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Peer Reviewed
Articles
Albert, L. R. (In press). Bridging the achievement gap in mathematics:
Sociocultural historic theory and dynamic cognitive assessment.
Journal of Thought.
- Abstract
In this paper I address the question, how can sociocultural
historic theory be applied within the discipline of mathematics
and to what extent is it relevant to bridging the achievement
gap? I discuss the relationship between social interaction
and the individual to illustrate how students' mathematical
learning is situated in sociocultural practices. I ground
this perspective in Vygotsky’s sociocultural historic
theory, which suggests that learning goes through an internalization
process resulting in the transformation of concepts, ideas,
and skills that have been socially constructed from interactions
with knowledgeable others. Then, I analyze and examine the
role of dynamic cognitive assessment in mathematics education.
I propose that dynamic assessment is critical to determining
the extent of individual’s mathematical learning. This
approach allows the monitoring of thought processes developed
‘outside-in’ through mediated practices assisted
by others to mature into thought processes developed ‘inside-out’
through mediated practices assisted by self (Albert, 2000,
p. 30). I conclude with a discussion suggesting that assessment
that involves aspects of mathematical learning and development
cannot and should not disregard the social and cultural context
within which the learner is situated.
Albert, L. Mayotte, G. and Cutler-Sohn,
S. (2002). Making observation interactive. Teaching Mathematics
in the Middle Grades. 7(7): 396-401.
- Abstract
- In this article, we focus on
a yearlong collaborative project regarding the role of observational
assessment in student learning of mathematical concepts. The
assessment technique was implemented in two sixth grade classrooms.
Many of the class activities involved algorithms and open-ended
problems in which students worked in collaborative groups, pairs,
or individually.
Albert., L. (2000).
Outside in, inside out: Seventh grade students' mathematical thought
processes. Educational Studies in Mathematics. 41(2): 109-142.
- Abstract
- Building on the
research of Vygotsky regarding the role of social interaction
and the zone of proximal development (ZPD) in learning and development,
this paper explored the relation between students' oral thought
processes and written thought processes. It is argued that the
practice of writing provides a context for a new learning zone:
the "zone of proximal practice" (ZPP). In this new zone, students
independently organize their thinking about mathematical concepts
and ideas. An interpretative case study of seven middle grade
students is presented to support this contention. The case study
describes the strategies and procedures students employed while
solving mathematical problems and documents students' oral and
written thought processes through interview protocols and writing
samples. The position that students' mathematical understanding
is further developed through writing as a communicative tool,
while taking advantage of mediated social practices, is discussed
to make clear the rationale for introducing a new learning zone.
Albert, L. R. &
Antos, J. (2000). Daily journals connect mathematics to real life.
Teaching Mathematics in the Middle Grades. 5(8): 526-531.
- Abstract
- This article
describes a journal-writing project developed in a fifth grade,
total inclusion classroom, and specifies the major features
of the writing project, including the framework used to assess
student learning.
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Zollers, N., Albert,
L., & Cochran-Smith, M. (2000). Pursuing social justice as
a teacher education faculty: Collaborative dialogue, collaborative
research. Action in Teacher Education.
- Abstract
Recent demographic
trends in American education have reaffirmed the need to teach
prospective teachers about social justice issues such as race,
class, and disability. With this goal in mind, fourteen members
of the Boston College Teacher Education faculty and three
administrators engaged in a year-long series of conversations
over the meaning of social justice. The goal of these "social
justice conversations" was to investigate individual understandings
of the meaning of social justice and find the commonality
necessary to "teach for social justice." A sub-group of faculty,
including the authors, studied these conversations. The authors
found that participants unanimously embraced the goal of teaching
for social justice, but that their definitions of social justice
ranged along a "continuum of beliefs." They identify three
categories of divergence about social justice: definitions
of fairness and equity; institutional vs. individual understandings
of injustice and responsibility of individuals to advocate
for social justice. In conclusion, the authors discuss the
implications of these discussions for the Teacher Education
faculty and individual faculty members.
Cochran-Smith, Albert,
L. R., M., Freedman, S., DiMattia, P., Jackson, R., McGee, L.,
Mooney, J., Neisler, Peck, A., & Zollers, N. (1999). Seeking
social justice: A teacher education faculty's self-study. The
Journal of Leadership in Education, 2, 229-254.
- Abstract
- Committed in
a general way to the idea of teaching and teacher education
for social justice, the nine co-authors of this paper embarked
upon a multi-year collaborative research and professional development
project that came to be known as "Seeking Social Justice." The
project was designed to allow group members (all faculty in
the same department) to examine their own understandings of
social justice issues as part of the process of helping their
students do the same as well as to encourage students to work
for social change and effectively meet the needs of the increasingly
diverse K-12 school population. In this article the authors
discuss the framework for the project and the first two years
of collaborative work. They suggest that their work together
provides a "proof of possibility" for faculty groups attempting
to emphasize or infuse social justice into pre-service teacher
education despite profound differences in politics, disciplines,
and perspectives. They argue that part of what made this possible
was a commitment to extended and repeated conversations that
evolved over time into a culture of careful listening. This
led to deeper and richer understandings of participants' own
biases as well as understandings of where colleagues were coming
from on particular issues. The article suggests that it was
these deeper understandings, and not consensus, that allowed
the group to take action--designing and implementing new administrative
policies and practices, establishing social justice as the centerpiece
of the curriculum, and beginning to look critically and publicly
at their own pedagogy as teacher educators.
Albert, L. R. &
Jones, D. (1997). Implementing the science teaching standards
through complex instruction: A case study of two teacher researchers.
School Science and Mathematics, 97, 283-291.
- Abstract
- In this case
study, an "interpretive collaborative" methodology is applied.
The experiences of two elementary teacher-researchers are described,
as they explore science teaching and learning in their two non-graded
primary classrooms through the process of complex instruction.
This study involves three strands: the theoretical base of complex
instruction , the on-going collaboration between two experienced
teachers, and the Science Teaching Standards in relation to
complex instruction. Findings suggest that, because the teacher's
role in conducting complex instruction activities is multifaceted
and complex, successful implementation of complex instruction
and the National Science Education Standards required ongoing
collaboration and support among teachers. The teacher-researchers
reported that it was their collegial relationship that encouraged
them to explore, prepare, and implement inquiry activities or
tasks for their students.
-
-
Book Chapters
Albert., L. and
McKee, K. (2002). In their own words: achieving intersubjectivity
through complex instruction. Learning and Instruction.
In V. Spiridonov, I. Bezmenova, O. Kuoleva, E. Shurukht, &
S. Lifanova, (Eds.). The summer psychology conference 2000, the
zone of proximal development. Moscow, Russia: Institute of Psychology
of the Russian State University for the Humanities.
- Abstract
- The theoretical
framework for this yearlong qualitative study is grounded in
Vygotskian theory to examine how forty children in two primary
grade classrooms came to experience shared understanding, "intersubjectivity,"
of mathematics and science content through "complex instruction,"
a collaborative group instructional approach. Data were collected
through classroom observations, students’ reflection sheets,
and in-depth, audio taped interviews with six students. Interweaving
the theories of the zone of proximal development and complex
instruction has implications for classroom instruction of problem-solving
activities. The instructional approach of complex instruction
promotes a collaborative problem-solving process in which children
are challenged to communicate ideas and understandings by speaking,
listening, observing, and analyzing the task at hand. The case
study presented in this paper substantiates this approach to
teaching and learning. Activities involving collaborative practices
require that children work together to achieve a common goal
as well as a common understanding. Findings suggest that when
children work to accomplish tasks in a collaborative context,
they are often able to achieve more than if they had worked
individually. However, in order for collaborative learning to
be successful, children must be taught to support and scaffold
each other’s understandings.
Albert, L. R. (2000).
Lessons learned from the five men crew: Teaching culturally relevant
mathematics. Strutchens, M, Johnson, M., & Tate, William F.
(Eds.). pp. 81-88. Changing the Faces of Mathematics: Perspectives
on African Americans. Reston, VA: National Council of Teachers
of Mathematics.
Albert, L. R. &
Ammer, J. J. (In press). Lesson Planning and Delivery. In K. Lenz,
Deshler, D., & Kissam, B. (Eds.). Inclusive Teaching in Secondary
School Classrooms. McGraw-Hill.
Clift, R., &
Albert, L. R. (1998). Early learning and continued development
for teachers. In B. Spodex and O. N. Saracho (Eds.) Issues in
Early Childhood Evaluation, Yearbook in Early Childhood Education,
V. 7. New York: Teacher College Press.
Curriculum Development
Albert, L. R. (2001). Reading and writing for math, using a problem-solving
approach, Grade 3. Columbus, OH: Zaner-Bloser.
Albert, L. R. (2001). Reading and writing for math, using a problem-solving
approach, Grade 3 Teacher Edition. Columbus, OH: Zaner-Bloser.
Albert, L. R. (2001). Reading and writing for math, using a problem-solving
approach, Grade 4. Columbus, OH: Zaner-Bloser.
Albert, L. R. (2001). Reading and writing for math, using a problem-solving
approach, Grade 4 Teacher Edition. Columbus, OH: Zaner-Bloser.
Albert, L. R. (2001). Reading and writing for math, using a problem-solving
approach, Grade 5. Columbus, OH: Zaner-Bloser.
Albert, L. R. (2001). Reading and writing for math, using a problem-solving
approach, Grade 5 Teacher Edition. Columbus, OH: Zaner-Bloser.
- Abstract
- The problem-solving
process featured in Reading and Writing for Math, Using a Problem-Solving
Approach is a recursive process that consists of five steps:
identify the problem, cross out unneeded details, organize details,
describe how the problem was solved, and show the mathematics
operations. Through Reading and Writing for Math, students quickly
become comfortable using this simple process and quickly show
a high level of success in solving real-life problems involving
important mathematics strands and concepts. The program also
reinforces basic literacy strategies (e.g., look for details,
use picture and context clues, write summaries, and record questions
and/or observations) that support computational skills. This
work emerges from my research on mathematical problem solving.
This work is important because it gives students the literacy
and mathematics strategies they need to solve real-world problems.
It is also designed to prepare students for standardized tests
that ask them to identify, describe, and organize the details
of a problem and to explain what they did to solve the problem.
It is important to note that Reading and Writing for Math was
field-tested in more than twenty-five elementary classrooms
across the country, including two schools in the Boston area.
Other
Albert, L. R. (2000).
The call to teach: Spirituality and intellectual life. Conversations
on Jesuit Higher Education. St. Louis: National Seminar on Jesuit
Higher Education.
Albert, L. R. (1994
November/December). Review of J. Countryman: Writing to learn
mathematics. Mathematics Teaching in the Middle School. Reston,
VA: National Council of Teachers of Mathematics.
Albert, L. R. &
Woodbury, M. (1995). 1993 Graduates of teacher education programs
at the University of Illinois (Technical Report). Champaign, IL:
Council on Teacher Education University of Illinois at Urbana-Champaign.
Articles Under
Review
Albert, L. R. & McAdam, J. F. (in review). Theory and Practice:
Decimal Fraction Algorithms Using Base-Ten Blocks. On-Math: An
NCTM Online Journal.
- Abstract
- This paper focuses on the experiences of prospective teachers
as they solve decimal fraction algorithms with Base Ten Blocks
(BTBs). In this paper, we discuss the processes involved in
assisting teachers in developing a conceptual understanding
of decimal fractions. We illustrate some of the essential components
and underlying principles for learning and teaching decimal
fractions involving the representation of multiplication algorithms,
using an array or area model. Readers are invited to work through
each problem presented by performing the algorithms with BTBs
and to analyze a videotaped activity of prospective teachers
solving decimal fraction algorithms with BTBs.
Work in Progress
Albert, L. R. (In
preparation). A classroom journey through the lens of Vygotsky.
Albert, L. R., Flores, S., Gallo-Fox, J., Manzon, S., & Paugh,
P., J. (In preparation). Sociocultural experiences in adult learning
communities: Group dynamic within the zone.
Albert, Lillie R.
(In preparation). On becoming a mathematics teacher: Professional
development of nontraditional middle school student teachers.
Albert, L. R. &
Rhoades, K. (In preparation) Imaging Mathematics: A study of teacher
candidates' perceptions of teaching and learning mathematics in
the past, present and future.
Top
of Page
My program of research focuses on the impact of the sociocultural
contexts within which learning and development occur and specifically,
how these contexts relate to the theories and practices of mathematics
pedagogy. Understanding the abstract nature of mathematics has
been the goal of traditional teaching and learning practices
that has been contextualized by rote memorization, rules and
formulas which emphasize only the procedural aspect of mathematics.
My research explores the relationship between the cognitive
act of learning mathematics and the cultural tools of written
and oral language to develop conceptual understanding of mathematics.
My empirical work, to date, involves case studies, phenomenology,
and interpretive analyses that elucidate the relationship between
cognitive processes and mathematical understanding using communicative
tools, writing and drawing.
Central to my research are the cultural historic learning theories
of Vygotsky, which emphasize how an individual's personal sociocultural
environment influences learning and development. Fueling my
research interest is my personal experiences as a child living
in Brookhaven, Mississippi, during the turbulence of the Civil
Rights Movement when cross burnings and lynchings were rampant
in the South. After a lynching in a nearby town, my teacher,
Miss Rainy, realized she must dissipate our fears before we
could learn fraction algorithms. She discussed this real-world
incident with us allowing give-and-take questions and answers
to ease our anxieties. From that point on, I understood the
importance of the cultural contexts in which children's lives
are situated and how their education coalesces with issues of
social justice.
My research and writing indicate a concept of learning that
is constructive and collaborative, leading to several promising
implications for pedagogical practices. The classroom is a learning
community in which goals and objectives are shared. Transformation
of teaching and learning demands engaging the individual in
purposeful activities as a whole person. The curriculum necessitates
that students become involved in activities that are personally
and socially meaningful. Such activities expand the student's
knowledge base, creating opportunities for new problems with
diverse and original solutions. The research projects and activities
that I have engaged in illustrate the progression of my research
advancing towards a reconceptualization of mathematical teaching
and learning practices. These projects are grounded in theory,
but are also rooted in practical inquires carried out in collaboration
with teachers, graduate students, and colleagues. The intent
is to assist teachers, teacher educators, curriculum developers
and researchers to better understand and improve the activities
of teaching and learning within a social justice framework.
My current research seeks to examine the visual and written
data generated by prospective teachers regarding their emerging
image of themselves as mathematics teachers to improve mathematics
teaching. I came to this topic through my association with my
colleague, Walter Haney. Walt has been actively engaged with
"drawings in education" in the area of assessment
for the past decade. In pursuit of this goal to improve mathematics
teaching, two questions emerge: How do educators provide opportunities
for prospective teachers to gain insight into their individual
mathematical learning experiences and their teaching practices?
And how may this awareness and knowledge affect their comprehension
of their students' learning processes and illuminate the process
of effective mathematics teaching? I posit that prospective
teachers' drawings and narratives about mathematics generated
during their academic experience may play a role in their preparation
and development as effective mathematics teachers. Tools such
as drawings and narratives may uncover their perceptions of
their prior personal teaching/learning experiences in mathematics;
these tools may provide rich material for self-reflection and
analysis of their present teaching strategies as they affect
their students understanding of mathematics. Drawings and narratives
may serve as a catalyst for self-reflection that will be the
basis for the emergence of qualitative changes in individual
teaching practices in mathematics.
It has become increasingly clear to me that I am at a point
in my intellectual life where I want to provide more than snapshots
or abstracted fragments of the complexity of mathematics teaching
and learning. Thus, my long-term plans include research that
will avoid fragmentation and put forth epistemological and theoretical
implications, considering methodological and practical questions
that are of use to teachers and researchers. Data will come
from my continuing work with teachers and their students in
K-12 classrooms and with students enrolled in my teaching mathematics
education courses. One project will be developed from data generated
by my current research study. It will provide an in-depth examination
and description of teacher-generated drawings. Another will
focus on the importance of the role of cultural historic theories
in mathematical research regarding the learning and development
of individuals, including children and adults. A major objective
is to "tease out" the particulars of this relationship
in order to gain new perspectives on how mathematical learning
is situated in sociocultural practices. Such understandings
are key, as they demonstrate that mathematical thoughts are
not acquired by learners in isolation, but rather are products
of sociocultural practices. The challenge for me as a researcher
and an educator is not to lose sight of the practical applications
inherent in cultural historic theory. Furthermore, I believe
that if my research is done with distinction and conviction,
then the quality of my professional and public work will reflect
my authentic commitment to social justice.
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