

Funding Source: State

Number of Each Impacted by Project: The training-of-trainer professional
development offerings trained approximately 325 trainers for the 4 modules. These
trainers represented universities, regional service centers, and school districts across the
state of Texas. The implementation of the professional development is supported by 20
funded entities within the Texas Mathematics Collaborative. This has the potential to
impact 3200 secondary mathematics teachers during the first year of this collaborative.
                   Math Best Practices Survey Results

Other Resources: This project contains
    Training-of-Trainers materials
    Technology-based activities for teacher designed to help teachers acquire content
      knowledge as well as pedagogical content knowledge related to technology
    Classroom-ready lessons to encourage implementation of teacher learning into
      instructional practices
    Technology tutorials to support teachers and students who may be less familiar or
      unfamiliar with the forms of technologies used
    Teachers who attend offerings related to the collaborative receive software and/or
      hand-held graphing technologies to support classroom implementation. On-line
      professional development modules for grades 6-8, Algebra I, Algebra II, and
      Geometry that lead to 12 hours of credit for each module completed

Project Contact:
Frank Ashley, Ph.D.
Texas A&M University-Commerce
P.O. Box 3011
Commerce, TX 75429-3011
Phone: 903-886-5180
Fax: 903-886-5905
Frank_Ashley@tamu-commerce.edu
http://www.tea.state.tx.us/research/pdfs/2006_comp_annual.pdf

Note: Education Service Center Region 4 in Houston developed the professional
development in partnership with Texas A&M University-Commerce for the Texas
Education Agency.
                    Math Best Practices Survey Results

Wisconsin Interactive Whiteboards and Learning

Through the support of the Enhancing Education Through Technology Title IID program
a consortium of school districts placed interactive whiteboards into the classrooms of
several teachers who are "trailbrazers" or "pioneers" in using instructional technology to
enhance teaching and learning. Initial intense professional developing in using
interactive whiteboards as an effective way to interact with digital content and
multimedia in a multi-person learning environment, their classroom was followed by
ongoing systemic professional training and support through face-to-face engangement
with consortium trainers and through virtual monthly sharing and learning sessions. The
interactive whiteboards were used for the following learning activities:
     manipulating text and images
     Internet research and systhesizing of information
     saving notes for review via e-mail, the Web or print
     modeling problem-solving strategies and math problem-solving and then posting
        the mini-videos on the teachers webpage
     demonstrating or using software at the front of the room
     creating digital lesson activities with templates and images
     showing and writing notes over educational video clips and video streaming
     using presentation tools buidt into the board's software
     showcasing and analyzing student work samples

The project data reports the this tool fostered student engagement and raised achievement
of intrinsic and extrinsic learners. It met student learning styles and special needs.

Grade Level: K-12

Role of Technology: The interactive white boards fostered students and teachers learning
new things in a new way. In other words they transformed their learning through the use
of instructional technology.

Cross Curricular Connections: Yes

Classroom Observers View Students:

Data or Formal Evaluations: The initial project showed a measurable increase in
student achievement as measured by the Wisconsin Knowledge and Concepts Exam.
Local data collection continues to show achievement growth. Plus the primary vendors
continue to collect national and international positive data. The project leaders present
their story at statewide and national conferences, as well as annually presenting
professional development training programs and one-on-one support through peer
mentoring and student "SMART SQUAD" support system. Their program is sustained
and expanded through local resources and student achievement and technology infused
instruction continues to accelerate from the first "trailbrazers" and "pioneer" teachers to
the "settlers" and the "stay-at-homers". Only the "fat-chancers" remain to be brought into
the program. This program has reached all content areas and all grade levels.
                    Math Best Practices Survey Results

Best Practices: Research studies are reviewed on the company website along with white
papers. The EETT project evaluation shows that student engagement, achievement and
and attendance increased and was sustained.

How does the project or initiative tie with federal or state requirements? This EETT
project supports the primary goal of the EETT program that "is to improve student
academic achievment through the use of technology in elementary and secondary
schools. It is designed to assist every atudent ... in becoming technologically literate by
the end of eight grade and to encourage the effective integration of technology resources
and systems with professional development and curriculum development to promote
research-based instructional methods that can be widely replicated."

Estimated Cost: $3500 for the board and projector installed with stand per classroom
and an Internet access compute

Funding Source: EETT Title IID plus local district and state TEACH funds (that are no
longer available)

Number of Each Impacted by Project:

Other Resources: There are several hundred lessons posted on a national and regional
website. Train-the-trainer program in place supported by the Cooperative Educational
Service Centers (CESA) and EETT project team. A fixed asset leasing program is
available to school districts and regional technical support is provided by the 12 CESAs.

Project Contact:
Donna Steffan
Wisconsin Department of Public Instruction
Instructional Media Education Consultant
donna.steffan@dpi.state.wi.us
608-267-1282
www.smarterkids.org/research
www.smarettech.com

				
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