ERIC Identifier: ED482722 Publication Date: 2003
Author: Ishii, Drew K.
Source: ERIC Clearinghouse for Science Mathematics and Environmental
Constructivist Views of Learning in Science and Mathematics.
Many educators may or may not be familiar with the term "constructivism,"
but probably recognize it as something to do with learning. The main tenet
of constructivist learning is that people construct their own understanding
of the world, and in turn their own knowledge. However, any theory of learning
has ramifications beyond the scope of learning itself. Simply put, subscribing
to a constructivist view of learning affects
teaching, classroom practices, and student classroom behavior. Von
calls constructivism a theory of knowing, as opposed to a theory of
knowledge. From his view it is easy to see how constructivism can be thought
of as a perspective or a lens with which to understand or know the world;
meaning that reality, knowledge, and
learning are considered to be constructed by individuals (See von Glaserfeld,
more philosophical issues regarding constructivism). So what does this
educational settings like the typical classroom?
CONSTRUCTIVISM IN MATHEMATICS AND SCIENCE... A CONTRADICTION?
It seems as though a belief in a constructivist approach to knowledge
or learning is
contrary to the fields of mathematics and science, where knowledge
is viewed as true
facts, principles, theorems, and laws. In literature, however, it makes
sense that the
reader constructs her own meaning of the works of William Shakespeare
Angelou because she is interpreting the writings and intentions of
the authors. But there
is only one interpretation of 2+2, and it is 4. There is a danger in
trying to apply that
logic with mathematics and science because constructivism is not questioning
interpretation of simple arithmetic or the notion of gravity; rather
it is saying that each
person comes to construct their own conclusions and conceptions. These
individually constructed conceptions are personally valued whether they are consistent
the field deems acceptable or not. A belief that the world is flat
is just one particular
view. It was once accepted by society, but now is not. Bodies of knowledge
mathematics and science change, and what is claimed to be known in
the fields is either
a logical derivation from the available conventions, or "the best way
of conceiving the
situation because, at the moment, it is the most effective way of dealing
with it" (von
Glaserfeld, 1993, p.33). In fact, some constructivists do not acknowledge
that there is a single truth to be known. Instead what is (traditionally)
"true" can be thought of as what is viable (von Glaserfeld, 1993.)
THE BASICS OF CONSTRUCTIVISM(S)
Using the term "constructivism" can be ambiguous because there are several
constructivism described in the professional literature. Good, Wandersee,
and St. Julien (1993) offer 15 different adjectives to place in front of
constructivism to clarify its meaning: contextual, dialectical, empirical, humanistic, information-processing,
methodological, moderate, Piagetian, post-epistemological, pragmatic,
realist, social, and socio-historical (p. 74). While many of these
terms relate to
overlapping concepts and assumptions, others have distinctions worth
forms of constructivism incorporate the notion of individually constructed
Weak constructivism, as Paul Ernest (1996) describes it, assumes that
construct their own knowledge (a local notion), while accepting the
objective knowledge (a global notion). Radical constructivism additionally
individual knowledge is in a state of flux, or constant reevaluation
by adapting and
evolving. In this view, the mind is characterized as problematizing
social constructivism is based on the assumption that individual knowledge
knowledge are one in the same. That is to say that the knowledge an
constructs is that which he or she constructs with society. This evokes
metaphor of knowledge, and the "social construction of meaning" (Ernest,
CONSTRUCTIVISM IN THE CLASSROOM
The various forms of constructivism present different implications when
it comes to
pedagogical concerns. There are some commonalities, however. According
Ernest (1996) the forms of constructivism identified above all lead
to the following
1. Sensitivity toward and attentiveness to the learner's previous constructions.
includes using students' previous conceptions, informal knowledge,
knowledge to build upon.
2. Using cognitive conflict techniques to remedy misconceptions. Engaging
like this allow students to trouble their own thinking, and it is through
this conflict that
they will develop their own meanings, or at least seek to rectify the
3. Attention to metacognition and strategic self-regulation. This follows
previous suggestion when students think about their thinking, and become
for their learning.
4. Use of multiple representations. In science and especially mathematics,
representations offer more avenues with which to connect to students'
5. Awareness of the importance of goals for the learner. This awareness
of goals refers
to the difference between teacher and learner goals, and the need for
understand and value the intended goals.
6. Awareness of the importance of social contexts. Various types of knowledge occur in various social settings for instance informal (street) knowledge versus formal (school) knowledge. (p. 346)
In addition to the suggestions proposed by Ernest, Brooks and Brooks
(1999) offer five guiding principles of constructivism that can be applied
to the classroom.
1. The first principle is posing problems of emerging relevance to students.
A focus on
students' interests and using their previous knowledge as a departure
students engage and become motivated to learn. The relevant questions
posed to the
students will force them to ponder and question their thoughts and
2. Another guiding principle is structuring learning around primary
concepts. This refers
to building lessons around main ideas or concepts, instead of exposing
segmented and disjoint topics that may or may not relate to each other.
"The use of
broad concepts invites each student to participate irrespective of
temperaments, and dispositions" (p. 58).
3. The third principle is seeking and valuing students' points of view.
allows for access to students' reasoning and thinking processes, which
in turn allows
teachers to further challenge students in order to make learning meaningful.
accomplish this, however, the teacher must be willing to listen to
students, and to
provide opportunities for this to occur.
4. Adapting curriculum to address students' suppositions is the fourth
adaptation of curricular tasks to address student suppositions is a function of the
cognitive demands implicit in specific tasks (the curriculum) and the
nature of the
questions posed by the students engaged in these tasks (the suppositions)"
5. The final principle is assessing student learning in the context
of teaching. This refers
to the traditional disconnect between the contexts/settings of learning
versus that of
assessment. Authentic assessment is best achieved through teaching;
between both teacher and student, and student and student; and observing
meaningful tasks. Brooks and Brooks (1999) offered these guiding principles
to serve as over-arching themes for educational settings that are consistent
with constructivist learning. They also identify 12 practices that distinguish
constructivist teachers. These practices apply to any subject or academic
1. Encourage and accept student autonomy and initiative.
2. Use raw data and primary sources, along with manipulative, interactive,
3. Use cognitive terminology such "classify," "analyze," "predict,"
and "create" when
4. Allow student responses to drive lessons, shift instructional strategies,
5. Inquire about students' understandings of concepts before sharing
understanding of those concepts.
6. Encourage students to engage in dialogue, both with the teacher and
7. Encourage student inquiry by asking thoughtful, open-ended questions
encouraging students to ask questions of each other.
8. Seek elaboration of students' initial responses.
9. Engage students in experiences that might engender contradictions
to their initial
hypotheses and then encourage discussion.
10. Allow significant wait time after posing questions.
11. Provide time for students to construct relationships and create
12. Nurture students' natural curiosity through frequent use of the
learning cycle model.
Teachers who embrace the constructivist view of learning are encouraged
to compare their classroom practices with those listed above, for they are the
indicators that practice matches theory.
FOR FURTHER STUDY
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a general search would yield over 140 items.
World Wide Web Resources
*Mathematics Education: Constructivism in the Classroom
The Math Forum http://mathforum.org/mathed/constructivism.html
*Constructivism and the 5Es
Miami Museum of Science
Mathematical Association of America
*Essays on Constructivism and Education
Maryland Collaborative for Teacher Preparation
Brooks, J.G., & Brooks, M.G. (1999). "In search of understanding:
The case for
constructivist classrooms." Alexandria, VA: Association for Supervision
and Curriculum Development.
Ernest, P. (1996). Varieties of constructivism: A framework for Comparison.
Steffe, P. Nesher, P. Cobb, G.A Goldin, and B. Greer (Eds.), "Theories
of mathematical learning." Nahwah, NJ: Lawrence Erlbaum.
Good, R.G., Wandersee, J.H., & St. Julien, J. (1993). Cautionary
notes on the appeal of the new "ism" (constructivism) in science education.
In K. Tobin (Ed.), "The practice of constructivism in science education."
Hillsdale, NJ: Lawrence Erlbaum.
Von Glaserfeld, E. (1993). Questions and answers about radical constructivism.
Tobin (Ed.), "The practice of constructivism in science education."
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