Building on What We Know: Cognitive Processing

The role of prior knowledge, expectations, context and repetition/practice in both processing and using information and making connections are covered in this episode. Fe MacLean, a first grade teacher at Paddock Elementary School, Milan, Michigan, and Sandie Gilliam, a ninth and tenth grade mathematics teacher and Kris Neustadter, a special education teacher at San Lorenzo Valley High School, Felton, California, are featured in this episode. Stanford University professor Roy Pea augments the teachers’ segments with expert commentary.

Key Questions

• How do we process information so that we can use it effectively later?
  How can teachers organize learning to support student understanding?

Learning Objectives

• Information processing – Teachers will understand how information is received, organized, and remembered.
• Associations and connections – Teachers will become familiar with strategies for helping students to make associations and draw connections among concepts and for enhancing memory and information use.
• Novices and experts – Teachers will understand how experts and novices differ in how they solve problems and use knowledge. Teachers will consider how to organize instruction to encourage the development of expert strategies.

Session Outline
How do we perceive and understand the world around us? How do we make sense of events and new information? What helps us to remember or forget? How do people think when they are solving problems? And why – and how – does an expert solve a problem more efficiently than a novice? In this session, we explore cognitive processing – the work we do to take in, organize, and make sense of new information. Teachers can assist students as they grapple with new ideas, organize, and communicate what they have learned.

How Does Experience Affect the Brain?
In How People Learn, Bransford and colleagues (2000) identify three major points about brain development that are important for education:

• Learning changes the physical structure of the brain,
• These structural changes alter the functional organization of the brain; in other words, learning organizes and reorganizes the brain, and
• Different parts of the brain may be ready to learn at different times.

Learning and the Physical Structure of the Brain
As we interact with the world around us, nerve cells, or neurons, send and receive information to and from other nerve cells. Communication between neurons takes place across microscopic gaps, or synapses, and nerve impulses are transmitted neurochemically across these synapses. The neuron integrates the information received from the synapses, which in turn project information to other parts of the body, such as the muscles. This process is the basis of how we think, move, talk, and make sense of the world around us.

New connections are added to the brain in two ways:

• Early in life synapses are overproduced,
  Then some are selectively lost (or pruned) because they are not used.

More complex cognitive processing occurs in the cerebral cortex – the blanket of cells that covers the brain and is divided into lobes, each of which performs many different functions.

It is a common misperception that individuals’ intelligence and brain development are entirely determined by biology. Education and experience do develop the brain.

Cognitive psychologists—those who study how we learn by conducting human experiments and observations—can help us to bridge understandings in neuroscience with implications for the classroom.

How Do We Perceive and Make Sense of the World Around Us?
We are constantly bombarded with stimuli and information, not all of which can be attended to at once. What is perceived and processed in the brain depends on several features of the stimulus as well as of the perceiver. Critical are –

• what captures our attention – the visual, auditory, or other attributes of the stimulus that cause us to pay attention
• how we selectively filter out aspects of the information that are unfamiliar or uncategorizable to us or that do not mesh with our expectations
• how we organize the information in our brain, connecting it through associations with other things we know.

Individuals process information differently in the brain. For example, people learn through different pathways and modalities – visual, aural, kinesthetic – and with different kinds of representations. These differences pose a challenge for teachers, requiring that they represent ideas and information in ways that allow for different kinds of processing and figure out what will allow certain students to process information most effectively.

Many researchers attribute specific learning difficulties to problems that occur when the brain processes language and other visual, auditory, and kinesthetic information.

Learning disabilities take different forms – they are related to language comprehension and production, motor skills, social skills, and attention, for instance.

It is important for teachers to have skills and tools for observing and cataloging the kinds of tasks with which students seem to have difficulty, as well as those with which they have greater success, as a guide to curriculum planning and instructional adaptations.

How Do We Remember?

• For learning to occur, facts, concepts, and ideas must be stored; connected to other facts, concepts, and ideas; and built upon. Cognitive theorists have studied the nature of memory to determine how and under what conditions people retain or forget information.
• How can memory be enhanced? Researchers have found that information is stored in several forms – visual, verbal, and by its meaning. When physical, auditory, and visual stimuli are combined with symbolic materials like language or numbers, the ability to retrieve information is likely improved.
• Research also demonstrates that when people are asked to remember a series of events or list of words, they will do better at recalling them if they create categories or meaningful connections among them, and if they “chunk” this information into smaller groupings.
• Other strategies for enhancing the retrieval of learned material include overlearning, learning with understanding, and relating material to an organized knowledge base.
• When the curriculum is organized in a manner that allows new material to build on earlier learning, and when new material is tied to what students already know, teaching effectiveness is increased.

How Do We Organize and Build Knowledge?

• Perceiving and remembering are influenced by our prior experience, our expectations for a given situation, and our ability to make connections among ideas.
• Cognition is cultural. The ways people categorize ideas, build knowledge, and reason are all influenced by the values and common activities of their culture.

Making Connections

• The simplest kind of association is developing a connection between two ideas.
• The way a set of new information is presented to students makes a difference in their learning and their ability to make new connections.

Developing Conceptual Knowledge

• Throughout their lives, individuals develop more complex associations among words, concepts, and ideas. Cognitive psychologists call these “schemas” or general knowledge structures used for understanding and memory storage. Schemas consist of information, in an abstract form, of the associations we have with a word, concept, or idea, and they in turn connect with other schemas.
• The schemas one brings to a learning experience – a person’s background knowledge – influence what is learned and what is retrieved. Part of the teacher’s role is to develop and enrich students’ existing schemas and the ways their minds organize information.
• As we develop understandings of concepts, we create new associations among ideas. One way to make these new associations visible to teachers and students is by creating a visual representation or diagram of the underlying features and structures of a concept.

Developing Explanations

• Another way we build knowledge is through the construction of explanations about different phenomena. Individuals carry around “mental models,” or explanations, in their heads for why things happen.
• Mental models may come from students’ intuitive theories – like theories of motion or theories of evolution – or they can be provided as a form of instruction by teachers or textbooks.

There are several ways teachers can support all children in organizing their learning, including those who experience challenges in cognitive processing.

1. 1. Teachers can structure the learning process.
      • Establish routines and procedures.
      • Simplify directions, cluster and sequence activities.
      • Demonstrate an idealized version of the task to be performed.
      • Organize and guide practice efforts.
   2. Teachers can organize information and help students organize what they are learning by taking appropriate steps.
      • Providing categories and labels for organizing information.
      • Providing alternative representations (e.g., pictures, metaphors, and analogies)
      • Using concrete examples of abstract ideas
      • Drawing attention to critical features or ideas
      • Using a multi-sensory approach to teaching: Providing opportunities for students to process and organize information through different pathways for input and output
      • Encouraging students to organize information by thinking out loud, talking with others, visualizing concepts, and making connections to personal experiences
   3. Teachers can identify students’ strengths, preferences, prior knowledge, and experiences.
      • Identifying and building on students’ preferences for information processing
      • Making connections to their prior knowledge and experiences
      • Using culturally familiar strategies for learning and responding
      • Using culturally familiar examples

Knowledge in Practice: How Do Experts Solve Problems?

• One of the ways researchers have discovered differences in cognitive processing is by comparing experts and novices as they solve problems in specific domains. Asking an expert and novice to solve the same problem reveals important differences in information processing, the organization of knowledge, and reasoning.
• Researchers have found that expert knowledge tends to be organized around core concepts or big ideas that guide their thinking and encompass a large number of interrelated facts or patterns.
• Experts not only have acquired a great deal of content knowledge, but they also understand how to determine the contexts in which particular kinds of knowledge are useful.
• Experts also use a number of different strategies to solve a problem.
• Experts tend to check their solutions to problems and monitor their own work more frequently,
• Conceptual understanding – that is, an understanding of the underlying ideas and relationships in a domain—influences what the learner pays attention to, what is remembered, and what kinds of errors are made in learning something new and with better results than novices.

Glaser (1992) suggests that teachers consider four strategies in designing experiences for students that will enable them to develop competence in solving problems:

• Provide increasingly complex opportunities to practice solving problems
• Create opportunities for self-monitoring
• Encourage principled performance (e.g., help students link their schemas for problem types to specific problem-solving strategies
• Consider the social context of learning

Conclusion
Attending to cognitive processing means taking into account and tapping into the often-invisible ways we develop knowledge, solve problems, and make sense of our worlds.

1. Automaticity – learning of a task or skill so well that retrieval is automatic or requires little conscious effort.
2. Cognitive Processing – the work the brain does to take in, organize and make sense of new information.
3. Cognitive Psychologists – scientists who study how individuals process information, build knowledge, and develop as problem solvers.
4. Conceptual Understanding – understanding of the underlying ideas and relationships in a body of knowledge or facts.
5. Expert Knowledge – information organized around core concepts or big ideas that guide thinking and encompass a large number of interrelated facts and formulas. Experts are particularly adept at recognizing patterns and recalling information because of the ways they chunk and organize information.
6. Hierarchical Presentation Strategy – Presenting new information beginning with simple, concrete ideas and later advancing to more complex, abstract concepts and principles.
7. Mapping – the creation of graphic organizers; visual and verbal diagrams of the knowledge to be remembered (Lambiotte et al., 1989, cited in Gage and Berliner, 1998).
8. Mediation – “the process of creating meaningful links between apparently unrelated items or ideas” (Gage & Berliner, 1998, pg. 288). The goal of mediation is to help make the second idea in a pair more memorable by linking it to the first idea in some meaningful way.
9. Mental Models – the explanations for facts that individuals carry around in their heads; they can be described as “constructed working models of the world used in the service of understanding” (Medin & Ross, 1992, pg. 359).
10. Neuroscientists – scientists who study how the brain changes as individuals learn and experience new things.
11. Novices’ Knowledge – information organized around relatively unrelated facts or patterns. Novices often get distracted by apparently important, but often irrelevant aspects of the problem.
12. Overlearning – the process of continuing to study and practice material after it has been mastered.
13. Schemas – an association of words, concepts, and ideas. Schemas are general knowledge structures used for understanding and for memory storage. Schemas consist of information, in an abstract form, of the associations we have with a word, concept, or idea, and they in turn connect with other schemas.
14. Top-down Presentation Strategy – Presenting new information with advance organizers, or a set of general concepts describing how ideas are grouped or structured.

Step 1. The video segments in The Learning Classroom were taped as teachers worked in their own classrooms. As you watch, jot down the questions you have about what you see the teacher do and how the students respond.

Step 2. When you’re done, click on the episode title from the list and compare your questions with the Questions for Reflection and responses that our project team has anticipated.

Step 3. Review the responses we have prepared to questions that match the ones you have asked. The expert responses are not “final answers,” they are provided to give you a starting point for your own reflection. What else might you add to the response you read?

Question 1: The teacher says she “asks questions to help them draw the kind of concepts that I want them to draw.” She appears to lead the children to decide on certain categories rather than telling them. Could the children build their own categories and then compare their categories with those developed by scientists?

Response 1: Generally, yes they could. One question about doing that is how important is it to understand the differences between “first grader categories” and “scientists’ categories” for these students? The teacher, Fe MacLean is giving the students an opportunity to describe the ways in which animals differ, and she is taking the students’ collective prior knowledge and structuring it in a new way to introduce a mode of inquiry used by scientists. That might be a sufficient objective for this exercise.

Question 2: The teacher is listing different theories from students without comment. There doesn’t seem to be much discussion of them – organizing them in any way.

Response 2: Sometimes MacLean will appear to be writing down thoughts of her students randomly across the whiteboard or easel pads she is using without comment. As we see, however, she may later draw a grid or some other structure to give the students an “aha”moment as they see the pattern she has anticipated for the information.

Later, MacLean enriched students’ schemas for classification of animals and extended their science understanding through their museum trip and their pop-up book and social studies understanding through their artwork and writing. In each case, the students worked problems out together.

Question 3: What was MacLean’s goal for the household items activity? How does that fit into her overall plan?

Response 3: MacLean is exploring basic concepts of community and the interrelationships of people and she does this using a process that her students use in many situations – facilitated brainstorming, starting with a very simple question or idea and building on it. In this case, she is developing the concepts that a community is made up of many people with special skills, and that these people use their skills to help each other. Earlier, students had discussed how people in a community depend on things (machines, appliances, utilities, etc.) to help them do their daily activities. On this day, MacLean and her students explored what happens when these things don’t work. After they agreed that people often call on other members of the community to help them fix things, the students extended their learning by matching each need to a person who could address it. As they continued work on their own reading/writing/drawing tasks, MacLean encouraged students to discuss their personal experiences with each other – in order to solidify the relationship between need and service. In general a community is made up of many people with special skills that use those skills to help each other.

Question 4: Fe MacLean and Sandie Gilliam make free-flowing classroom discussion look so easy. When I try that, my students either clam up or go off task. How do you get kids started in this process?

Response 4: Gilliam and MacLean both begin building their classroom communities in September, and then develop it throughout the year. Besides making connections that may assist their students’ cognitive processing, they use a variety of other learning theories that create learning communities in their classroom. For instance – they model and support taking intellectual risks; they manage discussions to include many participants; they expect and encourage students to listen and learn from the teacher and each other; and they make sure students’ home cultures are represented and respected in class.

Both Gilliam and MacLean also follow up their large group discussions with individual and small group work where they can address the specific learning needs of students – making sure no one is left behind. These steps not only support student learning – they also tend to reduce many typical classroom disruptions.

Question 5: Making the pop-up book and drawing the pictures – this looks like it took a lot of time away from instruction. How could MacLean be sure that her students were gaining deep understanding or proficiency as a result of this process?

Response 5: The “pop-up” feature of the books is a motivating factor for the students. As they make them students are also synthesizing what they have learned by manipulating the information in different ways. They are gaining a deeper understanding and proficiency by putting their skills to use in an integrative fashion. In a teacher-directed lesson the students recall the bits and pieces needed to answer questions, and this is helpful. In the process of creating their own book, however, students must draw upon the full array of their knowledge. More important, because they have spent time integrating this knowledge, they are more able to retrieve it later when they need it to solve new problems.

Question 6: What strategies are good for locating gaps in a student’s prior knowledge without embarrassing the student? I’ve given pre-tests before, but sometimes they backfire. I’m looking for more.

Response 6: Both Gilliam and MacLean have created a classroom culture that allows students to participate in these brainstorming sessions without risk. One part of that is introducing the academic concepts they are teaching with a discussion of something with which they know their students are already comfortable – such as animal photographs, living in a household, or basic supplies needed for travel. They ask students open-ended questions that relate to their daily experiences, and then engage the class in attempting to resolve these real life problems.

As you do the same, listen carefully to the discussion and shape your questions to draw out just what your students are thinking. Focus your attention more on the process than the answers themselves. In addition to giving you insight into what your students are thinking and how they are organizing their conceptions and misconceptions, this also fosters an atmosphere where students know that they are respected for their contributions to the class’s learning as they help each other figure out the answer.

Question 7: Gilliam seems to use top-down advance organizers and MacLean seems to move from bottom up – starting with simple, concrete examples and moving to abstractions. Is one better than the other? How do I know which approach to use with my students?

Response 7: Research tells us that each approach has its place, and that there’s nothing wrong with approaching each concept from a variety of perspectives. Students learn better when they have multiple pathways to understanding content. You will become more adept at knowing what works with your students by listening, questioning, and working through problems with your students, and by learning as much as you can yourself about the instructional content.

Question 8: Some of Gilliam’s students looked bored or uninvolved from time to time. There are a lot of kids like that in my class. How does she keep them all engaged?

Response 8: Gilliam does several things to keep students engaged in learning. One example is to keep going back to the dramatic storyline of the Overland Trail to maintain the connections between math and real-world situations. She also connects the Overland Trail scenario to students’ lives, because the mathematics that could make a difference of survival on the Trail also have an impact on the everyday life of 21^st Century students.

A second technique Gilliam uses is calling up individuals to solve problems for the group, and then calling on the group to help the individual. The give and take of that interaction keeps everyone engaged. As Gilliam’s teaching partner, Kris Neustadter mentioned, they also provide supports that give every student access to the information under discussion.

Question 9: Gilliam appears to have the benefit of a second teacher in her classroom. I’m a one-person show. How can I make sure that all of my kids are getting it when I’m all there is in the classroom?

Response 9: Gilliam has the support of a special education teacher in her classroom because her class includes a number of special education students. However, she also uses members of the class to support her instruction. She, as many other teachers, has created a culture where students are encouraged to ask each other to explain why they are solving a problem in a certain way. This isn’t a matter of “trying to make the job easier,” it benefits the learning of all the students who are sharing knowledge.

Linda Darling-Hammond
Charles E. Ducommon Professor of Education, Stanford University

Roy Pea
Professor of Education and Learning Sciences, Stanford University

Fe MacLean
first grade teacher, Paddock Elementary School, Milan, Michigan

Sandie Gilliam
tenth grade teacher, San Lorenzo Valley High School, Santa Cruz, California

Kris Neustadter
special education teacher, San Lorenzo Valley High School, Santa Cruz, California

Excerpts from an interview with Roy Pea, Director of the Stanford Center for Innovations in Learning, Stanford University

Discussion of “Building on What We Know – Cognitive Processing”

Cognitive processing refers to what the mind is doing as it listens, as it comprehends, as it produces symbol systems of all kinds, whether it is language, whether it is visualizations of different kinds of knowledge. And the term processing is used by analogy to the computer which processes information, does various transformations of it to get to results. And a lot of the work in cognitive science sought to understand how the mind worked by building computer models of how the mind worked. And they made some pretty good progress in creating programs that could play chess rather well and solve algebraic equations and things of that nature. Whether they’ve in fact provided an account of how the mind works, is quite up for grabs. But the term cognitive processing has stuck as a way for thinking about the reasoning and thinking that goes on and how it is that the structures and processes of the mind work to reason, to remember, to retrieve information when it’s appropriate, to transfer it to a new situation, to form concepts, and do many of the things that are integral to the learning enterprise. And so cognitive processing is an important thing to think about and learn about, both as a teacher, but also as a learner. I mean, it’s important to emphasize that young kids have pretty developed theories of cognitive processing themselves. People that have studied even elementary school children’s understanding of memory, of language, of reasoning, they’re quite reflective about these things. They recognize that when they’re tired or distracted, they don’t do as well, they don’t remember as much. So they’re attentive to cognitive processing. What teachers can help bring to the equation from the learning sciences is much more attention to teasing out what their learners are thinking and believing by having them represent that knowledge in conversations, in pictures and in other modalities.

How we process information is so variably influenced, it’s a miracle that we do as good a job as we do. We can be influenced by the energy we have at a particular time of day, hunger, things that are very common sense. Things that are less common sense, that teachers can do something about, involve how are students already thinking about the subject matter, that they’re doing some cognitive processing about. And for that, it turns out that the research tells us we don’t listen enough to how our students think. We don’t give them an opportunity to voice their beliefs, to draw pictures, to tell them what they think about and what they see. And many adults are surprised when you actually start to interrogate a child in the most positive sense, to understand how they think and believe, to find that their thoughts are very curious and unusual constructs. They might believe that a cloud really is alive, like a person, as a Piaget taught us years ago. Or that a moving tree is a living thing like a person. And these beliefs that they have are important to understand for us to go building on in instruction. So, prior conceptions, some call them misconceptions, we prefer to call them prior conceptions, are one very significant influence, that work in the learning sciences has helped reveal over the last number of years and that I think teaching can really pay attention to.

One of the highlights, and again work in the learning sciences, look at representations. Both mental representations – how is it, is it in images or words or in other symbol systems that students are thinking. So this we talk about as mental representation. But every bit as important are external representations, inscriptions. When someone writes something down, a written language, a picture, a diagram of how things work with little arrows for flows and so forth, processes of some kind or other, and, it can be of considerable aid for the teacher to understand how the learner’s thinking and to help advance that learner’s thinking to use these multiple representational forms. And they have different trade-offs. And this is part of what a learner needs to know. A graph may be wonderful for looking at a slope, but not so good for other purposes. So, each of the representations that we use for reasoning and for asking questions, has trade-offs affiliated with it. There are certain things that it’s good at and other things that it misses and, and part of what we need to help learners do is to understand the strengths of those representations, and when they’re appropriately used.

Visualizations are, as Rudolph Arnheim tells us in his famous book Visual Thinking, one of the more interesting inventions of human kind. Of course written language is a form of visualization, but usually we’re talking about many other things and they range from pictures of actual, unique situations to diagrams that represent a huge class of situations. They also include maps, concept maps where one can do concept mapping of the relations between concepts and something new that one is learning. And one of the things that visualizations do is they use vision to think. And so, that’s one of the strategies that humans have acquired to overcome their cognitive processing limitations. They can only keep so much in memory at once. The magical number is seven plus or minus two. And so they write things down in the world to serve in some sense as cognitive aids for their thinking. So as we go writing or drawing a diagram we can start to look at part/whole relationships in a way that’s very hard if we have to hold it all in memory. So a diagram can in a single glance, show the relation between the parts of the machine to the machine itself. McAuley’s wonderful book, How Things Work is one good example of this and in the computer world, more and more effort is going into creating visualization systems that can help students understand very complicated global phenomena like, issues in the environment, global warming, and changes of that kind.

Visualizations can help students depicting their thinking about a situation which might include the provision of an explanation. This is how it works because. And what visualizations can do is off-load from a pretty limited memory, not just in kids, but in adults, some of the work. That is to say you can draw in a picture something that you then no longer have to remember as you go building a complex story. So, I could create a diagram that describes my day and all the things that I do in it and what I need to do as part of a plan. We do that all the time – it’s called a to-do list. So the to-do list ends up being a visual organizer that helps solve a number of problems of memory and thinking. And the same thing that makes a to-do list useful for an adult, makes concept maps and other kinds of visualizations useful for kids. It becomes a cognitive tool for reasoning and for explaining and for communicating.

Well, many of the same strengths that make visualizations useful for reasoning and thinking are available as tools for the teacher, as well. The rub there, or the catch, is that if the teacher only uses these powerful visualizations to tell knowledge to students, they’re not going to get the opportunity to give students the power of these same tools. So, I did some research work in a number of, well-known high school classrooms some years ago on how geometrical optics is taught in physics. And this is an 18th century science – it’s nothing new, but it involves how does light interact with matter, like a lens or a mirror, to form images. People have experiences of this every day. And, diagrams are used to teach this subject matter. But in these classrooms where students did very well on tests, very famous schools actually, when they were asked to reason aloud at a chalkboard later, and by drawing a picture, they were very poor and didn’t reveal much understanding. And the simple reason was that they had memorized the formulas. They had memorized the diagrams they had seen the teacher put on the board, instead of having some facility with using this powerful visualization tool themselves. So if teachers only use visualizations in a lecture mode and don’t give the students an opportunity to construct visualizations, they’re missing a crucial learning and teaching opportunity.

So, visualizations provide a new window into thinking beyond hearing students talk. So a student who might be less verbally oriented, may be quite willing to draw a picture of how they’re thinking about things and to even label its parts in a way that can then become what we would call a conversational prop for a learning conversation – something that can be pointed at, refined, talked about in a learning community in which all of the kids in the classroom are creating visualizations. And part of what’s really interesting when a teacher does this, in virtually any subject matter – it can be math, science or humanities, social science, social studies, language arts – is that you find real differences in the diagrams and the pictures that kids create. And part of that is due to their having different beliefs. Some of it is due to their having idiosyncratic conventions for representing the knowledge in, some form of a visual representation. So this gives you opportunities as a teacher for doing several things at once. One is to introduce more canonical or typical forms of representing those ideas visually. Another is, learning about potential problematic conceptions in the way that the child is thinking as revealed through those pictures. And the third opportunity is that it provides their peers with a model for both appropriate ways of thinking in the domain and problematic ones. So it has many, many opportunities in making thinking visible.

The differences between novices and experts in any of the fields in which cognitive scientists have studied them, from chess to writing to mechanics to bartenders, all of these different areas are ones in which experts tend to among other things that differentiate them from novices, see the world differently. They see patterns in situations that are typical problems in the area. So if you’re a chess master, a classic finding that has chess experts versus novices, look very quickly at chess boards that are flashed with pieces that are in legal positions, that is ones that could’ve actually happened in the game, and you find, not surprisingly, that experts remember far more than novices do because they can see what the meaning of the different chess pieces in that position is, what possible states of play they could represent because they’ve had huge experience, usually over 50,000 hours to become a chess expert. But if you, interestingly enough, just scramble up the pieces and show the novices and experts those same boards, there’s no difference between an expert and a novice. So it’s not that experts have bigger memories. The novices do. But they’ve come to chunk the world differently and what they see. The same thing works for an expert teacher versus a novice teacher. When they look in a classroom in the to and fro of 25 to 30 kids all vying for attention and, in the context of some complex piece of teaching, novice and expert teachers see very different things. They see different opportunities. They see different problems arising. Like a chess player, they’re running ahead what are different scenarios. If I do this thing with that child’s question, what will happen to this other group? And so part of what it means to bring the child novice to being more of an expert in relation to, say mathematical problem solving, involves looking at what are the aspects of skills and concepts that an expert has and how can we help scaffold or support the learner to go building those. And so some of the things that differentiate mathematics experts from novices are, among other things, their facility with lots of representational systems. They don’t only use equations. They will write. They will draw diagrams. They will use computer programs. They will create graphs of different kinds for looking at functions. They will even do data tables, again, depending on what their purpose is. And so they have a meta-representational capacity. That is, they know what representational systems there are and what they’re good for and pick them. They also manage their mental work. They have a metacognitive capacity to think about the time that’s allotted, think about what they know and don’t know and focus their attention so if they go pursuing a process for a particular point in time, they don’t run it into the ground and run out of time. They’ll go to a certain point, see that it’s not gonna work, and shift course. And so, these are only some of the properties that differentiate novices from experts. But, part of the process of helping students become more expert involve modeling the kind of thinking that a more mature problems solver in the domain does, giving students opportunities to pursue that same kind of thinking aloud with support from the teacher and the distributed experts in the classroom, because some of the kids may know more than that particular child. And to, over time, fade that kind of support, having seen what expert problem solving looks like, and supported the student in trying to perform at a higher level and then, withdraw the support and see to what extent they can move themselves along an expertise continuum. This is, of course, at a level of abstraction, but I’m sure you’ll be playing that out in the series in the concrete examples.

There are various visualization techniques that are used heuristically. Now this is a word that is kind of, to mean rules of thumb. Things that may be useful, not necessarily guaranteeing a result which an algorithm does. So, heuristically, a matrix, or a table is often really good at brainstorming, and highlighting gaps in one’s thinking. So, if you’d like to take an example, you might have the faculty who teach your math courses, as rows, and the different topics that are covered in the curricula being the columns, and you might find from a process of curriculum mapping that low and behold, there are some missing topics that you should have been treating in the curriculum that you didn’t. This ends up being a useful value of the matrix for faculty work. Well it’s not surprising that it could be useful for kids as well. And, so in their case, you might want to, be using matrices for planning different kinds of story outcomes in a story writing task, or, science problem solving as well.

[looking at the segment in “Building on What We Know – Cognitive Processing” that features Sandie Gilliam]

Part of what this teacher does that’s extremely useful is setting the problem solving context in a motivational one of human narrative and drama. And that helps, attracts students’ attention, probably relates to situations they could imagine themselves in, as opposed to being simple, dry, decontexturalized formula. She then gives them the opportunity for reasoning quantitatively about their use of supplies during their trip, water in particular. And so they then have the opportunity to talk about what the shape of a graph would look like for water availability at different times in the trip – when they were trying to conserve and a period where they don’t know they’re going to get water, when they refill and so forth. And these issues of rate of change of a quantity are important not just for mathematics, but in physics and in a whole host of other subject areas. So, engaging students’ sense making around a narrative that then provides a kind of a smart tool, a graph, for helping reasoning with, is really a powerful strategy for bringing mathematical meaning into students’ reasoning and experience, even in what, in this case could easily be a social studies problem where no mathematics might normally be done. So, she’s doing a lot of work here weaving together some historical work, so the students’ making sense of situation and mathematical representations.

[looking at the segment in “Building on What We Know – Cognitive Processing” that features Fe MacLean]

So in Fe’s class, she has the students classify animals, with cards that represent those animals because she’s really interested in how these students think about the animals and on the basis of what features do they categorize them into groups. To hook back to our novice/expert distinction, a lot of the methodology there for distinguishing novices from experts has them sorting, different problems into piles. And experts tend to look at deep similarities, between problems situations, say in physics, whereas novices tend to categorize based on surface features of the similarity of, for example, the diagrams and the problems. Are there things going downhill in both problems? Whereas at a deep structural level in terms of Newton’s Laws, that might not be, those things might not be similar. So in this case she’s trying to tease out what are the student’s categories? And then she does some work tapping the distributed expertise of the group around what are the features for thinking about these concepts? Why are these different, species in one category rather than another? And she starts to get out what are the properties, that for these kids help define those categories. A very different approach would’ve been to just tell them the answer. What are the categories as we scientists have defined them, which doesn’t give the students an opportunity to, on the one hand do their own thinking about it, nor does it give the teacher an opportunity to learn what they’re already thinking. And, of course, it doesn’t mean that their results will be error-free. They may have concepts that need some work. But the point is, she’s engaged their thinking in a way that if she’d only told them the answers, she would’ve engaged only their memory in a way that after the course is over and their tests are done, they are most likely to go back thinking the same way that they did before. So, the opportunity of bringing out students’ concepts and then building them in a conversation in the moment, is the powerful idea in this scenario.

WEB-BASED READINGS

All Kinds of Minds. (n.d.). Our perspective: The approach. Retrieved September 11, 2002.

http://www.allkindsofminds.org/

Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000). How experts differ from novices (Chapter 2). In How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.

Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000). Mind and brain (Chapter 5). In How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.

D’Arcangelo, M. (1998, November). The brains behind the brain. Educational Leadership, 56(3). Retrieved 1/12/03.

Five authors of recent books about brain research identify what they regard as the most important implications of recent findings in neuroscience and how these ideas can translate to the classroom.

Greeno, J.G. & Hall, R.P. (1997, January). Practicing representation: Learning with and about representational forms. Phi Delta Kappan, 78(5). Retrieved 8/27/01, from http://www.pdkintl.org/kappan/kgreeno.htm

This article describes how knowledge can be represented inside and outside of the classroom.

LD basics, link on the National Center for Learning Disabilities Web site. Retrieved September 11, 2002.
http://www.ncld.org.

Related links

Learning Science Institute
The Learning Science Institute is a basic and applied research organization that focuses on how people learn, with a special focus on how learning can be enhanced through new uses of technology and through innovative teaching practices.

The Learning Research and Development Center – Research Institute
http://www.lrdc.pitt.edu/
University of Pittsburgh
3939 O’Hara Street
Pittsburgh, PA 15260
Phone: 412-624-7020
LRDC is a multidisciplinary research center whose mission is to understand and improve learning by children and adults in the organizational settings in which they live and work: schools, museums and other informal learning environments, and workplaces.

The Thinking Classroom
http://learnweb.harvard.edu/alps/thinking/
Developed as part of the Active Learning Practice for School site and Harvard Project Zero, the Thinking Classroom Web site offers resources for teachers about how to teach critical and creative thinking in the classroom.