Complex Thinking

This is Unit Six, on complex thinking: critical and creative thinking, problem solving, and the strategies teachers use to teach them. Unit Five closed on reading one lesson through four theories of learning. Unit Six turns to the most demanding kinds of thinking and how to teach them. Carry one idea through this unit: the kind of thinking a lesson seeks decides the strategy that suits it. At the final entry, the unit weighs teacher-directed against student-centered instruction and shows why good teaching uses both. By the end you will be able to tell divergent from convergent thinking. To apply the IDEAL method to a problem. To sequence a lesson by Hunter's model. To choose a cooperative structure for a goal. And to decide when teacher-directed or student-centered instruction fits.

Seven entries on critical and creative thinking: what each is, how to teach it, and for whom.

Three kinds of complex thinking.

EDP 0501 Three Kinds of Complex Thinking

Classrooms pursue three forms of complex thinking, critical thinking, creative thinking and problem solving, and each suits particular instructional strategies, as judging a source, inventing a design and fixing a broken circuit call on each in turn. Strategies range from teacher-directed to student-initiated, and the right one depends on the thinking sought.

What makes thinking critical.

EDP 0502 Critical Thinking

Critical thinking is skill at analyzing whether information is reliable and valid, plus the disposition to do so: asking key questions, weighing evidence and reasoning logically. Writing questions and comments in a text's margins produced better-reasoned essays than underlining. A critical thinker is astute, not negative, and metacognition is what makes thinking critical.

Infused, or taught on its own.

EDP 0503 Infusion or Free-Standing

Critical thinking can be taught infused into subject lessons, like evaluating historical sources in history class, or in free-standing courses in reasoning, and either works if it is implemented thoroughly and valued by teachers. The real question behind the choice is transfer: whether the skill will carry into other subjects.

Critical thinking for every student.

EDP 0504 Critical Thinking for All Students

Some teachers reserve critical-thinking instruction for high-advantage students, but little evidence supports that, and low-advantage students benefit too, as when a class discusses a personal incident in groups and analyzes it together. The evidence points to teaching critical thinking to every student, whatever their background.

What creativity is.

EDP 0505 Creativity

Creativity is making or doing something new that is also useful or valued, and it is not restricted to geniuses: ordinary students create too, like a student who invents a new way to organize the class library. Novelty alone is not creativity; the product must also be useful or valued by others.

Many answers, or one.

EDP 0506 Divergent and Convergent Thinking

Divergent thinking is open-ended, generating many possibilities, as in how many uses can you find for a cup; convergent thinking is focused reasoning toward a single correct answer, as in solving an equation. Mastering content feeds divergent thinking up to a point, but overemphasizing convergent work can stifle creativity.

Creativity and being judged.

EDP 0507 Creativity and Evaluation

Creativity flourishes when the activity is its own intrinsic reward and the creator is little concerned with how the work will be judged, so low-stakes play with ideas, alongside graded assignments, leaves room for creative risk. Motivation that comes from the activity itself returns in unit seven as intrinsic motivation.

Five entries on problem solving: kinds of problems, procedures and rules of thumb, getting stuck, and the IDEAL method.

Two kinds of problem.

EDP 0508 Well- and Ill-Structured Problems

Problem solving means resolving tasks with obstacles. Well-structured problems supply the information and clear rules, like a textbook word problem; ill-structured problems leave information missing and allow many solutions, like how to raise a school's attendance. Ill-structured problems have no single correct procedure, so defining the problem is part of solving it.

Procedures, and rules of thumb.

EDP 0509 Algorithms and Heuristics

An algorithm is a step-by-step procedure that guarantees a solution to a well-structured problem, like long division; a heuristic is a rule of thumb that often works but guarantees nothing, like start with the easiest part. Heuristics suit ill-structured problems where no algorithm exists, at the cost of occasional wrong turns.

Two ways to get stuck.

EDP 0510 Mental Set and Functional Fixedness

A mental set repeats an approach that worked before even when it no longer works; functional fixedness is one kind, seeing an object only in its usual use, like not seeing that a book could prop open a door. The terms are related, not synonyms: fixedness concerns objects, and mental set concerns approaches.

Strategies for solving.

EDP 0511 Problem-Solving Strategies

Useful strategies include problem analysis, breaking a problem into subproblems; working backward from the goal; and analogical thinking, applying the solution of a similar problem, as a student decodes an unfamiliar word by analogy with one she knows that rhymes. Mental set and functional fixedness are both failures of how a problem is represented.

A five-step method.

EDP 0512 The IDEAL Method

Bransford and Stein's IDEAL method organizes problem solving into five steps. Identify the problem, recognizing that one exists. Define its terms, so the goal and the givens are clear. Explore strategies, from problem analysis and working backward to analogy. Act on a chosen strategy. Look at the effects, and if the problem is not solved, return to an earlier step. When a class's garden keeps dying, students identify the problem, define healthy growth, explore watering, soil and light, act by testing the soil, and look at the results. The steps loop, and skipping the define step invites a strategy that solves the wrong thing.

Six entries on teacher-directed strategies, from advance organizers and notes to mastery learning and Hunter's lesson model.

Who directs the learning.

EDP 0513 Teacher-Directed and Student-Centered Instruction

Instructional strategies vary along two dimensions: how far the teacher directs the learning, from teacher-directed to student-centered, and whether students work individually or in groups. A lecture is teacher-directed and whole-class; independent study is student-centered and individual. The two approaches overlap in practice, and good teaching combines them.

A map before the journey.

EDP 0514 Advance Organizers

An advance organizer, Ausubel's idea, is a brief overview given before new material so students know where to place what follows, as in today we will see three causes of the war, then how each led to the next. Relating new material to prior knowledge and elaborating through questions and examples also help organize learning.

Notes and concept maps.

EDP 0515 Note-Taking and Concept Maps

Organizing strategies include outlining, note-taking and concept maps, such as a map linking photosynthesis to light, water and sugar with labeled arrows. For notes, the quantity recorded matters more than the style, and guides help inexperienced note-takers. Taking one's own notes aids encoding, which is why a teacher may decline to hand out slides.

Mastery for everyone.

EDP 0516 Mastery Learning

Mastery learning expects all students to reach the same high standard, some taking longer: brief instruction, an ungraded check, enrichment for those who pass or tutoring for those who do not, then a second check. It raises questions of fairness between enrichment and remediation, and needs a detailed curriculum broken into modules.

Scripted mastery learning.

EDP 0517 Direct Instruction

Direct instruction is highly scripted mastery learning: objectives stated first, small steps, immediate praise, and frequent review and practice, as a scripted early-reading lesson moves sound by sound with choral responses. It has proved very effective for early reading and arithmetic, the skills it was designed for.

Hunter's lesson model.

EDP 0518 Hunter's Lesson Model

Madeline Hunter's effective teaching model sequences a lesson in five parts. First, an anticipatory set focuses attention and states explicit objectives. Then the new material is presented in an organized, explicit way. Then comes checking for understanding, through responses from every student, choral answers or sampling individuals. Then guided practice, with the teacher close at hand, and finally brief independent practice with feedback. A teacher opens with a puzzle about fractions, presents the rule, has every student show an answer on a card, works problems together, then assigns five on their own. Checking for understanding keeps the rest honest.

Six entries on student-centered and cooperative strategies, ending with the payoff: which approach to choose, and when.

Giving students the initiative.

EDP 0519 Student-Centered Strategies

Student-centered strategies such as independent study and self-reflection give learners more initiative, but both still need a teacher's response to go deep: reflections on prejudice written alone stayed shallow, and teacher responses deepened them. Critics say teacher-directed instruction breeds passivity, yet research supports it when well designed and implemented.

Questions not answered directly.

EDP 0520 Inquiry-Based Learning

In inquiry-based learning, also called discovery learning, questions are posed but not answered directly; students investigate, guided by the teacher and their own interest, as students asked why ice floats design their own tests before hearing the explanation. How much guidance discovery needs is debated, and research on minimally guided instruction is contested.

What makes cooperative learning work.

EDP 0521 Making Cooperative Learning Work

Cooperative learning works when groups have time to work together, are taught collaboration skills, are held accountable as a group and as individuals, and value cooperation; a teacher who names each member's contribution gives every student equal status. Social prejudice can creep into groups, and rich tasks that need diverse skills help every member contribute.

Two ways group grading goes wrong.

EDP 0522 Freeloading and Overspecialization

Grading only the group invites freeloading, where some members let others do the work, as one student writes the report while three coast; grading only individuals invites overspecialization, where each writes one section and understands none of the others. Combining group and individual accountability guards against both problems.

Choosing a cooperative structure.

EDP 0523 Choosing a Cooperative Structure

Several cooperative structures suit different goals. Think-pair-share has students think alone, discuss with a partner, then share with the class, which suits quick checks of understanding. Jigsaw makes each student an expert on one part who teaches it to the group. Student Teams-Achievement Divisions reward teams for each member's improvement on individual quizzes, which guards against freeloading. Project-based learning organizes extended group work around a real problem or product. A class that must learn four causes of a war in one period fits jigsaw: each student masters one cause and teaches it. Think-pair-share takes minutes; project work takes weeks.

The payoff: teacher-directed or student-centered?

EDP 0524 Teacher-Directed or Student-Centered?

Here the unit's idea is decided. The choice between teacher-directed and student-centered instruction depends on what kind of learning is sought, how much organization students need, and how much initiative they can take. Teacher-directed approaches, from advance organizers to mastery learning, direct instruction and Hunter's model, organize information for students, and they have strong evidence for basic skills such as early reading and arithmetic when well designed. Student-centered approaches, from inquiry to independent study and cooperative groups, give students initiative and aim at complex thinking and transfer. Critics of teacher direction say it breeds passivity; critics of minimally guided discovery argue that novices learn less without guidance. Take a unit on electric circuits. A short, well-organized explanation with checks for understanding teaches the vocabulary and the rule; then groups investigate why some bulbs glow dimmer, guided by questions. Each half does work the other does poorly, and good teaching combines them.

Look at what you can now do. You can tell divergent thinking, generating many possibilities, from convergent thinking, reasoning to one answer. You can apply the IDEAL method: identify, define, explore, act and look, looping back when needed. You can sequence a lesson by Hunter's model, with checking for understanding holding the rest together. You can choose a cooperative structure for a goal, from think-pair-share to jigsaw, team achievement divisions and projects. And you can decide when teacher direction or student initiative fits, and why good teaching combines them. Unit Seven turns to motivation.