Motivational Strategies for Underachieving Math Students

By
Anne McCall, Mathematics Instructor
Champaign, Central High School
Champaign, Illinois
mccallan@cmi.k12.il.us

When drugs, gangs, crime, teen pregnancy, illiteracy, racial prejudice, poverty, and broken homes are terribly real issues confronting many of today's high school students, a set of thirty algebraic equations to solve might not seem like a top priority. This leaves teachers of mathematics, a subject already shunned by many students, to ask how they can possibly capture the attention of underachieving teens distracted by such serious problems and events in their daily lives.
Is it possible for math teachers to motivate these young people to find an interest in and a use for mathematics? Jaime Escalante thought so, and his math program at Garfield High School in the barrio of East Los Angeles affirmed that indeed even the most disadvantaged students can be "turned on" to and can succeed in higher level mathematics. Although responses on the 1988 National Assessment for Educational Progress indicated nearly 50% of 17 year-old Blacks and Hispanics reported Algebra I or below as the highest level of mathematics they had taken, Escalante has helped hundreds of minorities in East Los Angeles pass the Advanced Placement Calculus exam (Anderson, 1990; Escalante, 1990). Escalante's method and other successful math programs will be discussed in greater detail further in this paper. First, some of the problems and issues associated with current mathematics curricula will be discussed. Then, some of the teaching strategies and the educators who have already proven successful in motivating at-risk and underachieving math students will be more closely examined.
Before we take a look at the problem of underachieving math students, though, the subjects themselves should be defined more explicitly. Underachieving students could be characterized, in general, as lacking or concealing motivation to be academically successful. Thus, they do not work or perform up to their potential. Many such students fail to see the relationship between academic success and future opportunities. Another term often given to these students is "at-risk", which is defined by Midkiff and Thomasson as having an increased chance of failure in school due to personal behaviors, past educational records, or family problems (1993). Although underachieving students can be of any race or class, many are from minority groups and/or lower income families. Many also are raised in households in which the parents have not been to college or perhaps not even to high school. Thus, instead of emphasizing the value of education, these parents might encourage their children to get a job and help support the family. To counter this lack of parental involvement in their education, underachieving students frequently need the intervention of a concerned educator to establish academic goals. Rather than allow students to use their problems as excuses, teachers must inspire them to overcome the difficulties they face. As Escalante claims, "Yes, the barriers disadvantaged or minority students face are substantial, but it is the very possibility of their remaining trapped by them for an entire lifetime which requires that such students be urged to succeed in their academic studies." (1990, p.422)

Curricular Reform
The critical question that arises then is what exactly can a mathematics teacher do to stir such interest and motivation in students. When searching for an answer to this problem, teachers need to examine both the mathematics curriculum being taught and the teaching strategies being employed in the classroom. Looking first at the curriculum, one might see why low-achieving students are bored in their current math classes. Many have had repeated exposure to the same basic mathematical content for years in courses by such names as "Remedial Math", "General Math", "Consumer Math", or "Mathematical Applications" (Patterson, 1989). These classes often have a fragmented curriculum with an emphasis on rote memorization and lower-level computational skills, rather than the skills and content recommended by the NCTM Curriculum and Evaluation Standards (1989). The Standards urge a shift from repetitious drills to open problem situations that promote greater conceptual understanding through the making and testing of hypotheses and the communication of mathematical ideas.
Ironically, although many high schools have raised the number of math classes required for graduation, the types of courses offered in response to district-mandated course requirements are often just more lower-level classes, disguised under a variety of titles such as those listed above. Among 70 teachers across a four state sample in schools where graduation requirements had been raised, only 11% reported any increased student exposure to math or gain in knowledge. Only 7% felt there was any improvement in higher order reasoning (Patterson, 1989). This research indicates the quantity of math classes taken might not be nearly as important as the quality of the math classes. The Standards reiterate that "the long-standing practice of requiring lower-achieving high school students to repeat sixth-grade mathematics content over and over will be replaced by a study of content that we believe provides these students, as well as their classmates, with a central core of mathematical representation, mathematical processing, mathematical problem solving, and mathematical thinking." Thus, even though students might not be able to explore math content to the same depth or formalism, they should all be "guaranteed equal access to the same curricular topics." (1989, p.131)
Reforming content coverage is just one of several ways that the curriculum can be changed to make math more intrinsically interesting for students. Current research also overwhelmingly supports a greater use of technology in the mathematics classroom and the integration of math with other subjects. These two measures are expected to motivate students and to help them see important linkages between math and the real world.

Technology
Incorporating technology into the high school mathematics curriculum is advocated not only for increasing student interest but also for preparing them for jobs in the 21st century. As they are acquiring computer skills necessary in today's workforce, they also are more engaged in their own learning process. Rather than being passive receivers of information, students are more able to control the pace and mastery of their learning. Although students of all achievement levels have been shown to benefit from using computers in the classroom, a couple of studies by Signer and Christie focus on the effects of computer instruction and testing on high risk and minority youth.
Signer evaluated a year long project called MATH-R-US (Microcomputer Adaptive Testing High-Risk Urban Students) used in an urban high school that serves an at-risk, predominantly black population with a high rate of absenteeism (1992). In this program, students were given a computerized diagnostic test once a week and spent the other daily class meetings working on computer generated practice sheets. By the end of the year, results implied that computer assisted instruction increases students' motivation, self-confidence, and self-discipline. In this study, students engaged in much less off-task behavior (less than 5% of observed computer class time) and instead generated intense competition among themselves to perform well on tests. Whenever they completed one with 100% accuracy, a graphic of a hamburger would appear on their computer screen. Soon, the class made a contest to see who could get the most "hamburgers" in a class period! Actually, I have noticed similar student generated competitions in my own math classes when students use computer software, particularly a HpyerCard stack on functions with a computer quiz that rewards each correct answer with a smiling face. "Green Globs", another algebra program, also sparks competition since it provides a running list of the students with top scores. Naturally, the students compete to get their names on this scoreboard.
A second study on the usage of microcomputers with high-risk and minority adolescents was conducted by Christie and Sabers in the setting of a summer youth program (1989). An experimental group of students completed the mastery learning program using the computer while three other groups were in instructional settings that used lectures and worksheets. One purpose of the study was to investigate the claim that "traditional teaching methods are incongruent with the learning styles of high risk and minority students" (p. 2). To establish this congruence, some researchers suggest using mastery learning techniques. Two advantages of mastery learning are the well-defined body of content for the instructional encounter and the repeated exposure of content until the student has achieved the immediate goal of instruction. Christie and Sabers claim that the computer can be an excellent tool for implementing mastery learning since it can give repeated exposure to subject matter and consistent presentation, scoring, and feedback to students. Hess agreed when reporting that students perceived the computer as "fairer, easier, and more likable than teachers" (Christie, 1989, p.3). Furthermore, the use of computers gives students more ownership and responsibility over their learning, while enabling the teacher to provide more individualized help. Better teacher/student interactions often develop since the focus of their relationship is less on evaluation and more on assisting the student.
In the experimental setting of this study, the instructor would give a brief lecture on math and then assign computer-assisted-instruction lessons. At that point, students were responsible for deciding the order in which they worked on assignments, when to ask or offer help, when to take short breaks, and how to spend their time once they finished their assignments. This extra time was usually spent either finishing previous lessons, assisting other students, helping the teacher grade or record assignments, or using the computers recreationally. In contrast, students in the control setting typically listened to a lecture from their math instructor, helped work example problems on the board, and then were given worksheets to do individually at their seats. Student interaction was discouraged, but the teacher often had to monitor socialization and get the students back on-task. On the other hand, student interaction in the computer group was permissible and was almost always centered around learning.
Although the results of this study indicated that both types of instructional settings (alike in that both implemented mastery learning) produced similar gains in quantitative assessment scores, the qualitative analyses revealed the computer setting offered additional educational benefits. When using the computer, students learned to interact with each other in a cooperating manner and to interact with their teacher as an ally rather than an adversary. These positive interactions led to a sense of social integration, which is a very important experience for high risk students. They also learned responsibility and how to have a more substantial role in their learning outcomes and academic success.

A more specific use of computers in schools was described by Michele Wisnudel in an article entitled, "Constructing Hypermedia Artifacts in Math and Science Classrooms" (1994). Although hypermedia has already been commonly used to deliver information to teachers and students, a more innovative use, probably with greater educational benefits, is for students to design their own hypermedia artifacts. In doing so, the students would learn to organize information, make connections, and draw relationships between important ideas and concepts. This could also be an excellent motivational tool for math students. Wisnudel maintains, "By creating hypermedia artifacts, students are motivated because they are participating in authentic learning experiences" (1994, p.6). Other researchers agree that choice and control are critical factors in motivation. Daiute postulates that "when students ...select their own images, sounds, and text, their culture, values, and interests become a part of the curriculum, thereby creating familiar contexts and symbols with which to focus on their academic work" (Wisnudel, 1994, p.7).
Early examples of HyperCard stacks created by algebra students include the commutative, associative, and distributive properties, as well as adding polynomials and solving, simplifying, and rearranging formulas algebraically. Observations of these stacks being created reveal much enthusiasm and motivation among the students. Not only do they learn to work together in teams to design the HyperCard stacks, they learn in-depth the topics they are presenting. As they figure out how to structure the information, students improve their own conceptual linkages. According to Wisnudel, much more research is needed on how the process of designing hypermedia artifacts affects students' ability to develop conceptual organizations and to construct multiple representations of a single concept. She concludes that teachers must embrace powerful classroom technologies such as this to allow students to control their learning not only as a way of motivating them but also to improve students' cognitive and social skills (1994).

Another computer tool which can be adapted for a wide range of grade levels and math classes is the spreadsheet. In her article, "K-12 Teachers' Use of a Spreadsheet for Mathematical Modeling and Problem Solving," Sharon Dugdale lists many ways in which the spreadsheet can be incorporated into algebra and other classes (1994). She suggests having students create spreadsheet models to maximize area, to solve linear equations, to produce both numeric and graphical solutions for quadratic equations, to provide both graphical and tabular solutions to distance-rate-time problems that have travelers leaving different places at different speeds and meeting somewhere in between, to simulate population growth, to compute possible paths between two places on a grid, to compare linear and exponential growth, and to interpret data from surveys.
As with the computer activities previously described, the use of spreadsheets would enable students to play a more active role in their own learning process and would encourage creativity and autonomy. Especially when working with underachieving students, the models can be adapted to fit their particular interests. Since making money is a concern to most teens, a comparison of two daily allowance schemes would probably pique interest in the classroom. Students would be asked to compare which option is better: receiving $10 per day for a month or receiving a penny on the first day of the month and then each day thereafter doubling the number of pennies earned the previous day. A spreadsheet model for this problem could calculate and graph each day's income and the running total of each. This could lead to an interesting analysis of linear and exponential growth and when each is more profitable.
Other kinds of software that can facilitate the learning of mathematics but are more subject specific include Algebra Supposer, Geometer's Sketchpad, Data Insights (for statistics), and Mathematica (for Calculus). Actually, Mathematica is a versatile symbolic-manipulation package that can expedite instruction in all levels of math classes by eliminating tedious hand calculations and creating two and three dimensional graphs. This saves much time on "busy work" so that students can spend more time exploring relationships and making connections between mathematical topics. As graphing calculators continue to be updated and improved, however, expensive computer labs for math classes actually might become less necessary. The recently marketed TI-92 graphing calculators are much cheaper and more mobile than computers, yet have many of the capabilities of a computer. These calculators contain a version of the Cabri™ geometry program and the DERIVE® symbolic manipulation program. Texas Instruments also makes a Calculator-Based Laboratory™ System that allows users to collect real-world data, retrieve it directly into a TI-82 or TI-85 Graphing Calculator, and then generate graphs and analyze the results. The company has a growing supply of probes and other accessories to be used with this system to explore real-world connections between math and science.
One technological tool that the graphing calculators probably will not be able to duplicate from computers anytime soon, though, is the Internet. This exciting educational resource provides a boundless supply of material for both teachers and students to utilize. It allows students to be very interactive on the computer and to access up-to-date data from around the world. It also enables teachers to readily share lessons and disseminate ideas. Because of the newness of this tool, however, its educational potential is a topic on which more research is needed. As with all the different types of technology that have been described, the Internet should become a powerful motivational tool not only for students who are currently underachieving, but for math students at all grade and ability levels.

Linkages
A second critical change in the mathematics curriculum, besides technology, that should help motivate students is the linking of math to other subjects and to real-world applications. As already mentioned, technology will help to do this. However, written lessons and activities should also provide such connections. Some textbook companies are beginning to better integrate math with other subjects, but teachers usually are still left to find supplemental material on their own.
One resource that I found particularly helpful was a book entitled, The Power of Numbers: A Teacher's Guide to Mathematics in a Social Studies Context (Gross, Morton, & Poliner, 1993). This book, aimed toward both middle school and high school math classes, places mathematics in a social context to help students see that people in many different jobs need math to solve problems and make decisions. As part of a larger series of curricula designed to help students learn about active and constructive citizenship, this book encourages students who previously might have been hesitant to learn about issues or develop their own opinions because they could not understand the mathematical and scientific aspects of issues about which they were concerned. The authors provide mathematical experiences in real-world contexts that help students interpret, experiment, communicate, and look for multiple solutions to complex problems. Lesson topics include a poll about the lifestyles of young people, the census and redistricting for the House of Representatives, the doubling time of the U.S. population, mapping out a public rail transportation system for Los Angeles County, and graphing such information as the census data on American Indians, land use in Brazil, and U.S. dependence on foreign oil. Real life topics such as these should attract even the most underachieving students in class. Since the world is full of interesting facts and information, why not bring some of it into the classroom to be analyzed mathematically?
Another book with meaningful, multicultural lesson plans is Turning on Learning: Five Approaches for Multicultural Teaching Plans for Race, Class, Gender, and Disability (Grant & Sleeter, 1989). Each lesson plan contains a "before" version (as the lesson would traditionally be taught) and an "after" version (improved to "turn on" learning and offer a multicultural perspective). Although the book covers all subjects and grade levels from 1-12, there are several lessons appropriate for a secondary math class. Topics include graphs comparing poverty rates among different racial groups, maps and graphs for analysis of the distribution of agricultural land to Whites and American Indians, solving two equations with two unknowns using a jigsaw model of cooperative learning, factoring polynomials in teams, and studying functions by comparing and contrasting street language with mathematical language. As students complete these lessons, the authors hope that they will "become excited about learning and enthusiastic about living in and bettering their world" (p. v).
Plenty of evidence exists in support of the notion that students are more motivated to learn math and more likely to master the content when they see linkages like those just described. Patterson gave an example of students in a wiring class who finally saw a need for learning how to work with percentages and decimals and how to apply various algebraic and geometrical concepts (1989). The skills they never cared to master in their math classes, they were now willing and wanting to acquire.
There are some researchers, though, with concerns about what kinds of contexts that mathematics is situated in at schools and who decides those contexts. Stanic combines culture-practice theory and critical theory when posing the question, "Whose knowledge and whose ways to construct knowledge come to be valued in the culture of school mathematics? (1989, p.64). He claims that the lower performance of certain cultural groups on various measures of cognition reflects cultural differences embodied in the contexts of the assessments rather than real deficits in cognition. Although Stanic urges educators to find new contexts in which otherwise low achieving students are more able to demonstrate mathematical competence, he also warns against designing the school curriculum based on studies of what people do in their daily lives outside of schools. He advises, "One thing we must not do is to go back to the practice, prominent in the early part of this century, of basing the school curriculum on limited task analyses of home and vocational activities." (p. 65) Thus, even though linkages between math and the real world are undoubtedly important in motivating students, Stanic raises a valid concern about trivializing both the curriculum and daily life.

TEACHING STRATEGIES
Going beyond what is being taught in the secondary math classroom, let us now examine how it is being taught and what impact different teaching styles have on students' motivation. Even if the curriculum is enriched with technology and real world applications, will some student apathy remain if teachers do not adapt their instructional methods as well?
In his book, Winners Without Losers: Structures and Strategies for Increasing Student Motivation to Learn, Raffini provides several recommendations for stimulating student interest in any classroom (1993):
- Find ways to get students actively involved in the learning process
- Assess students' interests, hobbies, and extra-curricular activities to relate
content objectives to student experiences
- Occasionally present information and argue positions contrary to student assumptions
- Support instruction with humor, personal experience, incidental information,
and anecdotes that represent human characteristics of the content
- Use divergent questions and brainstorming activities to stimulate creative
thinking and risk taking
- Vary instructional patterns and activities
- Support spontaneity when it reinforces student academic interest
- Use vocal delivery, gestures, body movement, eye contact, and facial
expressions to convey enthusiasm
This last suggestion about conveying enthusiasm is discussed further by Raffini. Enthusiasm occurs when a teacher is committed to and values what he/she is teaching and then expresses that commitment with reasonable emotion, animation, and energy. For their own dedication to be of instructional value, however, teachers must be equally committed to helping students discover the same excitement and enjoyment. Thus, instead of fearing that enjoyable learning must be frivolous, educators should realize that "enjoyment and hard work often go hand in hand" (p. 241). And if teachers "truly want to motivate students to devote large amounts of effort to learning, then they must design the process of learning to meet or at least recognize students' need for fun" (p. 240).
When discussing strategies for motivating students, it becomes important to discern between external and intrinsic motivation. Raffini defines an intrinsically motivating activity as "one in which there is no apparent or compelling reason for doing the activity, beyond the satisfaction derived from the activity itself" (p. 64). Realistically, of course, students will probably encounter many assignments through the course of their education that are not particularly intrinsically motivating. Although some students may even appear to lack intrinsic motivation for performing any academic task, Edward Deci at the University of Rochester argues that intrinsic motivation is innate to humans and that people are driven to seek out and to master challenges that match their capabilities (Raffini, 1993). Hence, when students withhold effort and appear to lack motivation, many times they are simply putting up a defense mechanism to protect their sense of self-worth. Withdrawing from academic effort might have been found to be less painful than experiencing feelings of failure created by forced academic competition. Unfortunately, many educational practices do seem to limit the number of students who can feel good about their academic performance: for every "above average" student another is labeled "below average".
Another reason why intrinsic motivation might get stifled in some students is the use of external rewards such as candy, stickers, happy faces, coupons, and countless other types of awards. Although these tokens might temporarily increase performance, research suggests that they can eventually kill students' sense of autonomy and self-determination and thus decrease their intrinsic motivation. Nicholls and Thorkildsen also question the use of rewards and the camouflaging of mathematics with games (1995). These authors fear that using trinkets or bribes to coerce children into learning is an easy way for teachers to inflate a lesson without having to spend time creating more meaningful, intrinsically interesting lessons.
A booklet produced by the American Association of School Administrators offers some additional tips on the most effective ways to motivate students (Gonder, 1991). Among the 12 suggestions given are to state learning objectives at the outset, present information with intensity, add variety and playfulness, induce curiosity with invigorating warm-ups, encourage student responses, plan units so that students have a high chance of success, give positive reinforcement in the form of both verbal and non-verbal feedback, correct in a positive way by focusing on the behavior not the person, encourage risk taking by creating a classroom climate where students feel comfortable expressing opinions, and make the abstract more concrete, personal, or familiar by giving students something specific to identify with.
Midkiff and Thomasson suggest that students are often labeled as underachievers simply because their learning styles do not match the teaching styles of most classrooms. Even the physical environment can be important. Evidently, some students tend to work better in soft light and an informal room design wherein they could sit on the floor. These students prefer to work in groups, have a high need for movement, tend to be impulsive learners, and learn best through tactual or kinesthetic activities (1993). When trying to involve and motivate all students, teachers should be aware of these differences in learning styles and adapt accordingly when possible.

Successful Programs
The strategies delineated in the previous section are general ideas for teachers to think about incorporating into their current teaching styles. Naturally, there is not one particular style that is better than all the rest; rather, modifications must always be made to meet the needs of the specific population of students involved. As will be seen in this section, though, certain programs and educators have already proven to be very successful in motivating math students, even those formerly labeled as underachieving or at-risk. First, two educators, Jaime Escalante and Kay Toliver, who were highly effective at the schools in which they taught, will be described. Then, four other innovative programs in math education will be outlined.

The Jaime Escalante Math Program
The success achieved by this math teacher in East Los Angeles has already been briefly described. In an inner-city high school with about 3500 students, of whom 95% are Hispanic and about 80% qualify for the federal free or reduced cost lunch program, Jaime Escalante established a rigorous math curriculum and helped prepare hundreds of students for the AP Calculus exam (Gillman, 1990; Escalante, 1990). An astounding statistic is that of all the Hispanics taking this annual placement test nationwide, a quarter of them are from Escalante's program.
The key, according to this former Bolivian, is hard work. When both the teacher and the student are willing to work hard, he feels that the elements of his program and the successes he has experienced can be duplicated anywhere. He views it as the teacher's job to bring out the ganas (wish to succeed) in each student. To accomplish this, he would "entertain, challenge, cajole, encourage, praise, warn, scold, and threaten" (Gillman, 1990, p. 7). He used gadgets, gimmicks, and a special vocabulary; he played music, handed out candy, told jokes, had the class chant and clap and about anything else that got them going. Amidst this fun and creativity, though, existed high expectations of the students and how much time they spent on mathematics. They were expected to study math before school, during lunch, after school, and even on Saturday mornings in special classes. Much of this time they worked in teams, an important component of the program. Escalante used past graduates to come back to talk to current students and to serve as models of achievement. He also depended heavily upon parent involvement, claiming that "To succeed, a program as intense as mine must have 100 percent support from the parents." (Escalante, 1990, p. 418) Other important elements of his program were community resources and donations and the use of quality textbooks with lots of interesting practice problems and linkages between math principles and their real-world applications. Again, though, he emphasizes that the primary key to success is high expectations on the part of the teacher and diligence combined with unconditional love and humor.

The Kay Toliver Mathematics Program
A similar success story with minority math students can be found at East Harlem Tech, a public junior high school in New York City (Toliver, 1993). There Kay Toliver has been an extremely motivating teacher for over 25 years. As with Escalante, two fundamentals of her approach are to care about your students a great deal and to uphold high expectations. Toliver also sees it as her responsibility to get students "hooked" and "to the point that they anxiously look forward to coming to and participating in class" (p. 37). To present the whole body of mathematics as a unified subject and to emphasize relationships between math and the real-world, Toliver replaces the textbook with her own lesson material. Only for extra homework practice does she use the text and then she only assigns problems that require a sensible, well-thought-out answer. Instead of requiring students to work lots of repetitious problems, she sometimes has them give oral presentations or do research projects. To help students view mathematics as a tool for their futures, she blends history, culture, literature, writing, and other subjects with the study of mathematics. She is well known for a lesson called the "Math Trail" in which her class creates their own math problems based on real-life situations encountered in the neighborhood of the school. Students' progress in Toliver's math classes is monitored with constant contact and communication, and assessment is performance-based. As for discipline, she says the best form is to keep the students very busy and filled with a desire to learn. Like Escalante, this teacher relies on parental involvement and works hard to establish open lines of communication between herself, the parent, and the student, even going so far as to institute "family math" sessions. With the combination of all these techniques and tactics, Toliver succeeds each year in creating an exciting mathematics classroom comprised with intrinsically motivated students.

Although from the descriptions of both the Escalante and the Toliver math programs, creating a successful learning environment might appear relatively easy, any practicing teacher knows that motivation is a complex issue and that sparking intrinsic interest in math can be quite a challenge. To help teachers in doing this and to aid them in revising their curriculum, a variety of programs have developed across the nation. Four of them, EQUALS, FAMILY MATH, PUMP, and the Interactive Mathematics Program, will now be examined.

EQUALS
Although originally created as a gender equity program, EQUALS has evolved into a program with a much broader focus (Kreinberg, 1989). Designed in 1977 at the University of California at Berkeley, EQUALS was intended to help K-12 teachers address factors that lead to female attrition from mathematics and has since been proven to help all math students become better problem solvers and to feel less intimidated by the subject of mathematics. In a 30-hour inservice program, teachers discuss sex-role stereotyping, grouping, and tracking patterns in their own schools that might inhibit students in mathematics. They also learn to use manipulative materials and problem solving in the curriculum and to emphasize the role that mathematics plays in the work world. As their lessons become more oriented toward non-routine questions and problems that have more than one right solution, teachers assume the role of a guide encouraging students to take risks and then to learn from their mistakes.
Several studies have shown that the methodology of EQUALS has a positive impact on students. One study conducted in Cleveland, Ohio (Sutton & Fleming, 1987) on nearly fifteen hundred students indicated that problem solving skills of the EQUALS participants improved significantly over the year in contrast to the non-EQUALS students. The greatest improvement was found in white females and African-American males. EQUALS students in grades 4-6 also became less stereotyped in their perception of math as male domain, and their beliefs toward the perceived usefulness of math decreased less than those of non-EQUALS students. These attitudes have been found to be important predictors of future math course enrollments (Kreinberg, 1989).

FAMILY MATH
While expanding its focus to empower teachers and students to overcome not only gender issues but also race and class biases, EQUALS still did not address the needs of parents to help their children at home. In response to this need, FAMILY MATH was developed in 1981 with a grant from the U.S. Department of Education (Kreinberg, 1989). To better link home and school, FAMILY MATH offers courses in the evening for both parents and children to attend. These courses are usually lead by a teacher/parent/scientist team in a school, church, library, museum, or community center and meet for about 6 weeks. According to the FAMILY MATH Home Page on the Internet (http://theory.lcs.mit.edu/~emjordan/famMath.html), a typical group is approximately 25 people. At every session, which lasts about two hours, the group is taught three or four family games and activities that they can play at home. Parents are given explanations of how these activities relate to the topics covered at their children's grade levels and also learn how mathematics is connected to everyday life and to different careers. A primary goal of this program is to change people's habits and attitudes about mathematics, which it has been seen to do. As Kreinberg writes about parents, "Discovering that they know and use mathematics every day increases their understanding of the importance of mathematics as well as their confidence." (p. 136) Studies have also documented that FAMILY MATH is an effective medium for enriching communication between parents and children and is a politically neutral ground for minority communities and schools to come together. Since a 1985 grant by the National Science Foundation, more FAMILY MATH sites have been created to serve African American, Latino, and Native American families and continue to be very successful. Kreinberg concludes, "The spread of FAMILY MATH from low-income inner cities, to suburban and rural communities, throughout the U.S. and abroad, suggests that we have a mathematics program that can be adapted to the needs of very different communities." (p. 139)

PUMP Algebra Curriculum
In many urban high schools, underachieving math students either avoid taking algebra or really struggle through the course without finding it very relevant to their lives. In an attempt to provide the human and technological support to enable all students to enroll in and to be successful in algebra, The Pittsburgh Urban Mathematics Project (PUMP) was developed. This collaborative effort between teachers in the Pittsburgh public schools and the Anderson Research Group tries to make high school algebra accessible to all students through the use of situational curriculum materials and an intelligent computer based tutoring system. Other support includes a Chapter 1 reading specialist, after school tutoring, family algebra nights, the inclusion of special education students and teachers, summer workshops for the teachers, on-going help, and new assessment strategies. The curriculum is built around students' own informal knowledge of mathematics and on problem situations. In addition to more traditional assessment methods, the students are assessed on their performance on group tasks, portfolios, and their work on computer tutors. Like FAMILY MATH, the PUMP algebra program has a home page that can be accessed on the Internet (http://www.sands.psy.cmu.edu/ACT/awpt/pump-home.html). Also provided at this web site are two sample final exams administered in the PUMP curriculum. These assessment items are consistent with the National Council of Teachers of Mathematics Standards and require the use of problem solving skills to represent real world situations with equations and then to interpret those equations with tables and graphs.

The Interactive Mathematics Program
Another problem-based curriculum for high schools is the Interactive Mathematics Program, which began in California but, with funding from the National Science Foundation, has embarked on an ambitious nationwide dissemination plan. This program, designed to meet the needs of both college-bound and non-college-bound students, is meant to replace the four-course sequence typical of most high school mathematics curricula with an integrated course. The IMP curriculum consists of four-to-eight week units that are each organized around a central problem or theme. Motivated by this central focus, students solve a variety of smaller problems that develop the underlying skills and concepts needed for solving that unit's primary problem. Examples of problem contexts included in the IMP are games of chance, empirical models of periodic motion, the geometry of the honeycomb, rates of increase in human populations, and land use decision making. As they tackle these problems, students interact with each other in groups and make written and oral presentations to help clarify their thinking and refine their ability to communicate mathematically. More information is also available on this program through the World Wide Web at the following address: http://babe.math.uic.edu/~rdees/imp1.html.

Throughout this paper, I have tried to explain the characteristics of underachieving math students, the problems they have encountered in traditional mathematics classrooms, and the reforms needed to reach and to motivate these students. Research suggests that motivating students could be made easier through various reforms in the curriculum and the adoption of certain teaching strategies. A couple of effective teaching strategies to model were presented in the description of the Jaime Escalante and Kay Toliver math programs. The curriculum revisions needed, including the incorporation of technology and linkages to real world situations, were recapitulated in the descriptions of such model programs as EQUALS, FAMILY MATH, the PUMP algebra curriculum and the Interactive Mathematics Program.

References

Anderson, Beverly J. (1990) Minorities and Mathematics: The New Frontier and Challenge of the Nineties. The Journal of Negro Education, 59(3), 260-272.

Christie, Nancy, and Darrell L. Sabers. (1989) Using Microcomputers to Implement Mastery Learning with High-risk and Minority Adolescents. (ERIC Document Reproduction Service No. ED 326178)

Dugdale, Sharon. (1994) K-12 Teachers' Use of a Spreadsheet for Mathematical Modeling and Problem Solving. Journal of Computers in Mathematics and Science Teaching, 13(1), 43-68.

Escalante, Jaime. (1990) The Jaime Escalante Math Program. The Journal of Negro Education, 59(3), 407-423.

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