Habitat For Kids

Habitat for Kids Little Houses for Little People

“Project Synergy” Dade Middle School Trenton, Georgia School Based Student Business DMS Home Builders Inc. and Dade County Chamber of Commerce 2009-2010 August 26, 2009

learn 3D math by hand

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build a house 2

Energy Efficient and Environmentally Friendly Friendly Homes  Sun roof  Solar panel  Insulation Calking windows/doors 

 Turning off lights  Low energy light bulbs

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Students at Dade Middle School Trenton, Georgia with the Dade County Chamber of Commerce dedicate this “Habitat for Kids” service project to all children in Habitat for Humanity homes everywhere who need their own play house and President and Mrs. Jimmy Carter fellow Georgia home builders

Trenton, GA

Trenton, GA

Georgia Forrest Commission

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Colonial Style Construction

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Real Life Carpentry: “3D Math by Hand” Problem-Solving House Building Construction is all about applying math skills! 1. If you need to cut a board 9” long with a 45-degree angle at the end, what is the length of the board at the bottom of the angle? 2. Which is cheaper by the pound, a 5-pound box of nails for $4.35 or a 3-pound box for $2.10? 3. If you need to cut a board to exactly 7’ 8”, and you mark the line, where should you cut the board, to the left of the line, right of the line, or on the line? 4. If you cut 13 boards that are 7 ¼” long, and each board was carelessly cut 1/16” shorter than the one before it, how long would the 13th board be? 5. If you go to Lowes to buy 17, 2” X 4” X 8’ boards at $2.28 each, what is the total price after adding 9 percent tax? 6. If you add 2 boards together, 3’ 7/16” with 4’ ¾”, how long will be their length? 7. If you have a 2” x 4” x 8’ board and you need to cut it into 15 equal sections, how long will each part be? 8. If you need to cut a 2” x 4” x 8’ board into strips ¾” wide, how many strips will you have? 9. How many square inches of floor space will you have if your house’s foundation is 4’ by 28”? 10. What tool must you use to insure that the walls of your house are perfectly vertical? 11. How many degrees are in the corner angle of a rectangular house? 12. If you want to insure that the top level of a door is perfectly flat, what tool would you use? 13. What tool would use you to insure that a board is cut at a perfect-90 degree angle? 14. What would you use to cut a 38-degree angle for slanting roof? 15. If you needed a “stud” every 1 12/” for a 4” wall, how many studs would you need? 16. How would you determine 3/5ths of $34.56? 17. What is the easiest way to mark the exact center of a rectangular board? 18. If you wanted to evenly space 3, 1” hinges on a door 7 1/8” high, how much space is needed between each hinge and the top and bottom of the door? 19. Which would give you the greatest number of ¾” strips of wood, buying 3, “2 x 4” x 8’ boards or 1, 2” x 12” x 8’ board? 20. If you wanted a 5” wide window centered in a 28” wall, what is the width of the wall on each side of the window? 6

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VISION “Habitat for Kids” seeks to help support “Habitat for Humanity” as a partnership with public education to become a model to the nation. It will begin with Dade Middle School in Trenton, Georgia, in conjunction with the Dade County Chamber of Commerce. The project provides hands-on applications of math skills. Students build “little houses” as a construction project (4’ x 28” x 3’) for “little people” by building “little doll houses” for girls and “little castles and barns” for boys. These “buildings” will be donated or sold. Significant learning requires significant motivation! CONTACT Principal: Karen de Marche Dade Middle School 250 Pace Drive Trenton, Georgia 30752 School phone: 706-657-6491 Email: [email protected]

Teacher: Thomas Randolph Cell phone: 423-322-7849 Email: [email protected] Debbie Tinker Executive Director Dade County Chamber of Commerce 111 Railway Lane Trenton, Georgia 30752 Office phone: 706-657-4488 Email: [email protected]

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GOALS 1. Build doll houses from scratch (4 feet long, 28 inches wide, up to 3 feet high) on a moveable table with wheels approximately 3 feet high that can be rolled in and out of math classrooms. In this way, they do not have to remain in the class taking up space. They can be stored in the lobby for public viewing. 2. Each grade level math teacher’s classes would construct some kind of miniature building: house, school, castle, barn, etc. Students could decide what they want to build, but each teacher or at least grade level would build something different (differentiation). 3. Not more work but more relevance, rigor, and relationships. 4. Relevance: The boxes can be transported to any public building for display. This program can become a model for any school’s math classrooms that could receive widespread media coverage for the students and school. 5. Rigor: Students understand that they are creating a model for the nation. This will motivate them to do the very best job possible because their work is going out to the public on a state and national scale. 6. Relationships: Students will work in teams to be responsible for different aspects of the project. 7. Teachers and students will work together to develop specific math application lessons so that students can teach lessons to other students using their models as an example.

HOW 1. Math classes, or any kind of class, first compete for a design based on a blueprint and drawing of the building. 2. Students, in class, will cut small pieces of wood with a handsaw, nail, and glue the pieces together. 3. Students can decorate the inside and outside in addition to building furniture.

WHY 1. Math is the weakest area for students in American public education as proven by state test scores. 2. Learning abstract algebra equations apart from any real life context (carpentry, agriculture, mechanic, etc.) is very difficult. Students ask, “Where will I ever use this in my life?” 3. Using a “problem-solving” methodology to continually apply abstract math concepts to practical real life situations and careers will help make the necessary connections and prove its relevance as an essential job skill. 4. Illustrating practical applications, even better having students actually apply principles with authentic, hands-on work, is especially important for low achieving math students. 5. The math principles in building a small model house are not different from building a full-scale real house. Walls are walls. Space is space. Money is money. Time is still time. 6. A 1999 project by the Center for Occupational Research and Development research data suggested that less than 25% of students are abstract learners. This suggests that the majority of learners would benefit from some kind of real life, hands-on application of abstract math concepts. 7. The attached article published in the American Educational Research Journal, September, 2008, reviews supporting research for this methodology. 9

STRATEGY 1. This project is meant to last all year long if necessary. 2. Each week 20-30 minutes is spent on the project. 3. Can math teachers afford to spend even a small amount of time on a weekly basis on any project considering the intense pressure to raise CRCT math scores, especially for lower achieving students? 4. No significant learning happens without significant motivation. 5. This project will allow weekly, hands-on application all year long for a slowly growing vision. This will take 2-dimensional, paper, abstract ideas and transform them into 3-dimensional, wooden, concrete forms for public viewing. 6. This kind of project would be especially interesting and engaging for right-brained, visual, hands-on students who typically are the lower achieving students on the CRCT math tests.

STUDENT RUN COMPANY 1. DMS Home Builders Inc. is a student-based company for profit. 2. Its purpose is to help students better understand how to run business a business. 3. Students will develop a business plan for advertising and job responsibilities. 4. Homes will be donated as a service project or sold to cover materials cost with a small profit.

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FLAT WORLD 1. Students will be able to display their work daily, weekly, and monthly in the school lobby for every one to see along with their blueprints and drawings: students, teachers, parents, guests, etc. 2. When guests come to school, selected students can explain their projects to them and how they are applying their math concepts along with the math lessons they are developing. 3. Math teachers can take pictures and create a video of the project to be displayed each time the school is invited to share “Project Synergy.” 4. All the buildings would be displayed in the gym for both Synergy competitions. 5. Once enough of the building is erected, students with their math teachers can transport them to both elementary schools to be wheeled into each classroom for a presentation and our board of education. 6. President Obama said that he hoped the Apollo 11 moon mission would be an inspiration to schools and students for creative programs and learning for math and science.

FUNDING 1. The table base itself will cost approximately $100.00, but it can be used over and over again. The houses cost approximately $100.00. 2. Individuals, clubs, organizations, churches, etc., can donate money toward a table and/or building. Their name and date will be displayed on anything they donate money toward. 3. Lowes or Home Depot might be very happy to supply the wood with the understanding that their name also would be permanently displayed on the tables and/or buildings. Which ever company helps sponsor and financially supports the project, it will be pictured and advertized in the book and house.

BUILDINGS 1. Buildings could be build in two halves so that children could divide the house into two parts to play. Each half would be build on a separate piece of plywood that sits on top of the movable table so that students can take one half off and be able to work on both halves simultaneously in class. 2. The moveable table has shelf build below it to store materials. A small vice can be attached to hold wood while it is being gut. No electrical power tools would be necessary. 3. Buildings could be wired for lights using batteries. 4. At Christmas time and other holidays, the buildings could be decorated for the season. 5. Students could sign the bottom of the buildings with their names, date, school, and dedication.

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Doll Houses for Little Girls

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Castles and Barns for Little Boys

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DMS “Habitat for Kids” Construction Company MEDIA CREW * Maintain a daily diary (Day 1, Day 2, Day 3, etc. with weekly summary) with pictures of the building process from start to finish in order to create a book to present to the Ronald McDonald House in Chattanooga and President Jimmy Carter with “Habitat for Humanity.” * Visitor tour guides * Power Point presentation (continually building it) CONSTRUCTION CREW * Blue prints * Drawings * Transportation (bringing house to and from class) * Cutters * Sanders * Gluers * Nailers * Measurers * Clean up

INTERNET RESEARCH

PROPS (ex. Miniature ladders) EXTERIOR DECORATIOONS INTERIOR DECORATIONS FURNITURE 15

VIRTUAL REALITY CONSTRUCTION CREW

Each member of the company can buy or make a doll, figurine, (size and dress appropriate) to represent him or her on “construction site” of the model house. These “little people” will be working on the house each day as it displayed in the hall. The figurines will be no taller than eight inches. A photo of the actual construction crew will be laminated and hung inside the house when it i donated to Ronald McDonald. Crew members will sign the bottom of the house and date it for posterity. Crew members can choose to donate “themselves,” in addition to the house, in the form of their virtual reality figurines.

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REASONS TO EXPERIMENT IN PUBLIC EDUCATION “Everything in the world either remains to be done, or to be done better. The greatest picture has not yet been painted nor the greatest play been written.” “It is not the critic that counts.... The credit belongs to the man who is actually in the arena...who strives valiantly, who errs and often comes up short again and again...who at best knows in the end the triumph of high achievement, and who at worst, if he fails, at least fails while daring greatly, so that his place shall never be with those cold and timid souls who know not victory nor defeat.” President Theodore Roosevelt “All men dream but not equally. Those who dream by night, in the dusty recesses of their minds wake in the day to find that it is vanity, but the dreamers of the day are dangerous men, for they dream with open eyes to make it possible.” “The mere formulation of a problem is far more often essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advances in science.” Albert Einstein “Napoleon was accustomed to looking intently at war; he never added up figure by figure the tedious sum of details; the figures mattered little to him, provided they gave him this total: victory.” “Press on, nothing in the world can take the place of persistence. Talent will not; nothing is more common than unsuccessful men. Education will not; the world is full of educated derelicts. Persistence and determination alone are omnipotent.” President Grover Cleveland “The men who try to do something and fail are infinitely better than those who try to do nothing and succeed.” Teddy Roosevelt “Iron rusts from disuse; water loses its purity from stagnation and in cold weather becomes frozen; even so does inaction sap the vigor of the mind.” Leonardo da Vinci “No, I don’t know that it will work, but you don’t know that it will not work. And I would rather live with my hope than your doubt.” Mortimer Adler 17

Learn about Habitat for Humanity Our mission and history Take a quick tour of our mission, methods and current progress. Find in-depth answers to frequently asked questions in this fact sheet. Read the history of Habitat or view our photo timeline. Who we are We are a nonprofit, ecumenical Christian ministry founded on the conviction that every man, woman and child should have a decent, safe and affordable place to live. We build with people in need regardless of race or religion. We welcome volunteers and supporters from all backgrounds. Meet our Board of Directors and our CEO, Jonathan Reckford. Former U.S. President Jimmy Carter and his wife Rosalynn are Habitat's most famous supporters. The couple annually leads the Jimmy and Rosalynn Carter Work Project. What we build Our houses are simple, decent, and affordable to low-income families around the world. See what Habitat houses are like around the world. Whenever possible, we build energy-efficient, sustainable housing. Learn more about our construction and environmental resources. Why we build Nearly 2 billion people around the world live in slum housing and over 100 million are homeless. Habitat for Humanity is needed to help eliminate poverty by providing simple, decent shelter to those in need. Families left homeless by natural disasters, war and civil unrest often face dire housing situations as they struggle to rebuild their lives. Habitat for Humanity’s Disaster Response program provides shelter and housing solutions to help these families recover. How it’s possible Homeowners and volunteers build under trained supervision. Individuals, corporations, faith groups and others provide vital financial support. Learn more about Habitat's stewardship of these resources in our Annual Report and Financial Statement. In the U.S., Habitat for Humanity lends no-profit, no-interest mortgage loans to its beneficiary families. On a global scale, Habitat’s traditional model is not always possible. Our international housing finance programs consist of innovative housing finance practices and/or partnerships with microfinance organizations. Learn more HabitatLearns provides free in-depth knowledge on housing issues.Visit the Global Village and Discovery Center in Americus, Georgia. Learn about the devastating 18

effects of poverty everywhere. See life-size Habitat houses from countries around the world. Learn more about who we are and what we do around the world every day. Visit our newsroom for press releases, articles, photos and videos about Habitat for Humanity.

Volunteer! Get involved with Habitat for Humanity Join in the fight against poverty housing and homelessness around the world! Lend a hand and your voice today. Volunteer Locally. To volunteer in your community, use our search engine to find the Habitat affiliate group nearest you. Be an Advocate. Speak out to lawmakers and help change the systems that lead to poverty housing. Join or attend an upcoming Habitat special event. Jimmy and Rosalynn Carter Work Project. Find out how you can join the Carters in their upcoming building project. Special Events in your area Find your niche with one of these short-term volunteer programs. Global Village Program. Help build decent, affordable housing around the world. Youth Programs. Find Habitat’s opportunities for youth ages 5 to 25, their teachers and youth group leaders. Women Build. Learn construction skills alongside other women in an unintimidating environment and put them into action for families in need. Gulf Recovery Effort. Join in continuing recovery efforts to help hurricane-affected families in Louisiana, Mississippi, Texas and Alabama. RV Care-A-Vanners. Combine the fun of recreational vehicle travel with a fulfilling Habitat for Humanity experience! Commit to a long-term volunteer program. International Volunteer Program. Make a difference in the world! Spend 6 to 12 months volunteering in Habitat offices overseas. Volunteer at Habitat for Humanity’s Headquarters. Experience the place where Habitat for Humanity was started! Volunteer your skills for 2 to 6 months at our international headquarters in Americus, Georgia. Habitat AmeriCorps/VISTA. Service-minded individuals ages 18 and older live at and work with local Habitat affiliates while earning living allowances and receiving an education award upon completion of service. Get involved through Habitat for Humanity’s partnerships. 19

Your Church and Habitat. Find out more about church partnership opportunities, including volunteering, fund-raising and serving on committees. Corporate Partners. Partner with Habitat through product donations, financial support, or mobilizing your company’s employees as volunteers. Thrivent Builds with Habitat for Humanity. Members of Thrivent Financial for Lutherans, Lutheran congregations and Lutheran institutions are invited to demonstrate their care and concern for others by helping to build hundreds of Habitat homes around the world each year. Prison Partnership Program. A cooperative effort between local Habitat affiliates and correctional institutions. Eligible inmates are given the opportunity to participate in various aspects of house construction while learning marketable job skills and practicing social responsibility. Connect with Habitat on your own time. Do It Yourself Network created a five-part workshop, entitled "Lending a Hand: Habitat for Humanity," which provides an in-depth look at building a Habitat for Humanity house. You can view all five episodes online or watch and learn from other selections in DIY’s library.

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What are HFHI’s youth programs? Habitat for Humanity’s youth programs are a collection of resources and programs that capture the imagination, energy and hope of young people worldwide, ages 5 to 25, in order to productively and responsibly involve them as leaders in the work of Habitat.Read about the latest innovations and milestones from Habitat’s youth programs in the 2007 Summary Report (pdf). What is Habitat for Humanity?Habitat for Humanity International is a nonprofit Christian ecumenical housing ministry. We welcome all people to join us as we build simple, decent, affordable houses in partnership with those in need of adequate shelter. Since its founding in 1976, Habitat for Humanity has built more than 250,000 houses and had a presence in 100 countries. To find out more about Habitat for Humanity, please take the online tour. How have Habitat’s youth programs developed?In November 1987, Baylor University in Waco, Texas became the first university to form its own student-led, student-initiated Habitat for Humanity organization. The Habitat for Humanity International board of directors approved the Youth Programs department in December 1987. High school students became part of the youth programs family in 1988 when Marist School in Atlanta, Georgia formed the first secondary school campus chapter. The first international chapter was chartered in 1991 at the University of Technology in Lae, Papua New Guinea. Since 1987, more than 800 chapters have been chartered worldwide. While the vast majority of these student clubs are based in the United States, campus chapters exist in 35 countries. Collegiate Challenge was started in 1989 to provide young people with an opportunity to serve Habitat during their school breaks and continues to grow two decades later.As the department's programs expanded internationally, the Youth Programs department recognized that other youth program models were needed for those areas where schools were not close by or where the youth had graduated. Begun in the Philippines in 2001, community youth groups (CYGs) allow an entire community to be involved.For more than 20 years, we have been focused on creating and improving tools and programs that engage youth in this mission. In 2007, State Farm became the official corporate sponsor of Habitat’s youth programs. State Farm’s generous support continues to underwrite Habitat’s youth programs and is vital the success and growth of opportunities for youth with Habitat for Humanity.In 2008, Youth Programs joined forces with other departments within Habitat for Humanity International, including Global Village and the International and Domestic Volunteer Programs, to form the Volunteer Mobilization department. We look forward to continued success in supporting young people as they support Habitat and encouraging the world’s future leaders. What do we do?Habitat for Humanity International staff work to support Habitat’s youth programs, supporting national organizations and affiliates in promoting youth involvement. We are also responsible for providing ongoing support to youth volunteers and those that support them through resources, training and special programs. We help young people involved in Habitat for Humanity organize special events, participate in travel service teams and engage in decision-making at the local level. We also serve as a liaison between individual campus chapters and community youth groups and other Habitat for Humanity International departments. Staff members are stationed in the field and at Habitat for Humanity International headquarters in Americus, Georgia.

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T-squared: Build your community (ages 14-25) T-squared stands for “Today and Tomorrow.” You are not only the future of Habitat—there are tons of things you can do NOW to be leaders in Habitat’s work! Thanks to the generous support of State Farm, the official corporate sponsor of Habitat’s youth programs, there are lots of ways you can get involved! Explore the links to the left to learn more. Terry Pettus, owner of local State Farm Insurance Agency, is a proud sponsor of “Habitat for Kids.”

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Rigor and Relevance: Enhancing High School Students’ Math Skills Through Career and Technical Education James R. Stone lll, Corinne Alfred, Donna Pearson American Educational Research Journal, Washington: Sept. 2008, Vol. 45, Iss. 3, p. 767-795 (29 pp.) Accessed from ProQuest Abstract (Summary) Numerous high school students, including many who are enrolled in career and technical education (CTE) courses, do not have the math skills necessary for today's high-skill workplace or college entrance requirements. This study tests a model for enhancing mathematics instruction in five high school CTE programs (agriculture, auto technology, business and marketing, health, and information technology). The model includes a pedagogy and intense teacher professional development. Volunteer CTE teachers were randomly assigned to an experimental (n = 59) or control (n= 78) group. The experimental teachers worked with math teachers to develop CTE instructional activities that integrated more mathematics into the occupational curriculum. After 1 year of the math-enhanced CTE lessons, students in the experimental classrooms performed equally on technical skills and significantly better than control students on two standardized tests of math ability (TerraNova and ACCUPLACER®). [PUBLICATION ABSTRACT]

Full Text (11629 words) Copyright American Educational Research Association Sep 2008 [Headnote] Numerous high school students, including many who are enrolled in career and technical education (CTE) courses, do not have the math skills necessary for today's high-skill workplace or college entrance requirements. This study tests a model for enhancing mathematics instruction in five high school CTE programs (agriculture, auto technology, business and marketing, health, and information technology). The model includes a pedagogy and intense teacher professional development. Volunteer CTE teachers were randomly assigned to an experimental (n = 59) or control (n= 78) group. The experimental teachers worked with math teachers to develop CTE instructional activities that integrated more mathematics into the occupational curriculum. After 1 year of the math-enhanced CTE lessons, students in the experimental classrooms performed equally on technical skills and significantly better than control students on two standardized tests of math ability (TerraNova and ACCUPLACER®).

Rationale Most students are not being prepared to meet the demands of the workplace or college (American College Testing, 2004). The most recent National Assessment of Educational Progress results indicate that 37% of 12th-grade students performed at a below basic level on the math portion of the test. The most recent National Assessment of Educational Progress results available indicate that in 2005 less than one quarter (23%) of 12th-grade students performed at or above a proficient level on the math portion of the test (Grigg, Donahue, & Dion, 2007). There has been a significant increase in students' advanced coursetaking in math over the past 20 years. Still, only one third of high school graduates in 2004 completed advanced courses such as pre-calculus or calculus, even among those expecting to earn a baccalaureate degree (Dalton, Ingels, Downing, & Bozick, 2007). Of entering postsecondary students, 22% (35% at 2-year institutions) require remedial education in math (Parsad & Lewis, 2003). However, remedial classes at the college level are not a longterm solution but rather a bandage. Furthermore, what is the condition for students who do not enroll in postsecondary education? U.S. high school juniors and seniors are clearly unprepared for the math they will need in all settings after they graduate. More Math? The obvious solution to the problem-requiring more mathematics courses in high school-may not be effective. For example, after the Milwaukee Public Schools made Algebra I compulsory, algebra-passing rates for 9th graders went from 25% to 55%, but an average of 47% of 9th graders still failed Algebra I (Ham & Walker, 1999). These statistics indicate that dramatically more students are capable of succeeding in Algebra I than would enroll in the class on their own; however, the high failure rate may be indicative of larger issues surrounding student preparation, class instruction, and curriculum design. A recent study of teaching practices across the countries involved in the Trends in International Mathematics and Science Study (TIMSS) in fact found that U.S. teachers tend to focus more often on the execution of low-level math skills compared with higher achieving countries that use different methods and emphasized conceptual understanding, procedural skill, and challenging content (Hiebert et al., 2005).

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While school districts across the nation have increased academic coursework, mostly in math and science, by an average of four Carnegie units1 (see Levesque, 2003), National Assessment of Educational Progress assessments of mathematics show a flat growth curve over the past three decades (Perie & Moran, 2005), and the high school completion rate has been on a slow and steady decline (Swanson, 2004). Together, these data suggest that doing more of the same has not proven to be a viable solution to improving students' math skills. Different Math? Research has shown that disengagement or lack of interest is a factor in low student achievement (National Council of Teachers of Mathematics, 2000). Students may disengage from math because of difficulty with the subject, lack of support, or simply boredom. Students may disengage while still attending class. Many of these students believe that the math that they learn in school is not relevant to life after high school. However, it has become increasingly clear that math is in fact a component of most jobs in our increasingly technological society (National Research Council, Mathematical Sciences Education Board, 1995). Varying the curricular opportunities for high school youth may be a way to facilitate acquisition or mastery of algebra or other math concepts. Indeed, the National Council of Teachers of Mathematics makes it clear that preparing students to learn mathematics for the workplace or postsecondary entrance does not mean that all students can or should learn math in the same way. Students who lack a fundamental understanding of algebra and possess only a formulaic understanding of the course will struggle with applying the formulas in a testing environment, thereby differentially affecting their graduation and college entrance rates. The National Council of Teachers of Mathematics (2000) and the National Research Council, Commission on Behavioral and Social Sciences and Education (2000) encourage the design of engaging curricula that apply to realworld situations. More and Different Math We offer a potential solution: Enhance career and technical education (CTE) courses with more rigorous, relevant mathematics. CTE courses inherently provide contexts for applied or experiential learning (Owens & Smith, 2000; C. R. Rogers, 1969). Applied learning is the delivery of content area curricula within a relevant, authentic, and presumably more motivating context. Mathematical concepts are embedded in almost every CTE program, and within each specific labormarket preparation (SLMP) area, mathematics can be taught in the context of that occupation (Center for Occupational Research and Development, 1999). For example, horticulturists estimate the number of pots of various diameters that can fit in an area of a greenhouse, a problem that uses math skills to determine the area of the pot and the surface. However, there has been no empirical or quantitative evidence to suggest that math learned in such applied contexts transfers to the workplace, other educational settings, or real-world problems. The creation of explicit connections between situations is critical if students are to transfer their knowledge and skills outside the classroom, whether it is to another context or to an abstract testing situation (Fuchs et al., 2003). "Teaching via problem-solving is teaching mathematics content in a problem-solving environment. Learning in this approach involves learning through a concrete problem and eventually moving to abstraction" (Bay, 2000). Because the mathematics in the CTE curriculum is implicit, both to the teachers and to the students, we designed and tested a model to make it explicit. Overview of the Study In this study, we hypothesized that through occupational contexts (CTE courses), we could enhance CTE students' conceptual mathematics learning and ability to transfer math skills without forfeiting their technical skills. Since CTE educators are not trained to teach math, explicit math content, such as algebraic formulas, rarely makes it onto the blackboard. In our study, we encouraged CTE teachers to take a moment to show their students the mathematical formula behind a problem so that when students saw that formula in other situations, including on standardized tests, they would remember the problems they had solved in the applied context and would be more likely to know how to solve the novel problem. For example, when seeing the Pythagorean Theorem in a paper-and-pencil test, students would think back to their lesson on the T-square in carpentry class and remember how to solve the problem. The goal was to help students make the connection between a particular lesson situation and the abstract concept behind it (National Research Council, Commission on Behavioral and Social Sciences and Education, 2000), practicing the application of mathematical knowledge learned in one context to apply in multiple problem situations, including standardized tests. Through implementation of a model we created for this purpose, we sought to test the basic hypothesis that high school students in a contextual, math-enhanced CTE curriculum will develop a better understanding of mathematical concepts than those students who participate in the traditional CTE curriculum. Specifically, we asked the following primary research questions, each corresponding with the specific test used to measure the outcome (which will be explained in the Method section): 1. Does a math-enhanced CTE curriculum improve student math performance as measured by a traditional (TerraNova)

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test of math knowledge and skills? 2. Does an enhanced CTE curriculum decrease students' likelihood of requiring postsecondary math remediation, as demonstrated by improved scores on a college placement (ACCUPLACER®) test' 3. Does a math-enhanced CTE curriculum improve student math performance as measured by an applied (WorkKeys) test of math knowledge and skills? 4. Does enhancing a CTE curriculum with mathematics reduce students' acquisition of occupational skills they will need for the workplace? (as measured by a variety of technical skills tests; see Method) The model we created for this study began with the principle that the math content ought to emerge from the occupational content rather than from superimposing math into the curriculum of a particular SLMP course. Our model provides a pedagogic framework that makes explicit the mathematics concepts that naturally occur in occupationally specific CTE courses. Therefore, the CTE teachers first identified math concepts inherent in their curriculum and then created lessons that would move students from the fully embedded example in CTE toward less contextualized and more abstract examples of the math concept. We posited that through this contextualized approach, students would see the math as an essential component of the CTE content, a tool-like a saw, wrench, or thermometer-needed to successfully solve workplace problems. Background This approach is well supported in the literature. In CTE, students learn their trade in the context of actual work problems, and many perform best in areas in which their learning can be applied (Orr, Thompson, & Thompson, 1999; Slaats, Lodewijks, & van der Sanden, 1999). According to David KoIb, less than 25% of students are abstract learners (Center for Occupational Research and Development, 1999). For many of the remaining students, enhancing math in the CTE classroom may provide a valuable learning opportunity. In addition to applied learning, another way to teach concepts so that students see their application in multiple contexts is called curriculum integration (CI). Many schools have implemented programs such as "math across the curriculum," in which academic concepts are addressed in courses other than the core course in that subject. CI models attempt to move away from the traditional model of instruction, in which subjects are taught by themselves, completely isolated from any context. Traditional mathematics, for instance, is seen as abstract, disconnected from any real application (Brown, Collins, & Duguid, 1989). In the case of algebra, the equations are presented as things to be solved or symbols to be moved around or graphs to be drawn without any discussion of the real-life applications of the math (Kieran, 1990). Some math educators believe that students experience difficulty learning algebra in a decontextualized way (Boaler, 1998; Kieran, 1992). For many students, it becomes too abstract too quickly and does not make any sense. This issue is particularly acute among low achievers (Woodward & Montague, 2002). Perhaps more than other students, low achievers need an authentic lesson as a way to make sense of abstract mathematics. A contextual mathematics approach requires that educators change the way in which they deliver content in order to produce enhanced thinking about and use of mathematics concepts among students. According to this perspective, educators play a major role in helping students make connections between what they are learning in the classroom and ways in which that knowledge can be applied in the real world (Karweit, 1993)-that is, connecting the content with the context in which that content will be used (Berns & Erickson, 2001). The use of authentic situations serves to anchor the symbolic and abstract math in situations that are familiar and real to students, which serves to help them make sense of the content (Brown et al., 1989; Cognition and Technology Group at Vanderbilt, 1990). Contextual Learning and Situated Cognition One problem with contextual learning is that students may be unable to transfer the knowledge learned in one context or situation to another context or situation because it is so embedded (situated) in the original context where it was learned (Boaler, 1993, 1998; Lave, 1988; Lave & Wenger, 1991). The challenge with authentic, contextual learning is that "knowledge is . . . dependent upon and embedded in the context and activity in which it is acquired and used" (Karweit, 1993, p. 54) and may not be transferable to other contexts. Unless students are taught the abstract principle behind what they are learning in context and guided through other contextual examples to which it applies, it is unlikely that cognitive transfer will occur outside the classroom (see Fuchs et al., 2003). This is a critical problem because students will eventually need to use their math skills outside the classroom. Employers need students to have had experience with application of these skills (cf. Achieve, 2004). This implies that students need to practice math skills in a variety of ways so that they become proficient in knowing when and how to apply them. The workplace of today is filled with complex problems and rapidly changing environments and technologies where "the ability to cope with the nonroutine is perhaps the only knowledge worthy of instructional design in many cases" (Deny & Lesgold,

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1996, p. 791). Indeed, expert performance is characterized by an ability to adapt one's skills to novel situations and actively solve problems (Ericsson & Charness, 1994). Out Model: A New Pedagogy and Process For this study, we needed to teach CTE teachers how to enhance the mathematics that was already in the occupational curriculum. A systematic review of curriculum materials available through commercial and nonprofit vendors found none that was consistent with our operational definition of contextual learning. We therefore developed our own model for the experimental intervention, which involved both a pedagogy and a process. The pedagogy built on theories of contextual learning and transfer and was created by the research team and educational consultants to guide the development and instruction of math-enhanced CTE lesson plans. Based on both prior literature and experience, our team believes that in order for students to make links between concepts, they need to go through a process beginning with an introduction to solving a real, relevant problem; practicing on several similar examples; and then applying the concept to a more abstract problem. The Pedagogy: Seven Elements We called our pedagogical model the "Seven Elements of a MathEnhanced Lesson" (see Figure 1). Following the lesson plans they developed with these seven elements, teachers first introduced the lesson as a CTE lesson and then assessed students' initial understanding of the math concepts. The teachers then presented and worked through the math problems embedded in the lesson. When feedback from the students indicated that they understood the application, the teachers presented additional related contextual examples. The teachers then reviewed the same concepts as the students would encounter them in traditional forms in a math class or on a test and showed students any applicable formulas and the step-by-step procedures for solving the problem as encountered on a traditional test. The final two elements required the students to demonstrate their understanding of the math concepts and procedures, both in and out of context, through projects or learning activities directly linked to the lesson and as part of the formal assessment (quizzes and tests) for the overall instructional units in which the math-enhanced lessons were taught. The seven elements we outlined are very similar to the assessment framework that underlies the Program for International Student Assessment (PISA), sponsored by the Organisation for Economic Co-operation and Development (OECD) (2004). In addition, the seven elements in our pedagogical framework have many parallels with Gagne's (1965) Conditions of Learning and Hunter's (1982) Instructional Theory Into Practice. What differentiates our framework from theirs, however, is our increased emphasis on moving from specific contextualized applications to general mathematical principles. Elements 3 and 4 of the pedagogical model move the instruction from the original embedded CTE problem to additional contextual applications. In Element 5, the instruction moves to traditional examples in order to reinforce and expand the math to include that which students are likely to encounter in standardized tests. The Process: Professional Development The development of a pedagogical framework was only one aspect of our model. Our experimental intervention also required the creation of a process through which the CTE teachers could learn to develop and teach math-enhanced lessons. Hill, Rowan, and Ball (2005) found that improving teachers' mathematical knowledge can improve students' math achievement. Furthermore, a review of over 400 evaluation studies of mathematics and science curriculum and professional development models found that professional development that is tied to knowledge of the subject matter and/or how students learn the subject is more effective in terms of improving student achievement than is professional development that focuses only on teaching behaviors (Clewell, de Cohen, Campbell, & Perlman, 2004). The process we developed included partnering high school CTE teachers with math teachers, building curriculum maps that intersected math concepts with CTE curricula, providing professional development for the teacher teams, and implementing the math-enhanced lessons. Our basic requirement was that the mathematics taught in CTE courses should arise directly out of occupational content rather than be forced into it. It is this fundamental principle that differentiates this approach from other CI models. Also critical to this approach is the recognition that CTE teachers are not mathematics instructors and need assistance in identifying the math in their curricula and developing lessons to teach it; this is why we paired them with math teachers. However, we made an explicit decision not to refer to the math teacher as a coach or mentor, because these terms imply differing status. The CTE and math teachers were each full partners. Method This study began as a single-semester pilot test of the experimental intervention (the Math-in-CTE model) in six SLMPs and over 200 classrooms (see Stone, Alfeld, Pearson, Lewis, & Jensen, 2005). The results were promising enough to the funding agency that a full-year study of the same intervention, with minor modifications, in five of the SLMPs was

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undertaken.2 We report here the procedures and results for the full year test of the experimental intervention. A more detailed report is available elsewhere (Stone, Alfeld, Pearson, Lewis, & Jensen, 2006). The Design This study was designed as a field experiment with random assignment of teachers to the experimental and control conditions. The control or counterfactual condition permits the researcher to measure what would be expected if the students in the experimental classrooms had not received the intervention (Cook, 2002; U.S. Department of Education, 2003). Volunteer CTE teachers were assigned at random to the experimental or control group within each SLMP; thus, the primary unit of analysis was the classroom (i.e., aggregate class performance). We conducted the experiment across multiple occupational areas in order to address one of the key criticisms of experimental research in education: that findings are difficult to generalize to other sites (Magnuson & Waldfogel, 2005). The SLMP areas we chose for our study represented the breadth of CTE prograrnming. We chose one program (business and marketing) that is essentially classroom based, one program (auto technology) that is heavily skill oriented, two programs identified as high tech and high growth (health and information technology), and one program historically associated with CTE (agriculture). Replication of the Math-in-CTE Model: The Five Core Principles What would be required to replicate our findings in other CTE classrooms and programs? We identified five core principles of our intervention: (a) develop and sustain a community of practice among the teachers, (b) begin with the CTE curriculum and not the math curriculum, (c) understand that math is an essential workplace skill, (d) maximize the math in the CTE curriculum, and (e) recognize that CTE teachers are teachers of Math-in-CTE and not math teachers. Each is further explained below: 1. Community of practice. The necessary condition for successful replication of the Math-in-CTE model is a group of CTE teachers from a single occupational area and their math-teacher partners working together in a community of practice to identify the math inherent in the occupational curriculum (e.g., auto technology, health, information technology). The process of curriculum mapping and the subsequent development of math-enhanced lessons in a team environment produced a sense of ownership in the final set of lessons that emerged. Shared commitment and ideas are the defining characteristics of communities of practice (Wenger, 2005). As the Japanese practice of "lesson study" has shown us (C. Lewis, Perry, & Murata, 2006), teachers need the time and space to create a supportive community for professional development. The CTE teachers would not have had the expertise, confidence, or buy-in had they not spent the time in this process. 2. Begin with the CTE curriculum. This study tested one of the primary claims of CTE: that relevance facilitates learning. However, we also considered it essential to maintain the integrity of the CTE curriculum as it is linked to the labor market. These links to the workplace are what attract CTE students and provide the engagement that they often find lacking in academic courses. For these reasons, we required that the math to be taught as part of the CTE courses should emerge directly from the existing curriculum rather than superimposed onto it. While the CTE teachers made math applications in CTE more explicit by leading students from specific to general applications of math concepts, they were still teaching CTE lessons. 3. Understand math as an essential workplace skill. CTE courses have always included mathematics, but their instructors, who are not mathematics educators, often use "tricks of the trade" to address the immediate task and typically do not assist students to generalize beyond the specific application. Our approach was more explicit and fostered the mind-set among CTE teachers and students alike that, like any other tool in the workplace, math has its place in the toolbox required to solve genuine workplace problems. The mechanic, for example, may reach for a wrench or a formula to determine how to improve the performance of an automobile. 4. Maximize the math. Understanding the CTE curriculum to be rich with math, our fourth core principle is to encourage the CTE teachers to maximize the math whenever the opportunity arises in the curriculum (much like a "teachable moment"). That is, we encouraged the CTE teachers to begin to reinforce the concepts presented in the lessons they had developed whenever they were teaching content that touched upon the underlying math. Another aspect of maximizing the math included constant and consistent bridging of the math and CTE vocabularies, helping students make the link between them (modeling transfer).

5. Teachers of Math-in-CTE. Finally, just as we did not change the CTE curriculum into a math curriculum, we did not attempt to make CTE teachers into math teachers. In our model, the role of the math teacher is to serve as a resource, a source of information and support. The products of the collegial relationship between the CTE and math teacher were not

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only the lesson plans but also CTE teachers who had a fuller understanding of the math they taught. We wanted the CTE teachers to stay firmly grounded in their specialty and to teach math where it contributed to the learning of occupational skills. Communities of Practice and Issues of Reform In our opinion, the most important of these core principles is to develop and sustain a community of practice. The communities of practice that developed in our study fostered a shared purpose and high-level commitment among their members, which we believe is what led to their success. Indeed, Borman et al. (2005) found, in their recent evaluation of Urban Systemic Initiative funded by the National Science Foundation, that schools in which teachers reported the most involvement in learning communities showed the highest gains on student test scores. Borman et al. interpret this finding to indicate the importance of a supportive school culture. We believe that a supportive disciplinary culture is also critical; our study suggests that pedagogical change does not have to be top-down within a school but can occur within and across classrooms. The communities that emerged in our study were not from one school, and their principals were not involved in their activities. These communities cut across schools, school districts, and even state borders, connecting teachers within a discipline who provided their own leadership. They worked within a pedagogic structure developed by the National Research Center for Career and Technical Education and facilitated by local research staff, but the communities of teachers made the critical decisions. It was the communities who selected the math concepts to be emphasized, developed the lessons, and decided when these lessons would be delivered. While our communities lacked what most of the literature identifies as essential for school reform (e.g., strong, consistent leadership), they were able to improve measured performance in the academic area-mathematics-where the performance gap among students is most pronounced. Issues in Scaling Up While we would like to see our model continued, neither replication nor scaling up of the Math-in-CTE model can occur without a thorough consideration of several key issues. The first issue is the use of a volunteer sample in this study. The CTE teachers who participated in this research-both experimental and control-were clearly not a representative sample of CTE teachers. Marketing specialists and others often describe the general population in terms of the rate at which they will accept a new product or innovation. Innovators (2.5%) and early adopters (13%) are a small portion of the population on this innovation curve (E. M. Rogers, 1962, 1976). As teachers who continually seek ways to improve their professional skills and knowledge, the participants in our study probably fall into these two categories. The important next question in bringing a reform to scale is the extent to which the model works with the middle part of the curve, the early-majority and late-majority adopters. These are good teachers, competent professionals, but not readily inclined to embrace reform and innovation. A related question is the extent to which the teachers have truly accepted a changed approach to teaching CTE. As part of this study, teachers were provided with financial incentives; professional development; and various kinds of support, materials, and recognition. What happens when those incentives and support are not offered? Reform sustainability is another key issue in school reform literature. As many of our teachers reminded us, the educational landscape is littered with reforms that held promise but never really became part of the fabric of the school or the classroom. We recently completed a follow-up study to measure the extent to which the experimental teachers continued to use our model in their courses without our support during the school year following the intervention. We found that 73% of the experimental CTE teachers reported continuing to use the methods and materials from the study. An unanticipated finding was that 66% of the math teachers incorporated examples of applications of math from the CTE lessons into their own teaching (M. V. Lewis & Pearson, 2007). We believe that the investment that these teachers had made and the feeling of ownership of the process and product contributed to this high level of continued practice of the Math-in-CTE model. A third question that arises is a challenge to our community-of-practice core principle. Simple logistics and bureaucratic inertia militate against building such communities within school districts. Because many CTE teachers teach in singleteacher programs within comprehensive high schools or at regional CTE centers, assembling a community of practice following our guidelines will require cross-district and perhaps even cross-state cooperation. Conclusion We believe that, by using our five core principles, teachers and schools can begin to address students' math skills throughout the high school curriculum in a more organic way: incorporating explicit math lessons when they naturally occur. Mathematics in such diverse applications as statistical quality control, computer spreadsheets, and precision farming has become a basic component of many jobs, and mathematics will become increasingly pervasive in most occupations that require specialized preparation. We suggest that the Math-inCTE model is a way, but not the only way, to help U.S. youth, particularly traditionally low-achieving youth, gain greater mastery of the mathematics critical to their post-high school education and workplace success. Math should be treated as a necessary tool for problem solving rather than a separate-and for many students, abstract and irrelevant-subject. CTE courses have the best potential for

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demonstrating to students that rigorous math is in fact highly relevant.

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