Broad studies of the differences between novices and experts conclude that experts generally do more of the following than novices do: recognize patterns, focus on big ideas in a field, and conditionalize knowledge.
According to studies presented in How People Learn, experts in mathematics, radiology, electronic circuitry, computer programming, and even chess can quickly identify patterns that emerge in information they are presented with . For example, an expert computer scientist would see almost immediately that searching yellowpages.com for a person with the name Johnson and Netflix.com for movies which are ranked at 5 stars would both require first sorting the data.
The ability to recognize patterns is further discussed in cognitive psychology’s schema theory. A schema is a mental structure that contains generic conceptual knowledge; they are used to “represent knowledge as stable patterns of relationships between elements describing some classes of structures that are abstracted from specific instances and used to categorize such instances” . Educational psychologists who study experts and novices argue that schemas play a key role in the development of expertise; specifically, the growth of expertise involves the creation of many mental models and schema which are deeply interlinked in a knowledge hierarchy .
Curriculum then should encourage students to develop the correct schemas and link them in meaningful and useful ways. Students should create an arsenal of “canned solutions” to common problems or subproblems, as well as know when and how to apply them in unfamiliar situations. Such problem solving schemas are called plan schemas. A survey of cognitive psychology literature in computing reveals that “plan schemas are the basic cognitive chunk used in designing and understanding programs” . In fact, some argue that plan schemas are the single most important feature of the programming expert.
Focusing on Big Ideas
In addition to recognizing major patterns in data and problems, experts tend to understand problems in terms of the big ideas in their field . For example, when physics experts and novices are asked to sort problems (written on index cards) according to approaches used to solve them, expert and novice responses diverge greatly. On one hand, novices sort the cards according to surface attributes, like which equations they believe could be used to solve the problem. On the other, experts create piles of cards according to the big idea in the field of physics which is used to solve the problem – like Newtonian laws. Figure 1 from  shows one example problem pairing where novices and experts diverged.
Cognitive psychology studies of expert computer programmers suggest that an expert maintains two different forms of comprehension within his mental representation of a program: the program model and the domain model . A program model is strictly limited to the program code itself and concepts like elementary operations in the code, functions used, and the control of the execution flow. The domain model, in contrast, represents what problem a programmer is trying to solve and contains information about the problem sphere – including its components, relationships between them, the transfer of data between components, and the overall purpose of the program. In essence, the domain model grounds the program model in context by focusing on the big ideas in computing and how they pertain to the solution. It is important, then, that curriculum encourages students to develop both problem and domain models.
These studies together reveal that experts construct a domain model about the problem space that is founded on the big ideas in their field. Novice instruction, then, should be geared toward encouraging students to create similar domain models which emphasize the big ideas.
According to a survey of cognitive studies in How People Learn, experts display an ability to identify quickly which components of their knowledge base and plan schemas are appropriate in a given situation. They are able to use their classification of problems to identify similar scenarios that they may be more familiar with, giving them a context in which to solve a problem. According to How People Learn, word problems are especially useful for targeting a student’s ability to choose when to apply concepts: “if well designed, these problems can help students learn when, where, and why to use the knowledge they are learning” .
In line with the desire to encourage students learn when to apply their knowledge is the teaching theory of Problem-Based Learning (PBL). PBL drives education by presenting substantial and realistic problems which require students to use immediately the course material (with limited instruction from the teacher). How People Learn notes that a typical exam does not assess the degree to which a student’s knowledge is conditionalized, because it does not prompt the the student to apply their knowledge in the context of a real-world problem .
In order to encourage students to develop conditionalized knowledge and move toward expertise, curriculum should be built around contextualized problems which force a student to choose when and how to apply their knowledge.
I guessing that problem-based learning would target the sort of thinking that we want our novices to develop – viewing a problem in terms of its components and concepts rather than its surface features. I would expect that students who are taught in a problem-based learning environment would be more successful in classifying problems that have underlying similar structures (and require similar problem-solving techniques), because they would be learning from the beginning that analyzing a problem based on its surface features is not sufficient.
 S. Kalyuga. Schema Aquisition and Sources of Cognitive Load, pages 48–64. Cambridge University Press, 2010.
 C.D.S.L.C.L.R.E. Practice and N.R. Council. How People Learn: Brain, Mind, Experience, and School: Expanded Edition. National Academies Press, 2002.
 Juha Sorva. Visual Program Simulation in Introductory Programming Edu- cation. PhD thesis, Aalto University, 2012.
 G.P. Wiggins and J. McTighe. Understanding By Design. Gale virtual reference library. Association for Supervision and Curriculum Development, 2005.