According to Wikipedia, a schema is
“a pattern of thought or behavior that organizes categories of information and the relationships among them. It can also be described as a mental structure of preconceived ideas, a framework representing some aspect of the world, or a system of organizing and perceiving new information. Schemata influence attention and the absorption of new knowledge: people are more likely to notice things that fit into their schema, while re-interpreting contradictions to the schema as exceptions or distorting them to fit. Schemata have a tendency to remain unchanged, even in the face of contradictory information. Schemata can help in understanding the world and the rapidly changing environment. People can organize new perceptions into schemata quickly as most situations do not require complex thought when using schema, since automatic thought is all that is required”
Schema acquisition is necessary in order for students to effectively solve problems and think critically. In an attempt to achieve this, many teaching strategies focus on giving students a large amount of practice with a particular problem type. On the surface, this approach makes a lot of sense. If students are learning multiplication and division, then they need to practice the skill in order to become proficient. But evidence has shown that this conventional approach is not always the most effective.
The studies on this involved giving students problems to solve. The problems could be solved using either a means-ends analysis or by using a rule based on the problem structure (schema). Studies found that while the participants using a means-ends analysis were able to effectively complete the problems, they would not learn the essential aspects of the problem’s structure. Meaning that they would achieve success without much actual learning.
A means-ends analysis approach to problem-solving has two main weaknesses, selective attention and cognitive processing capacity. The means-ends approach involves a student keeping the current problem state and the goal state, along with the relationship between the problem state and goal state in mind at once. They do not necessarily think back on previously solved, similar problems. As a result, the cognitive load is much higher for someone using a means-ends approach (often involving working backward) as opposed to someone using a schema (working forwards). The cognitive load of a means-ends approach can interfere with the development of a schema because the cognitive load is so high.
Solving a problem using a schema allows for students to work forward because the schema holds the related problem states and the procedures associated with them. As teachers, we should strive to help our students develop their own, effective schemas for solving problems and applying concepts. One way to do this is to direct students to use a nonspecific goal strategy. We can do this by changing conventional (specific) goal questions to nonspecific goal questions.
- Conventional Goal Question: What direction does gravity pull the bird down?
- Nonspecific Goal Question: How does gravity act on the bird?
That being said, it is important for students to have a basic mental model in place before moving to nonspecific problems. If they don’t have a basic mental model, then nonspecific questions are often unhelpful. This fits with other cognitive science research such as concreteness fading. Basically, start concrete and get vaguer over time. An example of this is telling a student 2+2=4 by showing them two groups of two apples, then put the apples together and voila! Four apples. After the student has mastered two apples plus two apples, you can give them a problem that is two oranges plus two oranges. Eventually moving to strictly using numbers, 2+2=4.
Nonspecific goals are effective because this type of problem cannot be solved by a means-ends analysis (requiring a high cognitive load). Functionally this means that students will be using a problem-solving method that has a lower cognitive load, allowing them to devote more of their working memory towards building a schema. So, as teachers, we should strive to teach students how to solve problems, and we should develop that by giving nonspecific questions in order to help them develop the schemas necessary.