ERIC ED405171: [Statistics and School Mathematics.]

16 Pages·1994·0.37 MB·English

by  ERIC

DOCUMENT RESUME
SE 054 575
ED 405 171
Jacobs, Victoria R.; Lajoie, Susanne
AUTHOR
[Statistics and School Mathematics.]
TITLE
Wisconsin Center for Education Research, Madison.
INSTITUTION
Office of Educational Research and Improvement (ED),
SPONS AGENCY
Washington, DC.
94
PUB DATE
NOTE
15p.
National Center for Research in Mathematical Sciences
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Research /Technical (143)
NCRMSE Research Review; v3 n2 Spr 1994
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*Grouping (Instructional Purposes); Junior High
DESCRIPTORS
Schools; *Mathematics Achievement; *Mathematics
Curriculum; Mathematics Instruction; Middle Schools;
*Sex Differences; *Statistics
*Middle School Students
IDENTIFIERS
ABSTRACT
Statistics is assuming a new role in the mathematics
curriculum for K-12 students. This bulletin presents excerpts from
papers on two studies that were carried out to develop a knowledge
base that would enhance statistics instruction in middle school
classrooms. The first paper, "Statistics in Middle School: An
Exploration of Students' Informal Knowledge," reports the results of
introducing high-ability middle school students (n=10) to enrichment
activities designed to promote statistical discussion. By the end of
the 13-week program, students' test performance suggested that their
general level of statistical reasoning had increased. The second
paper, "How Do Group Composition and Gender Influence the Learning of
Statistics," reports a study designed to test the ways in which group
composition influences learning. Eighth-grade students (n=21) were
divided into eight same-gender groups consisting of either two or
three students. Results showed females performed as well as males in
statistical knowledge. Contains 25 references. (MKR)
***********************************************************************
Reproductions supplied by EDRS are the best that can be made
from the original document.
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NCRMSE RESEARCH REVIEW
The Teaching and Learning of Mathematics
Spring 1994
Volume 3, Number 2
Statistics and School Mathematics
In This Issue:
Students encounter numerous statistical claims in their daily lives. Data are
Integrating Statistics into the
country's
collected, summarized, analyzed, and transformed in most of this
5
School Curriculum
media, work places, and homes. The collecting, representing, and process-
statistics was
Review of
ing of data are assuming major importance in most nations. While
10
NCRMSE Research
students pursuing professional or academic
once taught primarily to college
of the school mathematics curriculum.
careers, it is now becoming a part
teach-
Mathematics reform documents developed during the last decade stress
NCRMSE
secondary mathe-
ing appropriate statistical content to students in elementary and
Research Review:
documents, develop students'
matics classes. This content should, according to the
The Teaching and Learning of
ability to use statistics to understand their worlds, to create and interpret sum-
Mathematics is published by the
of claims and argu-
maries of data and displays of information, and to be critical
National Center for Research in
Curriculum and Evaluation Standards for School
ments that are based on data. The
Mathematical Sciences Education,
Mathematics developed by the National Council of Teachers of Mathematics
Wisconsin Center for Education
Statistical
(1989) and projects, such as the Quantitative Literacy (American
Research, University of Wisconsin-
Association, 1987) and Used Numbers and Reasoning Under Uncertainty
Madison. The Center is funded
Consortium for
(Technical Education Research Center, Lesley College, and the
primarily by the Office of Educa
analysis could
Mathematics and Its Applications, 1989-1990), suK est ways data
tional Research and Improvement,
be implemented in the nation's schools.
U.S. Department of Education
mathematics
Few activities that involve statistics are now carried out in K-12
opinions expressed
(OERI/ED). The
from practi-
classrooms. While there is little information either from research or
in this publication do not necessarily
elementary- and
cal experience to aid teachers who would introduce statistics at
reflect the position or policy of
statistics at
secondary-grade levels, there is information on teaching and learning
no endorsement of OEM
OERI /ED;
that a
the college or university level. This research-based information suggests
or the Department of Education
elementary statistical
majority of higher education students do not understand
should be inferred. Send correspon-
after completing several courses
concepts (Garfield & Ahlgren, 1988), even
W.
dence to
NCRMSE, 1025
educators
(Poston, 1981). In its current form, according to a consensus among
Johnson Street, Madison, WI
1988;
and researchers (American Statistical Association, 1991; Mosteller,
53706. Telephone [phone];
education is inadequate.
NCTM, 1989; and Shaughnessy, 1992), statistics
FAX [phone].
Learning /Teaching of Statistics
National Center for
The Learning/Teaching of Statistics Working Group of the
U.S. DEPARTMENT OF EDUCATION
Improvement
Mice of Educational 'Research and
studying the ways
Research in Mathematical Sciences Education (NCRMSE) is
INFORMATION
EDUCATIONAL RESOURCES
)
CENTE
school mathematics
in which statistical content can best be integrated into the
reproduced BS
;Phis document has been
organization
received from the person or
the Working
curriculum. While NCRMSE Director Thomas Romberg initiated
originating it.
made to improve
o Minor changes neve been
reproduction Quality.
this doct
Points of view or opinions stated in
2
represent official
BEST COPY AVAILABLE
ment do not necessarily
OERI position or policy.
Wisconsin Center for Education Research, University of Wisconsin-Madison
that includes the testing of new
assessment models that use computer
ti
and videotape technologies.
Research Literature Database
'
)
r
Chair Lajoie and Affiliated Member
Joan Garfield collaborated on the
itPP'°'
development of a computerized
database of research, STAT-FILE,
related to the teaching/learning of
_
statistics. They combined their previ-
./461161."
ous resources and eliminated entries
that were duplicates. They then used
the database to develop an annotated
bibliography of the research litera-
Susanne Lajoie, an associate director of NCRMSE, is chair of the Working Group
ture on teaching/learning statistics.
on the Learning/Teaching of Statistics.
At the end of 1993, their bibliogra-
phy included 110 entries that were
orative program of research in June
Group, Susanne Lajoie of McGill
relevant to K-12 research. The data
1993. At their first meeting, these
University now chairs the group.
base can be searched by title, author,
members summarized their current
Sharon Derry and Richard Lehrer,
key words, and publication or pre-
University of Wisconsin-Madison,
research and knowledge on
sentation information. Copies of the
learning/teaching statistics. They then
are the group's principal investiga-
data base were sent to the members
tors. The group also includes 5 staff
identified the kinds of research they
of the Working Group.
thought would be necessary to extend
members and 17 affiliated members.
knowledge on the appropriate con-
Five Working Groups were
Cognitive Models Projects
tent, pedagogy, learning, and assess-
formed by NCRMSE early in 1991.
Richard Lehrer and Jeffrey K. Horvath
They focused on the topics: whole
ment of statistics for K-12 students.
are examining cognitive models of
Several studies by members of the
number, quantities, algebra, imple-
less- and more-skilled Grade 4-5 stu-
Working Group that are designed to
mentation of reform, and models of
dents' problem-solving performances
extend knowledge about statistics for
authentic assessment. A sixth
in statistics. They take the view that
K-12 students are now underway.
Working Group that focused on
curriculum-based performances
The studies address a) the develop-
geometry was formed during late
should be examined when informa-
ment of an international database of
1991. The Learning/Teaching of
tion about student knowledge and
research literature that relates to the
Statistics is the seventh and final
understanding is sought, and students
teaching and learning of statistics; b)
NCRMSE Working Group. It began
should be assessed in ways that pro-
the identification of the cognitive
its activities early in 1993. The oper-
vide opportunities for them to learn
components of probability and statis-
ation and research of each of the
more about the curriculum or provide
tics that are related to the K-12 cur-
other Working Groups have been
opportunities for them to receive assis-
riculum; c) the development of a
described in previous issues of
tance with their performance. Their
curriculum for statistics with Grade
NCRMSE Research Review.
work began with the spinner sum task,
7-8 teachers and the implementing
While each of the members had
a probabilistic assessment task devel-
of the curriculum in Grade 7-8 class-
completed independent research relat-
oped by the California Department of
es; d) the development of a technolo-
ed to the learning/teaching of statis-
Education (Lehrer & Horvath, 1993).
gy-based authentic statistics project
tics before the creation of the
They are now extending their work on
for Grade 8 mathematics students
Working Group, they began a collab-
cognition with a study of students'
3
National Center for Research in Mathematical Sciences Education
2
opment of reasoning, regardless of
ment the curriculum in 7th- and 8th-
developing understanding of the
classroom context.
grade classrooms. As an introduc-
nature of chance.
Investigators Derry and Osana are
tion to the curriculum, a film on
Kevin Collis has begun a study of
now investigating whether the simu-
concepts about statistics and medi-
cognitive functioning in probability
lations were more effective than the
cal research was shown to the stu-
and statistics as it relates to the
traditionally used instructional
dents. It provided a basis for discus-
school curriculum. It addresses
approaches in terms of the students'
sion and analysis. Students then
specifically the understanding of
development of concepts, use of sta-
listened to presentations by local
chance and data concepts in the
tistical concepts, quality of individu-
experts on statistics, argumentation,
wider social context. As a starting
al and social reasoning, and quality
and scientific research and discussed
point, he is developing a question-
of individual and group products
them in small groups. During the
.naire that uses the mediaexcerpts
such as presentations, written inter-
last days of the activity, students
from newspapers, for exampleto
pretations, or others that were based
were asked to assume the roles of
learn about students' understanding
on reasoning.
researchers, lawyers, legislators, con-
of the content. The questionnaire
sumers, or business owners. Acting
will include paper-and-pencil items,
Authentic Statistics Project
in these roles, students worked in
supplemented with graphical infor-
Working Group Chair Lajoie is
collaborative groups conducting
mation when relevant, that are con-
directing the Authentic Statistics
research and preparing and present-
structed to elicit statistical problem-
Project. Designed to test new forms
ing testimony at a mock legislative
solving skills. The four-part format
of statistics instruction and assess-
hearing on government regulation
(Collis & Romberg, 1992) and
ment, the project uses computer and
of the vitamin industry.
think-aloud techniques will be used
videotape technologies. Its assess-
The researchers collected field
in the construction of the items.
ment and instructional models are
notes, video recordings, and student
based on situated learning theory
and teacher ratings of class activi-
Statistics Curriculum Project
and the NCTM Standards. Of special
ties. They also administered a rea-
Sharon Derry and Helen Osana have
note is its attention to the problem
soning task. The data will be ana-
developed instructional simulations
solving, communication, reasoning,
lyzed to identify the specific events,
that will stimulate students to acquire
and connections emphasized by the
features of materials, procedures,
and use statistical concepts in the
NCTM Standards in both their
aspects of the classrooms, and
context of reasoning about realistic or
instructional and assessment aspects.
aspects of mentorship that were use-
non-trivial problem-solving situa-
The project also designed instruc-
ful in shaping the research activity
tions. They began with a plan to
tional activities in statistics that
or affecting the outcomes. Their
design situations that would improve
would provide students with oppor-
classroom observations suggest that
middle-school students' ability and
tunities to reflect, organize, model,
role-playing motivates most stu-
propensity to reason statistically
represent, and argue within and
dents, even some who are identified
about the problems they encounter
domains.
across other mathematical
by teachers as having behavioral or
in their daily lives. During the sum-
The Authentic Statistics Project
motivational difficulties. Despite
mer of 1993, they worked with a
developed an innovative approach to
the use of the same instructional
small group of classroom teachers to
of
assessment, a computerized library
game, the use of identical proce-
develop and refine the design for
exemplarstext and video examples of
dures, and common inservice pro-
instructional simulation activity that
student workthat convey to students
grams for teachers, each classroom
would be used by 7th- and 8th- grade
both models of and criteria for aver-
evolved as a unique social and learn-
students. The 3-4 week-long instruc-
age and above-average performance
ing environment during the activity.
tional game is called Vitamin Wars.
and can be used by students as
Some of the roles students played
During the academic year 1993-
benchmarks for their own statistics
also appeared to be more effective
1994, Derry and Osana and four
performances. When assessment
than others in promoting the devel-
classroom teachers began to imple-
4
3
Wisconsin Center for Education Research. University of Wisconsin-Madison
exemplars for reining statistical con-
criteria are made explicit to students,
Vigne, Steve Munsie, Helen Osana,
cepts. Paper presented at the annual
the researchers theorized, it can pre-
and Tara Wilkie. Two si-aff members
conference of the American
cipitate additional learning. A library-
are located at the University of
Educational Research Association
in Atlanta, GA.
Wisconsin-Madison and three are
of-exemplars study was then under-
Lajoie, S., Lawless, J., Lavigne, N., &
taken to examine the effectiveness of
located at McGill University in
Munsie, S. (1993). New ways to
the library as a tool for clarifying
Quebec.
measure skills of problem solving,
assessment criteria and for promoting
reasoning, communication, and con-
statistical understanding. The Project
Conclusion
nectedness. Paper presented at the
also developed a second study to
Future research on how statistical
annual conference of the American
Educational Research Association
content can best be integrated into
investigate whether tasks that require
in Atlanta, GA.
students to collect their own data are
the school mathematics curriculum
Lehrer, R., & Horvath, J. K. (1993).
more effective for promoting under-
should include an integrated frame-
Cognitive models of authentic assess-
standing than tasks that require stu-
work for the instructional and assess-
ment. Paper presented at the annu-
dents to use preexisting data.
ment process. Such a framework
al conference of the American
One portion of this project's study
would involve looking at the statisti-
Educational Research Association,
Atlanta, GA.
on the effects of text and video exam- cal content, the learner's conceptual
Mosteller, F. (1988). Broadening the
ples is reported in the next article in
understanding of the content, and
scope of statistics and statistical
this newsletter. Other portions of the
how instruction builds on the assess-
education. The American
ment of the learner in the context of
project's research were reported in
Statistician, 42(2), 93-99.
papers presented at the April 1993
an instructional situation. The
National Council of Teachers of
American Educational Research
Working Group members collabora-
Mathematics. (1989). Curriculum
and evaluation standards for school
Association Conference in Atlanta:
tively will seek answers to the research
mathematics. Reston, VA: Author.
questions they have identified.
New Ways to Measure Skills of Problem
Poston, H. 0. (1981). Review of sta-
Solving, Reasoning, Communication,
tistical teaching materials for 11-16
References
and Connectedness, by Susanne
year olds. The American
American Statistical Association.
Lajoie, John Lawless, Nancy Lavigne,
Statistician, 35(4), 258-259.
(1989). Quantitative Literacy Series.
and Steve Munsie (1993); and The
Shaughnessy, J. M. (1992). Research
Palo Alto, CA: Dale Seymour
in probability and statistics:
Use of Hypercard for Facilitating
Publications.
Reflections and directions. In D.
Assessment: A Library of Exemplars
American Statistical Association.
Grouws (Ed.), Handbook for
for Reining Statistical Concepts, by
(1991). Guidelines for the teaching
research in mathematics teaching
Susanne Lajoie, Nancy Lavigne, and
of statistics in K-12 mathematics
and learning (pp. 465-494). New
curriculum. Landover, MD:
John Lawless (1993).
York: Macmillan Publishing.
Corporate Press.
In addition to the principal inves-
Collis, K., & Romberg, T. A. (1992).
tigators Sharon Derry and Richard
For further information on the
Mathematics Problem Solving
Lehrer, the Working Group includes
Profiles. P. 0. Box 210, Hawthorn,
Learning/Teaching of Statistics
Affiliated Members George Bright,
Victoria 3122, Australia:
Working Group, readers may contact
Australian Council for Educational
Gail Burrill, Kevin Collis, Susan
its chair, NCRMSE Associate Director
Research.
Friel, Ido Gal, Joan Garfield,
Susanne Lajoie, Department of
Garfield, J., & Ahlgren, A. (1988).
Christopher Hancock, Victoria
Educational and Counselling
Difficulties in learning basic con-
Jacobs, Clifford Konold, James
cepts in probability and statistics:
Psychology, Faculty of Education,
Landwehr, Joel Levin, Kathleen
Implications for research. Journal
McGill University, 3700 McTavish,
Metz, Thomas Romberg, Andee
for Research in Mathematics
Montreal, Quebec, Canada H3A
Rubin, Richard Scheaffer, Ron
Education, 19(1), 44-63.
1Y2, telephone [phone];
Lajoie, S., Lavigne, N., & Lawless, J.
Serlin, Leona Shauble, and Michael
FAX [phone]; E-mail
(1993). The use of Hypercard for
Shaughnessy. It also includes Staff
([email protected]).
facilitating assessment: A Library of
Members Jeff Horvath, Nancy La
5
National Center for Research in Mathematical Sciences Education
4
Integrating Statistics into the,School Curriculum-
_
tatistics is assuming a new role in the mathematics cur-
Content
The content of the enrichment pro-
riculum for K -12 students in the 1990s. Because statis-
gram was designed to guide students
tics previously has not been taught to students in ele-
in explorations of the concepts that
make up inferential statistics. It was
-mentary or high school grades, little is known about students'
based on the assumption that chance
experiences with statistics acquired outside of their classrooms
and samplingthe use of results
obtained from a sample in reaching
and about instruction that can effectively enhance students'
conclusions about a larger popula-
understanding of statistics in their classrooms. This section
tionare the core concepts of inferen-
tial statistics. Specific lessons focused
presents excerpts from papers on two studies that were carried
on chance and its role in everyday
out to develop a knowledge base that would enhance statistics
decisions and on sampling and the
logic underlying the factors that affect
instruction in middle school classrooms. The first paper,
a researcher's ability to draw accurate
Statistics in Middle School: An Exploration of Students' Informal
conclusions about the population from
the sample results. The inferential sta-
Knowledge, was completed by Victoria R. Jacobs and Susanne
tistical content was selected because it
Lajoie. The second paper, How Do Group Composition and
is consistent with that recommended
for the middle school age group in the
Gender Influence the Learning of Statistics? was completed by
curriculum Standards published by
Susanne Lajoie and Nancy C. Lavigne.
the National Council of Teachers of
Mathematics and the guidelines pre-
pared by The American Statistical
An Exploration of Students'
Association. It was also selected
identified by teachers as interested in
Informal Knowledge
because, while there is little research on
challenges beyond their regular
students' understanding of any statisti-
mathematics curriculum. The
Much of the recent research in math-
cal content, many current projects
instructional activities that com-
ematics education underscores the
emphasize descriptive rather than
prised the program provided the
importance of understanding the
inferential statistics.
context from which students' statisti-
extent of children's informal knowl-
cal understanding could be studied.
edge before preparing formal instruc-
Pedagogy
Both the content and the pedagogy
tional programs. To some, students'
The NCTM Curriculum and
of the enrichment program were
prior knowledge is an essential start-
Evaluation Standards for School
designed to provide students with
ing point from which to build addi-
Mathematics (1989) recommend a
opportunities for extended thought
tional instruction. It can also provide
constructivist pedagogy that is based
and discussion about statistical prob-
teachers with a framework for think-
on a new vision of mathematics learn-
lems. They were also designed to
ing about their students' develop-
ing. Learning mathematics is defined
ment in this content domain. An
provide teachers with activities that
as doing mathematics. This view pro-
enrichment program was developed elicit or encourage discussion about
motes an activity-based curriculum
for middle school students who were statistical content.
6
Wisconsin Center for Education Research. University of Wisconsin-Madison
5
their decisions about everyday situa-
tions; some of the students, however,
had difficulty incorporating the results
into their discussions. Students were
also inconsistent in their ability to
explain representative sampling proce-
dures. This inconsistency seemed to
be linked to the context of research
questions. Opinion questions were
treated differently from other ques-
tions by students who seemed to think
that there should be an equal chance
Victoria R. Jacobs is a member of
Nancy C. Lavigne is a staff member for
for each possible optione.g., 50-50
the Learning/Teaching of Statistics
the Learning/Teaching of Statistics
or 33-33-33, and so forth.
Working Group.
Working Group.
Students' performance on a 50-
where students solve problems and
point test suggested that their general
pretest and posttest. All class dialogues
emphasis is placed on their informal
were audiotaped, and protocol analysis
level of statistical reasoning had
knowledge and their ability to com-
increased as a result of their participa-
provided the core of the analyses that
tion in the project. The test rewarded
municate about the processes they use
were completed.
to reach solutions. Classes emphasize correct explanations as well as correct
problem solving rather than computa-
answers. In addition to their cognitive
Results
gains, students indicated both through
At the conclusion of the 13-week
tional skills and explanations of how
verbal anecdotes and through individ-
enrichment program, students had
solutions are reached rather than single
ually written course evaluations that
developed a workable definition of
correct answers. Assessment is incorpo-
rated into instruction and modified to
they enjoyed the course
chance, could recognize it in their
.
reflect new beliefs about knowledge
daily lives, and describe how it affects
Usefid Instructional Materials
and learning.
the decisions they make. While most
Students were very articulate during
students were able to compute an
Method
classroom activities designed to stimu-
exact probability, all were able to use
the language of probabilitye.g., more
A researcher/teacher met with ten late discussion about statistical con-
tent. They responded verbally to open-
high-ability middle school students in
likely, less likely, impossible, etc. to
ended questions, shared their
describe chance events. They had lit-
a Wisconsin school once each week for
13 weeks during the students' regular strategies, and became comfortable
tle trouble distinguishing more likely
with questions that could have multi-
mathematics class. The enrichment
outcomes from less likely outcomes,
but difficulty understanding chance
ple answers. They struggled, however,
lessons were considered part of the stu-
dents' regular curriculum and the with open-ended written assignments.
events with outcomes that were equal-
The quality of reasoning in their
teachers incorporated the students'
ly likely. With regard to sampling, stu-
performance in the program into their
homework and essays on tests did not
dents easily identified its use and
match the level they demonstrated
importance in their daily lives. They
semester grades in mathematics.
during their oral interactions. This
The activities in the lessons were
also were able to apply sampling logic
designed to promote statistical discus-
to realistic situations. While all of the
finding suggested to the researchers
that students' conceptual understand-
sion. Measures of performance during
students participated in statistical dis-
the 13-week period included indices
ing may be underestimated if evalua-
cussions, some had difficulty in two
of class participation, weekly home-
tions are based only on written work.
areas. Students should be able to use
The study found that two activi-
work assignments, and a comprehen-
the results obtained from the applica-
ties were particularly useful in
sive examination administered as a
tion of inferential statistics to inform
7
National Center for Research in Mathematical Sciences Education
6
how best to instruct students and
uals working together on a common
promoting discussions that enabled
of
assess their learning in this new area
task. Constructivist and sitnaied learn-
students to learn from one another. A
school mathematics.
ing perspectives emphasize the impor-
student-generated test and a student-
According to the NCTM Standards,
that pro-
tance of social interaction
directed class can provide educators
8th graders should be provided with
development
motes thinking and the
with unique information about stu-
opportunities to do statistics-that is, to
of problem-solving skills in class-
dents' understanding. There is little
systematically collect, organize, and
based
rooms. These perspectives are
research to guide the implementation
describe data; to construct, read, and
cooperative
on the assumption that a
of these activities.
interpret tables, charts, and graphs; to
or shared learning environment per-
The study also found that students
make inferences and arguments based
mits students to learn from others
had difficulty identifying why the con -
based
on data and evaluate arguments
and can reduce students' anxiety
math-
..tent of statistics was classified as
develop an
on data analyses; and to
about learning when they feel willing
ematics. When they reviewed the pro-
appreciation for statistical methods as a
work
to share information. Group
gram, they viewed the division,
powerful means for decision making.
share their
encourages students to
multiplication, and fraction procedures
The study uses these guidelines by
knowledge with peers and exposes
they completed with numbers as
placing statistics instruction in an
them to multiple points of view. Small
mathematics. The students' views
experimental context carried out in the
students to develop
groups can enable
reflect society's view of mathematics as
classroom using computers that graph
mathematical power by developing
made up of
a nonconceptual field
and analyze student data. Groups of
higher-order thinking skills such as
numbers and their manipulation-a
students construct research questions,
problem solving, reasoning, and com-
view that is destructive because it
collect and analyze data, and display
munication, and behavioral attributes
algo-
encourages the use of memorized
their findings and interpretations for
such as persistence.
rithms without understanding.
the class. Both individual and group
Despite the success of small group
data are used to describe the transi-
learning situations, little attention has
Conclusions
tions that occur in student learning.
been paid to the nature of collaboration
This work provides some initial guid-
To ensure that students were
and the dynamics of small-group inter-
who
ance for mathematics educators
assessed fairly on their group projects,
actions that affect learning. Research
must begin to implement statistics in
developed: an
two conditions were
shows that peer collaboration can cause
the Grade K -12 curriculum. Its sugges-
exemplar condition-video and
students to shift perspectives but that
tions for instructional and assessment
text-where a computer hypercard stack
joint decision-making is necessary for
activities can provide an initial glimpse
describe assessment
was designed to
effective learning. Group interaction
of students' informal conceptions of
criteria, and a text-only condition, also
relying on
may result in some students
statistics. Although generalizing from
computer-administered, that provided
others, accepting little personal respon-
the results is limited by the size and
criteria with textual
a list of assessment
sibility, and doing little independent
ability level of the sample, the method-
descriptions of what these criteria
thinking. Collaboration is a complex
ology used in the study provides infor-
weighted.
meant and how they were
phenomenon and this complexity must
mation that can be used by others inter-
The criteria included: quality of the
be considered when collaborative class-
ested in examining students' thinking
research question-how clear and spe-
room activities are used.
about statistics.
cific the research question is; data col-
This study was designed to test the
lection-how students go about gather-
composition
ways in which group
The Influence of Group
ing information that pertains to their
influences learning. In particular, it
Composition and Gender
question; data presentation-how data
looked at group composition in terms
Theories of learning and instruction
and presented and the
are summarized
of gender to determine how gender
considering learning
are increasingly
andlor graphs
types of tables, charts,
influenced the learning of statistics by
that occurs in specific situations or
constructed to represent the data;
8th-grade mathematics students. The
contexts. The situations or contexts
data analysis and interpretation-what
goal of the research was to examine
often involve small groups of individ-
8
7
Wisconsin-Madison
Wisconsin Center for Education Research, University of
statistics are selected to analyze a data
and performance when compared to
together. Each of the groups worked at
set, and how students demonstrate
individual activity, but mixed- pairs
one Apple Macintosh computer work
their understanding and interpretation
did not. In this research, single-gender
station and were supervised by a
of the data analysis; presentation
pairs appeared to share task compo-
researcher for a period of two weeks.
stylehow the group explains the goals
nents and discuss possible solutions,
The eight groups were assigned ran-
and findings of their project to the
while mixed-gender pairs tended to
domly to the text only conditionin
class; and creativityhow unique the
separate task components and then
which textual descriptions of the crite-
project is. The video and text condition
complete them separately. Other
ria for assessing group projects were
added a video component that allowed
presented on the computeror the
research (Webb, 1984) indicated that
students to select one of the criteria
mixed-gender groups can be detri-
video and text conditionin which the
and obtain a textual and digitized
mental to females' mathematics
textual descriptions were supplement-
video demonstration of average and
achievement. Based on these findings,
ed with digitized video clips represent-
above-average performance by previ-
the current study was designed for
ing two levels of performance. The
ous students who had designed statis-
single-gender groups to see whether
randomization process resulted in
tics projects. The text only and video
gender differences would occur on
three groups of females and one of
and text conditions were prepared to
measures of statistics problem solving,
males being assigned to the video and
make the assessment criteria apparent
reasoning, or communication. All
text condition and three groups of
to students.
groups, regardless of gender, mixed
males and one of female being
Cognitive learning theories support
students with varying ability levels.
assigned to the text only condition.
small-group activities that have been
The predictions were that females
Instructional activities and assess-
found to facilitate learning for each
would perform as well as males in
ment tasks were designed to promote
individual by providing multiple
single-gender groups on measures of
learning and communication in an
perspectives as well as by negotiations
statistical knowledge and that groups
authentic learning environment. A
during problem-solving activities
exposed to the text and video condi-
pretest/posttest design was used to
(Blumenfeld, Soloway, Marx, Krajcik,
tion would outperform the groups
assess changes in student performance.
Guzdial, & Palinscar, 1991; Cognition
in the text only condition.
Journals were used as group measures
and Technology Group at Vanderbilt,
Subjects for this study were from
of statistical communication, problem
1990; Williams, 1992). There are few
an 8th-grade mathematics classroom.
solving, and reasoning. Structured jour-
guidelines for assigning students to
Twenty-one students, 9 females and
nals contained specific prompts
groups that are based on promoting
12 males, were divided into 8 groups
designed to encourage groups to define
learning for individual group mem-
consisting of either two or three stu-
and explain concepts, to reason about
bers or on how gender affects group
dents. Students were grouped with
data and graphs used in the tutorial,
activities. An earlier pilot project
same-gender peers, resulting in four
and to identify areas of difficulty. The
found that group work did not always
groups of females and four groups of
prompts were designed as a means to
result in a positive learning experience
males. Teachers' rankingse.g., high,
foster learning. Journals served as ongo-
for all group members. In the pilot,
medium, lowof each students' per-
ing measures of group performance
groups made up of mixed-ability lev-
formance as measured by classroom
and were analyzed in terms of the qual-
els completed a statistics project.
assignments and examinationswere
ity of statistical communication, prob-
Informal observations of group activi-
used to form groups of students with
lem-solving, and reasoning. All group
ty suggested that when females were
mixed mathematics achievement.
interaction and presentations were
in male-dominated groups they did
When groups were made up of two
audiotaped and videotaped.
not participate.
students, a high- and low-ability stu-
Other research that involved com-
Results
dent would be placed together. When
puter-based tasks (Underwood &
The prediction that females would
groups were made up of three stu-
McCaffrey, 1990) found that single-
dents, a high-, medium-, and low-
perform as well as males in single-
gender pairs improved participation
gender groupings on measures of
ability student would be placed
9
National Center for Research in Mathematical Sciences Education
8
References
There were also gender differences
statistical knowledge was not only
Blumenfeld, P., Soloway, E., Marx, R.,
in the way students documerited their
confirmed but the results exceeded
Krajcik, J., Guzdial, M., & Palinscar, A.
group projects. Structured journals
our expectations. The prediction
(1991). Motivating project-based learn-
ing: Sustaining the doing, supporting
were given to each group and stu-
that groups in the video and text
the learning.
Educational Psychologist,
dents were asked to document the
condition would outperform those
26(3 & 4), 369-398.
statistical concepts they were learning,
in the text only condition was not
Cognition and Technology Group at
as well as their project ideas. Females
confirmed. The statistical knowledge
Vanderbilt. (1990). Anchored instruc-
tended to document information
of all of the groups increased from
tion and its relationship to situated cog-
nition.
about statistical concepts and their
Educational Researcher, 19(5),
pre- to posttest, but groups of
2-10.
plans for how to conduct their group
females working together benefitted
Lajoie, S., & Lavigne, N. C. (1994). How
projects, whereas the entries for the
more from the instruction than did
composition and gender influ-
does group
male groups were sparse in such cate-
groups of males. Analysis of group
Paper pre-
ence the learning ofstatistics?
gories, but robust where they were
journals suggests they do provide use-
sented at the annual conference of the
asked how they would apply statistical
American Educational Research
ful information: Female groups
Association in New Orleans, LA.
concepts in certain situations.
responded to prompts more often
Jacobs, V. R., & Lajoie, S. (1994).
Statistics
Both of the conditions used in the
than male groups. Based on their
in middle schoot An exploration of stu-
study, video and text and text only pro-
responses, it appears that females
Paper present-
dents' infirmal knowledge.
duced significant changes in the statis-
were more interested in planning and
ed at the annual conference of the
tics performance of students. The
American Educational Research
in understanding concepts through
Association in New Orleans, LA.
finding was not expected because it
definitions, while males seemed
Johnson, D. W., & Johnson, R. T. (1985).
appeared that the video and text exem-
somewhat more inclined to deal with
Cooperative learning: One key to com-
plars would make scoring criteria
questions that required interpreting
puter assisted learning. In L. Rathje
more apparent to students and thus
the information that was presented in
(Ed.),
Software selection, evaluation and
serve as a more effective instructional
the data and graphs.
organization and software reviews.
University of Oregon, Eugene:
tool when compared to text only
International Council for Computers in
exemplars. Further study of this phe-
Conclusions
Education.
nomenon is needed before firm con-
This study suggests that gender plays
National Council of Teachers of
clusions are drawn about the compar-
an important role in group problem
Curriculum and
Mathematics. (1989).
ison. Future research on gender
solving using computer-based learn-
evaluation standards fir school mathemat-
Reston, VA: Author.
differences in learning statistics
ing environments. While gender dif-
ics.
Underwood, G. & McCaffrey, M. (1990).
through same-gender groups could
ferences did not exist on a pretest of
Gender differences in a cooperative
address the ability composition of
statistical knowledge, Grade 8
computer-based language task.
groups. Students were assigned to
females outperformed males after the
(1), 44-49.
Educational Research, 32
mixed-ability groups to ensure that
instruction. It appears that providing
Webb, N. (1984). Sex differences in inter-
action and achievement in cooperative
every group had a similar opportunity
females with opportunities to work
Journal of Educational
small groups.
for success. There may, however, be a
with other females on group projects
33-44.
Psychology, 76(1),
confounding between gender and abil-
that require computers has a more
Williams, S. (1992). Putting case-based
ity composition in groups that must be
positive impact than single-gender
instruction into context: Examples from
considered in fostering group problem
cooperative learning situations for
The Journal
legal and medical education.
2(4), 367-427.
solving in statistics using computers.
males. This finding is similar to
for the Learning Sciences,
That multiple means of assessment
that of Johnson and Johnson (1985),
Susanne Lajoie is an associate professor
provide a better profile of learning has
who found that a combination of
and Nancy C. Lavigne a project assistant
been established in previous research.
cooperative learning and computer-
at McGill University in Montreal,
What needs additional examination is
assisted instruction had a positive
Quebec, Canada. Victoria R. Jacobs is a
project assistant at the University of
the relationship between individual
impact on female students' attitudes
Wisconsin-Madison.
and group assessment.
toward computers.
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4.,
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Wisconsin Center for Education Research. University of Wisconsin-Madison