Teaching Mathematics and
Learning Community in Community College
Teaching Mathematics and
Learning Community in Community College
Dmitri Logvinenko
Department of Mathematics
The concept of a learning community has been used as a
powerful and successful instructional tool in various environments and places
(Lave, Wenger, 1999). Practices of the learning communities have been adopted
and successfully implemented at different times and by different cultures.
Attempts to use the learning community ideas and practices were made by modern
educators in a range of educational fields and areas (Treisman). This paper discusses
the principles, procedures, methods of learning communities and possible ways
of implementation of the Learning Community principles in teaching of Developmental Mathematics in Community College.
Learning Community in
Learning Community.
The concept of a Learning Community has been shown to be a
proven and effective method of instruction, successfully used by many interest
groups, professional and societal communities and associations. From Yucatec
midwives and Vai and Gola tailors, naval quartermasters (Lave, Wenger, 1991) to
insurance claims processors (Wenger, 1999) – all of these very different historical
and social groups naturally developed and applied the principles of learning
communities in gradually educating newcomers and apprentices to the professional
levels of the old timers and masters. The long way from a novice to an expert starts
from the minor participation in small and superficial yet productive and
important tasks that contribute to the overall goal of the community. Initially
peripheral participation in the activities of the learning community becomes
deeper and more central to the global functioning of the community. This legitimate
marginal participation (Lave, Wenger, 1991) allows the newcomers to become
acquainted and familiar with the tasks, organization principles and practices
of the community. Educational process in such a community occurs in continuous
interaction among the learners the learners of different skill level and in
lesser degree between the learners and mentors.
If we look closely at the principle components of a
learning community we can separate them into two important parts:
·
Participants – members of the learning community
differ in skills and knowledge which closely correlates to their levels of
engagement in the practices of the community.
Advanced learners are more involved in the life of the community;
accomplish more sophisticated, complex and central tasks. All the participants
of the learning community share one common goal – to reach the full mastery of
the skills, vocabulary and organizational principles of the learning community
and become a central member of a community.
·
Learning process, which is based on the
legitimate peripheral participation (Lave, Wenger, 1991), allows the novices to
understand the broader context and the final goals of the community’s
activities. Continuous change of members’ level of participation occurs with
the deeper engagement in the practices of the learning community. Participants
learn from continuous interaction with their peers and more advanced members.
This interaction changes learners, rules, and principles of the learning
community. Learning occurs in authentic situations, activities of learning
communities are natural, framed by the culture, and their meaning and purpose
are socially constructed through negotiations among present and current members
(Brown, et. al., 1989). The practices of the learning community are improved and
adjusted by each new generation of learners; the changes are influenced by their
inter-relationships. All the participants of the learning community are also
changing inside of those practices.
Learning community in a wide sense does not constitute learning
in a purely educational institution – it can be observed in many different
social environments. People getting professional training at work, in the work
environment itself, each of these circumstances possess necessary features for
the development of the learning community (Lave, Wegner, 1991). Some important
characteristics of a learning process in communities of practice and its
difference from leaning mathematics in modern community college instruction are
presented in Table 1:
|
Learning Communities |
Mathematics in Community Colleges |
|
Voluntary participation of
members in activities of the Learning Communities. |
Most of mathematical courses
offered in Community Colleges are mandated by program requirements. |
|
High levels of internal
motivation among the learners. Clear understanding of the objectives of the
learning process by apprentices from the very beginning. Learning activities are
authentic to the culture of the Learning Community and are embedded in it. The main goal of a learner is to
reach higher skill and knowledge level, become a true expert and
professional. |
Low motivation for learning
mathematics among the students. Acquired mathematical skills and knowledge
are considered highly abstract and completely useless by many students. Main goal of the Community College
instruction is to give the students some basic and mostly introductory level
of understanding of the taught concepts and skills. |
|
Instruction and learning are
carried on informally with high levels of interaction and support among the
learners. Cooperation and mutual assistance occur on all stages of learning.
Most of the learning occurs in interaction among the apprentices of different
levels and very limited interaction with the mentor. |
Most of the traditional Community
College mathematical instruction is conducted in a formal and regulated
manner with little interaction and cooperative learning among the students. Most
of the learning occurs during the instructors’ lecturing, with very little
interaction between the students of different levels. |
|
Movement to the new phases and
activities of the community of practice occurs only upon complete mastery of
the previously learned concepts. |
Often the students start and continue
their learning of mathematics in Community College with large gaps in
understanding and comprehension of the previous material. |
|
The practices of the Learning Community
are flexible; they are continuously modified and adjusted by the participants
and influenced by the changes in the outside world. |
Teaching and instructional practices
are highly artificial, rigid and not closely related to the outside of the
classroom experience of the students. |
Table 1.
Time proven effectiveness, usefulness of the Learning
Communities makes them and their possible application in Community College very
attractive for math educators. The question of implementation of the practices
of the Learning Communities is sitting on the top of the list of many educators
and educational institutions.
Leaning Community principles are
successfully implemented in Community Colleges in various craft and art
programs. Students of different levels are grouped in the same classes and go
through various activities based on their skill level. Majority of the students
are taking these classes voluntarily and are highly motivated to become experts
in learning the craft. Most of the knowledge and experience acquisition occurs
in watching the work of peers and interacting with more advanced students after
the short presentations made by the instructor. Students continue to take further
and more advanced classes with the sole purpose of becoming more proficient in
the field of their study. Practices of the Learning Communities are clearly in
place and are efficiently used in instructional process. Generations of
students obtain proficiency and some even become professionals in the learnt
crafts and trades. But these practices are efficient and easily adoptable in
teaching of art and craft programs, could they still be used in teaching of
mathematics?
Several attempts to incorporate
different aspects of the Learning Community into modern mathematical
instruction have been conducted by various educators. Perhaps the most successful of them include
the Professional Development Program (PDP), by Treisman at UC Berkley, the Excellence
in Mathematics, Science and Engineering Program (EMSE) in
Successful
Applications of the Learning Community in Higher Education.
In PDP and EMSE programs a group of
advanced pre-calculus and calculus level students were offered a special
program between semesters to better prepare them for Calculus course. The participants
were mostly highly motivated African-American students with significant
experience of learning in Community College or University environments. Both
programs were designed to prepare students for a regular calculus course and to
supplement their learning with more interesting, challenging, and difficult
calculus material based on real life applications, closely related to students’
experiences. The programs were conducted prior to a regular college semester. Strong
financial and academic assistance was offered to participants. Students studied
in groups and in a lab environment with instructor’s supervision and available
tutoring. Both programs resulted in significant improvement of the participating
students’ grades in the calculus course. Students were deeply engaged in their learning
process, performed on a significantly higher level in calculus, and developed a
strong understanding of the application value of learned concepts and principles
of calculus in various fields of activities in modern society.
The third program in De Anza
Community College, Math Performance Success (MPS), targeted the students who did
not have previous success in math courses. The Math Performance Success program
was open to all students who demonstrated a past difficulty in math classes: failures
in past math classes, difficulty with math in high school and math anxiety.
It offered a team approach by
linking increased instruction, counseling and tutoring. Participants received
double the typical daily instruction, academic and personal counseling, and
tutoring both in and out of class. The program attracted a large percentage of
underrepresented students. Participating students also took a series of consecutive
math courses over three consecutive semesters.
Some of the students later became
effective tutors in MPS. The program demonstrated direct positive effect on
students’ retention and completion. Its success can be attributed to the team-effort
approach and collaboration--collaboration
among students, who helped each other learn, and collaboration among teachers,
counselors, and tutors, who helped guide the students. Students received
individual attention that they could not obtain in a regular class. Extensive
group interaction was incorporated to ensure students’ bonding with each other.
Instructors in this program often referred to the students helping each. Instructors,
counselors and mentors/tutors collaborated to help students complete course
requirements from elementary algebra to college level mathematics. Counselors
attended class on a regular basis to assist students. Programs’ success and
retention rates of participating students are shown in Table 2, compared to
those of the entire Mathematics department:
|
|
Success |
Non-Success |
Withdrawal |
|
All |
62% |
17% |
21% |
|
MPS |
90% |
5% |
5% |
Table 2.
All of the above mentioned programs embody many of the core
characteristics of the learning community. The students in the programs
participated on the voluntarily basis, they possessed strong internal
motivation and from the beginning had clear understanding of their goals. The non-formal
instruction format in both programs allowed incorporation of considerable
amounts of group work, collaborative learning and tutor assistance, allowing
the students to learn in interaction with each other. Students reached
sufficient knowledge levels, mastered all required and necessary skills, and
learned important concepts before moving to the next steps of the program. They
were all developed from the Treisman Workshop model which focuses on believing
in students' ability to be excellent in mathematics and challenging them to do
superior work through collaboration with other students.
Possible Implementation of the Learning
Community at
The difficulties in adopting of
the Learning Communities in Community College include:
1. Linear
structure of mathematical learning.
New concepts in
mathematics are based on the clear understanding and proficiency in using
already previously learnt ideas. Developmental mathematics in Community
Colleges is sequential and cannot occur without complete mastery of the
previous material.
2. Mandated
curriculum.
The students are
required to take the sequence of mathematical courses for their programs of
study. Majority of the students are taking mathematical courses involuntarily
and with low levels of internal motivation.
3. Strict
regulation of the class pace and advancement level of the students.
The courses are
tightly and strictly regulated and the same pace is set for all students in the
class. Students in the same class are approximately of the same level in
mathematics, which limits the amount of possible help the students can provide
for their peers.
4. Little
interaction between the learners of different levels.
Students of
different levels do not interact with each other in the classroom. This does
not allow less advanced apprentices to learn from their more advanced peers and
the learners with higher levels of expertise improve and deepen their understanding
of already learnt concepts.
5. Abstract
nature of mathematics.
The concepts and
ideas taught in college level mathematics are highly abstract and seem foreign
to the developmental learners.
Suggested
Recommendations in the Implementation of the Learning Community in Community
College Environment
To address these
issues and implement powerful features of the Learning Communities in teaching
of the developmental mathematics in Community Colleges, we should take the
following measures:
1. Linear
structure of mathematical learning.
The courses
should be made more flexible, slower paced and be adjusted to the personal
levels of participating students. Transition to the next level should be done
only after the learner exhibits the complete mastery of the covered
topics.
2. Mandated
curriculum.
Curriculum
should modified to allow deeper and more extensive coverage of less amount but vital
concepts, with more time assigned for exercises, group projects, collaborative
learning and other instructional techniques allowing deeper levels of
interaction between the learners. The learners must go through the professional
counseling sessions and instructors must explain the necessity of the
mathematical knowledge in the student’s selected future professions to improve
their levels of internal motivation.
3. Strict
regulation of the class pace and advancement level of the students.
More
personalized level of instruction could be achieved by using computer based
labs, use of the tutors and TAs in the classroom for the material delivery and
student’s practical exercises. Addition of the in-class tutoring by the
student-tutors and work-and-study students from higher level math courses allow
the necessary for Learning Community peer – to – peer interaction and learning
from more advanced apprentices.
4. Little
interaction between the learners of different levels.
Students of
different levels can interact with each other in the computer or math lab
environment. Tutors and more advanced students can assist weaker students in their
learning, enhancing their level of expertise at the same time.
5. Abstract
nature of mathematics.
Taught concepts
must be represented through the real–life examples and applications, clearly
visualizing the relevance and life values of the delivered material.
Conclusions.
The necessary components for the
successful implementation of the Learning Community principles in Community
Colleges include:
1.
Strong counseling
support for low-motivated students.
Students have to
be interested in studying and motivated to learn prior to taking the course. In
Professional Development Program (PDP), by Treisman at UC Berkley, and
Excellence in Mathematics, Science and Engineering Program (EMSE) in
2.
Extensive
participation of the students with higher level of preparation used for
tutoring and instructional assistance.
These students
work as tutors for the students with lower levels of preparation and working as
such the students with higher level of preparation get a better grasp and
understanding of the new material taught. This is one of the strength’s of a
learning community – learning from peers. In PDP and EMSE programs tutoring and
communication with instructor were available during the lab hours and in MPS in
3.
Possibility of
the increased instruction time and relaxed time regulations.
EMSE and PDP were
created as supplementary, assistance programs targeting more challenging,
difficult, and interesting material in calculus and pre-calculus programs. The
workshops were not implemented as remediation of regular course work.
4.
Significant
amount of in-class tutor time, instructors and peers assistance.
During this time
the students should work on group projects, collaborative assignments and
develop necessary study relationships and habits.
The first goal of the Learning
Community program should be the improvement of the students’ motivation to
study the students with low levels of motivation must go through the set of
counseling sessions. The counselors’ work must continue through the course of
developmental program – every time the students would encounter any
motivational problems the counselors should be immediately available to address
and fix the issue.
Thus, the entry point and the first priority of the
program should be to address students’ enthusiasm and desire to study.
Confidence and interest to learn mathematics, motivation, self-concept and
self-esteem of the students are proved by many studies to be the most
significant predictors of continued success in post-secondary mathematics. A
person with low motivation, interest and self-esteem often fails in academic
achievement (Singh, Granville, Dika, 2002) and therefore it is unclear how to
deal with such students for the program to be effective. All the Learning
Communities, as described by Lave and Wenger, possess the same important and
crucial attribute – desire of participants to excel, improve skill and
participation levels inside of the Learning Community – community of practice
(Lave, 1993). In order for the Learning community to be effective, the
participants need to possess the willingness and desire to learn.
Moreover, instruction should
heavily rely on the practical applications of the taught concepts in everyday
life and experiences of the participating students and provide them with clear
sense of the utility and real life value of taught content. This should be delivered by utilizing
principles of collaborative learning that include group projects. Once students
achieve the higher level of motivation they should study in groups, consisting of
participants with both, higher and lower levels of preparation. It will help
the students with lower levels of preparation to learn from more advanced
students. At the same time, more advanced students will increase their mastery
of the material by tutoring.
The learning process
should take place under the continuous instructors’ and counselors’ supervision
of the students’ progress. These characteristics of the program are necessary
to achieve one of the most important and crucial conditions of the learning
community – learning by teaching and learning from the more advanced peers
(Lave, Wenger, 1991).
As in the MPS program in
At the beginning of the
program, participating students should become familiar with the college study
skills including note taking, time management, and other learning techniques.
New students should go through the set of counseling sessions to get acquainted
with these practices. Instructors and counselors should also introduce to
students the rules and policies of the community college.
Mathematics should not be taught as an abstract subject
matter, without any practical use. Research in cognitive science has clearly demonstrated,
that students “have difficulty learning and applying new knowledge and
information processing skills, when education and training occur out of
context. “(Roueche and Roueche, 1993).
Increased
instruction time allows instructors to deliver the conceptual knowledge in
depth and gives students an opportunity to improve their understanding of the
learned concepts and material through the group projects and collaborative
learning.
The Learning Community program
would have a good chance of success if it would incorporate the following
features of the community of practice:
Such organization and extensive program’s coverage of
various motivational and instructional issues will lead to significant benefits
for participating students, and to considerably increase in the success and
retention rates of Mathematical Departments and Community Colleges in general.
Great potential of the program should make the program
attractive to the Community Colleges and other secondary education
institutions.
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