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Dimensions of Inquiry
By Arthur H. Camins
Elementary Mathematics and Science Coordinator
Hudson Public Schools, Hudson, Massachusetts
Over the last two years I have been deeply embroiled in a
struggle over the content of the Massachusetts Mathematics
and Science and Technology/Engineering Curriculum Frameworks.
Much of the debate has centered on the role of inquiry in
mathematics and science instruction.
Two things have become clear to me. First, although many people
are using the term inquiry, we don’t all mean the same
thing. Second, people bring different values about the goals
of education to the discussion. Clarifying what we mean by
inquiry and its role in what we value about learning is essential
if we are to shed any light on what should be happening in
classrooms.
Although much of the recent discussions about improving mathematics
and science education has revolved around the term "inquiry,"
there is still a great deal of confusion about what it means.
A point of agreement is that all inquiry involves asking questions
and framing explanations. Over the years, I have witnessed
more than a few discussions that evaluated science curriculum
and instruction based on the degree to which they were perceived
as being inquiry-based. These discussions turned on the extent
to which questions and investigative methods were generated
by students or teachers.
This is not a trivial question, but it glosses over a number
of prior questions which, if explored thoughtfully, could
provide useful direction to teachers. A good place to start,
I think, is to ask the following questions.
What do we know about the process by which people learn?
How do scientists and mathematicians go about asking and answering
questions or solving problems? What are the skills that people
need to engage in scientific inquiry and mathematical reasoning?
What habits of mind support these modes of thinking? What
pedagogical strategies support these notions of learning and
thinking?
However, before we can sort out these dimensions of inquiry,
we need to set aside two ideas that tend to confuse the discussion.
The first such notion is that there can be "pure inquiry."
In designing instructional experiences, we need to make decisions
about the relative degrees of students’ self-direction
and teacher direction in relation to nature of the particular
subject matter, levels of student cognitive development, and
available time and resources.
Second, we need to be clear that although the urge to inquire
is a fundamental human trait, we are always inquiring about
something. We want students to learn how to inquire, so that
they develop more nuanced understandings about the world that
are grounded in reason and evidence.
Teacher professional development should help bring some clarity
to these questions in order to guide what happens in classrooms.
Unless teachers develop some passion for why inquiry is important,
not much will change. Teachers need to engage in inquiry themselves
and then reflect on the question of inquiry and how to implement
the practice in their classrooms.
There are a number of implicit values that are the foundation
upon which to build our work. I place a high value on scientific
thinking and mathematical reasoning as a way to make sense
of both the physical and social realms. This is related to
the notion that reason and logic, systematic testing and altering
of explanations in the light of evidence, and openness to
peer critique are superior to simple intuition or prejudice
as a way of knowing.
| As educators we are
faced with the challenge of preparing students to live
in a world that we cannot yet imagine.
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As educators we are faced with the challenge
of preparing students to live in a world that we cannot
yet imagine. This implies that learning how to learn and
how to make sense of and interpret information in the
natural and social spheres is our most important challenge.
Since knowledge and understanding inform the questions
we are able to ask, we also want children to gain as much
conceptual knowledge as is reasonable and age appropriate.
I also believe that the only chance we have of addressing
issues of inequality, poverty, prejudice, and environmental
degradation is for students to internalize the habits
of mind and skills associated with inquiry. They need
to learn how to utilize them to make sense of and interpret
information and to make decisions. If, as educators, we
can do this in a context that places value on respect
and dignity for all people, we will have done our jobs. |
What are the characteristics of inquiry?
I propose that we need to think of inquiry as having five distinct,
yet interdependent, dimensions.
- As a description of the cognitive processes by which
people make sense of patterns and relationships in
the natural and social world. This is a biologically-determined,
but socially-mediated process. That is, it is based
on how the brain works and how people interact with
one another in the social world.
- As the processes of investigation, problem solving,
and verification that are the essential core of mathematics
and science.
- As a set of skills or abilities that we want students
to develop in order to be effective thinkers and problem
solvers.
- As a description of the "habits of mind,"
attitudes, and behaviors related to learning and knowledge
that we value. Many of these are part of the ways
of thinking and problem solving that are part of the
enterprises of natural science, mathematics, and social
science.
- As a description of the instructional practices
that build upon the four categories above.
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The significance of these distinctions can be clarified by a
simple example. Measurement is an essential aspect of mathematics
and science. We can teach students how to use a graduated cylinder
to measure volume in a step-by-step fashion. However, unless
our teaching is informed by an understanding of how children
develop images of three-dimensional space and notions of standard
unit or how they come to understand measurement as an iterative
process, they will soon forget the skill. Unless students understand
the process of inquiry they cannot make judgment about when
it is appropriate to measure or how to use measurement as part
of a logical explanation. Finally, unless they develop not only
the skills to measure with precision and accuracy, but value
it as well, our teaching will ultimately prove useless. Teachers
will need to develop different strategies to address skills,
processes, and habits of mind.
What do we know about how people learn?
Inquiry Builds Upon Innate Cognitive Processes
Learning is an active process in which people identify new patterns
and relationships in the natural and social worlds. The ability
to decipher patterns grows out of innate human cognitive capacities,
and it develops in a fairly predictable order. These biologically-based
capacities need nurturing and a rich experiential base in order
to develop full expression in thought and behavior. Effective
teaching for particular educational goals makes full use of
and exercises these cognitive capacities through planned, developmental,
structured instructional experiences. It builds upon children’s
questions and natural curiosity, as well as seizes upon teachable
moments and opportunities for independent learning. These cognitive
capacities are the substructure upon which all thinking, attitudes,
and behavior are constructed. For the purposes of understanding,
organizing, and responding to teaching and learning experiences,
the following fundamental cognitive processes can be considered.
- Observing
Children observe the world through their senses, including
looking, touching, tasting, smelling, and listening.
- Communicating
Humans are by nature social animals with the unique
ability to communicate through invented language and
symbols. The development of knowledge, skills, and
understanding is, therefore, inextricably linked to
social interaction and communication.
- Comparing
This process builds upon observations and deals with
similarities and differences in both qualities and
quantities and between the known and the unknown.
Frequently comparing objects leads to finer observation.
- Organizing
Human brains have the capacity to bring order to observations
and comparisons by "putting objects or phenomenon
together on the basis of a logical rationale,"
including seriating, sequencing, grouping, and classifying.
- Relating
Seeing relationships involves under-standing interactions,
dependencies, and cause-and-effect.
- Inferring
This process involves our ability to draw logical
conclusions from events, phenomenon, or ideas that
may be remote in time and place based on orderly reasoning
from evidence or premises.
- Applying
This is the process by which humans bring all other
processes together to tie knowledge, relationships,
and inferences together into a comprehensive framework
or theory or to apply these in a new or novel situation.
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An awareness of these cognitive capacities and their developmental
trajectory should guide instructional design and questioning
strategies.
Inquiry Builds Upon Prior Knowledge
Current research indicates that children arrive in school with
fairly well-developed mental schema, ideas, and values about
how the natural and social world works. Conceptions are formed
through the construction of complex webs of interconnections
among neurons in the brain. These ideas or conceptions serve
as filters, constraints, and springboards for all school-based
learning. Research has demonstrated how resilient and powerful
these conceptions can be. Learners will often hold onto preconceptions
or intuitive ideas even in the light of new evidence or teaching.
There are two implications for acquiring new knowledge. First,
we know that new information is interpreted through existing
mental schema. Second, we know that contradictory or discrepant
information only alters existing schema when those contradictions
are realized and resolved on a conscious level (reflection).
People often hold simultaneous but contradictory conceptions;
however, the ideas with the more "hard-wired" interconnections
are most often used to interpret new information. Third, although
knowledge consists of constructions in an individual brain,
the process by which information is processed is socially mediated.
Therefore the social context for learning exerts powerful influence
on what is learned and how learning takes place.
How do scientists and mathematicians go about asking and
answering questions or solving problems?
Inquiry Models the Processes Used by Scientists and Mathematicians
Over the course of conscious human existence we have generated
an enormous body of knowledge that has sought to bring some
order to the natural world. Essentially, this order-seeking
is a uniquely human endeavor in which we look for patterns to
make sense of the world around us. The formal enterprises of
mathematics and science have developed systems of reasoning
and logic, rules of evidence, and means of verification and
revision. Our educational goal is for students to learn, practice,
and adopt these modes of investigation in their everyday existence.
- Questions and Conjectures
Scientists and mathematicians ask questions and make
conjectures that are answerable based on evidence.
(This is distinct from questions that can only be
answered based on personal feelings or faith.)
- Observation and Tools
Scientists and mathematicians use technology to extend
their senses, manipulate data, and to improve the
accuracy of observations.
- Evidence and Explanation
Scientists and mathematicians develop explanations
using observations (evidence) and what they already
know about the world.
- Reasoning and Proof
Scientists and mathematicians offer explanations and
proofs that are based on reasoning that is logically
consistent.
- Communication and Critique
Scientists and mathematicians make their explanations
public so that investigations are subject to replication
and verification.
- Revision and Change
Scientists and mathematicians consider alternate explanations
and revise their explanations in the light of new
evidence.
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Inquiry is Enriched by Rich Conceptual Knowledge
In discussions about learning, inquiry is often discussed as
a separate entity from content knowledge. However, research
that compares how novices and experts in particular disciplines
approach solving problems has highlighted the importance of
conceptual understanding in framing how individuals make observations
and incorporate those observations into new understandings.
Experts notice more features and nuances of a phenomenon or
situation than novices do. Their conceptual under-standings
make it possible for them to make connections among what may
seem like disparate phenomenon to novices.
In addition, experts monitor their own learning (meta cognition)
so that they can check for what they may not know or what requires
additional information. Being an expert is not innate. Novices
can learn to be experts. Being an expert in one field does not
imply expertise in another. An expert in microbiology may behave
as a novice in another area of inquiry such as astrophysics
or piano playing. However, experts’ habit of first seeking
to develop an understanding of a problem and search for patterns
tends to differentiate them from novices whose knowledge tends
not to be organized around big ideas. Inquiry, therefore, is
contextualized within specific areas of knowledge.
What are the skills that people need to engage in scientific
inquiry and mathematical reasoning?
Scientific Inquiry Skills
Our natural abilities are quite distinct from the extent to
which we exercise them. Being physically able to throw a baseball
is rather different from throwing a strike, much less throwing
strikes consistently. Being able to observe and see patterns
does not mean that we have the repertoire of experience and
practice to do so with care, refinement, or routine. There are,
therefore, skills that must be practiced in order to become
an effective learner. From an instructional point of view, it
is not only critical to be aware of the cognitive process available
to children, but also to organize engaging experiences for students
to practice these skills in a variety of meaningful and engaging
contexts. Below is a non-exhaustive list of some of these processes
drawn from science education, but which have application to
other subject areas.
- Identifying questions that can be answered through
scientific investigations;
- Systematic, careful, or refined observing;
- Sorting on the basis of single or multiple properties;
- Communicating through written expression (pictures,
words, sentences, paragraphs, reports, etc.);
- Graphing (concrete, pictographs, histograms, bar,
pie, Cartesian, etc.);
- Constructing and using data tables and charts;
- Measuring with a variety of tools and units;
- Using various types of scales (temperature, hardness,
etc.);
- Identifying variables;
- Predicting;
- Using the tools of scientific investigation to gather
data and extend the senses;
- Interpreting and organizing data;
- Designing and conducting scientific investigations;
- Making predictions on the basis of evidence;
- Constructing logical arguments on the basis of evidence;
- Locating information from a variety of sources;
- Working effectively as a team member; and
- Following directions.
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What habits of mind support scientific and mathematical
modes of thinking?
Habits of Mind
Research indicates that direct teaching of science process skills
or mathematical procedures without conceptual under-standing
does not result in effective learning. However, even if children
are taught to apply the methodologies of scientific and mathematical
inquiry in a school context, they may not ultimately assimilate
these ways of thinking, problem solving, or verifying into more
generalized thinking and attitudinal patterns. Neither our biologically
determined capacities nor the socially mediated skills needed
to exercise them necessarily mean that students will, in fact,
think or behave, for example, as a scientist or mathematician.
For students to be effective problem solvers or critical thinkers
they need to adopt and assimilate the values, attitudes, and
ways of thinking associated with the scientific inquiry and
mathematical investigation. This requires instructional direction
and focus. Most importantly, it means that students need regular
opportunities to apply these skills and process in personally
meaningful contexts. Listed below are some of these "habits
of mind."
- Curiosity: A willingness to ask questions
about the natural or social world; wonder;
- Open-mindedness: A willingness to change
ideas in the face of new contradictory evidence; valuing
both skepticism and theory; valuing and practicing
collaboration with others in the process of experimentation
and the creation of knowledge;
- Respect for Evidence: A desire for accuracy
and precision in observation and measurement; valuing
and practicing the use of data, evidence, and reason
in the construction of explanations; valuing and practicing
accuracy and precision in explanation;
- Persistence: A willingness to persist and
take risks to find answers and ask new questions in
the face of ambiguity, challenge, and contradictory
evidence; and
- A sense of stewardship and care: A sense
of responsibility for the well-being of others and
the environment.
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What pedagogical strategies support these notions of learning
and thinking?
Effective teaching based on inquiry in all the facets discussed
above is not simple or easy. It requires deep conceptual knowledge
on the part of teachers who have access to high quality curriculum
materials that are thoughtfully developed across at least a
K–12 continuum. It requires subject specific knowledge
about how particular conceptions typically develop, as well
as what confusions may arise. It requires a great deal of continual
planning and constant assessment and reframing of instruction.
It requires a supportive social context for students and teachers.
It requires ongoing, honest collaboration among teachers, administrators,
and parents. It requires time!
We can note some general features of inquiry-based teaching.
Inquiry-Based Teaching
- Focuses on learning with understanding.
- Is rooted in students’ knowledge.
- Is guided by student curiosity and questions.
- Engages students in active learning.
- Identifies, builds upon, and, when necessary, consciously
challenges students’ existing ideas and preconceptions.
- Provides opportunities for learning that build upon
students’ interests, questions, curiosity, and
existing knowledge.
- Engages students in self-conscious sense making,
self-assessment, and reflection.
- Engages students in applying knowledge, skills,
and understanding.
- Engages students in learning activities that require
collaboration in order to reach and verify conclusions.
- Engages students in critical questioning.
- Engages students in using evidence to reach and
verify conclusions.
- Engages students in communicating tentative thinking,
as well as ideas about which they are more confident.
- Self-consciously establishes goals in the areas
of significant content knowledge, skills of inquiry,
and modes of thinking and behaving consistent with
inquiry.
- Creates a positive social context that supports
inquiry.
- Uses ongoing assessment to improve instruction and
meet the diverse needs of children.
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Why should we care about inquiry?
Finally, inquiry-based teaching is rooted in a belief that inquiry
matters in children’s lives and in our own. One of my most
vivid enduring memories as a child recalls a bus ride home subsequent
to the arrest of Adolph Eichmann for his role in the extermination
of Jews in Nazi concentration camps. Although I was only about
7 or 8 years old, I was keenly aware of the events as well as
my minority status in my community. I don’t quite remember
the context that prompted the conversation, but I heard one
of my classmates, sitting behind me on the bus say, "He
should have killed six million more." Two things stand
out for me in this memory. The first, is that I did not yet
have the courage to speak up. I regret this even to this day.
Second, is the deeply troubling recurrence of unexamined prejudices.
For me, inquiry is about helping to build a community of inquirers
in which speaking up is not only safe, but encouraged and where
attitudes, values, and beliefs are able to be challenged in
the light of evidence. Each of us will have to find our own
set of motivations, but I believe that our efforts need to be
driven by a passion for personal and social values.
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for Elementary Science, Lawrence Lowery, ed.,
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