Constructivist Views of Learning
in Science and Mathematics
ERIC Identifier: ED482722
Publication Date: 2003-00-00
Author: Ishii, Drew K.
Source: ERIC Clearinghouse for Science Mathematics and Environmental Education Columbus OH.
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 Glaserfeld (1993)
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, 1993 for
more philosophical issues regarding constructivism). So what does this mean for
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 or Maya
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 the
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 with what
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 including
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 forms of
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, radical, rational,
realist, social, and socio-historical (p. 74). While many of these terms relate to
overlapping concepts and assumptions, others have distinctions worth mentioning. All
forms of constructivism incorporate the notion of individually constructed knowledge.
Weak constructivism, as Paul Ernest (1996) describes it, assumes that individuals
construct their own knowledge (a local notion), while accepting the existence of
objective knowledge (a global notion). Radical constructivism additionally assumes that
individual knowledge is in a state of flux, or constant reevaluation by adapting and
evolving. In this view, the mind is characterized as problematizing knowledge. Finally,
social constructivism is based on the assumption that individual knowledge and social
knowledge are one in the same. That is to say that the knowledge an individual
constructs is that which he or she constructs with society. This evokes a "shared"
metaphor of knowledge, and the "social construction of meaning" (Ernest, 1996, p.343).
CONSTRUCTIVISM IN THE CLASSROOM
The various forms of constructivism present different implications when it comes to
pedagogical concerns. There are some commonalities, however. According to Paul
Ernest (1996) the forms of constructivism identified above all lead to the following
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.
- Sensitivity toward and attentiveness to the learner's previous constructions. This
includes using students' previous conceptions, informal knowledge, and previous
knowledge to build upon.
- Using cognitive conflict techniques to remedy misconceptions. Engaging in practices
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 conflict.
- Attention to metacognition and strategic self-regulation. This follows from the
previous suggestion when students think about their thinking, and become responsible
for their learning.
- Use of multiple representations. In science and especially mathematics, multiple
representations offer more avenues with which to connect to students' previous
- 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 learners to
understand and value the intended goals.
- 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)
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 setting.
- Posing problems of emerging relevance to students
A focus on students' interests and using their previous knowledge as a departure point helps
students engage and become motivated to learn. The relevant questions posed to the
students will force them to ponder and question their thoughts and conceptions.
- Structuring learning around primary concepts
This refers to building lessons around main ideas or concepts, instead of exposing students to
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 individual styles,
temperaments, and dispositions" (p. 58).
- Seeking and valuing students' points of view
This principle allows for access to students' reasoning and thinking processes, which in turn allows
teachers to further challenge students in order to make learning meaningful. To
accomplish this, however, the teacher must be willing to listen to students, and to
provide opportunities for this to occur.
- Adapting curriculum to address students' suppositions
"The 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)" (p.72).
- 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; interactions
between both teacher and student, and student and student; and observing students in
Constructivist teachers ...
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.
- Encourage and accept student autonomy and initiative.
- Use raw data and primary sources, along with manipulative, interactive, and physical
- Use cognitive terminology such "classify," "analyze," "predict," and "create" when
- Allow student responses to drive lessons, shift instructional strategies, and alter
- Inquire about students' understandings of concepts before sharing their own
understanding of those concepts.
- Encourage students to engage in dialogue, both with the teacher and with one
- Encourage student inquiry by asking thoughtful, open-ended questions and
encouraging students to ask questions of each other.
- Seek elaboration of students' initial responses.
- Engage students in experiences that might engender contradictions to their initial
hypotheses and then encourage discussion.
- Allow significant wait time after posing questions.
- Provide time for students to construct relationships and create metaphors.
- Nurture students' natural curiosity through frequent use of the learning cycle model.
This digest was funded by the Office of Educational Research and Improvement, U.S.
Department of Education, under contract no. ED-99-CO-0024. Opinions expressed in
this digest do not necessarily reflect the positions or policies of OERI or the U.S.
Department of Education. ERIC Digests are in the public domain and may be freely reproduced.
FOR FURTHER STUDY
The ERIC database is the world's largest education-related, bibliographic database, and
it can be electronically searched online at: http://ericir.syr.edu/Eric/adv_search.shtml.
World Wide Web Resources
To most effectively find relevant items in the ERIC database, it is recommended that
standard indexing terms, called ERIC Descriptors, be used whenever possible to search
the database. The term constructivism is an ERIC descriptors, so this term could be
combined with other Descriptors, such as science education or mathematics education,
in constructing an ERIC search. Such a general search would yield over 140 items.
- Mathematics Education: Constructivism in the Classroom
The Math Forum - http://mathforum.org/mathed/constructivism.html
- Constructivism and the 5Es
Miami Museum of Science - http://www.miamisci.org/ph/lpintro5e.html
- Constructivism Bibliography
Mathematical Association of America - http://www.maa.org/t_and_l/sampler/construct.html
- Essays on Constructivism and Education
Maryland Collaborative for Teacher Preparation - http://www.towson.edu/csme/mctp/Essays.html
Brooks, J.G., & Brooks, M.G. (1999). "In search of understanding: The case for
constructivist classrooms." Alexandria, VA: Association for Supervision and Curriculum
Ernest, P. (1996). Varieties of constructivism: A framework for Comparison. In L.P.
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. In K.
Tobin (Ed.), "The practice of constructivism in science education." Hillsdale, NJ:
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