The bell rings, and a hot April sun pours down on a group of students hurrying to class at San Marcos High School in San Marcos, Texas. As a rule, most students would rather be anywhere than a pre-algebra class at this time of year, but these students are an exception.
A teacher greets them as they enter the classroom. Students are carrying calculators and notebooks, and they sit at tables of four in front of a rack of television monitors, three cameras, and a teacher work station. On one of the monitors the students see themselves; on another they see a professor from the university, with whom they exchange greetings.
Three months ago when these 20 9th graders entered the interactive television (ITV) classroom for the first time, they were apprehensive. They had been recruited for this class from remedial mathematics classes, where for eight years they had been conditioned to sit in straight rows doing skill work. Now they would be participating in a curriculum project that would use full two-way audio and video fiber-optic interactive television.
The second bell rings. On the monitor, the students see a split-screen image of a computer-generated problem and the professor. The professor reads the problem: “At a video store you can either pay a $15 annual fee and rent videos for $1.50 each or you pay no annual fee and rent videos for $1.75 each. When is it better to pay the annual fee?”
The classroom teacher instructs the students to work in their groups to solve the problem. Assisted by a graduate student tutor, he gives each student a chart to organize data and checks to see that each group understands the task. Students use guesses and work back and forth in their groups to find that with the annual fee, 60 videos cost $1.50(60)+$15= $105, and without the annual fee $1.75(60)=$105. If you rent more than 60 videos, it is better to pay the annual fee. The teacher calls on a group to come to the teacher station to show its work.
From another group, Rudy explains that he found the answer quickly by noting that there is a 25 cent difference in video price and $15 to make up, so it would take 60 videos to make up the difference. The professor asks the students to look at the pattern in the table to generate two rules where y is the cost and x is the number of videos. The students have been writing algebraic rules since the first week of class and easily come up with y=$1.5x + $15 for the cost with an annual fee and y=$1.75x for the cost without. “Now,” the classroom teacher asks, “can we write an equation for this situation to show when the costs would be the same?” Rudy answers, “So $1.50x + 15 would be equal to $1.75x.” The teacher works the solution on the overhead camera for the class to see, soliciting responses from the class. He then instructs the class to graph each of the rules on their graphing calculators.
Maria and Rebecca volunteer to demonstrate their work at the front. They place a calculator under the overhead camera so the class and professor can see the work on a television monitor. “So what is the point of intersection of the two lines?” the professor asks. Maria explains that it is (60, 105). The classroom teacher asks the class to interpret the result. A student explains that the point of intersection is the number of videos, 60, when the cost, $105, is the same.
A follow-up question and a challenge question appear on the monitor: “Suppose the annual fee is increased to $17.50. When is it better to pay the annual fee? Challenge: In the video problem, suppose you could pay $102 for 47 videos a year or $60 for 23 videos? What is the cost per video? What is the annual fee? Write a rule for the cost of videos. Graph it and check to see that your points satisfy the equation.”
Student teams work quickly through the follow-up question so that they can get to the challenge problem; they enjoy working as a team. In addition to experiencing an enriched curriculum, students interact with school social workers in weekly team sessions. Several of the students have sought the social workers' help with personal problems.
A few weeks ago these students and their parents met at the city park with the PATH staff for a picnic arranged by PATH social workers. Outside the pavilion, parents marvelled at a team of students estimating the distance across the San Marcos River using geometry, similar triangles, the Pythagorean Theorem, and calculators. They perform well when challenged.
The final bell rings. Students exit discussing the challenge problem and the lunch menu. Over the television network, the teacher and professor discuss the lesson and make plans to revise it for final entry into the curriculum document.
PATH Mathematics
Partnership for Access To Higher Mathematics (PATH Mathematics) is a two-year partnership funded by the U.S. Department of Education. It was formed to conduct research on mathematics teaching and learning and research in social services. PATH Mathematics aims to form a partnership among Southwest Texas State University, the San Marcos School District, San Marcos Telephone Company, and the community (families, social agencies, and professional associations) to significantly improve the mathematical skills of at-risk students. By providing them access to algebra and geometry, PATH Mathematics will increase their readiness for post-secondary education.
The project targets approximately 1,000 8th and 9th grade students (54 percent of each class) who have been tracked out of the algebra/geometry curriculum and are one or more years below expected achievement. These students are part of a school district where 60 percent of students are Hispanic-American, 36 percent Anglo, and 4 percent African-American. Forty-four percent of the students are economically disadvantaged.
PATH Mathematics provides students with a comprehensive, hands-on pre-algebra course early enough in their secondary education so that they can complete Algebra I, Geometry, and Algebra II. The pilot classes of 1992 and 1993 use the latest interactive communications technology, which links the university directly with the high school. The curriculum is an immediate intervention for all 9th graders who have been tracked out of algebra and subsequently will be implemented in off-track 8th grade classes.
The Curriculum
The scope and sequence of the PATH curriculum center on the appropriate use of manipulatives and technology coupled with a problem-solving focus in a cooperative setting. PATH's goal is to expand students' knowledge of mathematical concepts and the critical thinking skills necessary to apply those concepts. A variety of innovative instructional strategies is used. The curriculum is designed so that student outcomes are realized through an integrated, student-constructed approach. For example, the notion of variable and linear relations is not treated in isolation; it is developed throughout the year with an emphasis on graphing and solving equations and inequalities, as we demonstrated in our opening example.
The calculator-intensive curriculum is vastly different from the present curriculum for pre-algebra courses, which typically presents students with a review of whole numbers, drills in mathematical computations, a brief introduction to integers, and only a symbolic representation of algebraic systems. There is little problem solving and few concrete applications for the development of concepts. In contrast, the PATH activities focus on real-world applications that require quantitative and/or algebraic solutions. The lessons are designed so that the topics are connected across units.
In addition to regular instruction, the tutoring program both improves the mathematical skills of PATH students and increases their opportunities for continued education after graduation. The tutorial program uses ITV, including a locally broadcast television program called “Homework Hotline,” to facilitate the frequency of tutoring sessions conducted by university students. PATH students have regular tutorials in the ITV classroom, and they get additional hands-on experience from lessons in the regular class, where they also have the opportunity to interact with minority college students who are majoring or minoring in mathematics.
Social Support Program
The social support program is a critical element in PATH Mathematics. Joining the forces of diverse sectors of our community helps remove barriers to academic achievement (Chavkin 1990). Many of the low-income minority students who have been tracked out of higher-level mathematics courses face serious health, social, economic, and motivation problems that prevent them from attending class and completing assignments.
The PATH social worker and university social work interns collaborate with social service agencies, minority and majority businesses, parents, and the university to coordinate already existing social services to effectively serve the needs of students and their families. The San Marcos Interagency Council, a consortium of city and county social service agencies, helps provide appropriate services. Business and civic organizations—the San Marcos Chamber of Commerce, the San Marcos Telephone Company, the Hispanic Chamber of Commerce, the League of United Latin American Citizens (LULAC)—contribute by speaking to classes and providing mentors to students.
The social worker conducts parent education workshops and trains parents to work with the school district. In addition to empowering parents to understand and use the resources of the school and the community, the social worker facilitates collaboration between the university and families. Key linkages are being established between students/families and other university programs.
Interactive Television
To date, no educational partnerships have used fiber-optic technology to increase the mathematical skills of educationally disadvantaged students. PATH is the first digital fiber-optic network of its kind in the state of Texas that serves higher education and public schools. Oklahoma, Kansas, and Mississippi each have one digital fiber-optic project for public schools, but they do not emphasize the partnership of families and community members and do not employ advanced multimedia tools (San Marcos Telephone Company 1992).
The San Marcos Telephone Company is currently providing broad-band capabilities for integrated video, voice, and data uses. The system provides full motion, multi-way video, and voice and computer applications. Learners and instructors at the high school and at the university can see and hear each other simultaneously in real life settings. Equipment at each site is similar, allowing each interconnected site to function as a transmitting location (where the teacher is located) or a receiving site (where the students are located). Each classroom includes audio, video, and data equipment as well as a computer-controlled multi-media work station with peripheral devices. The teacher-controlled cameras in each classroom are arranged to allow the teachers to transmit their own image to the other sites, or an image of the students in the room where the instructional program is originating, or an image produced on the overhead camera. A passive switching device allows teachers to select which video source will betransmitted over the system. Multiple monitors and integrated audio systems permit participants in training and instructional settings to see and hear one another simultaneously in a live, continuous-presence arrangement.
In the PATH project, ITV is used primarily as a vehicle for field testing and revising curriculum. This is a dramatic departure from the usual ITV application, which typically involved a teacher at Site A working with students at Site A. The class at Site A was then broadcast to other sites where the course was not available. In the PATH Project pilot year, a university professor and a master teacher at the high school team-taught three classes of 20 each to field test, evaluate, and revise curriculum. The activities were taped for more in-depth evaluation. This unique use of ITV has proven to be an invaluable tool for curriculum development.
Project Outcomes
Many students who are enrolled in pre-algebra classes have been consistently tracked into lower-level classes, where they are subjected to low expectations and a boring curriculum. To provide students with a more engaging curriculum, PATH integrates activities of its three components: hands-on discovery learning, role-model tutoring, and personal links to social support services.
At the end of the pilot year, some interesting statistical results were noted (Kennedy, in press). Student grades during the pilot semester were significantly higher than the previous semester, and student attendance in the three pilot PATH classes significantly improved over the previous year. In addition, statistically significant correlations were noted between student attitude and use of calculator technology with achievement. There was no correlation between performance on a beginning-of-term arithmetic skills test and performance on an end-of-term algebra test. This is an interesting result since, contrary to the thinking of many mathematics teachers, arithmetic skill does not appear to be a prerequisite of higher mathematical thinking. At the end of the pilot semester, PATH students could generate a linear function given a graph, two points, or a real-world problem that could be modeled with a linear function. This is an uncharacteristic pre-algebra outcome. The PATH students scored significantly higher on the end-of-term algebra test than a comparable group of students in regular pre-algebra and algebra classes.
Perhaps the best indicator of success was the fact that 20 PATH students enrolled in a summer mathematics enrichment program. Joe Kopec, principal of San Marcos High School, commented that not only did the project outcomes “exceed his expectations” in the pilot semester, but he was particularly impressed that these students volunteered for a summer program to “learn for the sake of learning.”
What's Next?
In 1992–1993, the PATH Project serves three 8th grade and eleven 9th grade sections of students in three schools. Field testing with ITV continues with eight classes. The others serve as a beginning replication effort. The project is being documented with extensive qualitative and quantitative data, and the preliminary results suggest that all students can succeed in algebra as long as they are provided with an adequate support system including tutoring and social services. Teacher training in hands-on cooperative instruction, the use of peer tutoring, and the availability of social workers in the school will ensure the successful replication of a project like PATH Mathematics.
Critics will quickly point out that we could develop and implement a partnership for success without ITV. However, we see three distinct advantages to using ITV in PATH Mathematics. First, ITV removes logistical barriers to instructional delivery. Problems for most partnerships—distance, time, and schedule coordination—are nonexistent for our partnership. Second, ITV allows for more cost-effective use of instructional resources. We will be able to deliver more services to wider audiences for fewer dollars. Third, ITV allows at-risk students to see and interact with university faculty and students regularly in their high school career.
PATH Mathematics is clear about its expected outcomes for students—success for all students. Based on the studies reported by the College Board (Pelavin and Kane 1990), we expect that increasing students' skills in mathematics will lead to increased aspirations for college attendance. Because of the partnership effort, students in the PATH Mathematics program will make a successful transition into higher-level mathematics and post-secondary education, paving the way for productive lives in the 21st century.
Because every community in the United States, regardless of size, has access to a telephone company, our model can be replicated virtually anywhere. By joining forces, business and education can use their telephone company's fiber-optic technology to eliminate educational inequities and thereby significantly improve academic excellence and equality.
