Methods of didactic education assume a separation between knowing and doing, treating knowledge as an integral, self-sufficient substance, theoretically independent of the situations in which it is learned and used.
Recent investigations of learning challenge this separating of what is learned from how it is learned and used . The activity in which knowledge is conveyed (how it is learned)... is an integral part of what is learned.
Example (from the article) of knowlege not making sense out of context:
‘ Students can often manipulate algorithms, routines, and definitions they have acquired with apparent competence and yet not reveal, to their teachers or themselves, that they would have no idea what to do if they came upon the domain equivalent of a limping horse.’
This is actually relating to comparing knowledge to a pocket knife as an example tool, said in the text as being used for removing stones from horses’ hooves. The idea is that tools need their context to understand how to be used correctly, and so does knowledge.
Participants were told to measure a serving of cottage cheese. They were told they were allowed ¾ of 2/3 of a cup. The JPF filled a measuring cup 2/3 of the way with cottage cheese, then laid it out on the table and separated ¼ out from it.
At no time did the weight watcher calculate 2/3 x ¾ to get ½ cup of cottage cheese through multiplication. Why is the JPF solution better? Why is doing it the way school has taught us not as good a solution? ‘Because the problem is done naturally in its environment, and part of the cognitive task is off-loaded onto that environment.’
To enculturate students into authentic practices through activity and social interaction in a way similar to that evident – and evidently successful – in craft apprenticeship.
It’s a practical and theoretical framework for education, decidedly different from contemporary gradeschool, and perhaps more similar to doctoral (Phd) schooling. It advocates learning history as if one were becoming a historian, learning math as if one were becoming a mathematician, and so on...
In most classes, so-called ‘problems’ are exercises; you are done when you’ve shown that you’ve mastered the relevant technique by getting an answer. However, in a cognitive apprenticeship model like this class, you’re not done until you understand the mathematical nature of the square: explored other possible magic squares, discovered general principles, having more ways to solve the same problem.
(Shoenfeld, in press) Can you place the digits 1,2,3,4,5,6,7,8,9 in the box below, so that the sum of the digits along each row, each column, and each diagonal is the same? The completed box is called a magic square.
"using only nickels and pennies, make 82 cents.'' With such problems, Lampert helps her students explore their implicit knowledge. Then, in the second phase, the students create stories for multiplication problems.
By the creation of stories, students not only understand the multiplication to find a solution to the problem, but also learn that there are multiple right answers. Thus, they learn about being a mathematician in a culture of mathematics, not about succeeding at math just in its use for school.
By beginning with a task embedded in familiar activity, it shows students how to apply prior (implicit) knowledge to address unfamiliar tasks.
By showing different ways of solving or breaking down the same problem, it shows that methods and solutions are not absolute, but can be assessed and even improved upon.
By allowing students to generate their own solution paths, it encourages creativity and critical thinking. It also familiarizes students with the culture of mathematics, not just the culture of the school.
Collective Problem Solving – accumulating individual knowledge within the group (from a teaching point of view, this is an ideal and not always practical)
Displaying Multiple Roles – assumes that students may play different roles in solving the problem (however, this also assumes that students themselves will not typically play the same roles repeatedly)
Confronting Ineffective Strategies & Misconceptions – Teachers rarely have the opportunity to hear enough of what students think to recognize when the information that is offered back by students is only a surface retelling for school purposes, but student group members are more likely to draw out and confront these misconceptions (this is really idealizing the students and not flattering for these teachers)
Providing collaborative work skills – Students do need to learn collaborative skills, which may be best taught through group exercises.
The authors argue that Cognitive Apprenticeship, particularly when combined with collaborative learning, is a superior educational method than contemporary teaching methods in schools. This is because it places learning inside the context of a meaningful and intuitively relevant activity.