Guiding Inquiry to Adjust the Difficulty: During a process of guided inquiry leading to discovery learning, the level of difficulty — when we ask “how easily can students form a bridge from not-knowing to knowing?” — depends on the intrinsic difficulty of understanding a particular set of concepts (so each topic for inquiry should be chosen carefully) plus the guidance that increases students' ability to cope with an inquiry-challenge by helping them prepare before it, and coaching them during it. In coaching, a teacher (*) observes students while they work, and then does all (or none) of these — ask questions, answer questions, give clues, direct attention to useful information from past experiences or the current situation — to provide
guidance that will help students think productively and continue making progress toward solving the inquiry-mystery. Teachers can also coach afterward, by encouraging students to reflect on their experiences.
* Or coaching can be done by students. A common way to adjust difficulty (and stimulate educationally useful interactions) is by asking students to work in groups, where they naturally tend to coach each other, especially if this is encouraged by the teacher who explains how they can coach in productive ways.
Very few educators propose that teachers should frequently use pure discovery, in which "the student receives representative problems to solve with minimal teacher guidance. (Mayer, 2003)" Here are the main difficulties with pure discovery: for all students, pure discovery learning takes longer than with guidance; if discovery is to occur, the problems must be relatively easy; in a typical classroom, if a discovery is reasonably challenging for some students, other students will never discover a solution (or concept) without guidance.
For a variety of pedagogical reasons, almost all proponents of discovery learning propose guided discovery in which the teacher provides problems along with "hints and directions about how to solve the problem, to keep the student on track (Mayer, 2003)." For example,
• Scaffolding and Achievement in Problem-Based and Inquiry Learning by Cindy Hmelo-Silver, Ravit Golan Duncan, and Clark Chinn. This article is a pro-inquiry response to a criticism of “pure discovery” teaching in a journal. It examines the evidence, and explains why we should distinguish between various types of instruction (discovery, experiential, problem-based, inquiry) inspired by constructivism, because "problem-based learning and inquiry learning are not minimally guided instructional approaches but rather provide extensive scaffolding and guidance to facilitate student learning." They describe the types of scaffolding that are used, and suggest asking, "under what circumstances do these guided inquiry approaches work, what are the kinds of outcomes for which they are effective, what kinds of valued practices do they promote, and what kinds of support and scaffolding are needed for different populations and learning goals?"
• Scaffolded Inquiry by Karen Ostlund, with scaffolding gradually removed for the purpose of guiding students along a Continuum of Inquiry (from Directed Inquiry to Guided Inquiry to Full Inquiry) with descriptions of each stage, and tables to show differences in the types and amounts of scaffolding guidance by a teacher.
A Continuous Spectrum from Clear Explanation to Pure Discovery
Instruction spans a wide spectrum, ranging from clear explanation through moderate ambiguity (due to unclear explanation or intentional guided discovery) to pure discovery.
Even when totally clear explanation is the goal, this will not be achieved because “clarity is in the mind of the beholder” and some beholders will understand more accurately-and-thoroughly than others.
And even in the pure discovery described above [in the full page], students have guidance by getting "representative problems" and having the level of difficulty chosen by the teacher; in a sequence of problems with gradually increasing difficulty, there will be even more guidance.
Here are some techniques (from Collins, Brown & Newman, 1987) to guide inquiry in Cognitive Apprenticeship:
Modeling involves an expert's carrying out a task so that students can observe and build a conceptual model of the processes that are required to accomplish the task. In cognitive domains, this requires the externalization of usually internal (cognitive) processes and activities — specifically, the heuristics and control processes by which experts make use of basic conceptual and procedural knowledge.
Coaching consists of observing students while they carry out a task and offering hints, scaffolding, feedback, modeling, reminders, and new tasks aimed at bringing their performance closer to expert performance. Coaching may serve to direct students' attention to a previously unnoticed aspect of the task or simply to remind the student of some aspect of the task that is known but has been temporarily overlooked.
Scaffolding refers to the supports the teacher provides to help the student carry out a task. These supports can either take the forms of suggestions or help.
Articulation includes any method of getting students to articulate their knowledge, reasoning, or problem-solving processes in a domain.
Reflection enables students to compare their own problem-solving processes with those of an expert, another student, and ultimately, an internal cognitive model of expertise. Reflection is enhanced by the use of various techniques for reproducing or 'replaying' the performances of both expert and novice for comparison.
Exploration involves pushing students into a mode of problem solving on their own.
An Example of Computer-Adjusted Guiding: A computer program can be designed to adjust a problem's level of difficulty based on the quality of student responses. If a student’s answers for one problem are correct, the next problem is adjusted to a higher level of difficulty. If the answers now become less correct, the program provides guidance (in questions, comments, clues) to help the student cope with the challenge. This program is simulating a teacher, trying to imitate the guidance adjustments that would be made by a skillful teacher.
An Example of Student-Adjusted Guiding
Or a program can let each student decide how much guiding they want, and when. For example, a problem might have 3 levels of clues — labeled in a count-down (3, 2, 1) to the answer being revealed at “0” — with the clues at Levels 3, 2, and 1 offering increasing amounts of guidance, making it easier to construct a solution. A student works for awhile and then (if it's necessary, if they cannot solve the problem and don’t think they are making satisfactory progress) they can ask for the clue at Level 3, and then (if necessary) at Level 2, and then (if necessary) at Level 1. The program provides a clearly explained Answer (at “Level 0”) whenever a student solves the problem, or gives up after receiving all 3 clues. If a submitted solution is incorrect, the program can just say “this is wrong” or it could say “that was a nice try, but...” and provide an explanation for why it was wrong, and (perhaps) guidance about what to do next.
This process can be repeated for a second problem with a level of difficulty that is adjusted depending on success (did they solve the problem?) and guiding (did they request 0, 1, 2, or 3 clues?). If a student solved Problem #1 with no clues, #2 will be more difficult. But #2 will be easier if they failed to solve #1 even after using all 3 clues. Or the program could let each student choose the level of difficulty for Problem #2.
The process can be repeated for Problem #3, and #4,... until a student decides to stop working the problems.
Questions about Guidance, Motivation, and Metacognition
The computer programs described above raise questions about the process of teaching. With the Student-Adjusted Guiding, do you think it's better if students can solve problems by themselves, without using clues? Most teachers (perhaps all) will say “yes”, but there will be disagreements about timing. Is it best if students refuse to accept any clues, even when they don't seem to be making progress? Or is it better if initially (in Problem #1, #2,...) they learn from the explanations in clues and answers, then in later problems they begin to solve problems independently?
To what extent will their struggles without clues — shall we call this “clueless struggling?” :<) — help them improve their skills in “learning how to learn” and their long-term abilities for self-education? But if there is too much struggling and not enough solving, will this cause some students to become discouraged? These questions — about "an appropriate level of difficulty" and the value of struggle that leads to discovery — are important, and there are no simple answers that don't oversimplify in an unsatisfactory way.
Or, approaching these questions from another perspective, if the computer problems are graded would you give more points to students who solve problems without receiving clues, by subtracting points for every clue that is requested? If yes, would you begin this grading policy with Problem 1? or later?
A student's decision to request a clue now, or to wait and continue thinking without it for awhile, is a metacognitive strategy decision. How would you motivate students to be more patient, to work longer with minimal guidance before they request the next clue? Would you tell them that their patience will be rewarded with greater satisfaction? {This is usually true, and I think students know this intuitively.} By explaining the research-evidence showing that their learning will have higher quality if it's the result of their own discovery? {But I don't think this evidence exists in equal-time comparisons, which is one of the controversies about discovery learning.} Or in other ways?