However, once students are introduced to rational numbers, their assumptions about mathematics can hurt their abilities to learn. Consider learning about fractions. One cannot count things to generate a fraction. Formally, a fraction is defined as the division of one cardinal number by another: this definition solves the problem that there is a lack of closure of the integers under division.
To complicate matters, some number-counting principles do not apply to fractions. Rational numbers do not have unique successors; there is an infinite number of numbers between any two rational numbers. Neither the nonverbal nor the verbal counting principle maps to a tripartite symbolic representations of fractions—two cardinal numbers X and Y separated by a line. Related mapping problems have been noted by others e.
Overall, early knowledge of numbers has the potential to serve as a barrier to learning about fractions— and for many learners it does. Often, students construct understandings like those noted above. Strategies for such teaching are discussed in more detail in Chapters 6 and 7.
Prior knowledge is not simply the individual learning that students bring to the classroom, based on their personal and idiosyncratic experiences e. Prior knowledge is also not only a generic set of experiences attributable to developmental stages through which learners may have passed i. Prior knowledge also includes the kind of knowledge that learners acquire because of their social roles, such as those connected with race, class, gender, and their culture and ethnic affiliations Brice-Heath, , ; Lave, ; Moll and Whitmore, ; Moll et al.
School failure may be partly explained by the mismatch between what students have learned in their home cultures and what is required of them in school see Allen and Boykin, ; Au and Jordan, ; Boykin and Tom, ; Erickson and Mohatt, Everyday family habits and rituals can either be reinforced or ignored in schools, and they can produce different responses from teachers Heath, How teachers interpret this reticence or resistance has consequences for how intelligent or academically capable they judge students and their instructional approaches toward them.
For example, a primary school teacher is helping students to understand fractional parts by using what she thinks is a commonplace reference. Most African Americans are likely to serve sweet potato pie for holiday dinners. In fact, one of the ways that African American parents explain pumpkin pie to their children is to say that it is Something like sweet potato pie. For them, sweet potato pie is the common referent.
Even the slight difference of being unfamiliar with pumpkin pie can serve as a source of interference for the student. Rather than be engaged actively in the lesson, he may have been preoccupied with trying to imagine pumpkin pie: What does it taste like? How does it smell? Is its texture chunky like apple or cherry pie? In the mind of a child, all of these questions can become more of the focus than the subject of fractions that the teacher is attempting to teach. These differences have their roots in early adult-infant interactions Blake, The language that children bring with them to school involves a broad set of skills rooted in the early context of adult-child interactions.
What happens when the adults, peers, and contexts change Suina, ; Suina and Smolkin, ? This is an important question that relates to the transfer of learning. The meanings that are attached to cultural knowledge are important in promoting transfer—that is, in encouraging people to use what they have learned. For example, story-telling is a language skill. Topic-associative oral styles have been observed among African American children Michaels, a,b; In contrast, white children use a more linear narrative style that more closely approximates the linear expository style of writing and speaking that schools teach see Gee, ; Taylor and Lee, ; Cazden et al.
Judgments may be made by white and black teachers as they listen to these two language styles: white teachers find the topic-associative stories hard to follow and are much more likely to infer that the narrator is a low-achieving student; black teachers are more likely to positively evaluate the topic-associative style Cazden, African American children who come to school speaking in a topic-associative style may be seen by many teachers as having less potential for learning.
We began this chapter by stressing that the ultimate goal of learning is to have access to information for a wide set of purposes—that the learning will in some way transfer to other circumstances. In this sense, then, the ultimate goal of schooling is to help students transfer what they have learned in school to everyday settings of home, community, and workplace.
Since transfer between tasks is a function of the similarity by transfer tasks and learning experiences, an important strategy for enhancing transfer from schools to other settings may be to better understand the nonschool environments in which students must function.
Since these environments change rapidly, it is also important to explore ways to help students develop the characteristics of adaptive expertise see Chapter 1. The question of how people function in a number of practical settings has been examined by many scientists, including cognitive anthropologists,. One major contrast between everyday settings and school environments is that the latter place much more emphasis on individual work than most other environments Resnick, A study of navigation on U.
More recent studies of collaboration confirm its importance. For example, many scientific discoveries in several genetics laboratories involve in-depth collaboration Dunbar, Similarly, decision making in hospital emergency rooms is distributed among many different members of the medical team Patel et al. The use of tools in practical environments helps people work almost error free e.
New technologies make it possible for students in schools to use tools very much like those used by professionals in workplaces see Chapter 8. Proficiency with relevant tools may provide a way to enhance transfer across domains. A third contrast between schools and everyday environments is that abstract reasoning is often emphasized in school, whereas contextualized reasoning is often used in everyday settings Resnick, Reasoning can be improved when abstract logical arguments are embodied in concrete contexts see Wason and Johnson-Laird, A well-known study of people in a Weight Watchers program provides similar insights into everyday problem solving see Lave et al.
One example is of a man who needed three-fourths of two-thirds of a cup of cottage cheese to create a dish he was cooking. He did not attempt to multiply the fractions as students would do in a school context. Instead, he measured two-thirds of a cup of cottage cheese, removed that amount from the measuring cup and then patted the cheese into a round shape, divided it into quarters, and used three of the quarters; see Box 3.
Abstract arithmetic was never used. In similar examples of contextualized reasoning, dairy workers use knowledge, such as the size of milk cases, to make their computational work more efficient Scribner, ; grocery store shoppers use nonschool mathematics under standard supermarket and simulated conditions Lave, ; see Box 3. There are potential problems with contextualized reasoning, which are similar to those associated with overly contextualized knowledge in general. Could he generate a new strategy for molasses or other liquids? The answer to this question depends on the degree to which he can relate his procedure to more general sets of solution strategies.
Analyses of everyday environments have potential implications for education that are intriguing but need to be thought through and researched carefully. Opportunities to engage in problem-based learning during the first year of medical school lead to a greater ability to diagnose and understand medical problems than do opportunities to learn in typical lecture-based medical courses Hmelo, Attempts to make schooling more relevant to the subsequent workplace have also guided the use of case-based learning in business schools, law schools, and schools that teach educational leadership Hallinger et al, ; Williams, The transfer literature also highlights some of the potential limitations of learning in particular contexts.
Simply learning to perform procedures, and learning in only a single context, does not promote flexible transfer. The transfer literature suggests that the most effective transfer may come from a balance of specific examples and general principles, not from either one alone. A major goal of schooling is to prepare students for flexible adaptation to new problems and settings. The ability of students to transfer provides an important index of learning that can help teachers evaluate and improve their instruction. Many approaches to instruction look equivalent when the only measure of learning is memory for information that was specifically presented.
Instructional differences become more apparent when evaluated from the perspective of how well the learning transfers to new problems and settings. The amount and kind of initial learning is a key determinant of the development of expertise and the ability to transfer knowledge. Students are motivated to spend the time needed to learn complex subjects and to solve problems that they find interesting.
Opportunities to use knowledge to create products and benefits for others are particularly motivating for students. While time on task is necessary for learning, it is not sufficient for effective learning. Time spent learning for understanding has different consequences for transfer than time spent simply memorizing facts or procedures. In order for learners to gain insight into their learning and their understanding, frequent feedback is critical: students need to monitor their learning and actively evaluate their strategies and their current levels of understanding.
The context in which one learns is also important for promoting transfer. Knowledge that is taught in only a single context is less likely to support flexible transfer than knowledge that is taught in multiple contexts. With multiple contexts, students are more likely to abstract the relevant features of concepts and develop a more flexible representation of knowledge. The use of well-chosen contrasting cases can help students learn the conditions under which new knowledge is applicable. Abstract representations of problems can also facilitate transfer. Transfer between tasks is related to the degree to which they share common elements, although the concept of elements must be defined cognitively.
In assessing learning, the key is increased speed of learning the concepts underlying the new material, rather than early performance attempts in a new subject domain. All new learning involves transfer. Previous knowledge can help or hinder the understanding of new information. For example, knowledge of everyday counting-based arithmetic can make it difficult to deal with rational numbers; assumptions based on everyday physical experiences e. Teachers can help students change their original conceptions by helping students make their thinking visible so that misconceptions can be corrected and so that students can be encouraged to think beyond the specific problem or to think about variations on the problem.
Effective teaching supports positive transfer by actively identifying the relevant knowledge and strengths that students bring to a learning situation and building on them. Transfer from school to everyday environments is the ultimate purpose of school-based learning. An analysis of everyday environments provides opportunities to rethink school practices in order to bring them into alignment with the requirements of everyday environments.
But it is important to avoid instruction that is overly dependent on context. Helping learners choose, adapt, and invent tools for solving problems is one way to facilitate transfer while also encouraging flexibility. Finally, a metacognative approach to teaching can increase transfer by helping students learn about themselves as learners in the context of acquiring content knowledge.
One characteristic of experts is an ability to monitor and regulate their own understanding in ways that allows them to keep learning adaptive expertise: this is an important model for students to emulate. First released in the Spring of , How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior.
This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn?
How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methods--to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn.
The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.
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Do you enjoy reading reports from the Academies online for free? Sign up for email notifications and we'll let you know about new publications in your areas of interest when they're released. Get This Book. Visit NAP. Looking for other ways to read this? No thanks. Suggested Citation: "3 Learning and Transfer. Page 52 Share Cite. BOX 3. Page 53 Share Cite. In the discussion below we explore key characteristics of learning and transfer that have important implications for education: Initial learning is necessary for transfer, and a considerable amount is known about the kinds of learning experiences that support transfer.
Page 54 Share Cite. Page 55 Share Cite. Understanding Versus Memorizing. Page 56 Share Cite.
Page 57 Share Cite. Page 58 Share Cite. Page 59 Share Cite. Page 60 Share Cite. Motivation to Learn.
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hukusyuu-mobile.com/wp-content/husband/81-software-to-location.php Page 63 Share Cite. Problem Representations. Relationships Between Learning and Transfer Conditions. Page 64 Share Cite. Page 65 Share Cite. This makes it much easier to transfer new skills and knowledge to the job. Transfer of learning is the influence of prior learning on performance in a new situation. If we did not transfer some of our skills and knowledge from prior learning, then each new learning situation would start from scratch. Some learning professionals only think of transfer of learning or transfer of training in terms of the classroom to the job environment.
However, these trainers fail to realize the importance of task variation within the classroom. That is, practicing on a variety of tasks will enhance and quicken the learning process as compared to practicing in the same category or class. This helps the learners to become accustomed to using their newly acquired knowledge and skills in novel situations, thus encouraging transfer of learning to the job.
Transfer of learning is a phenomenon of learning more quickly and developing a deeper understanding of the task if we bring some knowledge or skills from previous learning to a new learning situation. Therefore, to produce positive transfer of learning, we need to practice under a variety of conditions and environments. Note that there is a brief slow down in the learning curve confusion occurs when the variation is first introduced. However, the variation soon begins to strengthen our previously acquired skills and knowledge.
This is perhaps why some trainers are reluctant to use task variation—they see the initial confusion and assume they are slowing and confusing the learning process. Hence, classrooms and other learning environments become sterile of transfer of learning. And since the learners have no practice in transferring their newly acquired skills and knowledge in the classroom, they have trouble transferring their learning when they return to the job as most work environments are neutral towards the transfer of new skills that is, they do very little to encourage the transfer of learning.
Do NOT fall into this trap. Variation is GOOD! Provide as many variations and conditions in the learning environment as possible. There are two main principles that work with transfer of learning:. We benefit or suffer from our prior experiences. People improve in their ability to learn new skills more proficiently because of prior practice on a series of related tasks. This helps us to acquire new views on a topic by looking at the task from a different approach, which strengthens our understanding of the topic.
For example, practicing to drive a variety of cars provides experience with different stimulus situations and makes new learning easier. Another example is that greater learning occurs not by rereading the same text, but by reading another text on the same subject matter. This can be carried further with the use of examples.
It comes as no surprise that when trainees perceive learning as relevant, useful, and valuable, they are more likely to apply their newly learned skills. Some factors that influence the perception of training as valuable include:. Encourage your organization to promote the importance of learning at work as a value.
A culture of learning promotes both formal and informal learning, It acknowledges that employees need opportunities to try out newly learned skills and that mastery or competence takes time. Supervisor support is an important dimension of the social aspect of learning. It refers to the extent that managers and supervisors reinforce and promote the use of new skills on the job. Training transfer is facilitated when trainees perceive that supervisors are supportive in this way.
An important qualifier here is that when supervisors are coercive, it wipes away the effect. Ways for managers and supervisors to promote transfer are to:. Support from peers and colleagues is another important dimension of the social aspect of learning.
Peer support may be even more important than supervisory support in promoting training transfer. Organizations can promote peer support by encouraging:.