Arc Design Group
I think the issue is how you are interpreting what the comb means. Heres another graphic I found describing this:
The length of the comb is the radius at any given point. So for the first image (G1) it means that there is a harsh transition between the flat and the radius - this is percieved as the jump in distance between the comb on one curve and the comb on the next.
With G2 - you see the comb ramp gradually back down to zero - this means the curvature at the end of that curve is the same as the curve it is connecting to. In the real world, this equates to a smoothness of the transition that is evident when viewing an objects highlight or reflection.
G3 and beyond are beyond this and the math is a bit easy to go over your head without diving really deep into it, but ultimately those combs help you understand where you will see tangent lines on a product. This is the reason that all automotive surfacing is done with G2 and beyond. A tangent break would show up as a hard crease on a shiny metal car body.
Mon, 29 Mar 2010 21:51:47 +0100
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Cognitive Learning Theories
Cognitive developmental research has also influenced the development of teaching and learning English in the area of learning capacity. Cognitive developmental research has had an impact on the constructivism movement in education and educational technology (Gilliani, 2003). Constructivism originated in the ideas of Piaget (1952) to account for the way in which children acquire cognitive abilities in an apparently regular order and children are engaged actively in constructing theories about how the world around them works.
It should be noted that Piaget’s observations and theories were not really targeted at language learning or development but at overall mental growth in general. One of his most famous statements about cognition in general was that “Intelligence is an adaptation…To say that intelligence is a particular instance of biological adaptation is thus to suppose that it is essentially an organization and that its function is to structure the universe just as the organism structures its immediate environment” (Piaget, 1963, pp. 3-4).To him, language was essentially just a representation of mental processes going on in the child’s mind, though his later work brought more focus to aspects of interaction and language ability (Lightbown, and Spada, 1999).
A key aspect of Piagetian psychology is the idea that cognitive development in young children stems from action and interaction with the world around them. This begins with physical objects in a problem-solving sequence that is gradually internalized and develops the child’s thinking ability. In terms of how this related to language acquisition in children, Piaget basically saw language as a representative system, one of a variety of ‘symbol systems’ developed throughout childhood to represent new knowledge acquired as children engage in a physical way with aspects of their environments (Lightbown & Spada, 1999, p. 23). In many ways, his theories were seen as working from the idea that right-hemispheric brain activity preceded left hemispheric brain activity, a notion which James Asher reiterates as one of the founding principles of his world famous Total Physical Response (TPR) method (Richards & Rodgers, 2001).
In addition, Piaget is known in for his theories about “stages of cognitive development” and the concepts of “assimilation” and “accommodation”. Piaget later went on from his early original theories to make observations about the way arguments among children are fundamental in the process of developing internalized reasoning skills, as cooperation in child play can be a major factor in the development of moral judgment (Richard-Amato, 1996, p. 427) Some of his theories had evolved to the point that they were considered to be from the same theoretical viewpoint as Vygotsky’s in terms of the central role they allocated to social interaction in language learning, and have even been considered fundamental in the growth of relatively contemporary notions such as Cooperative Language Learning (Richards & Rodgers, 2001).
The contemporary notions relates to Piaget’s general theory about how physical activity and the associated experience interacting with one’s environment which leads to mental growth:
Intelligence is assimilation to the extent that it incorporates all the given data of experience within its framework…There can be no doubt either, that mental life is also accommodation to the environment. Assimilation can never be pure because by incorporating new elements into its earlier schemata the intelligence constantly modifies the latter in order to adjust them to new elements. (Piaget, 1963, p. 6-7).
In the context of language learning, the way new information is found and utilized is considered to be a conceptual model (or ‘schema’). Activity can lead to mental development through two means: ‘assimilation’ and ‘accommodation’. Assimilation basically involves an action whereby the child does not actually “change” his or her knowledge, just reapplies the same action in different circumstances. Accommodation, on the other hand, indicates that some kind of alteration or adjustment of the knowledge occurs, as a result of interaction with new things present in the environment (Richards & Rodgers, 2001).
Other theorist, Bruner (1966) proposed a learning theory whose educational implications resemble the concrete to abstract concept of Piaget. Such a process is called scaffolding where the learner is initially dealing with concrete subjects, and the mentor provides a great amount of support. However, the support fades away as the learner begins to think abstractly. This shift can lead to very rapid learning, but is also risky process because it means abandoning old ways of viewing concept. This notion of scaffolding is useful, because it describes how new models of concept can be introduced to learners gradually and in a way lessens the risk (Gillani, 2003).
Furthermore Flavell (1985) has provided a more detailed discussion of three operations as the continuation of Piaget’s work in the area of cognitive development. The three operations are called; combination reasoning, propositional reasoning, and hypothetical-deductive reasoning. Combination reasoning refers to the ability to consider different factors to solve problem. This reasoning provides the learner with the ability to look at problems from an integrated approach. Propositional reasoning refers to the characteristic that learners acquire to reason on the basis of assumption to solve problems. Hypothetical-deductive reasoning allows the learner to consider different hypotheses in dealing with a problem. This also enables the learner to gather data and test different hypotheses to come up with a possible solution (Flavell, 1985). In brief, cognitive theories are useful theory to explain how, why, and when learners develop and learn new concept.
Cognitive Theories and Learning
Cognitive theories are not entirely perfect in their application to language learning especially in the classroom context. However, some of the key concepts are very solid and useful (Schwebel, et al., 1973). Piaget’s concept has given significant contribution to learning. First, he believed that the ability to take action to solve some kind of problem presented by the environment was neither innate nor a process of imitation – the child takes the action from the outset and through the experience acquires new mental knowledge. The second, first language development did not play anywhere near as much a role in children’s mental growth as did the key concept of taking action and learning from it (Riley, 1996). The third, he paid attention on children’s learning and cognitive development by focusing on biological factors as determining his famous “universal stages of development” theory (Richard-Amato, 1996) and then begun to focus a lot more on social factors in explaining cognitive development in children (Schwebel, et al., 1973). Fourth, Piaget essentially saw the concepts of “learning” and “mental development” as separate from each other, that “learning utilizes development but does not shape its course” (Richard-Amato, 1996, p. 38).
Despite his many critics, Piaget’s views on mental development in children have important implications for concepts in language learning. The idea that children try to make sense of the environment they find themselves in and actively seek to manipulate ideas and concepts, creating new knowledge for themselves as they go through this process and using these experiences to negotiate new situations and problems. The second important idea is the importance of a child’s environment in terms of affecting the number and type of opportunities available to apply or adapt new knowledge systems. On the first score, it needs to be acknowledged that what children have already experienced or know how to do with language is likely to have an effect on how they tackle the next ‘language problem’ to come their way, and that most children characteristically and instinctively want to find new solutions to new problems. In terms of the environment, such as English classroom in the middle of an EFL context affords very different opportunities to see the need for and try out new language than a natural environment where everything around them operates in the target language they are trying to learn (Gorman, 1972).
Cognitive Learning Theories and E-learning
Cognitive theories provide a frame of reference by which educators and educational technologies can analyze the behavior of the learner and design educational environments where the learners can construct their own knowledge. In the design of e-learning environment, such as SimCity, science exploration (http://www.exploratorium.edu/IFI/index.html) and many other similar programs which are mostly designed by using software called Macromedia Authorware, are examples of the influence of cognitive approach. These e-learning environments attempt to guide the learners to construct knowledge in the process of learning. In other words, the learners should be given opportunity in doing meaningful activities which facilitates the creation of personalized meaning. Good interactive online instructions facilitate knowledge construction because the learners have to take initiative to learn and to interact with other students and instructor (Murphy & Cifuentes, 2001). Furthermore, learners experience the information first-hand, which gives them the opportunity to contextualize and personalize the information themselves. According to Heinich et al. (2002), learning is the development of new knowledge, skills, and attitudes as the learner interacts with information and the environment. Interaction is also critical to creating a sense of presence and a sense of community for online learners, and to promoting transformational learning (Murphy & Cifuentes, 2001). Learners receive the learning materials through the technology, process the information, and then personalize and contextualize the information.
Flow Chart 2.2
In the transformation process, learners interact with the content, with other learners, and with the instructors to test and confirm ideas and to apply what they learn. Garrison et al. (2003) claimed that it is the design of the educational experience that includes the transactional nature of the relationship between instructor, learners, and content that is of significance to the learning experience. In the e-learning environment, the learners have the freedom to explore the learning materials and to experience the learning process as can be seen in flow chart 2.2. The learners have the freedom to take the path of their own. For example, the learner can login to the site and go directly to class forum to see what the teacher and peers have posted and discussed, then go to learning materials or even directly to the quiz. The learner also has the freedom to logout the program at anytime. In other words, constructivism underpins the understanding of how individuals learn in a social context and extends to the learning organization, which by nature its members learning together, improves its activities through group reflection and sharing of experiences. In this case e-learning has the potential to overcome some of the limitations of traditional learning, including the fixed times and locations for learning. E-learning allows for a synergy between advances in information and communication technologies (Holmes and John Gardner, 2006).
The web-based model for TEFL is adapting some of the cognitive theories. Various authentic learning materials are presented and the students have the freedom to explore the materials. Using the knowledge gained from the materials, students are given the opportunity to discuss and share their knowledge with other students. The discussion and sharing can be done online and offline.
To illustrate the influenced of cognitive learning theory, ‘Astro-Venture’ an educational multimedia web environment is a good example (http://astroventure.arc.nasa.gov). This website is intended for children and was developed by NASA Technology Team. In ‘Astro-Venture’, learners are first presented with the challenge of how to design a planet star system that would be able to meet their biological survival needs. Learners put forward with the aspects of Earth and solar system that allow human inhabitation. The learners are informed that they will be working with NASA scientists who will help them in their research to understand how the Earth meets human biological needs.
Learners conduct this research by engaging in multimedia training modules allowing them changing astronomical, atmospheric, and geological aspects of the Earth and solar system and see the effects of the changes on Earth. From these observations, learners draw conclusions about what aspects allowed Earth to remain habitable. Learners can interact with the NASA scientists by mean of forum discussion provided in the website. This site also provides special pages for teachers and parents allowing them to download texts about the facts of the Earth and Solar system so they can help their learners in explaining the astronomical, biological, geological and atmospheric facts.
When learners have a complete understanding of how the astronomical, biological, geological and atmospheric condition of Earth, they are ready to design a habitable planet. Learners then engage in a multimedia activity in the website to design a habitable planet. The learners are required to hypothesize various combinations of conditions, and test their hypothesis to see if it results in a habitable planet.
In other words, cognitivists see learning as an internal process that involves memory, thinking, reflection, abstraction, motivation, and metacognition. Cognitive psychology looks at learning from an information processing point of view, where the learner uses different types of memory during learning. Sensations are received through the senses into the sensory store before processing occurs. The information persists in the sensory store for less than one second (Kalat, 2007), and if it is not transferred to working memory immediately, it is lost. Cognitive psychology postulates that information is stored in long-term memory in the form of nodes which connect to form relationships; that is, in networks. In addition, information maps that show the major concepts in a topic, and the relationships between those concepts, should be included in the online learning materials. According to Stoyanova and Kommers (2002), information-map generation requires critical reflection and is a method for externalizing the cognitive structure of learners. To facilitate deeper processing, learners should be encouraged to generate their own information maps. The implication of cognitive theory for online learning:
· Strategies used should allow learners to perceive and attend to the information so that it can be transferred to working memory Ally (2005) suggests some strategies to promote perception and attention for online learning; (1) Important information should be placed in the centre of the screen for reading, and learners must be able to read from left to right. (2) Information critical for learning should be highlighted to focus learners’ attention. (3) Learners should be told why they should take the lesson, so that they can attend to the information throughout the lesson. (4) The difficulty level of the material must match the cognitive level of the learner, so that the learner can both attend to and relate to the material. Links to both simpler and more complicated materials can be used to accommodate learners at different knowledge levels.
· Strategies used should allow learners to retrieve existing information from long-term memory to help make sense of the new information. Ally (2005) suggests some strategies to facilitate the use of existing schema; (1) Use advance organizers to activate existing cognitive structure or to provide the information to incorporate the details of the lesson. (2) Provide conceptual models that learners can use to retrieve existing mental models or to store the structure they will need to use to learn the details of the lesson. (3) Use pre-instructional questions to set expectations and to activate the learners’ existing knowledge structure. (4) Use prerequisite test questions to activate the prerequisite knowledge structure required for learning the new materials. With the flexibility of online learning, students with diverse background and knowledge can choose the most appropriate path to review previous or prerequisite learning before new information is presented.
· A variety of learning strategies should be included in online instruction to accommodate individual differences and learning styles (Cassidy, 2004). Learning style refers to how a learner perceives, interacts with, and responds to the learning environment; it measures individual differences.
· Information should be presented in different modes to facilitate processing and transferring it to long-term memory. Textual, verbal, and visual information should be presented to encourage encoding. According to dual-coding theory (Paivio, 1986), information received in different modes (textual and visual) will be processed better than that presented in a single mode (text). Dual-coded information is processed in different parts of the brain, resulting in more encoding.
· Encourage learners to use their metacognitive skills to help in the learning process (Yorke & Knight, 2004). Metacognition is a learner’s ability to be aware of his or her cognitive capabilities and use these capabilities to learn. When learning online, learners should be given the opportunity to reflect on what they are learning, collaborate with other learners, and check their progress. Self-check questions and exercises with feedback throughout a lesson are good strategies to allow learners to check how they are doing, so they can use their metacognitive skills to adjust their learning approach if necessary.
Bibliography
Ally, M. (2005). Using learning theories to design instruction for mobile learning devices. In J. Attwell and C. Savill-Smith (Eds.), Mobile learning anytime everywhere (pp. 5–8). Proceedings of the Third World Conference on Mobile Learning, Rome.
Bruner, J. 1966. Toward a theory of instruction. Cambridge, MA: Havard University press,
Ertmer, P., & Newby, T. J. (1993). Behaviorism, Cognitivism, Constructivism: Comparing critical features from an instructional design perspective. Performance Improvement Quarterly, 6(4), 50-71.
Flavell, J.H.1985. Cognitive development (2nd ed.) Englewood Cliffs, NJ: Prentice Hall.
Galavis, B. 1998. Computers and the EFL Class: Their Advantages and a Possible Outcome, the Autonomous Learner. English Teaching Forum. Vol. 6, No. 4., Oct – Des 1998.
Garrison, D. and Anderson, T. 2003. E-learning in the 21st century: a framework for research and practice. London: Routledge Falmer
Gillani, B. 2003. Learning Theories and the Design of E-Learning Environments University Press of America
Good, T. L., & Brophy, J. E. (1990). Educational psychology: A realistic approach (4th ed.).White Plains, NY: Longman.
Gorman, R. 1972. Discovering Piaget : a guide for teachers. Columbus, Ohio, Merril.
Heinich, R., et al. 2002. Instructional Media and Technologies for learning, 7th edition. Merrill Prentice Hall,
Holmes, B., and John Gardner. 2006. E-learning: Concept and practice, London; Thousand Oaks, Calif. : SAGE Publications.Jonassen, D. 1991. Evaluating constructivist learning. Educational Technology, 31(9), 28-33.
Johns, T. & King, P. (eds) 1991. Classroom Concordancing. Special Issue of ELR Journal 4, University of Birmingham: Centre for English Language Studies.
Kalat, J. W. 2007. Introduction to psychology. Pacific Grove, CA: Wadsworth- Thompson Learning.
I was fortunate enough to go to the eLearning Guild’s Learning Solutions conference this year. I met lots of people – many for the first time in real life – but I’m going to talk about the people I met in a different post. I was going to put the entire wrap-up on one post, but it got too long. So here is the Wed wrap-up.
Breakfast Byte
This was the only day I went to a Breakfast Byte discussion. I sat in on Talking Shop about Learning Theories which was led by Cammy Bean. I got to talk about Mayers and his multimedia design principles. I couldn’t believe that either.
Keynote
The keynote was The Element: How Finding Your Passion Changes Everything by Sir Ken Robinson. He was a very engaging speaker. I agree with his main message – that to give our best, we should work in an area for which we have a natural talent and you should practice what you love. But this voice in the back of my head keeps nagging me – that’s fine if you have the social and economic standing and family situation to do that. What about everyone else? That voice got very loud towards the end of the conference.
Blending Informal Learning into your Formal eLearning
The session called Blending Informal Learning into your Formal eLearning was led by Bob Mosher. I really appreciated the references to what happened when eLearning started getting popular. Here were some of the main points I got:
- Learners own informal learning, but there is a difference between consuming learning and design
- The LMS puts an extra click between the performance need and learner consumption. We may need it for organizational reasons, but the extra click throws up a barrier to an individual reaching out for performance support. An LMS distances the learning from learning (e.g. log-in, search…).
- Performance support should be blended with the formal training event
- The best performance support is perceived by the learners to be part of the job
- Training people are great at building red shirts for people who want to by blue pants. Build to the need!
- Not all informal learning assets are digital. Think about cheat sheets, etc…
- A Performance Support broker (PS broker) is an over-arching system that helps a learner find info in the workflow, and makes it available in a particular order
- Create a learning asset analysis. This should include EVERYTHING that people use to learn, not just the formal assets in the LMS (e.g. user created and shared cheat sheets, experts that everyone talks to or emails, etc)
Assessing eLearning Results: Fundamentals, Myths, and Special Opportunities
This session was lead by Will Thalheimer. I already believed that smile sheets really don’t tell us much. The most interesting point for me is how measuring at the end of training doesn’t really tell us much either. Measuring at the end of training is a biased metric because studies have shown that people forget much of what they have learned in at most a week. Measuring during performance is much more telling.
And then I presented!
I headed over to the ID Zone to hear a presentation on Design Strategies for Leveraging Social Media for Learning, and there was some sort of issue with the speaker (ultimately he wasn’t there). I could not bear to watch my fellow New Englander Jean Marrapodi scramble in front of a packed group of people waiting to hear about social media and learning, especially when I had my laptop and the presentations I’ve been using internally.
So I did the EMC thing and volunteered on the spot to present. Of course my laptop then decided to act wonky, so I couldn’t get to my presentation (I posted a version of the slides after the fact). So I just talked about what we’ve started doing at EMC, and I showed everyone the Proven Professional Community using Jean’s teeny tiny laptop.
This was probably the craziest thing I’ve ever done. I didn’t even think about it, I just offered because of my social connections to Jean. Hopefully it was helpful for folks!
That’s all I did at the conference that day. Thursday and Friday posts coming soon
