Let's start with a paradox: Teachers should know their subject matter thoroughly, but it is impossible for one person to know any subject completely. Teachers are always traveling toward complete knowledge but never arriving. Of course, every person follows the same road, whether he notices or not. It's a good road to travel though, always fresh and challenging. Every day we can stretch again to reach a noble goal.

We meet people with vast stores of knowledge: computer technicians, doctors, financial planners, mortgage bankers, housing inspectors, auto mechanics. Some speak in a jargon so dense we struggle to grasp a fraction of what they say.

Why don't they make their knowledge comprehensible and usable? Maybe they don't know how. If my accountant said, "Here are 11 things to know about quarterly tax returns," my stomach would knot. To do 11 things, I need a checklist and time to comprehend each item. However, if he told me to do two things so that he could do the rest, I could confidently take appropriate action.

Communicating with the uninformed requires sorting key facts from less important details. The accountant above knew that two factors were absolutely critical, so he asked me to take action on these two only. From experience he knows that other factors are of second-tier importance. Factors that are central to basic understanding are called critical attributes. Wise experts concentrate on those things first.

Some experts choose words and examples so memorable that we can recall their words and concepts later. When we meet these jewels, we rave about the experience because it's unusual. Its rarity hints at how difficult it is to know and impart complex knowledge well.

Many issues are complex. It is difficult, using linear speech, to capture the multifaceted relationships within any given subject. We need to simplify to build understanding, yet we must also "re-complexify" the same subjects as our knowledge grows, or we remain partially ignorant. Consider a toddler learning about the kitchen stove. Although his mother warns him away, he touches it anyway, learning that hot stoves are dangerous. He has a simplistic understanding: Stove-hot-danger-stay away. Later in life he needs to know more. As he matures, he will "re-complexify" the original knowledge: A stove may be hot and might burn me (bad), but the heat can be used to cook food (good), so follow safety procedures around stoves (balanced).

Knowing exists on many levels, and understanding deepens as people gather more information over a lifetime. Communication skills influence how well people convey what they know. Every subject-matter teacher needs excellent writing and speaking skills, but even teachers may have learning difficulties or communication barriers. A teacher with dyslexia, for instance, may teach well, yet spell poorly on the board. In such cases, he must find coping skills to compensate for his limitation. As a teacher deepens his knowledge and develops his communication skills, he will teach facts differently.

The Unaware Teacher

Everyone is unaware of something—cheesecake recipes, quantum physics, properties of tanzanite. When the photocopy process was first developed, businesses were unaware of its useful value; the inventor leased machines to offices to create awareness. With hindsight the value seems clear, yet we surely remain blind to certain things that will someday be obvious.

The unaware teacher knows the subject and organizational methods incompletely

Novices begin with much to learn. Although they have completed the education department's coursework (or earned the HVAC certificate, MD, or BA), they are still wet behind the ears because there are thousands of facts and nuances that can be mastered only through experience. Incomplete knowledge is the normal state of the beginner.

Beginning teachers must study and then attempt to effectively organize the material. Their first efforts are often clumsy. They need to forgive themselves for not being perfectly prepared. We have learner's permits for young drivers, internships for doctors-in-training, and probationary periods for most new hires. No newcomer is as knowledgeable as a 20-year veteran in the same field. New doctors, consultants, and foremen all struggle to master details. With steady effort, teachers know more every year and present it better.

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For a quick introduction to the main ideas of a subject—butterflies, nutrition, Mayan math—look at children's nonfiction. Authors distill and simplify information for young readers, offering a brief, accurate overview we can appropriate.

Limited knowledge of the subject matter triggers anxiety. Beginners lament, "I never studied this in college." Neither the beginners nor the college failed. The body of knowledge in every subject is so deep and so wide that no matter what beginners have studied, it never matches what they need for all teaching assignments. Colleges offer a broad education, but in-depth mastery is a lifelong task.

Ms. Shinozaki, a preservice teacher who majored in history in college, offers an example. When she taught U.S. history for the first time, she read each section in the student textbook several times. She looked up additional information on the Internet and assembled lesson plans for hours, and she still made occasional factual errors. She couldn't predict what her students already knew or how to connect their knowledge to the new information; these skills develop through experience and experimentation. Provided she taught the course again and continued her efforts to grow as a teacher, her expertise in those areas would develop over time.

We hope that novices find out what they don't know. Normally, only students will hear a teacher's lectures, and only a few students will challenge the teacher's instruction. Either something—a student, a colleague, the media—challenges a novice's assumptions and gaps in knowledge, or, through continual voluntary study over time, a teacher reaches a broader and deeper understanding. Very knowledgeable teachers are usually those who feed their own curiosity, building knowledge year after year.

Beginners also lack skill in organizing information to increase the likelihood that students learn. Novices have a limited range of approaches. Because many have just experienced four years of college lectures, they gravitate toward lectures. Unfortunately, we recall only about 5 to 10 percent of what we hear; merely telling is a poor way to ensure student learning. Would a short video clip clarify the information? Is it best to go from a big idea to supporting details or start with details to lead to the big idea? Will a group discussion work? Should the teacher provide questions for students, create a diagram to be filled in, or invite personal experiences? Are kinesthetic materials needed?

Novices don't know how to organize their knowledge for learners because they are still sorting out their own understanding. Beginners have a hard time recognizing which facts are critical, which are fairly important, and which can be safely ignored. Although they may learn to prioritize facts for their lessons, dealing with the unexpected is still difficult. Preparing well to teach adjectives and adverbs, for instance, does not prepare them to explain gerunds to an inquisitive student.

The unaware teacher rarely makes connections

New teachers don't yet see clearly how knowledge fits into a bigger picture. College courses cover separate aspects of a major field. Integrating the information takes time and effort. Unaware teachers don't integrate various subject areas, and they rarely connect their own general knowledge to the subject matter or to other courses students are studying.

My second year as a high school teacher was my 14th year of teaching. In between I spent six years teaching adults seeking a high school diploma, six years teaching Job Corps students, and nearly two years leading workshops for teachers. I knew how to teach but was still a novice in teaching U.S. history to 10th graders. I had little idea of what students were learning about in other subjects from other teachers. Not until I had many teacher-to-teacher conversations did I understand what teachers of biology, math, art, and physical education were teaching in my high school and how these areas might connect to what I was teaching. As I learned, I connected history lessons to the other coursework students were taking. I teamed with the English teacher who taught the same students. Students read stories in English class about personal liberties while we studied the U.S. Constitution. They read the work of Native American writers or women writers or 18th century writers that dealt with issues covered in the history text. My partnering teachers and I gradually learned to use themes to improve our teaching.

The unaware teacher fails to link what students know to the subject

Beginners rarely check to see what students already know. Novice teachers often follow a plan developed by someone else—usually a textbook or a prescribed curriculum. Such outlines imply that the information must be covered in the order in which it's presented, so novices plunge forward. It may take months to notice that many students already know the material or that some lack the background information needed for full comprehension.

Novices avoid asking what students know because they want to avoid a very real problem: If everyone already knows this material, the teacher will have to teach another lesson entirely. This is an intimidating challenge for new teachers. Who could possibly prepare alternative lessons for every class? With experience, beginners become aware enough to assess student knowledge and brave enough to deal with the related difficulties.

Questions to grow by

• Do you read several sources to make sure you understand material thoroughly before planning lessons?
• Do you discuss with other teachers which issues seem most important in a given lesson or unit?
• Do you ask students to tell you what they already know about the subject under consideration?
• Have you tried asking students what they want to know or what they are curious or confused about?
• Do you help students connect what they are learning to ideas from other subjects or previous years?
• Do you write down what worked and what didn't so you'll teach the material more effectively next time?

The Aware Teacher

At the aware level, teachers are still spending a great deal of energy assembling facts and mastering intricacies of their subject matter because it is relatively new to them. They rarely think about the order that facts are presented in, how those facts relate to other matters, or their students' current understanding. Their knowledge of subject matter, while fairly broad, is still incompletely processed.

The aware teacher knows the subject adequately but organizes poorly for learning

When I took 10th grade biology, I was taught by Mr. Hammond, a recent college graduate. I remember the day he explained genes and chromosomes.

"Genes are located on the chromosomes," he said, "like beads on a string. During reproduction, they duplicate themselves before the cell divides. That way each of the new cells is just like the old cell."

My mind rebelled. How could beads on a string reproduce themselves? I memorized what he said without understanding how the process could possibly work. Perhaps he repeated to us the explanation he received in college. Still, I felt dissatisfied; his explanation didn't make sense to me. My knowledge of actual beads was a barrier.

The aware teacher sometimes checks prior knowledge

What the learner already knows is referred to as prior knowledge. Why would beginning teachers ignore prior knowledge? One reason is a human tendency to make assumptions: If the curriculum expects me to teach this, then the students must not know it. Another reason is that teachers fear coping with the results, such as inventing a whole new approach on the spot.

The knowledge of novice teachers is often tentative. Beginning teachers may be able to comprehend the material well enough to take a multiple-choice test or understand summaries and studies, yet they find explaining it to students much harder and they may stumble. At the aware level, teachers know more information and have some memorable ideas about organizing lessons, but they can do this only with focused effort. There is limited time for improving every lesson. Novices' lessons sometimes enhance learning; other times they don't.

We may be in a similar position after attending a seminar, a sales presentation, or a conference. An interested person asks what we learned and what seemed crystal clear as incoming data now sounds muddled and confusing as we hear ourselves trying to explain. Why is this true?

When we first hear or read new information, we have only a surface grasp of it, no matter how attentive we are. To have a deep understanding we must gradually construct a web of comprehension. On first hearing, we follow the line of thought as presented by the speaker or writer. This may be a good introduction, but it is a single strand of thought. We have not yet built a matrix of understanding.

Consider how memory works. If we hear "3rd grade" or "first job," a whole set of memories pops up. We remember things in sets and groups, with attached sensations and emotions. Sometimes a long-forgotten aroma will take us time traveling. We construct our own understanding by gradually making mental connections to the cognitive structures we have previously built.

Gary Rackliffe (1998) has used an activity with teachers-in-training to demonstrate how people construct knowledge.

"Form a group of four or five people," he says. "Then draw a poster to show the idea of a tree."

Each group creates a complex poster that includes many details: leaves, bark, branches, and seeds; green, brown, yellow, and red; birds, nests, squirrels, and nuts; swings, yards, and fences; sun, rain, clouds, and soil. All the posters are different, yet all do exactly the same thing. Each poster reveals dozens of facts that relate to trees, and each shows a complex understanding of what trees are, what they do, and where they come from. It is a re-creation of the sort of connections people have in their minds.

Rackliffe explains that we create mental filing systems for information. He compares the process to an old post office. The postmaster sorts all the incoming mail—into each box goes mail for one family. Similarly, in our minds we put new information into existing, related categories. When we first hear about birch bark canoes, the information may be filed with trees (because of bark), or with forms of transportation (because canoes are boats), or both, but every fact attaches to existing knowledge structures. Barring physical deterioration of the brain, people construct new knowledge for as long as they live.

What level of understanding can we expect for teachers who are still constructing knowledge in the subject area that they teach? Most states require incoming teachers to pass a test in their major and minor before receiving a teaching certificate. The tests may contain 200 multiple-choice questions on facts or issues that cover a whole field of study. To pass, candidates must answer three-fourths of the questions correctly. Some states also require essays or language proficiency tests. Future teachers must be familiar with a wide selection of details in order to pass, but how dense their matrix of understanding may be is not measured. We have to hope that they will continue to develop after they begin their jobs, in the same way that new drivers improve over time.

Beginning teachers are still in the process of constructing a complex matrix of understanding; they are often unaware of details regarding today's lesson and connections between those topics and other matters. Because they overlook interrelatedness, they are unable to guide students toward connections.

My daughter taught college courses as she worked on her PhD. She worked hard the first semester and received positive evaluations from her students. Nonetheless, when she started the second semester, she had a clearer idea of what students needed to know and how to present it. After the first week of the second semester she told me, "I feel like I should find all the students I had last semester and apologize to them!" This sentiment is familiar to many who have struggled through their first teaching experience and then seen growth in themselves. It can be embarrassing to look back at those first efforts.

Adequate knowledge means that presentations are free from major errors in fact and congruent with other information students are gleaning from text, handouts, authoritative Internet sites, and other reliable sources. If we state an error, we catch ourselves in the midst of it or have the guts to come back later and admit the error so it can be corrected in the students' notes and minds. Adequate knowledge means knowing basic grammar, dates, key definitions, correct procedures, and whatever else is central to the subject at hand. Although every teacher will occasionally make mistakes, adequate knowledge means that such errors are rare rather than pervasive. By this measure, my daughter's teaching displayed adequate knowledge, but for her, being merely adequate wasn't enough. She wanted to grow beyond that baseline.

The aware teacher may link the subject with other knowledge

Each time teachers or presenters point out how a subject connects to information we already understand, the new information is more firmly attached in memory. For most people, teaching this way is not automatic. Only through time and experience do we see these connections and learn to point them out. Teachers who are building this skill will gradually point out more and more of these links. They will also notice which links help learners most and which ones help very little. Naturally, over time teachers will reuse the effective examples and try to find good replacements for those that don't work well.

When I first heard about punctuating with colons in 7th grade English, I didn't understand their use. Mrs. MacFarland stood in front of us and explained, "A colon precedes something, like a list." We must have looked confused, so she tried a new approach. "Think of it as a warning light at a railroad crossing." She held one hand above the other, each index finger rhythmically poking the air as if in time with an imaginary flashing light at a crossing. "Something's coming. Something's coming. Something's coming," she chanted.

Instantly, the colon's job seemed perfectly clear. I never forgot her example and repeated it when I became a teacher. Mrs. MacFarland didn't teach the other punctuation marks in clever ways, but when it came to colons, she gave us exactly what we needed.

The absolute beginner rarely shows deep, broad knowledge or makes connections well; however, the person who has begun to improve does both at least part of the time. As teachers improve, the incidence of these two factors goes from somewhat rare to more common. When teachers connect new information to students' existing knowledge, the new information makes more sense to students and they remember it better. Connections contribute to congruence—the smooth fit between the old and the new. Information that doesn't overlap what is already known is harder to acquire. Information that conflicts with what is already believed to be true is integrated even more slowly or not at all. Therefore, if teachers point out overlaps with existing knowledge and also discuss perceived conflicts between new and old information, learners can better grasp and recall the lesson.

Events from the daily news may be used as a tie-in to a lesson. For instance, the actions of a well-known sports figure may illustrate a point in the lesson or appear as a character in a math problem. The teacher may refer to topics covered a week or a month ago and add new information from the current lesson to deepen understanding. Apparent contradictions are mentioned, clarified, and discussed so learners see a web of connections and build a place for these connections in their own minds. Teachers who take these steps are working to connect new knowledge to students' prior knowledge. Nonetheless, aware teachers still need extensive planning and comprehensive notes to make it happen. They deserve congratulations; they are working to develop greater skill.

Questions to grow by

• Do you subscribe to a magazine in your subject area?
• Are you reading books that broaden and deepen your subject-matter knowledge?
• Have you taken advantage of all the training opportunities your employer or school district offers?
• Do you seek out additional materials from the Internet, a regional resource network, or your library system?
• When your school district adopts new texts or materials, do you attend the introductory training sessions?
• Do you ask other teachers how they present various topics or issues?
• Is sharing lessons, materials, handouts, and ideas a part of the culture of your workplace? If not, what can you do to change this?

Self-Development

Assume there are things you do not know. Keep assuming this for as long as you teach. If you hear a fact that is "wrong" from students, friends, or the media, look it up to verify your own interpretation. Sometimes you will be humbled, but improved. Make a plan for deepening your knowledge and follow your plan. Read or listen to books. Subscribe to useful sources of information. Take a course. Join a professional organization and attend conferences. This will take time you do not have. Do it anyway. When you make an error, admit it to students, so they can know the truth. They may already know you were incorrect. If they don't, their respect for you will grow, along with their factual knowledge. Remember, you are their role model for lifelong learning.

Collegial Support

Share information and lesson plans with others. Build a culture of mutual assistance. There is so much knowledge in every field that no one has it all. Everybody benefits from sharing information. If mentoring an inexperienced person, you are likely to hear numerous errors in one session. Resist the urge to jump on every one. This will paralyze the person. Prioritize. Be sure to mention strengths. Then bring up only two or three significant errors. When a person comprehends significant concepts, smaller errors tend to disappear. If they don't, deal with errors during later sessions.

The Capable Teacher

A major difference between the aware level and the capable level has to do with ease and frequency. Aware teachers are like new drivers who recite the steps for shifting gears as they try to implement them. It takes a great deal of focused effort. At the capable level, drivers can rely on their hands and feet to shift fairly smoothly most of the time in normal driving situations. To carry the analogy further, not until they reach the inspired level will they instinctively downshift for control or master the shifting necessary to get out of a snowdrift.

The capable teacher knows the subject and organizes for learning

A teacher with extensive knowledge has probably studied several sources and holds a lot of information clearly in mind, more than will actually be used in a given lecture or explanation. She is aware of complexity and contradictions within the material, and she emphasizes important points to help students understand. She answers questions correctly and confidently. If the question is unexpected or slightly off track, she may promise to look up the answer and get back to the inquirer (and remember to do so). There is no hesitancy in the presentation because the information has become quite familiar. Notes are mostly unnecessary, used to help keep track of where she left off last time, not as a crutch. Teachers at this level may display a calm demeanor that springs from comfort with the topic. Nervousness abates because they no longer worry that they'll forget, become confused, or get lost.

The capable teacher connects information to prior knowledge

Think back to my story about being taught that genes and chromosomes resemble beads on a string. In college the topic came up again. My botany professor, Mr. Nebel, explained the process of cell division quite differently:

"Genes are components of chromosomes, like building blocks. During reproduction the paired chromosomes sort of unzip down the center and each gene on the chromosome attracts a new partner from the nuclear soup inside the cell, almost like a magnet. Once the new partners are all attached to the existing genes, you have two zippers, or chromosomes, one for each new cell."

I thought, Wow, that makes sense! Building blocks, zippers, soup, magnets—these were things I was familiar with. I had also been familiar with beads, but the examples in this analogy helped me picture the actual process of replication much better than the beads had. Mr. Nebel's explanation worked for me because the comparison was not contradictory: The reproduction of beads is not an idea that makes sense. A zipper actually does open down the middle. From there, attracting a new partner from the nuclear soup Mr. Nebel described, while an odd idea, was not completely unimaginable.

Many science students are given a paper with shapes representing genetic building blocks like adenine and guanine. They color each type, cut them out, and paste them on a sheet to demonstrate the way the replication occurs. The first time I saw teenagers doing this I envied them, wishing I had been taught this way by Mr. Hammond.

Both Mr. Hammond and Mr. Nebel used a technique very helpful to learners—analogy. The best analogies present unfamiliar information by comparing it to familiar things and then pointing out similarities and, where appropriate, differences. Analogies use learners' prior knowledge. The beads-on-a-string analogy that Mr. Hammond provided gave a picture of the sequential nature of genes on a chromosome, but it didn't go very far to explain other characteristics of cell reproduction. Mr. Nebel combined the ideas of building blocks, zippers, and magnetism to describe a process. His comparisons stimulated in me a real understanding. He demonstrated higher skill in the use of subject-matter knowledge by organizing it in a way that greatly enhanced learning—definitely putting him at the capable level, or maybe even higher.

The capable teacher connects the subject with other knowledge

Capable teachers have a mental road map of today's lesson, the unit it belongs to, and the semester plan. This road map supports the making of connections. Teachers recall where they have been with this class and foresee where they will go next. They understand the relationship between the parts of the subject and the course. Such teachers often refer back to a previous lesson or experience to reinforce a point. They may promise to delve into a certain issue in the next unit, not to put students off but because these teachers know some matters will be better understood at that point. These teachers may answer the relevant part of a question, promising to cover more details at a future time. They actually do cover them later, because they teach their way along a mental road map and don't skip any important sites along the way.

Capable teachers have built a repertoire of examples and links that are held in memory. Tried and true ways of making information understandable enrich the lessons. A variety of links will be used to help students connect new knowledge to old, and to do so more often and more thoroughly.

Good teachers are open to unexpected connections that students make spontaneously. Thus, if May Belle blurts out that today's fraction lesson about eighths reminds her of Grandma, instead of squelching her, the teacher may ask why. May Belle can explain that Grandma always cuts pies into eight pieces so all the cousins can have a piece. This provides a chance for the teacher to discuss a complicated idea: the smaller the denominator, the larger the pieces. The larger the denominator, the smaller the pieces, but the more pieces there are. This concept is made more memorable when Grandma's pies and May Belle's clamoring cousins enliven it.

Questions to grow by

• Do you look for new ideas everywhere, even from presenters who repeat things you have already learned?
• Does your school or department make mutual assistance and learning a part of every meeting?
• Have you formed a support group with other teachers to brainstorm new approaches to each topic?
• Have you read research to ensure your understanding matches developments in the field?
• Do you design assessments before planning lessons in order to guide your explanations?

The Inspired Teacher

Inspired teachers' subject-matter knowledge is extensive, and they know from experience how to organize and present information to make it interesting and memorable to students. They integrate their subject-matter knowledge with other fields and help students to do the same. These teachers pay attention to students' prior knowledge and help students make connections to the topic under study, so that students' previous understandings are linked and integrated with new information.

The inspired teacher understands the subject and organizational methods deeply

If you have ever heard it said of someone that they "live and breathe" physics or Civil War history or psychology, that individual is likely to demonstrate an inspired command of a topic. When the individual is a teacher, this deep interest and curiosity can be sensed by students, and such interest is contagious. An impressive command of the subject underlies all planning, comments, and responses to questions. For the learner it feels like a guided tour through a complex maze—difficult but delightful.

Sometimes when experts try to answer questions or explain points, their eyes drift upward as they pause briefly to formulate their comments. I imagine that they are mentally poring over mounds of data to choose just those specific items that are needed by a specific listener with a specific question. When the answer is clear and responsive, I marvel at how much knowledge experts have brought to bear in that simple but effective answer. The inspired teacher has this kind of grasp of what makes lessons work and uses this knowledge constantly.

The inspired teacher integrates knowledge of the subject with other fields

Inspired teachers' deep, clear understanding includes thousands of facts, but facts alone are not enough. These teachers also see the relationships within a subject and across subject boundaries. They may point out similarities between parenting and the presidency, sociology and nuclear physics, economics and courtship rituals, or basketball and typing, not because these comments are required in the curriculum outline, but because such teachers perceive that pointing out the relationship will clarify some points for learners or help keep them interested and on track.

Questions from students are no longer interruptions but wonderful invitations to explore more deeply along some related trails of thought. The inspired teacher asks the student what he already knows or what he guesses the answer might be. Or the teacher answers by telling the class two or more theories or interpretations and asking students to evaluate each. This teacher is willing to explore complexity and is comfortable with the possibility that neither theory can be proven "right" or "wrong," yet both make interesting points. Such reactions are possible only if the teacher has command of a large body of knowledge.

Imagine a geography teacher with a deep understanding of cartography. Rather than merely presenting a list of the strengths and weaknesses of various map styles, she may present a series of situations to the class, asking how maps might be made to meet certain criteria. A map that attempts to show the relative size of nations looks very different from one that is designed to maintain the grid lines of latitude and longitude. A map designed to demonstrate the populations of nations rather than the land masses is distorted and odd-looking, yet still correct for its own purpose. Discussion based on a book like How to Lie with Maps (Monmonier, 1996) will give students a deeper understanding of the strengths and weaknesses of maps and the multiple purposes they might serve. This is a very different experience from memorizing one map and moving on.

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Teachers often say they have no time to read. An average 5th grader reading at the 50th percentile for just 11 minutes a day would read, over the course of one year, about 465,000 words (Nathan, 1990). Maybe every teacher could find 11 minutes a day. That might be enough.

The inspired teacher guides students to link prior knowledge to the subject

It is important to work from what students already know, adding new information along the way. Repeating the known can lead to boredom and mischief; telling only the unknown soon overwhelms the listener. A technical writer once told me that he tried to structure his sentences so the new information was at the end of the sentences. He said that people seemed to follow his instructions best when he started sentences with something he'd already covered and added new details at the end.

Starting with the known and moving to the unknown sounds relatively simple—if everyone in the group has a similar level of existing knowledge. But everyone in a given audience or classroom brings a different set of experiences and thus a different body of existing knowledge. In some cases the difference is relatively small; in other cases it is immense.

Great teachers develop the ability to find the heart of the lesson, the few key factors that cause the subject to make sense. We already named these key factors as critical attributes. Key factors form the skeleton upon which all the rest of the details hang. For example, the moment a toddler can tell a dog from a cat, she has isolated the key attributes of "dogness" and "catness." People of all ages can identify attributes but may find it challenging when faced with a brand-new subject. A great teacher identifies critical attributes and points them out as soon as possible to help students comprehend. The teacher must sort through a mountain of details and isolate those few that are central to understanding.

It can be tempting to include too many details too soon or to dwell on exceptions. But teachers who can concentrate on the critical attributes make every topic accessible. Students who are studying under such instructors say that the topic is "easy" without realizing that it might seem impossible if presented by a less skilled teacher. Some say it is possible to teach very sophisticated ideas—philosophy, for instance—to very young children as long as ideas are presented at an age-appropriate level. To do this, finding and pointing out critical attributes is indispensable.

Mentioning critical attributes at the beginning of a presentation takes a fairly short time. This is not boring to the knowledgeable listener, who may just nod in agreement, while his completely uninformed neighbor may be able to absorb enough at the onset to make the rest of the discussion intelligible. If the presenter follows with diversified assignments, then all levels of understanding can be served. Admittedly, diversifying is quite difficult. One method is to provide work stations for student learning. The teacher must spend time preparing these learning experiments, but once class begins, students do all the work.

Inspired teachers also sense that sometimes it is best to begin with interesting facts that are peripheral to the core subject because they rivet the attention of the learner. Choosing an effective approach hints at how inspired their work is. A thorough grasp of best practices feeds an intuition about when to disregard the typical approach and when to use it.

It's easy to forget that how we teach is as important as what we teach. A teacher, speaking as a parent, related this experience: "When my son was in 11th grade," she said, "our high school hired a retired chemist to teach chemistry. We were all delighted because he really knew his stuff. But once he started teaching, the kids were lost. He was the worst teacher my son ever had. After that year the teacher quit. What a disappointment."

This chemistry teacher had a deep understanding of his subject without an accompanying ability to use and organize the information to effectively guide learners. Even the teacher-parent overlooked how important this skill is and that the skill must be developed over time. Effective teaching is not automatic, but rather a set of habits assembled through reflective practice. Reflective practice means thinking back on one's own work with questions: What reaction did each of my actions get? What might I do differently to elicit different responses? Inspired teachers know that when they change their own behaviors, they have the power to cause new responses and increase learning.

Donald Cronkite, a science professor at Hope College, consciously designs activities to increase learning. When studying the brain, his students wear shower caps bearing labeled diagrams of the brain. His students perform square dances based on cell division and create costumes to illustrate important features of various phyla (Reinstadler, 2005). No wonder Cronkite was named Michigan's College Teacher of the Year.

Tests given to potential teachers can show us whether they have a basic command of their subject; however, there is no written test to show us whether they can see connections or guide students to make them. These skills emerge over time in the context of the classroom. We learn whether teachers can demonstrate this skill by observing. Are connections made over hours, days, weeks, and months? Teachers develop these skills through daily consideration of whether their lessons and approaches achieved the desired results. If the answer is yes, the teachers will repeat or adapt the approach. If no, they will try something different.

Actions to grow by

• When you read, mark all terms or references that are unfamiliar. Look them up to increase your depth and breadth of knowledge.
• Compare several versions of the material about a subject—preferably unfamiliar versions—looking for differences and contradictions. Ponder what these variations tell you.
• To test your own knowledge, take the tests associated with your class's textbook before preparing any lessons.
• Be a mental adventurer. Expose yourself to fields you have never studied before.
• Ask listeners to share their knowledge of the subject before giving yours.
• Look for connections between the subject at hand and other courses, events, or memories listeners are familiar with. Mention connections as you teach.
• Think of three or more ways to present a concept and then select the one that seems most effective.
• Write notes to yourself about the experiences of your audience. For instance, people born after 1980 will understand comparisons to iPods and cell phones, but not record players or Sputnik.

For Information and Inspiration

The following professional organizations offer teachers a forum for improvement in various curriculum areas. Joining such organizations, reading their publications, and attending their conferences can inspire and inform teachers.