Students at Risk in Mathematics: Implications for Elementary
Schools
Two groups of students in schools are learning substantially
less mathematics than they should. They are entering the work-force unable
to use mathematics effectively, and probably account for a significant amount
of the reason national assessment scores in mathematics do not show much improvement.
The first group consists of the "typical or usual" potential
school dropout and underachiever. The second group of students, the group
we term "nominal mathematics students," stay in high school and may even
go on to college, but their mathematics education is not adequate to allow
them maximum educational and life choices. Both of these groups, the potential
dropout and the nominal mathematics student, are at risk of not developing
adequate mathematical knowledge and skills and contributing less than what
they might to their own lives and to society.
What can the elementary school staff do to address the problems
of these at-risk students? This digest and the publication on which it
is based were developed to help schools and teachers know some of the problems
the students have, what the elementary school staff can do, and what elementary
classroom teachers can do. Most of the recommended actions will help not
only these students, but also others.
WHO ARE THE POTENTIAL DROPOUTS?
Data have been accumulated and analyzed on the numbers
and characteristics of potential dropouts. Recent data indicate over 20
percent of the students who enroll in American schools become part of this
group. In many urban and rural areas the percentage of students who dropout
is much higher.
It is estimated that two-thirds of these students are from
families at the poverty level. They frequently differ from their more successful
peers in development of self-esteem, task performance, school achievement,
and career and cultural aspirations. They often develop behavior patterns
that create problems in school.
These students may never fulfill their personal potential
and they may become an economic burden on society.
WHO ARE THE NOMINAL MATHEMATICS STUDENTS?
Analyses of National Assessment of Educational Progress
(NAEP) data and achievement test scores from states indicate that from
20 to 25 percent of the school population who complete high school do not
perform at a satisfactory level on many basic test questions. Correlations
from research studies indicate most of these students only complete the
basic required mathematics courses. They usually have taken no mathematics
elective courses.
Unlike the potential dropout, "nominal mathematics students" seldom
cause mathematics teachers major difficulties in school. They do not manifest
behavior problems and they are not viewed as potential problems for society.
These students are at risk because their level of understanding and competence
in mathematics is substantially below desired levels. These students are
not likely to continue in mathematics beyond basic requirements in high
school, nor are they likely to consider a career that uses mathematics.
Many of these students also will not be able to use mathematics when needed
in their daily lives.
WHAT ARE SOME OF THE CAUSES OF AT-RISK STUDENTS IN MATHEMATICS?
There are several variables that tend to cause students
to fall into the at-risk groups in mathematics. Several of these causes
can be prevented, reduced, or modified to help make students more successful
in school and in mathematics in particular.
Some students, especially minority students, are not able
to see themselves and their backgrounds reflected in the curricula. The
curriculum in many cases does not provide for cultural differences.
Females have tended to be especially at risk in many mathematics
courses or classrooms because mathematics has frequently been viewed as
a male domain. Instructional materials, family and peer behaviors and expectations,
and teacher behaviors and expectations have frequently reinforced this
attitude.
Some students develop anxieties that interfere with studying,
learning, and using mathematics. These anxieties can interfere with learning
and performance and cause the student to underperform and/or to elect to
avoid mathematics courses and experiences.
Some students have not succeeded in mathematics classes due
to learning and behavior problems, sensory handicaps, and physical and
health impairments. These conditions do not need to limit the mathematical
learning of these students. In many cases, mathematically related careers
can provide these students with excellent employment opportunities.
Some school age youth are less likely to complete elementary
and secondary school mathematics programs successfully and/or to acquire
the skills necessary for higher education and employment because they are
enrolled in classes where the curriculum and instruction are not appropriate
to foster desired attitudes, aspirations, skills, and understandings related
to mathematics. For many students the curriculum is neither interesting
nor relevant; the very structure of the curriculum serves to "turn off" students.
The mathematics curriculum often lacks real world problems and applications,
is repetitious, and focuses too much on product and not on process.
Mathematics instruction also frequently suffers from at least
five problems.
- the usual classroom routine is not effective for developing
new concepts
- the pace is wrong for many students
- drill and practice are ineffective
- diagnosis and treatment of error are often superficial
- instruction does not provide sufficient hands-on experiences
WHAT CAN AN ELEMENTARY SCHOOL STAFF DO TO HELP REDUCE THE
NUMBER OF MATHEMATICALLY AT-RISK PUPILS?
Data indicate a strong relationship exists between early
mathematics achievement and later mathematics achievement. Mathematics
competency appears to be learned. Mathematics programs that are planned
and operated to attempt to ensure success tend to have fewer remedial pupils
and fewer nominal mathematics pupils. Prevention is far more successful
than remediation; early remediation is more successful than late remediation.
While more research is needed to develop better models, combinations
of the following variables are associated with school programs that tend
to have a lower percentage of dropouts and a lower percentage of nominal
mathematics students.
The elementary school mathematics program:
- stresses goals and objectives
- stresses building knowledge and developing and using skills
in a coordinated curriculum
- provides mathematics instruction early (kindergarten and
grade 1) and continues
- provides time for mathematics instruction on a regular
basis
- stresses real-life use of mathematics
- uses activity based learning
- uses a variety of instructional approaches to accommodate
learning styles, preferences, and needs
- provides enrichment and adequate resources for all classes
- provides for transition from grade to grade
- emphasizes a continuous progress approach and/or cooperative
learning techniques
- stresses effective use of homework
- has a program for involving parents
- uses a diagnostic and prescriptive approach in instruction
to help identify pupil errors and to keep them from falling behind grade
level expectations
- has an early identification and intervention program for
pupils with learning problems
- uses frequent monitoring to identify pupils with possible
problems
- maintains careful records of pupil progress
- frequently uses a special program (in class or pull-out)
and special assistance (tutoring)to help pupils who have had difficulty
in mathematics
- provides intensive individual attention to individuals
with sustained problems for a period of time
WHAT EFFECTIVE PROGRAMS FOR ELEMENTARY SCHOOL MATHEMATICS
ARE AVAILABLE TO HELP PREVENT AND REDUCE THE NUMBER OF AT-RISK PUPILS?
Research and development on programs for elementary school
mathematics continues. There are, however, several programs available through
the National Diffusion Network (NDN) and also listed in the ERIC database.
For assistance in identifying programs available through
the NDN, contact your NDN state facilitator or: National Diffusion Network
Program, Office of Educational Research and Improvement, U.S. Department
of Education, 555 New Jersey Avenue, NW, Washington, DC 20208-1525, Telephone:
(202) 357-6134
To purchase a publication containing a listing of programs
contact: ERIC Clearinghouse for Science, Mathematics, and Environmental
Education, 1200 Chambers Road, Room 310, Columbus, OH 43212, Telephone:
(614) 292-6717
References
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