We feel, therefore we learn: the relevance of affective and social neuroscience to education

Immordino-Yang, M.H. & Damasio, A. (2007) We feel, therefore we learn: the relevance of affective and social neuroscience to education. Mind, Brain and Education,1: 3-10.
The authors contend that the relationship between learning, emotion and body state runs much deeper than many educators realize and is interwoven with the notion of learning itself. It is not that emotions rule our cognition, nor that rational thought does not exist. It is, rather, that the original purpose for which our brains evolved was to manage our physiology, to optimize our survival, and to allow us to flourish.

In brief, learning, in the complex sense in which it happens in schools or the real world, is not a rational or disembodied process; neither is it a lonely one.

Emotions are not just messy toddlers in a china shop, running around breaking and obscuring delicate cognitive glassware. Instead, they are more like the shelves underlying the glassware; without them cognition has less support.

Two important hypotheses:

• First, because these findings underscore the critical role of emotion in bringing previously acquired knowledge to inform real-world decision making in social contexts, they suggest the intriguing possibility that emotional processes are required for the skills and knowledge acquired in school to transfer to novel situations and to real life. That is, emotion may play a vital role in helping children decide when and how to apply what they have learned in school to the rest of their lives.
• Second, the close ties between these patients’ decision making, emotion, and social functioning may provide a new take on the relationship between biology and culture. Specifically, it may be via an emotional route that the social influences of culture come to shape learning, thought, and behavior.

Without adequate access to social and cultural knowledge, these children [with prefrontal damage] cannot use their knowledge efficaciously. As Vygotsky posited more than three quarters of a century ago, social and cultural functioning actually does underlie much of our non-social decision making and reasoning. Or, more precisely, social behavior turns out to be a special case of decision making and morality to be a special case of social behavior.

The more people develop and educate themselves, the more they refine their behavioral and cognitive options. In fact, one could argue that the chief purpose of education is to cultivate children’ s building of repertoires of cognitive and behavioral strategies and options, helping them to recognize the complexity of situations and to respond in increasingly flexible, sophisticated, and creative ways.

The authors' goal in presenting their model is not to devalue established notions of cognition and emotion but to provide a biologically based account of this relationship and to begin to specify the nature of the overlap between cognition and emotion in a way that highlights processes relevant to education. These processes include learning, memory, decision making, and creativity, as well as high reason and rational thinking. They also include the influence of the mind on the body and of the body on the mind.

In teaching children, the focus is often on the logical reasoning skills and factual knowledge that are the most direct indicators of educational success. But there are two problems with this approach. First, neither learning nor recall happen in a purely rational domain, divorced from emotion, even though some of our knowledge will eventually distill into a moderately rational, unemotional form. Second, in teaching students to minimize the emotional aspects of their academic curriculum and function as much as possible in the rational domain, educators may be encouraging students to develop the sorts of knowledge that inherently do not transfer well to real-world situations.

Simply having the knowledge does not imply that a student will be able to use it advantageously outside of school.

It is not enough for students to master knowledge and logical reasoning skills in the traditional academic sense. They must be able to choose among and recruit these skills and knowledge usefully outside of the structured context of a school or laboratory.

Neurobiological evidence regarding the fundamental role of emotion in cognition holds the potential for important innovations in the science of learning and the practice of teaching.

Preparing Teachers to Learn from Teaching

Hiebert, J., Morris, A. K., Berk, D., and Jansen, A. (2007). Preparing Teachers to Learn from Teaching. Journal of Teacher Education, 58(1):47-61.

Four skills needed to learn from teaching:
1. What were the learning goals? What were students supposed to learn?
2. To what extent were the goals achieved in the lesson? What did students learn?
3. Why do you think the lesson did or did not work well? (How did teaching help [or not] students learn?)
4. How would you revise the lesson if you were to teach it again? How could teaching more effectively help students learn?

Skill in reflecting on these questions can improve teaching performance and understanding the connections between instruction and student outcomes.

Genres of Teacher Ed Research

Borko, H., Liston, D., and Whitcomb, J. A. Genres of Empirical Research in Teacher Education. Journal of Teacher Education, 58(1):3-11.

Is empirical research on teacher education really so bad? Critics decry its inconsistent quality and inability to respond convincingly to some of the field’s most vexing problems. At the same time, teacher education is a relatively new field of study. Those who have traced its development observe that rigorous, large-scale research on teacher education is difficult, time-consuming, and expensive to conduct; thus, some of the theoretical and methodological advances seen in more mature fields, for example, research on student learning, are just beginning to emerge in research on teacher education.  

In an effort to broaden and stimulate the conversation, this editorial office offers an assessment of four genres that have been central in empirical teacher education research, namely (a) effects of teacher education, (b) interpretive, (c) practitioner, and (d) design. 

"Effects of teacher education" research refers to a body of scholarship concerned with understanding the relationships between teacher education experiences and student learning.

Interpretive research is, at its core, a search for local meanings. Unlike effects of teacher education research, it aims for particularizability, not generalizability (Erickson, 1986). It seeks to describe, analyze, and interpret features of a specific situation, preserving its complexity and communicating the perspectives of participants.

In Zeichner’s (1999) assessment of scholarship in teacher education, he observed “research about teacher education [that] is being conducted by those who actually do the work of teacher education” as “probably the single most significant development ever in the field of teacher education research” (p. 8). This genre, which we label practitioner research, includes action research, participatory research, self-study, and teacher research. Like interpretive research, it aims to understand human activity in situ and from the perspective of participants; however, it differs in two critical ways—the role of the researcher and the overarching purpose for the research. Practitioner research examines practice from the inside; instead of research on teacher education by an outside party, it is research by teacher educators about their practice.

Intentionality refers to the planned and deliberate nature of practitioner research, which can be contrasted to other versions of reflective practice that are typically more spontaneous in nature.

Systematicity refers to organized ways of gathering information, keeping records of experiences and events, and analyzing the information that has been collected and recorded.

Design research is characterized by an intimate relationship between the improvement of practice and the development of theory: The research team works to simultaneously improve practice and contribute to theory by creating models of successful innovations and developing explanatory frameworks about the processes of learning and the tools that are designed to foster learning (Brown, 1992; Cobb, Confrey, diSessa, Lehrer, & Schauble, 2003).

Situating learning in communities of practice - Lave 1991

Lave, J. (1991). Situating learning in communities of practice. In L. Resnick, J. Levine, and S. Teasley (Eds.), Perspectives on socially shared cognition (pages 63-82). Washington, DC: APA.


Key ideas:
p63. Lave views learning as an emerging property of whole persons' legitimate peripheral participation in communities of practice.

p64. Learning is recognized as
+ a social phenomenon constituted in the experienced, lived-in world , through legitimate peripheral participation in ongoing social practice;
+ the process of changing knowledgeable skill is subsumed in processes of changing identity in and through membership in a community of practitioners;
+ and mastery is an organizational, relational characteristic of communities of practice

p65. Lave asks us to consider learning not as a process of socially shared cognition that results in the end in the internalization of knowledge by individuals, but as a process of becoming a member of a sustained community of practice. Developing an identity as a member of a community and becoming knowledgeably skillful are part of the same process, with the former motivating, shaping, and giving meaning to the latter. which it subsumes.


Theories of Situated Experience
Three genres of simulative approaches
1. Cognition plus - cognitive theory that takes into account people, process, relationships, etc., in a social world
2. Interpretive view - Interpretivists argue that we live in a pluralistic world composed
of individuals who have unique experiences and perspectives; the use of language and social interactions contribute to situativeness
3. Situative social practice – Lave’s POV: This theoretical view emphasizes the relational interdependency of agent and world, activity, meaning, cognition, learning, and knowing. It
emphasizes the inherently socially negotiated quality of meaning and the interested, concerned character of the thought and action of persons engaged in activity. But unlike the first two approaches, this view also claims that learning, thinking, and knowing are relations among people engaged in activity in with, and arising from the socially and culturally structured world. This world is itself socially constituted. This third position situates learning in social practice in the lived-in world; the problem is to translate this view in to a specific analytic approach to learning.

Learning as Legitimate Peripheral Participation
Legitimate peripheral participation offers a two-way bridge between the development of knowledgeable skill and identity, the production of persons and the production and reproduction of communities of practice.

Newcomers become old-timers through a social process of increasingly centripetal participation, which depends on legitimate access to ongoing community practice. Newcomers develop a changing understanding of practice over time from improvised opportunities to participate peripherally in ongoing activities of the community. Knowledgeable skill is encompassed in the process of assuming an identity as a practitioner, of becoming a full participant, an old timer. p68

Example 1: Yucatan Mayan Midwifery
Girls/women learn to become midwives through apprenticeship. p70
Broad exposure to ongoing practice, such as that described for the midwives' apprentices is in effect a demonstration of the goal toward which newcomers expect, and are expected, to move. The other is the notion that knowledge and skill develop in the process - and as an integral part of the process - of becoming like master practitioners within a community of practice. p71

Example 2: Alcoholics Anonymous
Cain argues that the main business of AA is the reconstruction of identity, through the process of construction of these life stories, and with them, the meaning of the teller's past and future action in the world. p73

Communities of Practice and Processes of Learning
Participation as members of a community of practice shapes newcomers' identities and in the process gives structure and meaning to knowledgeable skill. p74

The process of becoming a full practitioner in a community of practice involves two kinds of production: the production of continuity with, and the displacement of, the practice of old-timers (Lave & Wenger, 1991). Newcomers and old timers are dependent on each other: - newcomers in order to learn, and old-timers in order to carry on the community of practice. At the same time, the success of both new and old members depends on the eventual replacement of old-timers by newcomers-become-old-timers themselves. The tensions this introduces into processes of learning are fundamental. p74

Apprentice forms of learning occur in graduate programs in universities and in the practice of medicine, law and the arts.

Lave argues that learning occurs under just the circumstances where the fashioning of identity and the gradual mastery of knowledgeable skill are part of an integral process of participation. p77

Questions:
+ What learning curriculum is afforded by the legitimate participation that makes it possible for newcomers to become old-timers in a given setting?
+ What are the characteristics of communities of practice that make broad accessibility to the whole steadily available to newcomers?
+ What are the conditions that make deep transformations possible?

Summary:
+ The main part of the chapter explored ways in which communities of practice and cultural processes of identity construction shape each other. p80
+ Lave recommends a conception of learning as  “legitimate peripheral participation in communities of practice” p81

Ecological theory of knowing; affordance networks, effectivity

Barab, S.A. & Roth, W.M. (2006). Curriculum-based ecosystems: Supporting knowing from an ecological perspective. Educational Researcher, 35(5), 3–13.

Key ideas
p4: James J. Gibson and colleagues have conducted numerous studies that demonstrate how the environment perceptually specifies possibilities for action (chairs as sittable, doorways as passable, platforms as crawlable, etc.). Central to their work is the belief that the environment includes qualitative regions of functional significance (affordances) that are visible to individuals with reciprocal skills (effectivities) and the intention to act (Gibson, 1986).

p8: an affordance is a possibility for action by an individual

p5: affordance network
An affordance network is the collection of facts, concepts, tools, methods, practices, agendas, commitments, and even people, taken with respect to an individual, that are distributed across time and space and are viewed as necessary for the satisfaction of particular goal sets.

pp6-7: effectivity
Gibson introduced the concept of effectivities as complementing affordances. If an affordance is a possibility for action by an individual, an effectivity is the dynamic actualization of an affordance. Functionally defined, an effectivity set constitutes those behaviors that an individual can in fact produce so as to realize and even generate affordance networks. When an individual has a particular effectivity set, he or she is more likely to perceive and interact with the world in certain ways—even noticing certain shapes of networks that are unavailable to others. This view has overlap with Foucault’s (1975) notion of gaze or Shaffer’s (2004) discussion of epistemic frames. For example, Foucault suggests that experts perceive the world very differently from novices and outsiders, and Shaffer suggests that an important aspect of learning is to support the learner’s adoption of a new way of knowing and caring about the world.

p8 knowing
knowing is described as the process of being able to realize affordance networks; that is, the coupling of affordance networks and effectivity sets in the service of particular goals.

p7: life-world
To understand living beings, theoretical biologists distinguished between the material bodies of the animals, demarcating inner worlds, and the surrounding, material outer worlds. However, the behaviorally relevant concepts are not the inner and outer worlds, but the developmental, functionally related worlds that the organism perceives and the world that the organism affects through its actions; in fact, these two worlds are not independent but co-emerge in the course of development and therefore mutually presuppose one another.

p7: Different (physical) individuals relate to the same material environment in different ways and therefore inhabit different, personal life-worlds, which nevertheless share family resemblances across individuals. In other words, the contents of any life-world are dependent both on the individual’s effectivity sets and on the available affordance networks (Roth, 2003), leading to a continuous evolution of both individual life-world and communicative patterns with others (Roth, 1999).

p8: ecological theory of knowing
At the very core of an ecological orientation and distinguishing it most sharply from prevailing approaches to the study of human development is the concern with the progressive accommodation between a growing human organism and its immediate environment, and the way in which this relation is mediated by forces emanating from more remote regions in the larger physical and social milieu. (Bronfenbrenner, 1979, p. 13)

Problem / Goal / Challenge:
p3: It is one thing to learn about the concept of erosion to pass a test (having exchange value) and quite another to use it as a conceptual tool (having use value) for understanding why the water quality of a local river is deteriorating (Lave, 1988).

p3: When educators fail to engage students in meaningful relations and instead impart core ideas as isolated facts or abstract concepts, these facts and concepts are no longer connected to the situations that allow them to be powerful tools in the world.

p3: The irony is that we then wonder why children appear unmotivated to learn after we have disconnected meaning from the learning situation, assuming that the learner somehow will attribute the same functional value to the information as the teacher does.

p7: A core goal of education is how best to support learners in developing personal life-worlds that overlap with those socially agreed-upon life-worlds that are engaged by more knowledgeable others. Similarly, a core challenge of education is how to develop curricular contexts that extend themselves meaningfully into the personal life-worlds of individuals.

p8: As educators, we want to support both functioning in a particular context and participation that carries over to other places and times—not simply a short-lived or local adaptation to an immediate situation (i.e., the classroom, the next unit test). Such cross-contextual application requires that learning environments, beyond aiding students in appreciating the contextual value of that which is being learned, also serve as a mechanism for attuning the learner to the underlying invariance. This type of knowing involves not just succeeding in one situation but developing the capacity and interest to create new action possibilities, even reconstructing relations that might not have been readily apparent in the dynamic structure (Shaffer, 2004).

p9: Thus knowing, as described here, is the process of successfully engaging an intentionally bound system such that particular goals can be accomplished.

Learning Environments as Curriculum-Based Ecosystems

p.9 : The design challenge lies in establishing contexts that support user-adopted intentions that give rise to an appreciation for, even creation of, sets of relations that are consistent with socially agreed-upon ones. From our perspective, this involves establishing rich contexts through which students attend to the socially agreed-upon formalisms and at the same time appreciate the situations for which those formalisms have value.

p9 These curriculum-based ecosystems begin by setting up the problem and then making available various resources and suggested activities through which students assemble the necessary networks for solving the introduced problem.

This should not be taken as a move toward formalism-free contexts.

Formalisms are useful in that they provide an important organizing role for a discipline, can mitigate contextual ambiguity about core conceptual meanings, and help reveal the common deep structure underlying different contextual phenomena, thereby potentially supporting transfer and theory building (Nathan, 2005).

However, while disciplinary formalisms clearly serve a useful role for experts, our ecological framework implies that they are less useful for facilitating the conceptual development of an individual who is learning about the discipline or just beginning to recognize the value of disciplinary formalisms for meaningfully interacting with the world.

Barab et al. suggest that it is a balancing process in terms of the quality of formalism (explicit versus implicit) and the quality of context (noisy versus tailored).

p10: Barab et al.’s work has focused on building rich contexts-of-use and determining which tasks will most likely facilitate students in enlisting formalisms as conceptual tools.

Project: virtual park, virtual fish, declining fish population

In Year 2 of their research Barab et al. redesigned the curriculum, ensuring that each of the tasks involved one of the key standards and target concepts to be learned—mapping out the trajectory and aligning the various activities with the target formalisms.

In addition to increasing the diversity of contexts, Barab et al. also decreased the number of contextual specifics so that over time students were required to understand the formalisms in increasingly tailored contexts, until the abstracted formalism itself became the focus almost explicitly. More generally, in supporting students in attending to the cross-context applicability of specific nodal content, Goldstone and Son (2005) advocated a process that they referred to as concrete fading: In their experiment, students first were immersed in a rich context and then worked with more abstract representations of the same underlying conceptual tools—a process that effectively facilitated transfer.

When using contextually rich problems, Barab et al. have found that, in addition to contrasting cases, some type of meta-contextual decomposition in which learners interrogate the problem in terms of the invariant and variant aspects is an important step in fostering the development of a cross-contextual appreciation for the underlying invariant structures.

Summary:
+ Barab et al. argued that learning is not simply scoring high on a test or assignment, but should involve increasing possibilities for action in the world.
+ Learning and participation, with respect to this project and our ecological framework, is about successfully participating as part of an ecosystem, an intentionally bound network, and it fundamentally involves increasing possibilities for action in the world.
+ Life-world expansion, as the ultimate trajectory of learning, involves engaging in sets of experiences that have overlapping core components such that children build up “effectivity sets” that span multiple affordance networks—potentially evolving into new ways of interacting with the world.
+ Transfer can occur when individuals begin to see different contexts as having similar underlying affordance structures—even in the context of differing contextual particulars.
+ In the best cases, individuals appreciate the power of, or adopt commitments with respect to, a particular effectivity set and begin to assert this “toolset” in multiple situations even when the affordances are not readily apparent on the surface.
+ Educators need to better understand the types of curriculum that will engage children while also supporting disciplinary learning and future-oriented trajectories.
+ At its core, our pedagogical argument highlights the primacy of rich experience and the importance of enmeshing students in such experience—not simply describing abstracted contents.

Situated cognition and the culture of learning; cognitive apprenticeship

Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18, 32-41.

Key ideas:

1. The activity in which knowledge is developed and deployed is not separable from or ancillary to learning and cognition. Nor is it neutral. Rather, it is an integral part of what is learned. Situations might be said to co-produce knowledge through activity. Learning and cognition are fundamentally situated. (p32)

2. Concepts are like tools. Like physical tools, it is quite possible to acquire a conceptual tool but to be unable to use it. (p33)

3. People who use physical tools actively rather than just acquire them, by contrast, build an increasingly rich implicit understanding of the world in which they use the tools and of the tools themselves. (p33)

4. Learning how to use a tool involves far more than can be accounted for in any set of explicit rules. The occasions and conditions for use arise directly out of the context of activities of each community that uses the tool, framed by the way members of that community see the world. The community and its viewpoint, quite as much as the tool itself, determine how a tool is used. Thus, carpenters and cabinet makers use chisels differently. (p34)

5. Activity, concept, and culture are interdependent. No one can be totally understood without the other two. Learning must involve all three. p33

6. Students are too often asked to use the tools of a discipline without being able to adopt its culture. [i.e., acquire conceptual tools but not use them in authentic ways] p.33

7. The ways schools use dictionaries, or math formulae, or historical analysis are very different from the ways practitioners use them (Schoenfeld, in press). Thus, students may pass exams-(a distinctive part of school cultures) but still not be able to use a domain's conceptual tools in authentic practice. p34

8. Authentic activities are defined simply as the ordinary practices of the culture. p35

Examples of authentic activity (p35)
a. Weight-watchers: take 3/4 of 2/3 cup of cottage cheese. Mathematically 3/4 of 2/3 cup is 1/2 cup (.75 x .6666 = .500). But the dieter solved this problem by measuring out 2/3 cup of cottage cheese, dividing the portion into 4 parts, and removing one part.

9. Authentic activity is important for learners, because it is the only way they gain access to the standpoint that enables practitioners to act meaningfully and purposefully. It is activity that shapes or hones their tools. p36

10. Most school experiences encourage students to learn about a subject rather than learn a subject with understanding (surface learning vs. deep understanding, low meaning vs. high meaning)
Example of teaching multiplication using authentic activity approach: Lampert (1986) p38
+ First phase of teaching starts with simple coin problems, such as "using only nickels and pennies, make 82 cents." With such problems, Lampert helps her students explore their implicit knowledge.
+ Second phase of instruction:  the students create stories for multiplication problems.  They perform a series of decompositions and discover that there is no one, magically "right" decomposition decreed by authority, just more and less useful decompositions whose use is judged in the context of the problem to be solved and the interests of the problem solvers.
+ Third phase of instruction: gradually introduces students to the standard algorithm, now that such an algorithm has a meaning and a purpose in their community. The students' procedure parallels the story problems they had created. Eventually they find ways to shorten the process, and they usually arrive at the standard algorithm, justifying their findings with the stories they created earlier.

11. characteristic of cognitive apprenticeship approach to teaching: p38
+ beginning with a task embedded in a familiar activity
+ stress that multiple solutions are possible
+ allowing students to generate their own solution paths
+ by enculturating through activity, learners acquire some of the culture's tools-a shared vocabulary and the means to discuss, reflect upon, evaluate, and validate community procedures in a collaborative process.

12.  Craft apprenticeship enables apprentices to acquire and develop the tools and skills of their craft through authentic work at and membership in their trade. Through this process, apprentices enter the culture of practice. [this might be a better way to train teachers than traditional teacher prep programs] p.39

13. In this model, the relationship of the teacher to the student is one of master to apprentice [does this requires the avg. K-12 teacher to "know" a lot more and/or be better trained than most K-12 teachers to teach this way] p.40

Misconceptions reconceived

Smith, J. P., diSessa, A. A., & Roschelle, J. (1994). Misconceptions reconceived: A constructivist analysis of knowledge in transition. Journal of the Learning Sciences, 3, 115-163.

Summary:
+ Casting misconceptions as mistakes is too narrow a view of their role in learning
+ Misconceptions are faulty extensions of productive prior knowledge
+ Misconceptions are not always resistant to change; strength is a property of knowledge systems
+ Replacing misconceptions is neither plausible nor always desirable
+ Instruction that confronts misconceptions is misguided and unlikely to succeed
+ It is time to move beyond the identification of misconceptions

Notes:
p115: basic premise of constructivism: that students build more advanced knowledge from prior understandings

p117: The knowledge system framework makes it easier to understand how novice conceptions can play productive roles in evolving expertise, despite their flaws and limitations.

p124: Learning Paradox: How is it possible for our existing cognitive structures to transform themselves into more complex forms? Smith et al. suggest that misconceptions, especially those that are most robust, have their roots in productive and effective knowledge.

p125: If concepts are more like complex clusters of related ideas than separable independent units, then replacement looks less plausible as a learning process (disessa, in press; Smith, 1992).

p128: Smith et al. show that novices can exhibit expert-like behavior in explaining how a complex but familiar physical system works. Specifically, novices are willing to search for appropriate underlying mechanisms that are independent of salient surface representations. The heart of this analysis is that explanation is an everyday activity.

p132: These analyses have generally asserted that the flaws in students' understandings result from overgeneralized applications of prior mathematical knowledge-for example, using only knowledge of whole number order and place value to order decimals. Although many students eventually work through and beyond their flawed conceptualizations, mastery of these elementary mathematical domains is neither easy, rapid, nor uniformly achieved

p137: Smith et al. claim that learning in both of these cases involves shifts in the applicability of strategies more than changes in the content of the strategies themselves. The examples suggest that mastery is achieved, in part, by using what you already know in more general and powerful ways and also by learning where and why pieces of knowledge that are conceptually correct may work only in more restricted contexts.

p139: Larkin's analysis emphasized fundamental differences between novice and expert reasoning. She claimed that her expert and novice subjects used different representations and different concepts. Without disputing that experts' reasoning is different in important ways from that of novices, we emphasize the substantial continuities between them.

p145: Smith et al. have argued that there is often more similarity between expert and novice than meets the eye. Historically, elements of prior knowledge have played essential roles in the development of scientific theory. Prior knowledge has provided new concepts for scientific theory by abstracting objects and processes from everyday experience.

p145: In the final section, Smith et al. identify a set of theoretical principles that represents a step beyond the epistemological premise of constructivism.

+ Knowledge in pieces: A shift toward viewing knowledge as involving numerous elements of different types
+ Continuity: Persistent misconceptions, if studied in an evenhanded way, can be seen as novices' efforts to extend their existing useful conceptions to instructional contexts in which they turn out to be inadequate. p147
+ Functionality: Learning is a process of finding ideas that sensibly and consistently explain some problematic aspect of the learner's world. Conceptions that do not work in this way (or are linked to other conceptions that do) are unlikely to take root, be applied in reasoning, and subsequently defended by students
+ A Systems Perspective: Smith et al. for an analytical shift from single units of knowledge to systems of knowledge with numerous elements and complex substructure that may gradually change, in bits and pieces and in different ways.


Implications:

Discussion rather than confrontation. Classroom discussion, when freed of its confrontation frame, can play an important role in learning, particularly when it concerns problematic situations in which students' ideas are strongly engaged and the impact of reformulation may be most clear. But the purpose of discussion changes when we conceptualize learning in terms of refinement rather than replacement. We still need to have students' knowledge -- much of which may be inarticulate and therefore invisible to them -- accessed, articulated, and considered. Rather than opposing those ideas to the relevant expert view, instruction should help students reflect on their present commitments, find new productive contexts for existing knowledge, and refine parts of their knowledge for specific scientific and mathematical purposes. The instructional goal is to provide a classroom context that is maximally supportive of the processes of knowledge refinement.

Analytic microworlds can foster interactive learning and reflection; Three types: simulation environments, computer-based graphics packages, and knowledge spaces