ERIC ED355117: Mathematics and Middle School Students of Mexican Descent: The Effects of Thematically Integrated Instruction. Research Report No. 5.

23 Pages·1992·0.4 MB·English

by  ERIC

DOCUMENT RESUME
ED 355 117
SE 053 484
AUTHOR
Henderson, Ronald W.; Landesman, Edward M.
TITLE
Mathematics and Middle School Students of Mexican
Descent: The Effects of Thematically Integrated
Instruction. Research Report No. 5.
INSTITUTION
National Center for Research on Cultural Diversity
and Second Language Learning, Santa Cruz. CA.
SPONS AGENCY
Office of Educatioral Research and Improvement (ED),
Washington, DC.
PUB DATE
92
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R117G10022
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DESCRIPTORS
*At Risk Persons; *Context Effect; Cooperative
Learning; Grade 7; Junior High Schools; Low
Achievement; *Mathematics Achievement; Mathematics
Education; *Mathematics Instruction; *Mexican
Americans; Middle Schools; Minority Groups;
Multivariate Analysis; Self Esteem; Student
Attitudes; Student Motivation
IDENTIFIERS
Hands On Experience; *Hispanic American Students;
*Middle School Students
ABSTRACT
This paper reports the effects of thematically
integrated mathematics instruction on achievement, attitudes, and
motivation in mathematics among middle school students of Mexican
descent. A school-university collaborative effort led to the
development and testing of a thematic approach undertaken as a means
of contextualizing instruction for students considered to be at risk
for school failure. Instruction relied heavily on small collaborative
learning groups and on hands-on activities designed to help students
make real-world sense of mathematical concepts. As hypothesized,
experimental and control students made equivalent gains in
computational skills, but experimental students (who received
thematic instruction) surpassed controls in achievement on
mathematical concepts and applications. The two programs did not have
a differential effect on students' attitudes toward mathematics or
self-perceptions of motivation in mathematics, but motivational
variables did predict achievement outcomes for both groups. Issues
related to the opportunity to learn the full range of mathematics
content of the curriculum within a thematic approach are examined.
(Contains over 50 references.) (Author)
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Reproductions supplied by EDRS are the best that can be made
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RESEARCH REPORT.. 5
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MATHEMATICS AND MIDDLE SCHOOL
GeZ
STUDENTS OF MEXICAN DESCENT:
THE EFFECTS OF THEMATICALLY
a
INTEGRATED INSTRUCTION
ts
RONALD W. HENDERSON &
EDWARD M. LANDESMAN
U.S. DEPARTMENT OF EDUCATION
Once of Educational Rssrch and Improvement
EDUCATIONAL RESOURCES INFORMATION
CENTER (ERIC)
),C This document has been rePrOduCed as
received from the parson or organization
It
originating
0
Minor changes have been made to improve
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OERI
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VI
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2
BEST COPY AVAILABLE
MATHEMATICS AND MIDDLE SCHOOL STUDENTS OF MEXICAN DESCENT:
THE EFFECTS OF
THEMATICALLY INTEGRATED INSTRUCTION
RONALD W. HENDERSON
EDWARD M. LANDESMAN
UNIVERSITY OF CALIFORNIA, SANTA CRUZ
NATIONAL CENTER FOR RESEARCH ON CULTURAL DIVERSITY AND
SECOND LANGUAGE LEARNING
1992
This report was prepared with funding from the Office of Educational Research and Improvement (OERI) of the U.S. Depart-
ment of Education, under Cooperative Agreement No. R117G10022. The findings and opinions expressed here are those of
the authors and do not necessarily reflect the positions or policies of OERI.
NATIONAL CENTER FOR RESEARCH ON CULTURAL
DIVERSITY AND SECOND LANGUAGE LEARNING
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MATHEMATICS AND MIDDLE SCHOOL STUDENTS OF MEXICAN DESCENT
ACKNOWLEDGEMENTS
The work reported here was supported in part by the University of
California Presidential Grants for School Improvement, via the Bilingual
Research Group at the University of California, Santa Cruz. Additional support
was provided by the Social Sciences Divisional Research Committee of the
University of California, Santa Cruz.
This work was prefatory to follow-up
research now being conducted as a project of the National Center for Research
on Cultural Diversity and Second Language Learning, funded in part by the
Office of Educational Research and Improvement, U.S. Department of Educa-
tion. We are gratc.fi.:; to the teachers and administrators who collaborated in this
effort and especially to mathematics teachers Tammy (Wilcox) Mullen and M.
Fisher and to Project Coordinator Stephanie Locke. We also thank Greg Peters,
Dagoberto Garcia, and Michelle Marshall for their contributions to the project.
MATHEMATICS AND MIDDLE SCHOOL STUDENTS OF MEXICAN DESCENT
MATHEMATICS AND MIDDLE SCHOOL STUDENTS OF
MEXICAN DESCENT: THE EFFECTS OF
THEMATICALLY INTEGRATED INSTRUCTION
ABSTRACT
This paper reports the effects of thematically integrated mathematics
instruction on achievement, attitudes, and motivation in mathematics among
middle school students of Mexican descent. A school-university collabora-
tive effort led to the development and testing of a thematic approach
undertaken as a means of contextualizing instruction for students consid-
Instruction relied heavily on small
ered to be at risk for school failure.
collaborative learning groups and on hands-on activities designed to help
students make real-world sense of mathematical concepts. As hypoth-
esized, experimental and control students made equivalent gains in compu-
tational skills, but experimental students (who received thematic instruction)
surpassed controls in achievement on mathematical concepts and applica-
tions. The two programs did not have a differential effect on students'
attitudes toward mathematics or self-perceptions of motivation in math-
ematics, but motivational variables did predict achievement outcomes for
both groups. Issues related to the opportunity to learn the full range of
mathematics content of the curriculum within a thematic approach are
examined.
6
MATHEMATICS AND MIDDLE SCHOOL STUDENTS OF MEXICAN DESCENT
within a thematic approach, of providing comprehen-
INTRODUCTION
sive coverage of topics designated for the middle
school mathematics curriculum.
The fact that Hispanic students are perpetually
It is important at the outset to acknowledge
at risk for underachievement and failure in American
recent improvements in the mathematics perfor-
schools is well documented (Laosa & Henderson,
mance of Hispanic students. Data from the National
1991; Orum, 1986; Valencia, 1991). The problem is
Assessment of Educational Progress (NAEP) dem-
especially acute in mathematics (Haycock & Navarro,
onstrate steady gains by Hispanic students at all of
1988; MacCorquodale, 1988; Policy Analysis for
the levels tested: ages 9, 13, and 17 (National
California Education, 1990). The difficulties His-
Council of Teachers of Mathematics, 1988). Some
panic students face in school, and particularly in
reports in the mass media have attributed these
mathematics, are compounded by the demands of
results to the "back to basics" movement (Fisk,
an increasingly technological work force. The prob-
There may be some justification for this
1988).
lem of underachievement in mathematics is pro-
attribution, because the pattern of improvement ap-
found not only because it imposes limitations on the
pears to mirror the different ways in which the educa-
educational and career opportunities available to the
tional reform movement has been implemented. In
individuals affected, but also because it poses a
minority schools, the bulk of resources and energy
broader problem for the nation. An increasing num-
has been focused on basic skills, whereas, accord-
ber of new scientists and engineers must come from
ing to Simmons (1985), schools with predominantly
populations that are currently underrepresented in
white enrollments have devoted more of their atten-
that sectcr of the workforce (Holden, 1989). This
tion to higher order abilities. Therefore, it is probably
challenge must be met by schooling that is appropri-
no coincidence that improvement in scores of minor-
ately constructed to help underrepresented students
ity students has been confined primarily to lower-
develop competence and confidence in mathemat-
level computational skills.
ics and science (Massey, 1989).
Several researchers and educators have ar-
This paper reports on the first two years of an
gued that the problem of Hispanic underachieve-
effort to address the problem of underachievement
ment in schools should be addressed through cur-
and low participation in mathematics among stu-
ricular restructuring to achieve cultural compatibility
dents of Mexican descent. The project was part of a
A series of
(Moll & Diaz, 1987; Trueba, 1988).
larger effort that brought an interdisciplinary group of
studies by Laosa (1978, 1980, 1982) offers insights
university-based researchers together with middle
into processes that may contribute to the problems
school teaners in a collaborative effort to enhance
Hispanic children and their teachers have in making
the educational experience of a population of at-risk
sense of one another's behavior. Laosa (1980) iden-
(See Garcia, 1990;
students in a middle school.
tified significant differences in the maternal teaching
Henderson & Landesman, 1990; Matute-Bianchi &
styles of Hispanic and non-Hispanic white mothers,
Alvarez, 1990.) The present paper reports on math-
but these differences virtually disappeared when the
ematics outcomes and associated patterns of atti-
amount of formal education completed by the moth-
tudes and self-perceptions of academic motivation
ers was controlled statistically. Less educated moth-
over the first two years of the project. Our more
ers used a modeling or demonstration approach,
specific purpose is to examine the effects of themati-
whereas more educated mothers used more ques-
cally organized instruction in mathematics, to de-
tioning, with praise for correct responses (Laosa,
scribe student attitudes relevant to mathematics,
1978). Hispanic mothers with more education appar-
and to test hypotheses regarding the relationship of
ently imitated the instructional style of school class-
motivational variables to mathematics outcomes.
rooms: i.e., the recitation script that serves as the
We also examine some of the special difficulties,
PAGE 1
MATHEMATICS AND MIDDI i. SCHOOL STUDENTS OF MEXICAN DESCENT
pervasive protocol of instruction in American class-
would enable students to encounter mathematical
rooms (Tharp & Gallimore, 1988).
concepts within socioculturally relevant problem-
Mexican-American children consistently have
solving contexts that would be more meaningful than
the traditional basal-text oriented approach. Specifi-
been found to exhibit a more field dependent cognitive
style than their Anglo-American peers (Garcia, 1983).
cally, we hypothesized that students participating in
The causes and implications of the field dependent/
the thematic curriculum would make greater achieve-
independent construct are subject to debate
ment Gains than their counterparts in traditionally
organized mathematics classes.
Because tradi-
(Henderson, 1980), but the consequences for instruc-
tion of differences in cognitive style remain an impor-
tional instruction has emphasized computational skills
for minority students, we anticipated that perfor-
tant issue. The more field dependent style of Mexi-
can-American children may reflect what Tharp (1989)
mance in computational skills would not differ for the
calls holistic/visual thought. Because children from
two groups.
cultures that employ holistic/visual patterns of cogni-
tion tend to learn in their natural environments, Tharp
(1989) suggests greater curricular contextualization
THEORETICAL PERSPECTIVE
as a means of making instruction more compatible
Contextualized Instruction
with the home culture of these students.
Thematic instruction may provide an effective
Although the advantages of thematic instruc-
way to contextualize instruction.
It incorporates a
tion remain to be demonstrated, there are sound
concrete learning-by-doing orientation and has the
theoretical reasons to think that such an approach
potential to facilitate cooperative and interactive learn-
holds promise. The rationale for the thematic inte-
ing opportunities in the classroom.
Cooperative
gration of instruction might be seen most clearly by
learning can provide opportunities for hands-on ac-
means of contrast with the dominant mode of teach-
tivities that result in products on which students
ing mathematics in contemporary schools.
perform mental operations, and in situations that
As usually practiced, mathematics instruction
engage students in the use of concepts and materi-
is dominated by bottom-up information processing
als (Tharp, 1989). These features have been iden-
Individual concepts and skills are
assumptions.
tified as characteristics of classrooms that have
presented, followed by practice in their application.
proved effective for Hispanic students with limited
Instruction follows the recitation script, described by
proficiency in English (Garcia, 1991).
Tharp and Gallimore (1988) as the dominant form of
The central features of the collaborative ap-
interactive teaching in American schools for over 90
proach reported here include "untracking," that is,
years. Teachers ask questions requiring convergent
assigning students to c'asses on a heterogeneous
answers, and successful students respond with
basis; developing a thematic (rather than the tradi-
known (presumably correct) information. There is
tional subject-based) approach to instructional orga-
little demand to think about what specific problems
nization; and emphasizing cooperative learning
mean or how to approach them, because all of the
groups. The approach was designed to incorporate
problems are generally of the same type.
instructional strategies that emphasize higher order
Students are expected, on the basis of such a
thinking and have been identified as attributes of
foundation, to be able to combine skills and concepts
schools that are effective for students with limited
appropriately to solve future problems.
The de-
English proficiency (Tikunoff, 1983; Wong Fillmore,
manding nature of this challenge may be appreci-
Ammon, McLaughlin, & Ammon, 1985), especially
ated when one considers that the mathematics cur-
Hispanic students (Garcia, 1988, 1991). We as-
riculum has been "chopped into small pieces, which
sumed that thematic integration of the curriculum
focus on the mastery of algorithmic procedures as
PAGE 2
MATHEMATICS AND MIDDLE SCHOOL STUDENTS OF MEXICAN DESCENT
ent with the often abstract learning experiences of
isolated skills" (Schoenfeld, 1988, p. 162). Unfortu-
nately, many students are unable to put these iso-
traditional classrooms (Tharp, 1989).
lated skills together (Sternberg, 1988) and to derive
Thematic Integration and Opportunity to
mathematical meaning from them on their own. They
have special difficulty relating the mathematical prob-
Learn: Tensions and Prospects
lems they have practiced to the varieties of environ-
We have argued that thematic instruction of-
mental and contextual information to which they
fers a potentially powerful way to assist Hispanic
In information processing terms, many stu-
apply.
students to connect mathematical concepts and
dents lack environmentally relevant, conceptually
problem-solving strategies to socioculturally relevant
driven information to give meaning to the problems
experiences. Although there is strong theoretical
posed in mathematics classes.
justification for this view, we must acknowledge a
If instruction is to overcome barriers to learning
certain tension between instruction that organizes
that result from an inadequate match between the
content around themes, on the one hand, and the
culture of the school and the community backgrounds
need for comprehensive coverage of the mathemat-
of cultural minority students, the schools must, as
ics curriculum on the other. School administrators
Tharp (1989) suggests, help these students by dem-
and parents are not without justification when they
onstrating how rules, abstractions, and verbal de-
ask the practical question, 'Will students who partici-
scriptions are drawn from the everyday world and
pate in thematic instruction cover the mathematics
If the fragmented and
how they are applied to it.
curriculum for this grade thoroughly?" Data from the
decontextualized nature of contemporary mathemat-
Second International Mathematics Study (Travers,
ics instruction poses barriers to achievement and
1988) provide convincing evidence of a substantial
participation for important segments of the popula-
relationship between what schools actually teach
tion, then the practices that promote integration and
and what students learn. Students tend to do well on
provide a meaningful context for learning offer a
the topics that are emphasized in the actual curricu-
potential remedy worth trying.
lum, and conversely, they tend to achieve poorly on
Cooperative learning and heterogeneous group-
those topics that received little attention in their
ing do not, by themselves, guarantee success. But
schools. Patterns of curricular emphasis vary from
they can be employed to involve students in finding,
nation to nation, and to some extent, from school to
inventing, and solving problems in familiar contexts,
school within nations. Thus, there are variations in
and these procedures enable students and teachers
Thematically inte-
students' opportunity to learn.
to engage in authentic, subject-based exchanges.
Small groups organized around specific tasks make
grated instruction may provide an effective means of
it possible for assisted learning (Tharp & Gallimore,
helping students to learn the skills and concepts they
use in this context by connecting them to
1988) to take place, leading to the internalization of
the metacognitive skills students need to regulate
socioculturally relevant experiences. But we must
their own learning (Henderson, 1986). Such autono-
be concerned whether the thematic approach af-
mous learning is considered essential to the devel-
fords students the opportunity to learn the full scope
opment of higher order thinking in mathematics
and sequence of mathematics content that will en-
(Fennema & Peterson, 1985). Learning based on
able them to move on to more advanced learning of
concrete activities rather than on textbook abstrac-
mathematics. We therefore will report on initial
tions enables learners to make real-world sense of
efforts to examine the fit between thematic instruc-
their school experiences. Such opportunities are
tion and the prescribed mathematics curriculum.
likely to be especially important for students whose
(Set page 9.)
out-of-school experience may not be highly congru-
PAGE 3
MATHEMATICS AND MIDDLE SCHOOL STUDENTS OF MEXICAN DESCENT
Attitudinal and Motivational Dimensions
ematics. Considering the integrated nature of the
thematic approach, in which a variety of mathemati-
In addition to examining the effects of thematic
instruction, we were interested in determining the
cal skills and concepts are applied to broad problems,
we also hypothesized that students would develop
nature of attitudes toward mathematics among Mexi-
broader perceptions of mathematics as a discipline.
can-American students and the effects of instruction
on those attitudes.
Attitudes toward mathematics
The final purpose of the research reported here
was to examine student self-perceptions in a way
and beliefs about the nature of mathematics appear
to play an important role in students' mathematics
that would enable us to begin to link our work with this
achievement and participation (Haladyna,
population to models of motivation that have been
developed with non-minority populations and to as-
Shaughnessy, & Shaughnessy, 1983; McLeod, 1985;
Silver, 1985). There is a widely held belief among
certain the applicability of those models to Hispanic
students. Our aims were guided by Carol Dweck's
educators that children of Hispanic descent experi-
ence early and repeated failure in school, which
model of academic motivation (Dweck, 1986; Dweck
& Leggett, 1988), which postulates a chain of causal
results in poor academic self-concept, negative atti-
associations between students' interpretation of
tudes toward school subjects, and alienation from
events and their adaptation to challenging academic
It was important for us to know whether the
school.
situations. Dweck suggests that some students are
students with whom we were working liked or disliked
motivated by learning goals, whereas others are
mathematics. Cocking and Chipman (1988) review
motivated by performance goals. Those who are
reports suggesting that parental attitudes toward
oriented to performance are concerned about being
mathematics may direct Hispanic children away from
correct. They tend to make choices that are likely to
MacCorquodale (1988) argues that
the subject.
invite favorable judgments of their performance or
Hispanic girls, in particular, may be discouraged
that will minimize the chances of negative judgments
from pursuing mathematics. Cocking and Chipman
of their competence by others. Thus, they may
report the following for Hispanic and Native Ameri-
undertake a difficult task if they believe they can
can populations:
However, when their
accomplish it successfully.
There is a negative image of math, whereby
confidence in a successful outcome is low, they are
tmaticians are perceived as remote, sloppy,
likely to pursue a less challenging task. In contrast,
obsessive and (no pun intended) calculating. No
students who are oriented toward learning goals are
matter what your socioeconomic status happens
to he, it is not likely that you will strive hard to
more likely to explore, take initiative, and pursue
become an unscrupulous, calculating, cold,
tasks that promote intellectual growth, even when
sloppy, and obsessive number cruncher. (1988,
they are not confident that their efforts will be re-
p. 32)
warded with success.
Although goal orientation has been identified
We did not know if this generalization would
as a potentially important factor in academic achieve-
apply to our sample of students of Mexican descent.
ment in general (Dweck, 1986; Dweck & Leggett,
Therefore, for both descriptive and follow-up pur-
1988; Elliot & Dweck, 1988) and in mathematics
we wished to ascertain these students'
poses,
achievement in particular (Peterson, 1988), little is
percepticns of the usefulness of mathematics, their
known about the dynamics of goal orientation in
intention to take more mathematics, and their inter-
natural classroom settings or for different ethnic
est in careers that involve the use of mathematics.
groups. A learning orientation is normally associated
We expected the thematic approach to result in
with an inclination to seek intellectual challenge and
improvement in students' attitudes toward math-
to persist in the face of difficulty. We expected the
ematics (relative to attitudes of comparison stu-
two variables, goal orientations and challenge seek-
dents) and in their view of the importance of math-
MATHEMATICS AND MIDDLE SCHOOL STUDENTS OF MEXICAN DESCENT
PAGE 4