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Getting to "Got It!"

by Betty K. Garner

Table of Contents

Chapter 1. Cognitive Structures: What They Are and Why They Matter

Imagine what it would be like to sit in a classroom and have nothing make sense. There are far too many students in our schools today who don't have to imagine this, even though today's schools are filled with dedicated teachers working hard and using research-based instructional practices in an effort to help their students learn. When we present a very well planned, logical lesson, we wonder why some students "get it" and others do not. After reexamining our methods and our curriculum, and after trying and failing again and again to reach a subset of students, we ask ourselves some hard questions: Are the students who don't get it learning disabled? Are they unmotivated? Are they unfocused, inattentive, lazy? Are they just "slow"?

To try to reach these students, our schools offer after-school study programs, remedial reading and math programs, summer school, tutoring, resource services, and special education. Still there are students who do not understand and do not achieve. Concerned parents take these students to tutors and specialists or enroll them in expensive learning centers. Still these students struggle.

Meanwhile, sitting in the same classroom with the struggling students are the high-achieving students. They thrive on our well-prepared lessons, and secretly we suspect that they could learn from anyone at any time with any kind of method. They can do this because they know how to gather, process, and output information. They have well-developed cognitive structures.

Cognitive Structures Defined

Cognitive structures are the basic mental processes people use to make sense of information. Other names for cognitive structures include mental structures, mental tools, and patterns of thought. To clarify how cognitive structures function, I group them into three interdependent categories:

  1. Comparative thinking structures process information by identifying how bits of data are alike and different. They include recognition, memorization, conservation of constancies, classification, spatial orientation, temporal orientation, and metaphorical thinking. Comparative thinking structures are foundational to learning. As the prerequisites to the more complex cognitive structures in the other two categories, they are the focus of this book.
  2. Symbolic representation structures transform information into culturally acceptable coding systems. They include verbal and nonverbal language; mathematics; music and rhythms; movements, dance, and gestures; interpersonal interactions; graphics (two-dimensional drawings, paintings, logos); sculpture and constructions; and simulation, drama, and multimedia.
  3. Logical reasoning structures use abstract thinking strategies to systematically process and generate information. They include deductive and inductive reasoning, analogical and hypothetical thinking, cause–effect relationships, analysis, synthesis, evaluation, problem framing, and problem solving.

One reason that educators don't immediately identify underdeveloped or underused cognitive structures as a source of learning difficulties is that we assume they operate automatically. Our own ability to process information quickly and work easily with abstract ideas can make it difficult for us to imagine what it is like to struggle to do these things, or to grasp that it is even possible for someone over the age of 7 or 8 to not be able to gather and organize information, recognize patterns, or see "obvious" connections.

Often, neither the struggling students nor their teachers are aware of what lies behind the students' failure. The teachers get frustrated and conclude that the students need to pay more attention, work harder, or change their attitudes. The students have no idea why they don't get it; they think that the schoolwork is simply too hard or doesn't make sense. They may quit trying and become behavior problems, or they may slip through the cracks in the system, passing from grade to grade with minimal competency. Those who do get by typically do so by using memorization or imitation strategies. Although these tricks can help students find right answers, using them gets students no closer to experiencing the joy and excitement of deep understanding. They get no closer to developing metability.

Two Key Points

The more educators learn about how cognitive structures affect learning, the more cause there is for us to be optimistic. There are two key points to keep in mind:

  1. Each individual has to develop his or her own cognitive structures. However, just as good coaching helps athletes improve their performance, good teaching provides learning opportunities that stimulate students' reflective awareness and visualization and help them develop their cognitive structures.
  2. It is never too late to develop cognitive structures. From infancy through old age, everyone who has the neurological capacity to communicate, to be reflectively aware, and to use visualization can develop cognitive structures. When I work with students who are struggling in school, I explain that they already have the capability to learn; what they need to do is learn how to use their "mental tools."

Andre: An Unmotivated 7th Grader

Andre was one of those seemingly unmotivated students who barely did enough to get by and really disliked school. I used an analogy to help him understand cognitive structures.

"Andre, do you know anyone who is really good at working on cars?" I asked.

"Yeah, my Uncle George."

"Has he got some tools he uses?"

"Oh, yeah! His garage is full of wrenches and stuff."

"He's good, right? He knows how to use his tools and make them work for him?"

"You bet!"

"If you had his tools but didn't know how to use them, would they do you any good?"

"Not really."

"What if you found out that you have mental tools in your head?"

Andre looked at me suspiciously. "What do you mean?"

"Your mind has tools, called cognitive structures, that will make learning a whole lot easier," I explained. "They'll do the work for you. Would you like that?"

"Wow!" Andre responded. "I didn't know I had tools in my head. How do I use them?"

In class, Andre normally sat back and waited for the teacher to tell him what to do. He just followed directions. When I worked with Andre, he began to use his cognitive structures to create meaning, change his understanding, and learn. He actually became excited about his "mental tools" and enjoyed the challenge of figuring things out on his own.

How Students Use Cognitive Structures to Process Information

Students use cognitive structures to process information and create meaning by (1) making connections, (2) finding patterns, (3) identifying rules, and (4) abstracting principles.

Making Connections

Cognitive structures help students make connections with prior knowledge and experience by bridging from the known to the unknown. It is very important to ask students what sense they make of information we share with them. As we listen to their connections, we show respect for their uniqueness, encourage them to bring something to the learning situation, and identify the need to clarify misconceptions.

Finding Patterns and Relationships

Cognitive structures help students compare, analyze, and organize information into patterns and relationships. Patterns are repeated motifs or units. Relationships are logical or natural associations between any two or more things. All learning is based on relationships; that is, something has meaning when compared and contrasted with something else. From early childhood, patterns are part of the curriculum. However, patterning activities remain just imitation unless the teacher uses them to mediate students' cognitive structure development. Here is an example of how Sandra came to understand patterns.

Sandra: Making Patterns

When I worked with Sandra, a 4th grader who was struggling in school, I gave her an assortment of colored paper shapes and asked her to make a pattern. She selected three big red circles and three big blue circles and then arranged them in an alternating red–blue line. She shoved all the other pieces into a pile.

When I asked Sandra to tell me about her pattern, she said, "Red–blue, red–blue, red–blue."

"What makes it a pattern?" I asked.

"The same thing goes over and over."

"What about all the other pieces?"

"They don't make a pattern."

"Help me understand," I prompted.

Sandra then became a little impatient. "That's all the big red and blue circles!"

"Are there other ways to arrange the pieces to make a pattern?" I asked.

She looked puzzled. "Huh? I don't know what you mean."

I was tempted to arrange a pattern element for her to imitate. However, for Sandra to develop her cognitive structures, she had to form patterns and relationships on her own. Too often, teachers make connections and point out patterns for students without realizing we are teaching them to imitate what we do rather than to construct meaning for themselves. Then we wonder why they cannot find patterns in reading, math, science, social studies, and life.

Sandra then asked, "What do you want me to do?"

I responded by asking her to tell me what she noticed.

"There's different colors and shapes and sizes," Sandra said.

"Tell me more," I prompted.

She started to move the pieces around and group some together. "There are big and small ones. Red, blue, yellow, green circles, squares, triangles. . . ." Sandra continued to slowly move pieces around. "Wait a minute!"

"What do you notice?" I asked.

"Wow! There are lots of different ways to make patterns!"

I watched Sandra organize a complex matrix pattern. She was smiling now. "Hey! This is fun!"

"Are there other ways you could use the pieces to make patterns?" I asked.

She paused and studied the pieces. "Let me think. Oh, yeah! Lots of ways."

"When do you see patterns in reading and writing?" I asked.

Sandra gave me a blank look and shrugged her shoulders. "I don't."

"What if you could find patterns in stories, spelling words, and sentences?"

"I don't know what you mean," Sandra replied. "Reading and spelling and stuff aren't like this. . . ."

"Everything has a pattern," I explained. "The secret to learning is finding patterns and relationships." I opened her reading book and asked what she noticed.

"What am I supposed to be looking for?" she asked. "I don't understand."

"What do you notice? See if there are patterns."

As she read, Sandra began to comment to me about how periods, commas, quotation marks, and capital letters were used. Since 1st grade, Sandra had completed many worksheets on punctuation. Now, for the first time, she noticed their patterns.

Formulating Rules

Cognitive structures help students formulate rules that make processing information automatic, fast, and predictable. When students notice relationships that are always or nearly always the same, they do not have to expend time or energy to think about them. They can divert their mental resources to new learning instead of constantly relearning the same things. Adults' definitions of rules and students' definitions often differ. Here's a conversation I had with Greg, a 5th grader.

Greg: Exploring the Meaning of Rules

I started our exploration by asking Greg, "What is a rule anyway?"

He responded, "Something you can't do."

"Give me an example," I prompted.

"Don't run in the hall. Don't fight. Don't talk out in class."

"Those are school rules. Do you have any rules at home?"

"I have to be in at a certain time," he said. "I have to clean my room."

"Do adults have rules?" I asked.

"No, they can do whatever they want. I will too, when I get big."

"Do adults have to be at work at a certain time or do what their boss tells them?"

"Well, yeah!"

"What about laws? Are laws like rules that we all have to follow?" I asked.


"Where else do you have rules?"

"At restaurants you have to pay for your food and act a certain way. Don't steal."

"OK," I said, nodding. Then I prompted Greg to think beyond the negative constraints. "Have you ever thought of rules as being there to help you and keep you safe?"

"Not really."

"What about games? Could you win a game if there were no rules?"

"Sure! You can cheat!"

"How would you know if you were cheating if there were no rules? How would you know if you had any points, or won or lost?"

"Oh," he said and then paused. "I never thought of it like that."

"What if you thought about rules as being there to help you win, to make learning easier?" I suggested.

"What do you mean?"

"In math, for example, if you know the rules for multiplying and dividing, it's a lot easier to do the work," I explained. "In language arts, if you know the rules for punctuation or how to spell a word, you don't have to look it up each time." Through our interaction, Greg realized that a rule was a guide you could count on to be the same in most cases.

When working with rules, the ability to automatically predict builds confidence and enables students to quickly process more difficult and complex information. We cannot assume that knowing a rule is the same as knowing when and how to use that rule. Most teachers are trained to first teach rules and then have students apply these rules by making connections with content. I recommend instead inviting students to make connections and find patterns and relationships before asking them to formulate rules. For example, rather than teaching rules about punctuation and quotation marks, give students texts and have them work together to identify when, where, and why punctuation is used. When they identify patterns and formulate rules, they can test these rules with other texts. In addition, students are more likely to remember these rules because they created them. Does this approach take more time? Yes. Is it more effective, and will it save time in the long run? Yes.

Abstracting Generalizable Principles

Cognitive structures help students abstract generalizable principles that apply or transfer to situations other than the original learning context. Let's pause for some quick definitions. To abstract means to draw out or separate from a specific object or instance. A generalizable principle is the critical essence or fundamental guiding certainty that clarifies understanding and can be applied to diverse situations. For example, a high school sociology class studies a series of documents on social justice, and students generalize that the rights of individuals and the rights of society need to coexist in a delicate balance of power. This principle can be applied to many different historical and social settings as well as personal choices, economics, politics, literature, and the arts, just to mention a few. Many students never reach this step, because they know they can get good grades in school by just memorizing specific content. They are rarely challenged to identify generalizable principles to help them understand other information or situations in real life.

Harold: Abstracting a Principle

One afternoon I was explaining to a group of educators how students need to make connections, find patterns, formulate rules, and abstract principles. Harold, a psychologist in the group, suddenly made a connection with a childhood experience. He was 10 years old, and he and his dad were in their basement, building a birdhouse. The floor was covered with sawdust. Harold dropped a screw and immediately tried to find it by searching through all the sawdust. His dad stopped him. "Son, look where the screw fell from," he said. "Based on that, where do you think it will be?" Harold immediately looked on the floor directly below the edge of the table, reached down, and found the screw. Then his dad asked, "Will it always be that way?" This made Harold stop and think about how abstracting a generalizable principle would save time and energy.

Several things happened here. Harold's dad coached his son—in other words, he mediated meaning—by asking questions rather than telling him what to do or solving the problem for him. He not only let Harold find the screw but also taught him a valuable lesson for life. He was helping Harold develop cognitive structures by first helping him to be reflective (urging him to stop and think about an experience) and then by encouraging him to notice a relationship that was predictable. Harold's dad then went one step further to encourage him to think about abstracting a generalizable principle that would affect future experiences.

Little interactions like this have lifelong impact. Notice that Harold's father did not make fun of him, embarrass him, or call him clumsy or stupid for making a mistake. He recognized a teachable moment. We have many opportunities to coach students in such a way that helps them develop cognitive structures. As I thought about Harold's story, I realized how we often assume students are making connections, finding patterns, formulating rules, and abstracting principles, especially when things are so obvious to us. A student named Sean helped me become aware of this challenge.

Sean: A 2nd Grade Enigma

Sean's teacher described him as an enigma. He was not a behavior problem, and although he worked very hard in class, he just didn't "get it" in any content area. Sean took all his work home and brought back correctly completed worksheets. However, he could never do assignments by himself in class, nor could he explain responses on his homework papers. When I worked with Sean, he gradually began to make connections and notice patterns. Before he left, I asked him to write his name on his paper. Remembering Harold's story, I pointed to his name and asked, "Will those letters in that order always spell Sean?" He paused, looked at what he had written, then looked at me, and said in all sincerity, "I don't know."

I realized how critical it was for Sean to be able to generalize, so he sat back down and we worked with some math counters. We did several hands-on activities, such as moving a set of five blocks around to see how many different ways he could make them equal 5. As Sean made each arrangement of blocks, I asked rule-oriented questions. For example, "Would 1 + 4 always equal 5?" He would have to check it out several times before being certain that 1 + 4 and 4 + 1, or 2 + 3 and 3 + 2, would always equal 5. We did this with several different numbers.

Then I had Sean write the words rat and tar.

I asked, "What do you notice about these words?"

Sean said, pointing to rat and tar, "These two have the same letters, but they're lined up different."

"Will r-a-t always spell rat?" I asked him.

Sean thought for a few minutes. Then he looked at me and responded cautiously, "Yes, I think so."

"Will t-a-r always spell tar?"

Sean responded a little more confidently, "Yes."

I then asked him what had changed and what had stayed the same. He pointed out that the letters had stayed the same but that the order and meaning had changed. After practicing with several words, Sean looked up at me and said confidently, "I get it! Some things are the same even when some things change!"

Sean's teacher noticed an immediate change in his participation and productivity in class. A couple weeks later, I went to Sean's classroom to check on him. Students were quietly doing a spelling worksheet. When Sean saw me at the door, he smiled and motioned for me to come over to his desk. As I looked to see what he was doing, he pointed to a word on his paper. He said, "That's cake, and it will always spell cake!" I was as happy as he was. Sean was a young man who worked very hard with little or no understanding or enjoyment in learning until he figured out that simple principle: Some things change; some things stay the same. Before he learned to generalize, every piece of information was new and different, and he felt completely overwhelmed. Now he was looking for connections, patterns, rules, and generalizable principles that would make it easier for him to learn.

Three Important Questions About Cognitive Structures

When educators begin to understand what cognitive structures are and how they work, they ask three important questions.

  1. How do students develop cognitive structures?
  2. Why have some students already developed them and other students have not?
  3. What can a teacher do to help students develop cognitive structures?

How Do Students Develop Cognitive Structures?

Students develop cognitive structures through reflective awareness and through visualization. The more students become reflectively aware of what their senses are telling them and mentally represent this information through visualization, the stronger their cognitive structures will become and the more likely they will be to develop metability to learn, create, and change (see Figure 1.1).

Figure 1.1. Reflective Awareness and Visualization Develop Cognitive Structures and Foster Metability

Reflective awareness. Reflective awareness is conscious perception. Reflection is thoughtful consideration. Awareness is alert attention. To be conscious means to be mindfully attentive of oneself as a thinking, feeling person. To perceive means to mentally take hold of or consciously grasp something while assigning meaning to it. The mind accepts mental representations of information as fact. Perception is reality for the person doing the perceiving. Perception is filtered through values, beliefs, and feelings, which color and shape how the information is processed. Perception can be intuitive and unsystematic, or it can be reflective and logical. Although reflective awareness is similar to metacognition, it is, more simply, thinking about your thinking.

Students take in sensory data every waking minute. To be reflectively aware, students need to notice and thoughtfully consider the information that they see, hear, touch, taste, and smell. We have all had students with learning problems and ones who have demonstrated inappropriate behavior, a disrespectful attitude, poor cooperation, a lack of productivity, or a lack of motivation. When I work with students like these, I focus on helping them develop more effective cognitive structures. Here is the story of one such student.

Tim: An Unproductive 8th Grader

Tim slouched in a chair across from me, gazing into space as if he were bored to death. I placed an open box of 24 crayons and a pile of 5 pencils on the desk in front of him. "What do you see?" I asked.

Tim glanced at the materials. "A bunch of stuff," he replied.

"Tell me more," I prompted.

"It's just a bunch of stuff—crayons, pencils. That's all."

Once we make a judgment such as "that's all," we cut off sensory input, and with little sensory data, there is little information to process. My objective was to help Tim become reflectively aware of the millions of bits of sensory data available to him.

"What do you notice?" I asked, gesturing to crayons and pencils on the table.

"Huh? What do you mean?" he asked me.

Tim was waiting for me to tell him what I wanted for a response, to tell him what he should see and notice. Too often, well-meaning parents and teachers short-circuit students' cognitive development by doing the mental work for them. For example, we give them some objects to sort and tell them how to sort those objects rather than giving them the objects and letting them figure out several possible criteria for sorting. We unintentionally encourage them to become passive recipients, to depend on others rather than on their own capabilities or need to know.

"Trust your eyes and your brain," I told Tim. "What do you notice?"

"Well, OK, I notice the box is open," Tim said. "And inside there's lots of different colors. Some are just different shades of the same color. Like here." He sat up in the chair and reached out to slide the crayons out of the box onto the desk. "There's light green, regular green, kelly green," Tim said, reading the labels on the crayons. "There's blue-green and turquoise."

"Tell me more," I said.

Tim started feeling the crayons and pencils, gathering tactile data. "They're round, or really kinda shaped like. . . ." He paused. "I forget what you call that shape."

"Cylinder shape," I said.

"Yeah, cylinder, that's it. And they're made of wax. When I was a kid, I used to like to color," Tim said. He smiled as he cocked his head to one side and pretended to be coloring a picture. "These pencils are made of wood and have a little rubber on the end with metal around to hold it on. I like to draw, too."

"I bet you are good at drawing," I commented.

"Yeah," Tim said. "It's fun, you know? I look at something and then draw it on the paper. I make up stuff to draw too, like from my mind."

"Have you ever thought of using your imagination to learn?" I asked.


"I bet that before you draw something, you can actually see it in your mind, right?"

"Yeah. I know exactly what it's going to look like."

"You think about it, too, right?" I asked. "You see in your mind how all the parts fit together?"

Tim smiled and nodded. "Yeah," he replied.

"What if you found out that you could use that same ability to reflect and picture things in your mind to learn stuff in school?"

"That would be pretty cool."

Teachers often form an unspoken agreement with unproductive students like Tim. It goes something like this: "You don't bother me, and I won't bother you." These students drift through their schooling, putting in time, staying out of trouble, and doing just enough work to squeak by. Tim knew he wasn't dumb because he could figure out what to do in many different kinds of real-life situations. But he had decided, back when he was in elementary school, that the "school stuff" was hard, no fun, and not worth his time and energy. The way to reach these students is to encourage them to notice data available to their senses. The process of reflective awareness helps students develop their cognitive structures to process information and create meaning. If students fail to notice what their senses are telling them or fail to reflect on the information they take in, they quickly discard it, unprocessed.

Students who demonstrate ADD or ADHD behaviors use a kind of blurred and sweeping perception that limits sensory input. This kind of superficial information gathering is reinforced by the value that our fast-paced society places on speed. Movies, TV shows, commercials, and video games with rapidly flashing images and sounds foster lack of attention. Noise and commotion overload senses without processing. Students are often hurried from one activity to another with little time for reflection. Without sufficient data and reflection, students have difficulty determining what is relevant.

Visualization. As students become reflectively aware of the messages or stimulation their senses are sending to their brains, they need to visualize the information so that they can process it. Visualization is the ability to mentally represent and manipulate information, ideas, feelings, and sensory experiences. It is essential in abstract thinking and planning. Without visualization, students are dependent on specific information within sensory range and have a very difficult time with abstract thinking.

When we visualize, we use images, symbols (e.g., numbers, words, pictures, designs, and diagrams), and other forms of mental coding to represent sounds, tastes, smells, feelings, experiences, and information. These mental representations are so real that the mind often cannot differentiate between what is outside (in the material world) and what is inside (in the mind).

Imagination is important, but being able to differentiate what is real and what is imaginary is important too. This is especially true when students get so engrossed in virtual characters—TV, movie, or video game superheroes, for example—that they walk around acting like and thinking they are the character, even trying to do super-karate maneuvers or gravity-defying tricks they have observed.

Jerry: In Trouble on the Bus

Jerry, a 2nd grader, was constantly getting in trouble on the bus. No amount of behavior modification seemed to change his bizarre reactions to other students and his apparently uncontrollable jumping around and yelling. Although Jerry was doing well academically, his teacher was very concerned about his inappropriate behavior on the bus because it was resulting in suspensions and missed classes.

Using reflective awareness and visualization, Jerry was able to identify the causes of his behavior. He described how the other kids made him feel and act like the title character from TV's Buffy the Vampire Slayer. When I asked him to help me understand, Jerry said, "Well, I'm like Buffy: fighting and overcoming evil forces. When the other kids say something mean, I jump over the seat and try to knock them out, or I crawl under the seats to escape." In a matter-of-fact way, he demonstrated how he swung his imaginary sword to take on his foes. I asked Jerry if he really thought the other kids were vampires or other evil monsters, and he replied confidently, "That's what they look like to me!"

Together Jerry and I did some sensory input exercises and some visualization exercises to help him differentiate between what his senses were seeing and hearing, and what his mind was making up. I also worked with him to identify alternative behaviors he could use to deal with the situation. One of the exercises took advantage of his very active imagination: practicing thinking "beautiful thoughts" that made him feel calm and happy inside. "Picture something that makes you feel so good that you don't want to quit thinking about it," I advised. He liked that idea. He was soon able to ride the bus without further incident.

A couple weeks later, I saw Jerry on the playground and asked if he was still thinking beautiful thoughts. He said smilingly, "Oh, I don't have to think them anymore. They just come all by themselves!" In general, I've found the "beautiful thought" exercise to be a marvelous way to help students settle themselves and encourage both reflective awareness and visualization.

Here's an example of how John's teacher helped him discover that his ability to visualize could make his schoolwork more enjoyable.

John: Using His "Mental Hands"

John was an 8th grader who hated school and did just barely enough work to pass each year. Although he was not a behavior problem, his teachers and parents became frustrated because he refused to do his work. However, John loved to draw and often amazed the other kids with his exceptional drawing abilities. One day his teacher took some time to work one on one with John to find how he could use his strengths to be successful in school.

John's teacher used an assessment instrument called the tower, which is designed to identify and develop a student's cognitive structures. The instrument consists of six small boards, five by five centimeters square and about one and a half centimeters thick. The boards are painted black, and each is drilled with nine evenly spaced holes. Each hole is fitted with a black peg, about two centimeters high, and on each of the boards, one of the pegs is glued into its hole. The six boards with their pegs are stacked to form a tower (see Figure 1.2). The positions of the glued pegs all together form an asymmetrical pattern.

Figure 1.2. The Tower: An Instrument for Cognitve Structure Assessment and Development

When John and his teacher started working together, the teacher asked him to describe what he saw (what his senses were telling him). Instead of saying that he saw six black blocks stacked on each other, John said that he saw a parking garage, a building under construction, and a jail. He never mentioned the color, shape, size, position, or other sensory data. Like so many creative students, John immediately visualized, processed, and interpreted his perception instead of the information itself. This is a real gift for creative expression; however, when it comes to schoolwork it can be a problem because the information processed is not what is required for assignments and tests. This is one reason so many creative students have problems in school. John's teacher explained that he was "seeing with his mind," which was a wonderful ability to have, but that it was important for him to also see with his eyes and notice what his eyes were telling his brain. John then described the visual characteristics of the tower.

Next, his teacher asked him to twist the pegs on each board to find the glued peg. As he found each one, he identified its location in relationship to the other pegs; for example, "On Block 1, the glued peg is in the middle left." Identifying the position was easy for John; however, if students do not effectively use spatial cognitive structures, they have a difficult time naming the position. As he found each glued peg, he removed the block from the stack and set it on the table. Every time he found a glued peg, John closed his eyes and made a mental map; that is, he visualized glued positions in relationship to each other. He repeated unstacking the tower several times until he was confident that he could visualize the pattern. To confirm that John had visualized the information and to have him symbolically represent it, his teacher drew a tic-tac-toe grid on a piece of paper and asked John to write the numbers 1 to 6 on the grid to show where the pegs were glued. Without hesitation, John identified the positions (see Figure 1.3). "I can see it," he said, pointing to his head.

Figure 1.3. John's Mental Map of the Tower

His teacher removed the paper, stacked the blocks, and rotated the tower clockwise one quarter-turn. Then the teacher said, "Use your mental map and pick up each block by the glued peg." John smiled and quickly unstacked the blocks without error.

"How did you do that so quickly?" his teacher asked.

John said, "Well, I just took my mental hands and turned it around in my head."

"Mental hands? Tell me about your mental hands," his teacher prompted.

John responded, "Well, when I want to draw something, I take my mental hands and turn it around in my head. Then I can see it from all sides, and I can draw anything."

With enthusiasm, the teacher followed up and asked John if he'd ever thought of using his mental hands to do math, language, science, or history. John said no and then asked how he could do that. His teacher suggested visualizing what the numbers stand for in math or what the story is saying in history.

John was a bit surprised that he could use what he was good at—his mental hands—to do schoolwork. Within three months, he went from the bottom of his class to the 8th grade honor roll. An even more important accomplishment was that John continued to use his mental hands over the next four years and graduated from high school in the top 10 percent of his class. Learning to use his own visualization ability made school much more meaningful and enjoyable for John. He no longer had to avoid schoolwork because now he could make sense of it.

Why Have Some Students Developed Cognitive Structures and Others Have Not?

As noted, students develop cognitive structures by being reflectively aware of sensory input and by visualizing information for processing. It's often the case that many so-called "smart" students are those who have received the most effective mediation at home. Encouraged to visualize and reflect from an early age, they come to school with well-developed cognitive structures. Students who appear "slow" due to underdeveloped cognitive structures may have grown up with little mediation or encouragement for reflection and visualization. Other circumstances that can inhibit cognitive structure development include

  • Physical impairments or psychological disorders
  • Living in poverty with limited access to resources
  • Trauma or abuse
  • Fragmented family structures, isolation, or insecurity
  • Limited verbal interaction or communication difficulties attributable to language barriers
  • Extended illness
  • A home life in which learning is devalued
Although these circumstances are outside educators' control, we can accept students and believe it is possible for them to develop their cognitive structures.

What Can a Teacher Do to Help Students Develop Their Cognitive Structures?

Because students have to develop their own expertise in using cognitive structures, teachers can help by encouraging them to develop the following skills:

  • Become reflectively aware of sensory data
  • Visualize information
  • Ask questions and conduct experiments to figure things out on their own
For students to believe and trust us, we teachers must have a caring relationship with them. We also need to ask stimulating questions and provide opportunities for them to make mistakes in safe environments where they don't need to worry about "feeling stupid."

We can use everyday lessons, activities, and content to help students develop cognitive structures (see Figure 1.4). Although we work within a set curriculum, this goal can influence our choices about what and how we teach. If, for example, our goal is simply raising test scores, we will only teach what is tested. If our goal is developing metability, we will use lessons designed to develop the cognitive structures that equip students to learn, create, and change.

Figure 1.4. Use Content, Activities, and Assessment to Develop Cognitive Structures

As teachers begin to understand how students need to use cognitive structures to make sense of information presented in class, they analyze their lessons in terms of these two questions: (1) Which cognitive structures are needed for this content, activity, and assessment? (2) How can I use the content, activity, and assessment to help students develop these cognitive structures?

Teachers often complain they don't have time to cover all the required content, and they are right. I worked with a history teacher who was expected to cover everything from the European Middle Ages through the Renaissance in six weeks. She said, "I feel like I'm flying an airplane but nobody's on it!" Similar situations exist in other content areas. Because students are exposed to new concepts almost every day without time for processing, they memorize as much as they can and usually forget it within a week or two.

Sometimes teachers get caught up in doing lots of activities that keep students busy and may even produce wonderful products or displays. However, the time would be more effectively spent designing and implementing activities to help students develop the cognitive structures that will equip them for independent learning. For example, Tami, a 5th grade teacher, came to one of the group meetings after doing a science lesson on bubbles. She was exhausted, frustrated, and disgusted.

Tami's Bubble Lesson for 5th Graders

"I'm never doing bubbles again!" Tami complained at our meeting. "My kids made such a mess, just goofed off, started squirting soap and chasing each other around. It was awful!"

"Did you ask them what they noticed about bubbles?" I asked. "Or what they learned from doing the activity?"

"No. I forgot to do that," Tami said. "I just followed the plan in the book."

Tami told me that although she usually enjoyed doing fun activities with her students, she was sometimes disappointed when students seemed to miss the point of the activity. Although Tami was an experienced teacher, she had the courage to admit that it was difficult for her to make the connection between activities and cognitive structures. She began to seriously analyze how she could plan activities to help the students develop and use their cognitive structures.

Through discussion with colleagues in the seminar, she realized that she could have interacted with the group and with individuals as they were experimenting with the bubbles and stimulated reflective awareness by asking questions. For example, she could have asked: "What do you notice?" "Why do you think this is happening?" "What if . . . ?" "What do you understand about bubbles?" "What questions come to mind?" "What do you wonder about?" "Why do you need to know this?" "What does this have to do with life?"

After the discussion, Tami asked her students these questions and requested that they submit responses in writing. At first, her students moaned and groaned, because they just wanted to do another fun activity. However, Tami encouraged them to reflect on what they had learned from the bubble activity. As the students began to share their "notices," questions, and what they wondered about, Tami suddenly realized that every activity could be an opportunity for her students to use and develop their cognitive structures. With this activity, her role was to help them do the following:

  • Notice what changed and what stayed the same (conservation of constancy).
  • Compare and contrast attributes (classification).
  • Notice where and when bubbles formed and floated (time and space).
  • Find ways to describe and document observations and experiences (symbolic representation).
  • Analyze cause–effect relationships (logical thinking).
  • Make creative comparisons (metaphorical thinking).
By using their cognitive structures to process the information and components of the activity, Tami's students were developing their metability.

It took time for Tami to become comfortable with this approach. Several weeks later she came to the group meeting and confessed that she was feeling a little guilty. "I'm not up there doing my 'teacher thing' anymore," she said. "Now, I get the kids started, they begin asking questions, and then they do their work. I go around and help as needed, but they're so involved, it's like they're teaching themselves. I can't believe how relaxing it is!"

Traditionally, we use standardized, formal, and informal testing to assess learning. Students may come to think the grade is more important than understanding. Sometimes teachers give students study guides to memorize for a test. However, if the questions are rephrased on the test, students are lost.

Assessments encourage effective use of cognitive structures when students integrate and apply information. We can assess understanding by encouraging students to formulate questions (not ones they can copy an answer to from the text). The true level of understanding is evident in the kinds of questions students ask. Teachers who model asking open-ended questions stimulate student reflection and the need to know more. We can also encourage students to assess their own understanding by asking them to explain information to a younger student.

We are trained in content, methods, and assessment. We are under immense pressure to cover material and raise test scores. We have limited resources and time for instruction, and we still must deal with other issues, such as schedules, discipline, classroom management, administrative paperwork, special needs students, and so on. Therefore it is more efficient (not more effective) to simply give the students a worksheet and have them fill in the correct responses. Some teachers will object and say, "I don't do that!" Interestingly, it is challenging for most teachers to step back and analyze their beliefs and practices about teaching and learning. As I work with teacher groups, I encourage them to videotape their lessons and bring the tapes to the group for analysis. It is truly a "eureka" moment when they realize they do most of the talking (even answering their own questions) and encourage imitation rather than cognitive processing. They also notice how they assume everyone in class understands when one student responds correctly, and how they (not the students) are doing most of the work. Through discussion, the teachers also begin to see how their curriculum can help develop the cognitive structures needed for metability.

Although I see that it is challenging for these teachers to transform their thinking and embrace this new focus, they always express relief and renewed energy when they see their students learn, create, and change. One teacher with 28 years of experience commented, "Why weren't we taught this in our teacher training? How did I ever get through all these years not knowing this? This is so much more enjoyable and satisfying for me and the kids!"

Suggestions for Practice

  1. Build caring relationships with your students. They will believe you and work with you if they trust you and know you care for them. Spend time with them. Listen to them.
  2. Encourage students to be reflectively aware. Prompt them to notice what their senses are telling them. Allow time for them to wonder about their thoughts and reactions. Encourage them to suspend judgment and delay output to allow for effective processing of information.
  3. Encourage students to use their imaginations to visualize. When students can picture (or hear, feel, taste, or smell) data in their minds, they can carry it with them when the information is out of sensory range. Visualizing helps transform physical data into abstract representations.
  4. Encourage students to use cognitive structures to process information in the following ways:
    • Make connections with prior knowledge and experience and share what they bring to the learning situation. Ask them to explain how they put things together in their mind and why they do it the way they do.
    • Look for patterns and relationships among bits of information to integrate and make meaning. Ask students how they can move the bits of data around to make different kinds of patterns.
    • Formulate rules to process information quickly and automatically. Rules are guidelines or predictable patterns that provide structure. Applying rules in appropriate situations uses less mental energy than constantly relearning information or ways of doing things.
    • Abstract generalizable principles to transfer learning from one situation to another.
  5. Mediate meaning for students. Model, coach, question, listen to, and encourage students. Analyze content, activities, and assessments to identify which cognitive structures are needed for the lesson and how to use the lesson to develop cognitive structures.
  6. Encourage students to ask questions and to wonder. This is especially important to clarify their interpretations of what they see, hear, and experience so they don't form misconceptions. Encourage students to ask themselves: "What does this mean to me?" and "How would I explain this to someone in my own words?" When students begin to ask themselves these questions, they become their own teachers.
  7. Instead of "telling," use open-ended prompts and questions.

Here are some examples:

  • What sense do you make of this?
  • What questions come to mind as you think about this?
  • Which part do you know for sure? Which part do you understand?
  • What do you notice?
  • What kind of pattern do you notice?
  • What do you wish was easier? (Students will respond to let you know where they need help.)
  • Why? (Ask this question to encourage students to elaborate on their responses—without giving them nonverbal clues about whether their responses are correct.)
  • What did you understand the question to be?
  • What do you wonder about?
  • How is this like life?
  • If you were going to explain this to someone, how would you do it?
  • If you did know, what would you say? (Use this when students respond to a question by shrugging their shoulders or saying, "I don't know.")
  • Tell me in your own words what you understand.
  • Tell me more.
  • Help me understand.


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