INQUIRY LEARNING AT THE HIGH SCHOOL LEVEL:  A POSSIBLE ANSWER TO THE DEPTH-COVERAGE TRADE-OFF

Dr. Patrick Leighton, 6/15/00

Inquiry learning of science is strongly advocated by many state science frameworks (for example, the Inquiry Strand in the Massachusetts Curriculum Frameworks for Science and Technology, 1996) and both the National Science Education Standards (National Academy of Sciences, 1996) and the American Association for the Advancement of Science’s national science frameworks, Project 2061  (AAAS, 1993).  Inquiry-based curriculum programs in science, such as INSIGHTS and FOSS, have become well known at the elementary level, with about a dozen elementary or early middle school inquiry-based science programs presently available.  The situation is different at the upper secondary level where only a few inquiry-based programs are widely available, such as ChemCom, Insights in Biology, and Active Physics.  Commercial and non-profit publishers, as well as the National Science Foundation, which funds much of the national curriculum development in science, are increasingly focusing on developing more high school inquiry-based programs, and the next decade will almost certainly see more options become available.

This trend brings up the question of how inquiry learning might differ between the elementary and high school levels.   Given the large changes in students’ cognitive development, not to mention physical and social development, over twelve years of schooling, it might well be that the implementation or appearance of inquiry learning would change as students mature.  An increasing use of the inquiry approach at high schools might also imply changes in classroom practice and the curriculum materials designed to promote inquiry teaching and learning.   This paper discusses two core aspects of inquiry learning that might be distinctly shaped at the high school level.  First, this paper proposes that over the K-12 spectrum hands-on investigation becomes increasingly minds-on, to the point where mental investigations predominate at the high school level. Second, this paper proposes that deep, meaningful, transferable understanding of concepts results primarily from extensive application of the concept AFTER it is has been discovered and comprehended by the student.

HANDS-ON CAN WEAR DIFFERENT GLOVES
Inquiry learning emphasizes the student’s role in actively investigating and manipulating the natural world, yet not all lab or hands-on activity necessarily constitutes inquiry learning.  At one end of a spectrum, hands-on activities can be formulaic, predictable exercises.  Ask students what they are doing, and the answer might well be, “I’m doing Step Six on the lab sheet.”   Hands-on can also consist of investigations that are designed and orchestrated by students even while being guided by the teacher or curriculum materials.  At the other end of the spectrum is what is often called authentic or open inquiry learning.  An authentic or open inquiry investigation or activity often begins by leading students to the type of questions that are to be investigated.  Careful planning and guidance by the teacher helps students establish appropriate hypotheses that will likely lead to the content goal, often with extended discussion that elicits multiple options for the class to investigate.  The teacher anticipates that students, investigating from the basis of different hypotheses, will share different insights garnered from the different approaches.  Different hypotheses can require different background information, and teachers will emphasize the research skills that students need to find, interpret and organize needed content knowledge.  Teachers attempt to form in their students a generic ability to manipulate tools, materials and equipment so that they can design and assemble investigations and measurements for themselves.  Class time is dedicated to choosing and creating appropriate formats for presenting data and observations.  Students are expected to evaluate their own lab technique, the accuracy of their data, and its usefulness for addressing their original hypothesis.  Finally, students are expected to share their results with the rest of the class, and synthesize what the class as a whole learned.  If all goes well, this synthesis constitutes the content that was the initial goal.

THE TRADE-OFF BETWEEN DEPTH AND BREADTH IN THE HIGH SCHOOL CURRICULUM
It seems self-evident that authentic, inquiry-based learning of science would take more time than the lab-a-week approach and much more time than the text-and-test approach.  As a result, high school science teachers often perceive a trade-off between conventional approaches and authentic inquiry in terms of time.  Teachers are increasingly accountable for the considerable content requirements of college entrance and state competency exams.  Such lengthy lists of required topics often produce an emphasis in the classroom on rapid and superficial coverage.  For example, schools in Massachusetts will typically translate the Science and Technology Curriculum Frameworks (1996) into a spiral curriculum for grades and courses, where each standard is introduced, reinforced and mastered at different grade levels.  Some simple arithmetic and generous assumptions (does learning really occur on all 180 school days?) show that, on average, a teacher has three contact hours to dedicate to each topic listed in the grade or course curriculum that s/he is responsible for teaching.   Conventional approaches to curriculum often seem the only logical recourse.  The result is a curriculum that is a mile wide and an inch deep (Elmore, R. 1997).  In contrast, an inquiry approach often sees the coverage challenge as futile.  Quality is preferred over quantity.  Appropriate time, considerably longer than three days, is allocated to chosen topics so that deep or meaningful learning may result.  Inevitably, some topics are dropped.

Many high school teachers are deeply ambivalent about such curricular triage.  It is often difficult for high school teachers to jeopardize their students’ maximum-possible coverage of the required wide-ranging content, regardless of their reservations about the shallowness of student understanding.  Many of the standardized tests upon which they and their students are judged, including high-stakes state competency exams upon which a high school diploma depends, emphasize superficial knowledge of many different topics; the tests primarily measure the width of knowledge, not its depth.  Even if a teacher might feel intuitively, philosophically, or professionally that an emphasis on quantity is not best in the long-term for her students, in the short term the best way for her students to progress on the educational game-board is to do well on tests that emphasize quantity.  Thus inquiry-based programs at the high-school level that come down on the other side of the time trade-off must fight for adoption against content requirements and teacher accountability for their students’ performance on standardized tests.

MENTAL INVESTIGATIONS
Perhaps a closer look at the purpose of authentic inquiry will provide a fresh perspective that could shrink, or even evaporate, the time trade-off at the high school level.  Student-centered investigating and experimenting are actually a means towards an end.  Inquiry is a means of reaching the goal of meaningful understanding of content; call it “minds-on.”   Science is not an encyclopedic collection of information.  It is a way of thinking about and making sense of the natural world.  One profound implication is that investigating can be mental as well as manipulative.  A large part of “thinking” science is carrying out imaginary investigations.  The skill of investigating a question can be an internal one, particularly as students mature and develop intellectually.

High school students can physically carry out investigations, of course.   Or, they can think it through, harking to previous knowledge and carrying out an if-then thought experiment.  Trial-and-error can consist of physically working with objects and phenomena, but it can also consist of playing with a question internally, trying out different conjectures to see how they fit with what is already known.   Students can play with a question mentally, hypothesizing, “collecting” and discussing data from prior related observations, proposing conclusions at a level of generality that fits their level of curiosity, identifying (but not necessarily pursuing) prerequisite knowledge, skills or resources, “testing” insights by seeing how they in turn help to understand familiar past experiences.

Such mental inquiry is necessarily highly social, with students contributing to an often free-wheeling and passionate discussion.  This process is very similar to what might happen in a literature class that is beyond identifying the facts of vocabulary, plot, and character.  Students interpret, analyze, and evaluate a piece of literature intellectually.  They refer to the text, of course, just as in science students refer to concrete, verifiable observations pertaining to their question.  Yet the “minds-on” literature class emphasizes the intellectual processing and application of past knowledge and experience in a highly interactive discussion.  Likewise, inquiry-based science in the high school can be as much an imagined process, a way of knowing or a habit of mind, as a hands-on process.  The goal of one final, correct answer becomes secondary, as it is in the literature class, with the fun and benefit clearly in the consideration of multiple answers (Cardellichio and Field, 1997).  The goal is to foster intellectual fluency, or “the ability to retrieve relevant knowledge in a manner that is relatively ‘effortless’… Instruction that focuses solely on accuracy does not necessarily help students develop fluency” (Bransford et al., 1999, p. 37). 

By high school, students have considerable life experience, whatever its specifics and context.  This experience creates a wealth of background knowledge, forming a kind of internal library that is adequate for “researching” many, if not most, of their questions. When considering a particular question, they have often had enough prior experience with related phenomena that they can reasonably summarize or hypothesize plausible answers or useful insights.  It is as if they had a large internal store of data that they selectively manipulate and analyze in many different ways.   A teacher must guide mental inquiry carefully, particularly to provide opportunities for students to confront some of their pre-conceived notions that might well be less than accurate or useful.  The rapidity and flexibility of mental inquiry, and particularly the conversational sharing among students, can provide many opportunities for students to sort out their mis-conceptions.

There are many caveats.  Mental investigating must be based on previous hands-on experiences and skills that can be re-created in the imagination.   Elementary level students need regular hands-on practice with observation, measurement and experimenting for these skills to eventually become innate and intuitive.  As students climb through the grades, the external activity can become an internal, highly efficient, mental re-creation.  There will be high school students who will not have internalized investigative skills and processes. Neither should mental investigating totally replace actual hands-on experiences. There are many times in high school that lab experiences are needed to focus student observation, particularly on subtle or complex interactions.  An optimum balance between the two is possible.  The mental approach must eventually be harnessed by the reality of objective observations if insights and answers are to be reliable.

This said the time and effort to carry out an actual investigation for most questions, even if necessary equipment and resources were available, comes with a price beyond the necessary class time.  The price is largely extracted from that most valuable of scientific attributes, curiosity.  How does the wind-chill factor affect how easily a car starts?  Why do tall chimneys have better drafts?  Do grapes contain all the good vitamins and minerals that raisins do?  Why does a finger with a serious wound feel so much warmer than the other fingers?  Are Homo sapiens still evolving?  Curiosity is where science begins, and it is a delicate attribute.  Elementary students are abundantly curious, but curiosity seems to have largely evaporated by the time they reach high school.  If inquiry is thought of as hands-on investigating, then its major alternative, when hands-on is not practical, seems to be “finding” answers from either the teacher, textbook, library or Internet (Wheeler, 1997).  Think of the five questions just posed.  Either form of research would be tedious enough to quickly dampen student enthusiasm and curiosity.  Why ask a question if the only ways to answer it are either days in the lab or days in the library?  Rarely are a student’s curiosities so compelling.  Rarely does a student really even want the “full and complete” answer, even if there were such a thing.   Such flexibility in understanding the natural world is common among early elementary children, brimming over in their curiosities: “They will not ask to know the “real” answer, or worry about whether their answers were correct.  Perhaps this is because many of their questions were so complex, and, as they say to each other, ‘scientists don’t even know the real answer for sure.’ It is the asking and the talking that are the focus” (Gallas, 1995, p. 70).  Such a focus can be preserved through the high school years, with the increasing sophistication and coherence derived from life experience and school learning creating ever-increasing verisimilitude.  The discipline of the lab and library generally produces clearer and more reliable conclusions, important for scientific research.  The flexibility and rapidity of mental investigation and knowledge transfer often create more excitement and wide-ranging creativity that reinforce and feed curiosity.  For many questions there are many right answers, depending upon one’s perspective.  What is important educationally is to teach the fluent, skilled application of different perspectives rather than the precision and accuracy of researched information.

WHAT IS SCIENTIFIC LITERACY?
The flexibility and rapidity of mental investigation and knowledge transfer are also practical and useful in everyday life. In other words, they directly build to scientific literacy.  Both of the national (National Academy of Sciences,1996;  American Association for the Advancement of Science, 1993) and many of the state science curriculum framework standards describe the type of learning they are attempting to promote, called scientific literacy.   “Scientific literacy means that a person can ask, find, or determine answers to questions derived from curiosity about everyday experiences.  It means that a person has the ability to describe, explain and predict natural phenomena.  Scientific literacy entails being able to read with understanding articles about science in the popular press and to engage in social conversation about the validity of the conclusions.  Scientific literacy implies that a person can identify scientific issues underlying national and local decisions and express positions that are scientifically and technologically informed” (National Academy of Sciences, 1996, p. 22). Remarkably, this quote from the National Science Education Standards does not mention correctness or “truth” of information.  The underlying, common element among the italicized processes is the ability to transfer knowledge.  A scientifically literate person refers to previous knowledge or experience that is somehow relevant and useful to a question, phenomenon, reading, conversation, or issue, invoking verifiable observations, generating insights, extensions, and judgements.

If knowledge is transferred, the question becomes, What is it that is transferred?  The details and peculiarities of specific experiences are filtered out, and what remains to be transferred is a generic concept that can be applied widely.  Ultimately, scientific literacy is the ability to apply the basic concepts and principles of science to a wide variety of previously unconsidered questions and circumstances in a proactive, self-initiated manner.

Even though the term concept has many less distinct meanings in everyday use, a category of ideas can be defined that does conform to a more rigorous definition based on how effectively they travel.  Those generic ideas that can be extracted from one situation, phenomenon or investigation and transferred to seemingly unrelated contexts are, in a rigorous definition, called concepts (Ausubel 1978, Erickson 1995, 1998, Leighton 1997, Novak 1977).  For example, the concept of energy transformation can be deduced from observations of, say, shooting arrows into a hay bale, and then transferred to, for example, the ocean-atmosphere interaction or photosynthesis.  Students have learned to identify the various forms and grouping of energy that might be contained within any system, so a stretched bow primarily contains elastic energy, radiation contains wave energy, tropical oceans contain considerable thermal energy, and the plant matter contains chemical energy.  Observation and description of any event or change leads to the an analysis of the energy transforming as it flows from entity to entity, greater inputs creating greater outputs: stretching the bow further makes the arrow go faster; a warmer ocean means a warmer atmosphere; increased light makes a plant grow bigger.  Some learning theorists (e.g. Erickson, 1998) distinguish among concepts, principles, and laws, but such distinctions are essentially a way of describing the hierarchical relationships among the members of the

DISCOVERY LEARNING OF CONCEPTS
Discovery learning, often considered a defining characteristic of the inquiry approach, considers how students’ use their existing knowledge to create new knowledge and meaning from experience and through social interaction.  What does it mean for students to discover powerful, key concepts of science?  At the elementary level many of the concepts (e.g. growth, chemical change, phase, interdependence) are more obvious and simple than those found in high school curricula (e.g. inertia, chemical equilibrium, regulation).  So student discovery at the elementary level is often a matter of familiarity with and close observation of common objects or processes.  Many of the inquiry-based, elementary curricula use trial-and-error, playing around, and directed questioning and observation to reveal some of the more elementary concepts of science (e.g. FOSS, Insights).   Once the concept has been uncovered, it is often transparently applicable to many other situations.  For example, once a student has generalized the concept of growth from, say, the pea plants on the windowsill, it is easily transferred to all manner of organisms and even physical phenomena.  The application of the growth concept follows quickly from its discovery.

Yet the concepts that high schools must teach are often complex and subtle.  Application does not necessarily follow discovery.   The ability to use such higher-order concepts for scientific literacy is not always, or even often, produced from having derived, recognized or enunciated it.   Obviously Isaac Newton understood deeply the concept of gravity after having discovered it, but his very personal genius and context of discovery cannot be routinely duplicated in the minds of many students today.  A student may be led through an artificial discovery process, finally enunciating and describing the concept of gravity.  But how well can the student use the concept for scientific literacy, applying it to different contexts, problems and questions.?  Why doesn’t the atmosphere just float away into empty space?  Why is there a high tide on the OPPOSITE side of the Earth from the moon?   How would a satellite orbit a potato-shaped asteroid?  Should ballpoint pens be stored right side up?

When a discovery approach is used for teaching students a concept, they engage in activities and conversation designed to elucidate the pattern of observations or behaviors that is the concept. 
At the end of what is generally called discovery learning students have become conscious of the concept.   They can name, summarize and describe it.  They can give original examples.  They can recognize it in different forms of expression.  In short, they comprehend the concept (Bloom, 1956). If the concept is fairly simple and obvious, students can usually apply it and transfer it to new situations and contexts with relatively little additional effort.  The metaphor of the light bulb turning on is well placed.  Once the bulb is on, the act of seeing is fairly automatic. 

For the complex and subtle concepts that form the grist of high school science the process of discovery itself might well not carry over quickly to the higher-thinking literacy described in the national standards.  The ability to transfer the concept to unfamiliar and novel situations, contexts and phenomena does not automatically follow from its comprehension.   Students must practice applying the concept to a wide variety of questions and situations before it can become part of the warp and woof of their critical thinking and problem solving.  Such wide-ranging practice provides opportunities for students to reconcile the new perspective with past understandings.  They experience the range, limits and benefits of their new intellectual tool.  Eventually the concept is cognitively assimilated and becomes a new, comfortable habit of mind.

THE LEARNING CYCLE
Discovery learning implemented in a curriculum program often follows a pattern called a (discovery) learning cycle.  Most of the inquiry-based curriculum programs presently available incorporate or emphasize that instruction should follow such a learning cycle.  Different curriculum programs have different versions, such as ExplorationàConcept DevelopmentàApplication (Comprehensive Conceptual Curriculum for Physics) or EngageàExploreàExplainàElaborateàEvaluate (BSCS Middle School), or Focusà Exploreà Reflectà Apply (Science and Technology for [elementary level] Children).  The original learning cycle was developed by Robert Karplus (Atkins and Karplus, 1962; Karplus, 1977) in the 1960’s as part of the Science Curriculum Improvement Study that produced the elementary-level, inquiry-based curriculum generally referred to as SCIS.  Virtually all of the present incarnations of the learning cycle, including the above examples, mimic Karplus’ original, three-stage pattern (Beisenherz and Dantonio, 1996).  In short, during the first stage, students are guided to explore their prior knowledge and new experiences in order to direct them towards the desired content, often a concept.  In the second stage the concept becomes explicit and comprehended.  The third stage consists of applying the concept to new situations to produce a robust habit of mind.

THE LEARNING CYCLE AT THE HIGH SCHOOL LEVEL
Obvious, simple concepts can be derived from direct observations of the natural world, so much of stage one in elementary curricula emphasize interactive experiences with students’ environment.  The subtle, complex concepts of high school, sometimes referred to as super-ordinate or higher-order concepts, are mostly derived from combinations of the simpler, more fundamental concepts.  Indeed, these higher-order concepts are largely defined by their relationships to subordinate concepts (e.g. the concept of force field is built from subordinate concepts of property, force, interaction, direction and measurement, each of which is itself built from other, even more subordinate concepts).  Thus at the high school level the first stage of the classical learning cycle often consists of re-examining prior knowledge and drawing connections among pre-requisite concepts.   This new experience and perspective births a unitary, coherent idea that has its own identity and unique intellectual usefulness, constituting the second stage of the learning cycle.  Students explain or enunciate what they have learned.  At the end of this second stage students recognize, summarize and give examples of the concept.  They explain how the introductory experiences of the first stage can be understood in terms of the concept.

Once high school students comprehend a concept, they then move on to the third stage of the learning cycle.  They practice extensively with applying the concept to a wide variety of different situations and contexts.  The third stage of the learning cycle is critically important at the high school level.  The real discovery of a complex, subtle concept occurs AFTER it has become explicit. There is only a weak relationship between how students arrive at the explicit comprehension of a higher-order concept (i.e. stage one) and the difficulty they will experience in the third-stage practice required to apply and transfer it effectively (Ausubel 1978, p. 24-29).

Deep understanding of a concept results from the practice of applying it widely to many different topics and contexts.  Students learn to transfer knowledge by identifying the part that is transferable and then practicing its transfer.  Each different topic, context or phenomenon to which it is applied provides another insight into the concept’s range, limits, power, and relationship to previous understandings.   These topics and contexts can become increasingly different from those that were used during the first stage of the learning cycle, when the purpose was to elicit, form, and illustrate the concept.  As students range further a-field in their applications, they become increasingly adept at transferring the concept.  Meaning comes from applying what is already known to what is new.  The already-known becomes richer and stronger; the new becomes transparent and comfortable.  At the beginning of the third stage, many of the activities and exercises will be teacher directed, perhaps applying the concept to topics that are required by state curriculum frameworks or college entrance exams.  By the end of stage three students should be directing their own inquiry, either mental or hands-on investigating, wherein they are using the concept to pursue a mixture of required topics and their own curiosities.  They are able to orchestrate the concept they are learning with previously learned concepts, forming and strengthening the connections among concepts and back-loading ever-deeper understanding and elaboration of previously learned concepts.  The concept(s) become the intellectual vehicles with which students may travel deeply into a wide variety of different contexts and topics.  Students can delve into topics far more deeply and far more quickly than most teachers hope for.  Using concepts as intellectual vehicles, the topics required by most state curriculum frameworks can be (un)covered, more or less, in about half of a course’s time, leaving the other half for deeply exploring the interests and preferences of the students, teacher, school or community.

The purpose of stage three is to build and augment a web of generic concepts within the student’s intellect.  Such a conceptual structure is useful for addressing and progressing on any manner of questions, whether they deal with people, planets, parasites, protons, or potatoes.  It is this third-stage practice using the concept that produces long-lasting, meaningful, and practical understanding.  As a matter of fact, it is precisely the ability to use the basic concepts of science to carry out such flexible, inquiry-based problem solving and critical thinking that is the evidence of deep understanding and the definition of scientific literacy.

A RESOLUTION TO THE DEPTH-BREADTH TRADE-OFF
Inquiry at the high school level has been differentiated from what it commonly looks like at the elementary level with two contentions:  mental investigation is often as viable as hands-on experiences, and  deep, transferable knowledge of the types of concepts encountered at the high school level is especially dependent upon practice with applying concepts to a wide variety of situations and contexts.  These two contentions have become closely interwoven, even suggesting a possible resolution of the time trade-off of quality versus quantity that has impeded the adoption of inquiry methods by many high school teachers. 

High school students generally have deep and wide knowledge bases derived from their personal and well as educational experiences.  They characteristically have the neurological maturity and agility to manipulate their internal “databases” to create new connections, perspectives, and organizational schemes.  Students’ prior conceptual knowledge becomes the “soil” from which new, more subtle, complex concepts sprout.  Indeed, a new concept is largely defined by its connections to these other concepts.  During the first stage of a learning cycle a high school teacher can often plant and germinate subtle, complex concepts more effectively than student inspiration, serendipity, trial-and-error, or historical re-creation.  At the high school level, a well constructed lecture, Socratic questioning, demonstrations, student discussion and even theatre can be effective strategies for moving students quickly to the third stage of a learning cycle, where precious classroom time can then be concentrated  (Bransford et al, 1999, p. 11).  A careful combination of both hands-on and mental investigating during stage three of a learning cycle can produce deep, meaningful learning that ranges across the many topics on the lengthy lists imposed by state curriculum frameworks and college entrance requirements.  The concepts become an efficient “chunking” mechanism to organize these lists according to how people learn intellectually (Bransford et al., 1999).  Students see the conceptual connections among the disparate topics and are able to quickly transfer learning from one to the other.  The web of concepts provides the learning efficiency, retention and recall needed to accomplish BOTH deep and wide learning.  Once the required content has been understood, students discover the fun, power, and deep satisfaction of using concepts, in concert with their previous knowledge, to literally play with their own curiosities, regardless of what their interests may happen to be.

CONCLUSION
Many of the popular conventional high school curriculum materials organize and present content in a manner that is less that conducive for the kind of mental inquiry described in this paper.  The hope is that many of the high school inquiry programs that are now beginning to be developed will have the opposite effect, encouraging and facilitating mental inquiry.   These new programs will need to focus clearly on the goal of literacy for all as exemplified by the ability to transfer knowledge.  A broad outline of how these impending high school materials might organize and present content can be derived from the nature of mental investigating and discovery learning that has been discussed.  For example, identifying, defining and organizing concepts according to their “ease of transfer” will be a central task, particularly since it has to be based on what we know of the development of children.   But these next subjects must be left to another day.

 

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