**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 DERIVEŽ 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**

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